NMR Spectroscopic and quantum chemical characterization of the (E)- and (Z)- isomers of the penta-1,3-dienyl-2-cation

Dilute solutions of the (E )− and (Z )− isomers of pent-1,3-dienyl-2-cations (1) were obtained from reaction of 4-chloro-1,2-pentadiene (2) with SbF5 in SO2ClF/SO2F2 at −135 °C using high-vacuum co-condensation techniques. The experimental NMR spectra of the mixture of the two isomers were compared with quantum chemical 13C NMR chemical shift calculations at HF-SCF, MP2, CCSD and CCSD(T) levels using MP2/tzp geometries. Quantum chemical shift calculations were performed with a tzp basis (9s5p1d/5s3p1d) for carbon and a dz basis (4s/2s) for hydrogen using gauge-including atomic orbitals (GIAOs). The HF-SCF calculations deviate significantly for the positively charged carbon atoms of the ally…

Approximate treatment of higher excitations in coupled-cluster theory.

The possibilities for the approximate treatment of higher excitations in coupled-cluster (CC) theory are discussed. Potential routes for the generalization of corresponding approximations to lower-level CC methods are analyzed for higher excitations. A general string-based algorithm is presented for the evaluation of the special contractions appearing in the equations specific to those approximate CC models. It is demonstrated that several iterative and noniterative approximations to higher excitations can be efficiently implemented with the aid of our algorithm and that the coding effort is mostly reduced to the generation of the corresponding formulas. The performance of the proposed and …

Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory

We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from st…

Analytic gradients for Mukherjee’s multireference coupled-cluster method using two-configurational self-consistent-field orbitals

Analytic gradients for the state-specific multireference coupled-cluster method suggested by Mahapatra et al. [Mol. Phys. 94, 157 (1998)] (Mk-MRCC) are reported within the singles and doubles approximation using two-configurational self-consistent field (TCSCF) orbitals. The present implementation extends our previous work on Mk-MRCC gradients [E. Prochnow et al., J. Chem. Phys. 131, 064109 (2009)] which is based on restricted Hartree-Fock orbitals and consequently the main focus of the present paper is on the treatment of orbital relaxation at the TCSCF level using coupled-perturbed TCSCF theory. Geometry optimizations on m-arynes and nitrenes are presented to illustrate the influence of t…

Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level.

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing …

The route to high accuracy in ab initio calculations of Cu quadrupole-coupling constants.

We report nonrelativistic and scalar-relativistic coupled-cluster calculations of the copper quadrupole-coupling constants for eleven small copper-containing compounds. It is shown to be necessary to treat both electron-correlation and scalar-relativistic effects on the same footing even for a qualitatively correct description, because both effects are significant and are strongly coupled in the case of Cu electric-field gradients. We show that the three scalar-relativistic schemes employed in the present study--the leading order of direct perturbation theory, the spin-free exact two-component theory in its one-electron variant, and the spin-free Dirac-Coulomb approach--provide accurate tre…

Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree–Fock case

The theory and implementation of approximate coupled-cluster (CC), in particular approximate CC singles, doubles, triples, and quadruples methods, are discussed for general single-determinant reference functions. While the extension of iterative approximate models to the non-Hartree-Fock case is straightforward, the generalization of perturbative approaches is not trivial. In contrast to the corresponding perturbative triples methods, there are additional terms required for non-Hartree-Fock reference functions, and there are several possibilities to derive approximations to these terms. As it turns out impossible to develop an approach that is consistent with the canonical Hartree-Fock-base…

Thermochemical properties of small open-shell systems: experimental and high-levelab initioresults for NH2and

The first adiabatic ionization energy and the first singlet–triplet splitting of the amidogen radical (NH2) have been determined by high-level ab initio quantum chemistry based on the coupled-cluster approach (90 041 and 10 319 cm−1, respectively) and by high-resolution pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy (90 083.8 ± 1.0 and 10 222.0 ± 1.3 cm−1, respectively). A comparison between the theoretical and experimental values demonstrates the predictive powers of high-level ab initio theory in the derivation of the thermochemical properties of small molecular systems. The absolute accuracy of better than 100 cm−1 alleviates the experimental search for…

Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit

In the present letter, it is demonstrated how full configuration interaction (FCI) results in extended basis sets may be obtained to within sub-kJ/mol accuracy by decomposing the energy in terms of many-body expansions in the virtual orbitals of the molecular system at hand. This extension of the FCI application range lends itself to two unique features of the current approach, namely that the total energy calculation can be performed entirely within considerably reduced orbital subspaces and may be so by means of embarrassingly parallel programming. Facilitated by a rigorous and methodical screening protocol and further aided by expansion points different from the Hartree-Fock solution, al…

Hybrid Particle-Field Molecular Dynamics Simulations of Charged Amphiphiles in an Aqueous Environment.

We develop and test specific coarse-grained models for charged amphiphilic systems such as palmitoyloleoylphosphatidylglycerol (POPG) lipid bilayer and sodium dodecyl sulfate (SDS) surfactant in an aqueous environment, to verify the ability of the hybrid particle-field method to provide a realistic description of polyelectrolytes. According to the hybrid approach, the intramolecular interactions are treated by a standard molecular Hamiltonian, and the nonelectrostatic intermolecular forces are described by density fields. Electrostatics is introduced as an additional external field obtained by a modified particle-mesh Ewald procedure, as recently proposed [Zhu et al. Phys. Chem. Chem. Phys.…

Communication: The performance of non-iterative coupled cluster quadruples models

We compare the numerical performance of various non-iterative coupled cluster (CC) quadruples models. The results collectively show how approaches that attempt to correct the CC singles and doubles energy for the combined effect of triple and quadruple excitations all fail at recovering the correlation energy of the full CC singles, doubles, triples, and quadruples (CCSDTQ) model to within sufficient accuracy. Such a level of accuracy is only achieved by models that make corrections to the full CC singles, doubles, and triples (CCSDT) energy for the isolated effect of quadruple excitations of which the CCSDT(Q–3) and CCSDT(Q–4) models of the Lagrangian-based CCSDT(Q–n) perturbation series a…

Quantitative prediction of gas-phase F19 nuclear magnetic shielding constants

Benchmark calculations of (19)F nuclear magnetic shielding constants are presented for a set of 28 molecules. Near-quantitative accuracy (ca. 2 ppm deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gauge-including atomic orbitals are used to ensure gauge-origin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/cc-pVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections…

On the convergence of perturbative coupled cluster triples expansions:Error cancellations in the CCSD(T) model and the importance of amplitude relaxation

Recently, we proposed a novel Lagrangian-based perturbation series-the CCSD(T-n) series-which systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the Møller-Plesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(T-n) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(T-n) series at fourth order (the CCSD(T-4) model), we are able to separate th…

Incremental Treatments of the Full Configuration Interaction Problem

The recent many-body expanded full configuration interaction (MBE-FCI) method is reviewed by critically assessing its advantages and drawbacks in the context of contemporary near-exact electronic structure theory. Besides providing a succinct summary of the history of MBE-FCI to date within a generalized and unified theoretical setting, its finer algorithmic details are discussed alongside our optimized computational implementation of the theory. A selected few of the most recent applications of MBE-FCI are revisited, before we close by outlining its future research directions as well as its place among modern near-exact wave function-based methods.

33S hyperfine interactions in H2S and SO2 and revision of the sulfur nuclear magnetic shielding scale

Using the Lamb-dip technique, the hyperfine structure in the rotational spectra of H2(33)S and (33)SO2 has been resolved and the corresponding parameters--that is, the sulfur quadrupole-coupling and spin-rotation tensors--were determined. The experimental parameters are in good agreement with results from high-level coupled-cluster calculations, provided that up to quadruple excitations are considered in the cluster operator, sufficiently large basis sets are used, and vibrational corrections are accounted for. The (33)S spin-rotation tensor for H2S has been used to establish a new sulfur nuclear magnetic shielding scale, combining the paramagnetic part of the shielding as obtained from the…

The prediction of molecular equilibrium structures by the standard electronic wave functions

A systematic investigation has been carried out of the accuracy of molecular equilibrium structures of 19 small closed-shell molecules containing first-row atoms as predicted by the following standard electronic ab initio models: Hartree–Fock (HF) theory, Mo/ller–Plesset theory to second, third, and fourth orders (MP2, MP3, and MP4), coupled-cluster singles and doubles (CCSD) theory; CCSD theory with perturbational triples corrections [CCSD(T)], and the configuration-interaction singles and doubles (CISD) model. For all models, calculations were carried out using the correlation-consistent polarized valence double-zeta (cc-pVDZ) basis, the correlation-consistent polarized valence triple-zet…

A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy.

Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDTQ) energies, considering the CCSD state as the unperturbed reference state and the fluctua- tion potential as the perturbation. Since the Lagrangian technique is utilized, the energy corrections satisfy Wigner’s 2n + 1 rule for the cluster amplitudes and the 2n + 2 rule for the Lagrange multi- pliers. The energy corrections define the CCSD perturbation series, CCSD(T–n) and CCSD(TQ–n), which are ter…

Analytic CCSD(T) second derivatives

A general-purpose implementation of analytic CCSD(T) second derivatives is presented. Its applicability is demonstrated by calculations of vibration-rotation interaction constants for the astrophysically important molecule cyclopropenylidene (C3H2) in which the required cubic force constants have been determined by numerical differentiation of analytically evaluated second derivatives of the energy.

Reinhart Ahlrichs (1940-2016).

Reinhart Ahlrichs, Professor Emeritus of Theoretical Chemistry at the Karlsruhe Institute of Technology (KIT) and one of the leading figures of both the German and international theoretical chemistry communities, passed away aged 76 on October 12, 2016. His work shaped the field of quantum chemistry and took the interplay between theory and experiment to new levels. He was also the founder of the TURBOMOLE program package.

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and MS = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calcul…

Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory

Schemes for the analytic calculation of the diagonal Born-Oppenheimer correction (DBOC) are formulated and implemented for use with general single-reference configuration-interaction and coupled-cluster wave function models. Calculations are reported to demonstrate the convergence of the DBOC with respect to electron-correlation treatment and basis set as well as to investigate the size-consistency error in configuration-interaction calculations of the DBOC. The importance of electron-correlation contributions to the DBOC is illustrated in the computation of the corresponding corrections for the reaction energy and activation barrier of the F + H2 --FH + H reaction as well as of the atomiza…

Mass-independent analysis of the stable isotopologues of gas-phase titanium monoxide – TiO

More than 130 pure rotational transitions of $^{46}$TiO, $^{47}$TiO, $^{48}$TiO, $^{49}$TiO, $^{50}$TiO, and $^{48}$Ti$^{18}$O are recorded using a high-resolution mm-wave supersonic jet spectrometer in combination with a laser ablation source. For the first time a mass-independent Dunham-like analysis is performed encompassing rare titanium monoxide isotopologues, and are compared to results from high-accuracy quantum-chemical calculations. The obtained parametrization reveals for titanium monoxide effects due to deviations from the Born-Oppenheimer approximation. Additionally, the dominant titanium properties enable an insight into the electronic structure of TiO by analyzing its hyperfin…

Analytic second derivatives for the spin-free exact two-component theory

The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting "electrons-only" two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exp…

Relativistic corrections to electrical first-order properties using direct perturbation theory.

Direct perturbation theory (DPT) is applied to compute relativistic corrections to electrical properties such as dipole moment, quadrupole moment, and electric-field gradient. The corrections are obtained as second derivatives of the energy and are given via method-independent expressions that involve the first derivative of the density matrix with respect to the relativistic perturbation as well as property integrals with additional momentum operators. Computational results obtained using Hartree-Fock (HF), second-order Moller-Plesset (MP2) perturbation theory, and the coupled-cluster singles and doubles approach augmented by a perturbative treatment of triple excitations are presented for…

Generalized Many-Body Expanded Full Configuration Interaction Theory

Facilitated by a rigorous partitioning of a molecular system's orbital basis into two fundamental subspaces - a reference and an expansion space, both with orbitals of unspecified occupancy - we generalize our recently introduced many-body expanded full configuration interaction (MBE-FCI) method to allow for electron-rich model and molecular systems dominated by both weak and strong correlation to be addressed. By employing minimal or even empty reference spaces, we show through calculations on the one-dimensional Hubbard model with up to 46 lattice sites, the chromium dimer, and the benzene molecule how near-exact results may be obtained in a entirely unbiased manner for chemical and physi…

Vibrational Energy Levels via Finite-Basis Calculations Using a Quasi-Analytic Form of the Kinetic Energy

A variational method for the calculation of low-lying vibrational energy levels of molecules with small amplitude vibrations is presented. The approach is based on the Watson Hamiltonian in rectilinear normal coordinates and characterized by a quasi-analytic integration over the kinetic energy operator (KEO). The KEO beyond the harmonic approximation is represented by a Taylor series in terms of the rectilinear normal coordinates around the equilibrium configuration. This formulation of the KEO enables its extension to arbitrary order until numerical convergence is reached for those states describing small amplitude motions and suitably represented with a rectilinear system of coordinates. …

The Grignard Reaction − Unraveling a Chemical Puzzle

More than 100 years since its discovery, the mechanism of the Grignard reaction remains unresolved. Ambiguities arise from the concomitant presence of multiple organomagnesium species and the competing mechanisms involving either nucleophilic addition or the formation of radical intermediates. To shed light on this topic, quantum-chemical calculations and ab initio molecular dynamics simulations are used to study the reaction of CH3MgCl in tetrahydrofuran with acetaldehyde and fluorenone as prototypical reagents. All organomagnesium species coexisting in solution due to the Schlenk equilibrium are found to be competent reagents for the nucleophilic pathway. The range of activation energies …

The hyperfine structure in the rotational spectrum of water: Lamb-dip technique and quantum-chemical calculations

Seven ortho rotational transitions have been recorded for the main isotopic species of water in the mil- limeter- and submillimeter-wave region using the Lamb-dip technique in order to resolve the hyperfine structure due to the hydrogens and to provide accurate hyperfine constants. The experimental determi- nation has been supplemented by high-level quantum-chemical calculations of the hyperfine parameters thereby focusing in particular on a systematic study of the basis-set convergence and on vibrational effects.

CCSDT calculations of molecular equilibrium geometries

Abstract CCSDT equilibrium geometries of CO, CH2, F2, HF, H2O and N2 have been calculated using the correlation-consistent cc-pVXZ basis sets. Similar calculations have been performed for SCF, CCSD and CCSD(T). In general, bond lengths decrease when improving the basis set and increase when improving the N-electron treatment. CCSD(T) provides an excellent approximation to CCSDT for bond lengths as the largest difference between CCSDT and CCSD(T) is 0.06 pm. At the CCSDT/cc-pVQZ level, basis set deficiencies, neglect of higher-order excitations, and incomplete treatment of core-correlation all give rise to errors of a few tenths of a pm, but to a large extent, these errors cancel. The CCSDT/…

Mechanically interlocked calix[4]arene dimers display reversible bond breakage under force.

The physics of nanoscopic systems is strongly governed by thermal fluctuations that produce significant deviations from the behaviour of large ensembles1,2. Stretching experiments of single molecules offer a unique way to study fundamental theories of statistical mechanics, as recently shown for the unzipping of RNA hairpins3. Here, we report a molecular design based on oligo calix[4]arene catenanes—calixarene dimers held together by 16 hydrogen bridges—in which loops within the molecules limit how far the calixarene nanocapsules can be separated. This mechanically locked structure tunes the energy landscape of dimers, thus permitting the reversible rupture and rejoining of the individual n…

A comparison of density-functional-theory and coupled-cluster frequency-dependent polarizabilities and hyperpolarizabilities

The frequency-dependent polarizabilities and hyperpolarizabilities of HF, CO, H2O and para-nitroaniline calculated by density-functional theory are compared with accurate coupled-cluster results. Whereas the local-density approximation and the generalized gradient approximation (BLYP) perform very similarly and overestimate polarizabilities and, in particular, the hyperpolarizabilities, hybrid density-functional theory (B3LYP) performs better and produces results similar to those obtained by coupled-cluster singles-and-doubles theory. Comparisons are also made for singlet excitation energies, calculated using linear response theory.

Unravelling the fine structure of stacked bipyridine diamine-derived C-3-discotics as determined by X-ray diffraction, quantum-chemical calculations, Fast-MAS NMR and CD spectroscopy

An in depth investigation of the fine structure adopted by the helical stacks of C3-discotics 1 incorporating three 3,3'-diamino-2,2'-bipyridine units is described. In the bulk the molecules display liquid crystalline behaviour in a temperature window of >300 K and an ordered rectangular columnar mesophase (Colro) with an inter-disc distance of 3.4 Å is assigned. X-Ray diffraction on aligned samples has also revealed a helical superstructure in the liquid crystalline state, and a rotation angle of 13–16° between consecutive discs. The proposed superstructure in the bulk phase has been further substantiated by a combination of quantum-chemical calculations and solid-state NMR spectroscopy…

Revisitation of Nonorthogonal Spin Adaptation in Coupled Cluster Theory.

The benefits of what is alternatively called a nonorthogonally spin-adapted, spin-free, or orbital representation of the coupled cluster equations is discussed relative to orthogonally spin-adapted, spin-orbital, and spin-integrated theories. In particular, specific linear combinations of the orbital cluster amplitudes, denoted spin-summed amplitudes, are shown to reduce the number of contractions that must be explicitly performed and to simplify the expressions and their derivation. The computational efficiency of the spin-summed approach is discussed and compared to orthogonally spin-adapted and spin-integrated approaches. The spin-summed approach is shown to have significant computationa…

The equilibrium structure of propadienylidene

Abstract A coupled-cluster study of the equilibrium geometry of propadienylidene (C3H2) is presented. Deviations between a recently reported experimental re structure and those computed at the CCSD(T)/cc-pVQZ and CCSD(T)/cc-pCVQZ levels are larger than expected. A closer analysis reveals that this discrepancy is due to inaccuracies in the cubic force field that was used to correct the measured rotational constants for vibrational effects. A satisfactory agreement between theory and experiment is obtained if the vibrational effects on the rotational constants are computed from harmonic and cubic force fields determined at either the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pCVTZ levels. Revised values…

Temperature dependent mechanical unfolding of calixarene nanocapsules studied by molecular dynamics simulations.

Using atomistic molecular dynamics simulations, we study the temperature dependence of the mechanical unfolding of a model supramolecular complex, a dimer of interlocked calixarene capsules. This system shows reversible transitions between two conformations that are stabilized by different networks of hydrogen bonds. We study the forced dissociation and formation of these networks as a function of temperature and find a strong impact of the nonequilibrium conditions imposed by pulling the system mechanically. The kinetics of the transition between the two conformations is ideally suited to investigate the range of validity of the stochastic models employed in the analysis of force dependent…

Deuterium hyperfine splittings in the rotational spectrum of NH2D as revealed by Lamb-dip spectroscopy

Abstract In the context of radio-astronomical observations, laboratory experiments constitute a cornerstone in the interpretation of rich line surveys due to the concomitant presence of numerous emitting molecules. Here, we report the investigation of three different rotational transitions of mono-deuterated ammonia (NH2D), a species of astrophysical interest, for which the contribution of the deuterium nuclear spin to the rotational spectrum has been resolved for the first time in the millimeter- and submillimeter-wave domain. The effect of hyperfine interactions on the rotational spectrum has been unveiled by a combined theoretical and experimental approach. Quantum-chemical calculations …

Die Bindungsverhältnisse in schweren Analoga des Cyanwasserstoffs: der merkwürdige Fall des HPSi

The first excited singlet state of s‐tetrazine: A theoretical analysis of some outstanding questions

The equation‐of‐motion coupled cluster method for excited electronic states (EOMEE‐CC) is applied to study the structure and selected properties of the first excited singlet state of s‐tetrazine. Adiabatic S1←S0 excitation energies obtained with large basis sets containing up to 270 functions are uniformly somewhat above the experimental 0–0 value of 2.238 eV, but nevertheless are the most accurate calculations reported to date for this quantity. The equilibrium geometry of S1 predicted in this study is in excellent agreement with another high‐level calculation, and moreover is quantitatively consistent with both the intensity of vibrational progressions observed in absorption and measured …

Reversible hydrogen bond network dynamics: molecular dynamics simulations of calix[4]arene-catenanes.

We present detailed molecular dynamics (MD) simulations of mechanically interlocked calix[4]arene-catenanes under external force. Single-molecule force spectroscopy experiments revealed that the separation of dimers with two aliphatic loops results in reversible hydrogen bond breakage through an intermediate in a triple-well potential, while the tetra-loop species separates in a one-step manner (Janke, M.; et al. Nat. Nanotechnol. 2009, 4, 225). MD simulations show that calix[4]arenes interlocked by four loops (1) display a complete restructuring of the hydrogen bond network under mechanical force. All hydrogen bonds of the closed structure open, and new ones are formed in the extended stru…

Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies

The recently presented linear-response function for Mukherjee's multireference coupled-cluster method (Mk-MRCC) [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044115 (2012)] is employed to determine vertical excitation energies within the singles and doubles approximation (Mk-MRCCSD-LR) for ozone as well as for o-benzyne, m-benzyne, and p-benzyne, which display increasing multireference character in their ground states. In order to assess the impact of a multireference ground-state wavefunction on excitation energies, we compare all our results to those obtained at the single-reference coupled-cluster level of theory within the singles and doubles as well as within the singles, doubles, and…

Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations.

We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for p…

A simple scheme for the direct calculation of ionization potentials with coupled-cluster theory that exploits established excitation energy methods

Vertical ionization potentials can be obtained from existing computer programs for the high-level treatment of excited states by simply including a continuum orbital in the basis set. Exploiting this feature easily allows final state energies for ionized states to be calculated at several previously untested levels of theory that go beyond the equation-of-motion coupled-cluster singles and doubles model. Values obtained for N2, CO, and F2 with the most theoretically complete approximations studied here (those based on the CCSDT-3 and CC3 parametrizations of the neutral ground state) are in excellent agreement with experiment when a large basis set is used.

Spin-restricted open-shell coupled-cluster theory

Spin-restricted CC theory is suggested as a new approach for the treatment of high-spin open-shell systems in CC theory. Spin constraints are imposed on the wave function in the sense that the projected spin eigenvalue equations are fulfilled within the (truncated) excitation space. These constraints allow a reduction in the number of independent amplitudes, thus decreasing the computational cost when implemented efficiently. The approach ensures that the spin expectation value always corresponds to the exact value, though the wave function is (for truncated CC treatments) not rigorously spin-adapted. For the specific case of high-spin doublets, detailed equations are derived for amplitudes…

Microwave, High-Resolution Infrared, and Quantum Chemical Investigations of CHBrF2: Ground and v4 = 1 States

A combined microwave, infrared, and computational investigation of CHBrF(2) is reported. For the vibrational ground state, measurements in the millimeter- and sub-millimeter-wave regions for CH(79)BrF(2) and CH(81)BrF(2) provided rotational and centrifugal-distortion constants up to the sextic terms as well as the hyperfine parameters (quadrupole-coupling and spin-rotation interaction constants) of the bromine nucleus. The determination of the latter was made possible by recording of spectra at sub-Doppler resolution, achieved by means of the Lamb-dip technique, and supporting the spectra analysis by high-level quantum chemical calculations at the coupled-cluster level. In this context, the…

Perturbative treatment of the electron-correlation contribution to the diagonal Born-Oppenheimer correction.

A perturbative scheme for the treatment of electron-correlation effects on the diagonal Born-Oppenheimer correction (DBOC) is suggested. Utilizing the usual Moller-Plesset partitioning of the Hamiltonian formulas for first and second orders (termed as MP1 and MP2) are obtained by expanding the wave function in the corresponding coupled-cluster expressions for the DBOC[J. Gauss et al., J. Chem. Phys. 125, 144111 (2006)]. The obtained expressions are recast in terms of one- and two-particle density matrices in order to take advantage of existing analytic second-derivative implementations for many-body methods. Test calculations show that both MP1 and MP2 recover large fractions (on average 90…

Towards highly accurate ab initio thermochemistry of larger systems: benzene.

The high accuracy extrapolated ab initio thermochemistry (HEAT) protocol is applied to compute the total atomization energy (TAE) and the heat of formation of benzene. Large-scale coupled-cluster calculations with more than 1500 basis functions and 42 correlated electrons as well as zero-point energies based on full cubic and (semi)diagonal quartic force fields obtained with the coupled-cluster singles and doubles with perturbative treatment of the triples method and atomic natural orbital (ANO) triple- and quadruple-zeta basis sets are presented. The performance of modifications to the HEAT scheme and the scaling properties of its contributions with respect to the system size are investiga…

Vibrational Excitation Hindering an Ion-Molecule Reaction: The c−C3H2+−H2 Collision Complex

Experiments within a cryogenic 22-pole ion trap have revealed an interesting reaction dynamic phenomenon, where rovibrational excitation of an ionic molecule slows down a reaction with a neutral partner. This is demonstrated for the low-temperature hydrogen abstraction reaction $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{2}}^{+}+{\mathrm{H}}_{2}$, where excitation of the ion into the ${\ensuremath{\nu}}_{7}$ antisymmetric C-H stretching mode decreased the reaction rate coefficient toward the products $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{3}}^{+}+\mathrm{H}$. Supported by high-level quantum-chemical calculations, this observation is explained by th…

Comparison of full-configuration interaction and coupled-cluster harmonic and fundamental frequencies for BH and HF

The harmonic and fundamental frequencies are calculated for the potential-energy curves of BH and HF using the full-configuration interaction model and two hierarchies of coupled-cluster wavefunction models. The anharmonic contributions are also obtained using second-order vibrational perturbation theory. A consistent and systematic improvement is seen for both the harmonic and anharmonic contributions when increasing the level of the correlation treatment. The changes are largest for the harmonic contributions. This is also the case when including valence or diffuse functions in the basis set. Second-order perturbation theory gives a good approximation to the anharmonic contribution and in…

Gas-phase detection of HSOD and empirical equilibrium structure of oxadisulfane

We present the first gas phase spectra of singly deuterated oxadisulfane, HSOD, in its vibrational ground state. More than 100 transitions have been recorded with highest frequency accuracy using the Cologne Terahertz Spectrometer. The molecular parameters derived from a least squares fit analysis proof HSOD to be an almost accidental symmetric prolate top molecule with an asymmetry parameter kZK0.9985. Spectra of c-type and weaker b-type transitions have been recorded in the range from 716 to 772 GHz. The ratio of the dipole moments mc/mbZ2.4(3) has been derived from measured line intensities. The c-type transitions are split by the tunneling motion of a hindered internal rotation, whereas…

Unveiling the Sulfur–Sulfur Bridge: Accurate Structural and Energetic Characterization of a Homochalcogen Intermolecular Bond

open 12 si MIUR “PRIN 2015” funds (Grant Number 2015F59J3R) By combining rotational spectroscopy in supersonic expansion with the capability of state-of-the-art quantum-chemical computations in accurately determining structural and energetic properties, the genuine nature of a sulfur–sulfur chalcogen bond between dimethyl sulfide and sulfur dioxide has been unveiled in a gas-jet environment free from collision, solvent and matrix perturbations. A SAPT analysis pointed out that electrostatic S⋅⋅⋅S interactions play the dominant role in determining the stability of the complex, largely overcoming dispersion and C−H⋅⋅⋅O hydrogen-bond contributions. Indeed, in agreement with the analysis of the…

Complex Ground-State and Excitation Energies in Coupled-Cluster Theory

Since in coupled-cluster (CC) theory ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper we discuss the appearance of complex energy values in CC calculations from a mathematical perspective. We analyze the behaviour of the eigenvalues of Hermitian matrices that are perturbed (in a non-Hermitian manner) by a real parameter. Based on these results we show that for CC calculations with real-valued Hamiltonian matrices the ground-state energy generally takes a real value. Furthermore, we show that in the case of real-valued Hamiltonian matrices complex excitation energies only occur in the context…

The temperature dependence of vibronic lineshapes: linear electron-phonon coupling.

We calculate the effect of a linear electron-phonon coupling on vibronic transitions of dye molecules of arbitrary complexity. With the assumption of known vibronic frequencies (for instance from quantum-chemical calculations), we give expressions for the absorption or emission lineshapes in a second-order cumulant expansion. We show that the results coincide with those obtained from generalized Redfield theory if one uses the time-local version of the theory and applies the secular approximation. Furthermore, the theory allows to go beyond the Huang-Rhys approximation and can be used to incorporate Dushinsky effects in the treatment of the temperature dependence of optical spectra. We cons…

Analytic gradients for the state-specific multireference coupled cluster singles and doubles model.

The general theory of analytic energy gradients is presented for the state-specific multireference coupled cluster method introduced by Mukherjee and co-workers [Mol. Phys. 94, 157 (1998)], together with an implementation within the singles and doubles approximation, restricted to two closed-shell determinants and Hartree-Fock orbitals. Expressions for the energy gradient are derived based on a Lagrangian formalism and cast in a density-matrix notation suitable for implementation in standard quantum-chemical program packages. In the present implementation, we exploit a decomposition of the multireference coupled cluster gradient expressions, i.e., lambda equations and the corresponding dens…

Closed-shell coupled-cluster theory with spin-orbit coupling

A two-component closed-shell coupled-cluster (CC) approach using relativistic effective core potentials with spin-orbit coupling included in the post-Hartree-Fock treatment is proposed and implemented at the CC singles and doubles (CCSD) level as well as at the CCSD level augmented by a perturbative treatment of triple excitations [CCSD(T)]. The latter invokes as an additional approximation the neglect of the occupied-occupied and virtual-virtual blocks of the spin-orbit coupling matrix in order to avoid the iterative N(7) steps in the treatment of triple excitations. The computational effort of the implemented two-component CC methods is about 10-15 times that of its corresponding nonrelat…

Electron-Correlated Approaches for the Calculation of NMR Chemical Shifts

On the geometry of the HO3 radical

Abstract We discuss the equilibrium structure of the hydrogen trioxy radical (HO3). The CCSD(T) geometry at the approximate basis set limit, in conjunction with the geometry obtained using the CCSDT method and a moderate basis set, suggests an equilibrium HO–OO bond length of approximately 1.59 A.

Calculation of electronic g-tensors using coupled cluster theory.

A scheme for the calculation of the electronic g-tensor at the coupled cluster (CC) level is presented. The reported implementation employs an effective one-electron spin-orbit operator, allows the inclusion of arbitrary excitations in the cluster operator, and offers various options concerning the treatment of orbital relaxation and choice of reference determinants. In addition, the use of gauge-including atomic orbitals (GIAOs) is possible to overcome the gauge origin problem. Benchmark calculations for the NH ((3)Sigma(-)) radical reveal the importance of electron correlation effects for the accurate prediction of the g-shift as well as the slow basis set convergence of such calculations…

Quantum-chemical determination of Born–Oppenheimer breakdown parameters for rotational constants: the open-shell species CN, CO+ and BO

The quantum-chemical protocol for computing Born-Oppenheimer breakdown corrections to rotational constants in the case of diatomic molecules is extended to open-shell species. The deviation from the Born-Oppenheimer equilibrium rotational constant is obtained by considering three contributions: the adiabatic correction to the equilibrium bond distance, the electronic contribution to the moment of inertia requiring the computation of the rotational g-tensor, and the so-called Dunham correction. Values for the Born-Oppenheimer breakdown parameters of CN, CO+, and BO in their (2)sigma(+) electronic ground states are reported based on coupled-cluster calculations of the involved quantities and …

The empirical equilibrium structure of diacetylene

High-level quantum-chemical calculations are reported at the MP2 and CCSD(T) levels of theory for the equilibrium structure and the harmonic and anharmonic force fields of diacetylene, HCCCCH. The calculations were performed employing Dunning's hierarchy of correlation-consistent basis sets cc-pVXZ, cc-pCVXZ, and cc-pwCVXZ, as well as the ANO2 basis set of Almloef and Taylor. An empirical equilibrium structure based on experimental rotational constants for thirteen isotopic species of diacetylene and computed zero-point vibrational corrections is determined (r_e^emp: rC-H=1.0615 A, rCtripleC=1.2085 A, rC-C = 1.3727 A) and in good agreement with the best theoretical structure (CCSD(T)/cc-pCV…

Triple excitation effects in coupled cluster calculations of Verdet constants

Abstract The CC3 approach has been employed to calculate the Verdet constants of N 2 ,C 2 H 2 , and CH 4 . For N 2 and C 2 H 2 , relatively large triples contributions are found which need to be included in order to reach close agreement with the experimental constants.

Flexibility of phenylene oligomers revealed by single molecule spectroscopy

The rigidity of a p-phenylene oligomer (p-terphenyl) has been investigated by single molecule confocal fluorescence microscopy. Two different rylene diimide dyes attached to the terminal positions of the oligomer allowed for wavelength selective excitation of the two chromophores. In combination with polarization modulation the spatial orientation of the transition dipoles of both end groups could be determined independently. We have analyzed 597 single molecules in two different polymer hosts, polymethylmethacrylate and Zeonex. On average we find a 22 degrees deviation from the linear gas phase geometry (T = 0 K), indicating a rather high flexibility of the p-phenylene oligomer independent…

A fundamental catalytic difference between zinc and manganese dependent enzymes revealed in a bacterial isatin hydrolase

Scientific reports 8(1), 13104 (2018). doi:10.1038/s41598-018-31259-y

The hyperfine structure in the rotational spectrum of CF+

Context. CF+ has recently been detected in the Horsehead and Orion Bar photo-dissociation regions. The J=1-0 line in the Horsehead is double-peaked in contrast to other millimeter lines. The origin of this double-peak profile may be kinematic or spectroscopic. Aims. We investigate the effect of hyperfine interactions due to the fluorine nucleus in CF+ on the rotational transitions. Methods. We compute the fluorine spin rotation constant of CF+ using high-level quantum chemical methods and determine the relative positions and intensities of each hyperfine component. This information is used to fit the theoretical hyperfine components to the observed CF+ line profiles, thereby employing the h…

Frequency-dependent polarizabilities and first hyperpolarizabilities of CO and H2O from coupled cluster calculations

Abstract Frequency-dependent electronic polarizabilities and first hyperpolarizabilities for CO and H 2 O have been investigated in coupled-cluster response theory calculations. Triple excitation effects have been considered by means of the CC3 model which has recently been implemented for frequency-dependent polarizabilities and first hyperpolarizabilities. The final estimates for polarizabilities and first hyperpolarizabilities are in good agreement with experimental results.

Hyperfine structure in the rotational spectra of trans-formic acid: Lamb-dip measurements and quantum-chemical calculations

Context. Formic acid, HCOOH, is the simplest organic acid and the first that has been identified in the interstellar medium. Its astrophysical relevance has motivated this spectroscopic study. Aims. The aim of this investigation is to provide very accurate rest frequencies for the trans isomer of HCOOH as well as to improve the spectroscopic and hyperfine parameters available in the literature for this molecule. Methods. The Lamb-dip technique has been exploited in order to record the rotational spectrum of trans-HCOOH at sub-Doppler resolution in the millimeter- and submillimeter-wave frequency ranges and, when possible, to resolve the hyperfine structure due to the hydrogen nuclei. THz me…

Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level

In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorp…

Structural Origin of Metal Specificity in Isatin Hydrolase from Labrenzia aggregata Investigated by Computer Simulations.

We performed quantum-chemical calculations, ab initio molecular dynamics, hybrid quantum mechanics/molecular mechanics (QM/MM) and enhanced sampling metadynamics simulations to investigate the origin of metal specificity in isatin hydrolase from Labrenzia aggregata. The peculiar octahedral binding geometry of the Mn2+ ion in the Michaelis complex includes both the isatin substrate and the catalytic water within the first coordination shell of the cation. Our calculations show that the same arrangement of the ligands cannot be efficiently achieved in the presence of other small divalent metal cations such as Zn2+ or Cu2+ . On the contrary, bulkier alkaline-earth cations such as Mg2+ , which …

The Born–Oppenheimer equilibrium bond distance of GeO from millimetre- and submillimetre-wave spectra and quantum-chemical calculations

The millimetre- and submillimetre-wave spectra of the five common isotopologues of (GeO)-O-16 in their electronic and vibrational ground state have been recorded in the spectral region 115-732GHz; for (GeO)-Ge-74-O-16, the rotational spectrum in the v = 1 state has been detected as well. Exploiting the high precision of the measurements, the Born-Oppenheimer breakdown parameter Delta(Ge)(01) could be determined from a Dunham analysis of the spectral data, whereas Delta(O)(01) was obtained from quantum-chemical calculations, because of the lack of high-precision measurements for the (GeO)-O-18 isotopologues. From the rotational equilibrium constant, the Born-Oppenheimer equilibrium distance …

Comparative Study of the Mechanical Unfolding Pathways of α- and β-Peptides

Using molecular simulations, we analyze the unfolding pathways of various peptides. We compare the mechanical unfolding of a β-alanine's octamer (β-HAla8) and an α-alanine's decamer (α-Ala10). Using force-probe molecular-dynamics simulations, to induce unfolding, we show that the 3(14)-helix formed by β-HAla8 is mechanically more stable than the α-helix formed by α-Ala10, although both structures are stabilized by six hydrogen bonds. Additionally, computations of the potential of mean force validate this result and show that also the thermal stability of the 3(14)-helix is higher. It is demonstrated that β-HAla8 unfolds in a two-step fashion with a stable intermediate. This is contrasted wi…

Equation-of-motion coupled cluster perturbation theory revisited

The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]

Germanium Dicarbide: Evidence for a T-Shaped Ground State Structure

The equilibrium structure of germanium dicarbide GeC2 has been an open question since the late 1950s. Although most high-level quantum calculations predict an L-shaped geometry, a T-shaped or even a linear geometry cannot be ruled out because of the very flat potential energy surface. By recording the rotational spectrum of this dicarbide using sensitive microwave and millimeter techniques, we unambiguously establish that GeC2 adopts a vibrationally averaged T-shaped structure in its ground state. From analysis of 14 isotopologues, a precise r0 structure has been derived, yielding a Ge–C bond length of 1.952(1) A and an apex angle of 38.7(2)°.

Analytic first and second derivatives for the CCSDT-n (n = 1–3) models: a first step towards the efficient calculation of CCSDT properties

Analytic first and second derivatives of the energy are implemented for closed-shell systems described by the CCSDT-n (n=1, 1b, 2 and 3) and CC3 electron correlation models. A detailed discussion of the computational requirements of these calculations is given, along with diagrammatic formulas for all relevant quantities. The method is applied to calculate the nuclear magnetic shielding of H2O, CO and N2O and the structure and properties of propadienylidene.

The barrier height of the F+H2 reaction revisited: coupled-cluster and multireference configuration-interaction benchmark calculations.

Large scale coupled-cluster benchmark calculations have been carried out to determine the barrier height of the F+H2 reaction as accurately as possible. The best estimates for the barrier height of the linear and bent transition states amount to 2.16 and 1.63 kcal/mol, respectively. These values include corrections for core correlation, scalar-relativistic effects, spin-orbit effects, as well as the diagonal Born-Oppenheimer correction. The CCSD(T) basis-set limits are estimated using extrapolation techniques with augmented quintuple and sextuple-zeta basis sets, and remaining N-electron errors are determined using coupled-cluster singles, doubles, triples, quadruples calculations with up t…

Critical analysis of the spin-rotation constants of CF2 and CCl2: A theoretical investigation

Quantum chemical ab initio calculations for the spin-rotation constants of difluorocarbene (CF2) and dichlorocarbene (CCl2) were carried out using coupled-cluster techniques with sequences of correlation-consistent basis sets. Theoretical best estimates were obtained using extrapolation to the complete basis-set limit and taking into account corrections for core correlation, additional diffuse functions and zero-point vibrational effects. It is demonstrated that such accurate theoretical estimates can be used either to support or to challenge the analysis of the experimental spectra and the reliability of the resulting data. 2005 Elsevier B.V. All rights reserved.

Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory.

In this work, we present relativistic corrections to first-order electrical properties obtained using fourth-order direct perturbation theory (DPT4) at the Hartree-Fock level. The considered properties, i.e., dipole moments and electrical-field gradients, have been calculated using numerical differentiation techniques based on a recently reported DPT4 code for energies [S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011)]. For the hydrogen halides HX, X=F, Cl, Br, I, and At, we study the convergence of the scalar-relativistic contributions by comparing the computed DPT corrections to results from spin-free Dirac-Hartree-Fock calculations. Furthermore, since in the DPT series spin-…

Internally Contracted Multireference Coupled Cluster Calculations with a Spin-Free Dirac-Coulomb Hamiltonian: Application to the Monoxides of Titanium, Zirconium, and Hafnium

We combine internally contracted multireference coupled cluster theory with a four-component treatment of scalar-relativistic effects based on the spin-free Dirac–Coulomb Hamiltonian. This strategy allows for a rigorous treatment of static and dynamic correlation as well as scalar-relativistic effects, which makes it viable to describe molecules containing heavy transition elements. The use of a spin-free formalism limits the impact of the four-component treatment on the computational cost to the non-rate-determining steps of the calculations. We apply the newly developed method to the lowest singlet and triplet states of the monoxides of titanium, zirconium, and hafnium and show how the in…

Accuracy of Rotational Parameters Predicted by High-Level Quantum-Chemical Calculations: Case Study of Sulfur-Containing Molecules of Astrochemical Interest

The accuracy of rotational parameters obtained from high-level quantum-chemical calculations is discussed for molecules containing second-row atoms. The main focus is on computed rotational constants for which two statistical analyses have been carried out. A first benchmark study concerns sulfur-bearing species and involves 15 molecules (for a total of 74 isotopologues). By comparing 15 different computational approaches, all of them based on the coupled-cluster singles and doubles approach (CCSD) augmented by a perturbative treatment of triple excitations, CCSD(T), we have analyzed the effects on computed rotational constants due to (i) extrapolation to the complete basis-set limit, (ii) …

Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS

An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (12Π) and first electronically excited (12Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 12Π→12Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities…

Gas-Phase Vibrational Spectroscopy of the Hydrocarbon Cations l-C3H+, HC3H+, and c-C3H2+: Structures, Isomers, and the Influence of Ne-Tagging

We report the first gas-phase vibrational spectra of the hydrocarbon ions C3H+ and C3H2+. The ions were produced by electron impact ionization of allene. Vibrational spectra of the mass-selected ions tagged with Ne were recorded using infrared predissociation spectroscopy in a cryogenic ion trap instrument using the intense and widely tunable radiation of a free electron laser. Comparison of high-level quantum chemical calculations and resonant depletion measurements revealed that the C3H+ ion is exclusively formed in its most stable linear isomeric form, whereas two isomers were observed for C3H2+. Bands of the energetically favored cyclic c-C3H2+ are in excellent agreement with calculated…

Determining Factors for the Unfolding Pathway of Peptides, Peptoids, and Peptidic Foldamers.

We present a study of the mechanical unfolding pathway of five different oligomers (α-peptide, β-peptide, δ-aromatic-peptides, α/γ-peptides, and β-peptoids), adopting stable helix conformations. Using force-probe molecular dynamics, we identify the determining structural factors for the unfolding pathways and reveal the interplay between the hydrogen bond strength and the backbone rigidity in the stabilization of their helix conformations. On the basis of their behavior, we classify the oligomers in four groups and deduce a set of rules for the prediction of the unfolding pathways of small foldamers.

Cyclic SiS2: a new perspective on the Walsh rules.

Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. I. Triples expansions

The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species …

Spin-orbit coupling constants from coupled-cluster response theory

A scheme for the calculation of spin-orbit coupling constants using coupled-cluster (CC) electronic structure methods is described based on response-theory expressions for transition properties. An implementation is reported for singlet–triplet transitions within the coupled-cluster singles and doubles (CCSD) approximation. An atomic mean-field representation of the spin-orbit interaction is used to simplify the calculation of spin-orbit coupling constants. Sample calculations are presented for spin-orbit couplings for the 11Σ+→13Π transitions for BH and AlH and for the 11A′→13A″ and the 13A″→11A″ transitions for the silylenes HSiX, X=F, Cl, Br, and are compared to results obtained from ful…

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles

Abstract The shape and size of self‐assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long‐range interactions. Combining small‐angle X‐ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry br…

Cyclisches SiS2 - die Walsh-Regeln in neuem Licht

Exotic SiO(2)H(2) Isomers: Theory and Experiment Working in Harmony.

Replacing carbon with silicon can result in dramatic and unanticipated changes in isomeric stability, as the well-studied CO2H2 and the essentially unknown SiO2H2 systems illustrate. Guided by coupled-cluster calculations, three SiO2H2 isomers have been detected and spectroscopically characterized in a molecular beam discharge source using rotational spectroscopy. The cis,trans conformer of dihydroxysilylene HOSiOH, the ground-state isomer, and the high-energy, metastable dioxasilirane c-H2SiO2 are abundantly produced in a dilute SiH4/O2 electrical discharge, enabling precise structural determinations of both by a combination of isotopic measurements and calculated vibrational corrections. …

The rotational spectrum of 17O2 up to the THz region

Abstract The investigation of the pure rotational spectrum of the 17O2 isotopic species of molecular oxygen has been extended with respect to previous investigations to the submillimeter-wave region, from 230 GHz up to 1.06 THz. The resulting spectroscopic parameters, which have an accuracy comparable to that of the constants obtained from an updated isotopic invariant fit involving data for three electronic states and six isotopologues [Yu et al. High resolution spectral analysis of oxygen. IV. Energy levels, partition sums, bandconstants, RKR potentials, Franck–Condon factors involving the X 3 Σ g − , a 1 Δ g , and b 1 Σ g + states. J Chem Phys 2014;141:174302/1–12], permit the prediction…

Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory

The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections t…

Orbital instabilities and spin-symmetry breaking in coupled-cluster calculations of indirect nuclear spin–spin coupling constants

Abstract The effect of orbital instabilities is investigated for spin-symmetry breaking perturbations, namely the Fermi-contact (FC) and spin–dipole (SD) contributions to the indirect nuclear spin–spin coupling constants. For the CO and N 2 molecules the FC and SD contributions have been calculated and orbital-stability analyses for various interatomic distances have been carried out. This includes calculations at the Hartree–Fock self-consistent field (HF-SCF), coupled-cluster (CC) singles and doubles (CCSD), CC3, CCSD(T), CCSDT-4, CC singles, doubles, and triples (CCSDT) levels, and for the first time also at the CC singles, doubles, triples, and quadruples (CCSDTQ) level of theory. For c…

Gas-Phase Spectroscopic Detection and Structural Elucidation of Carbon-Rich Group 14 Binary Clusters: Linear GeC3Ge

Guided by high-level quantum-chemical calculations at the CCSD(T) level of theory, the first polyatomic germanium-carbon cluster, linear Ge2C3, has been observed at high spectral resolution in the gas phase through its remarkably complex fundamental antisymmetric C-C stretching mode ν3 located at 1932 cm(-1). The observation of a total of six isotopic species permits the derivation of a highly accurate value for the equilibrium Ge-C bond length. The present study suggests that many more Ge-C species might be detectable in the future using a combination of laser-ablation techniques for production and high-resolution infrared and/or microwave techniques for spectroscopic detection.

Mechanical unfolding pathway of a model β-peptide foldamer.

Foldamers constructed from oligomers of β-peptides form stable secondary helix structures already for small chain lengths, which makes them ideal candidates for the investigation of the (un)folding of polypeptides. Here, the results of molecular simulations of the mechanical unfolding of a β-heptapeptide in methanol solvent revealing the detailed unfolding pathway are reported. The unfolding process is shown to proceed via a stable intermediate even for such a small system. This result is arrived at performing non-equilibrium force ramp simulations employing different pulling velocities and also using standard calculations of the potential of mean force, i.e., the free energy as a function …

The semi-experimental equilibrium structures of AlCCH and AlNC

Abstract Based on experimental rotational constants available in the literature (Walker and Gerry, Chem. Phys. Lett. 278, 9 (1997); Walker et al., J. Mol. Spectrosc. 209, 178 (2001); Sun et al., Chem. Phys. Lett. 553, 11 (2012)) [14,17,19] for five isotopologues of AlCCH and three isotopologues of AlNC as well as quantum-chemical computations for the vibrational corrections to rotational constants, the semi-experimental structures of these two aluminum compounds are determined. These empirical equilibrium structures (AlCCH: r e (Al C) = 1.957 A, r e (C C) = 1.222 A, r e (C H) = 1.065 A; AlNC: r e (Al N) = 1.850 A, r e (N C) = 1.181 A) compare favorably with theoretical best-estimate structu…

New Carbaalanes − (AlMe)8(CCH2Me)5(C≡C−Me) and the THF Adduct (AlMe)8(CCH2Me)5H·2THF

The hydroalumination of Me2Al−C≡C−Me with a large excess of Me2AlH afforded the arachno-carbaalane (AlMe)8(CCH2Me)5H (4) by the release of AlMe3. 4 is almost insoluble in noncoordinating solvents and could not be purified by recrystallization. On an attempt to recrystallize 4 from a THF solution, the adduct (AlMe)8(CCH2Me)5H·2THF (5) was isolated as the first stable ether adduct of a carbaalane. Crystal structure determination revealed a cube of eight aluminium atoms, five faces of which are bridged by C−CH2Me groups. The sixth face is µ2-bridged by a hydrogen atom, and two opposite aluminium atoms of this face are coordinated by one THF ligand each. When the excess of dimethylaluminium hyd…

Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties

An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for…

W3 theory: robust computational thermochemistry in the kJ/mol accuracy range

We are proposing a new computational thermochemistry protocol denoted W3 theory, as a successor to W1 and W2 theory proposed earlier [Martin and De Oliveira, J. Chem. Phys. 111, 1843 (1999)]. The new method is both more accurate overall (error statistics for total atomization energies approximately cut in half) and more robust (particularly towards systems exhibiting significant nondynamical correlation) than W2 theory. The cardinal improvement rests in an approximate account for post-CCSD(T) correlation effects. Iterative T_3 (connected triple excitations) effects exhibit a basis set convergence behavior similar to the T_3 contribution overall. They almost universally decrease molecular bi…

The Equilibrium Structure of Benzene

The re structure of benzene is revised on the basis of high-level quantum chemical calculations at the CCSD(T)/cc-pVQZ level as well a reanalysis of the experimental rotational constants using computed vibrational corrections. A least-squares fit to empirically determined Be constants yields re(CC) = 1.3914 ± 0.0010 A and re(CH) = 1.0802 ± 0.0020 A; the latter distance is significantly shorter than the best previous estimate based on experimental data. Comparison of computed rg and rz distances with experiment as well as considerations of bond lengthening due to anharmonicity are consistent with the estimated re distance, indicating that the recommended structural parameters are very accura…

Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals

In this contribution, we present the implementation of a second-order complete active space–self-consistent field (CASSCF) algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called norm-extended optimization, guarantees convergence of the optimization, but it involves the full Hessian and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance …

High-resolution rovibrational spectroscopy of c-C3H2+: The ν7 C–H antisymmetric stretching band

Abstract The ν 7 antisymmetric C–H stretching fundamental of c- C 3 H 2 + has been characterized in a cryogenic 22-pole ion trap by a novel type of action spectroscopy, in which the rovibrational excitation of c- C 3 H 2 + is detected as a slowing down of the low-temperature reaction c- C 3 H 2 +  + H2 → C 3 H 3 + + H. Ninety-one rovibrational transitions with partly resolved fine structure doublets were measured in high resolution. Supported by high-level quantum chemical calculations, spectroscopic parameters were determined by fitting the observed lines with an effective Hamiltonian for an asymmetric rotor in a doublet electronic ground state, X ˜ A 1 2 , yielding a band origin at 3113.6…

Equation-of-motion coupled-cluster methods for ionized states with an approximate treatment of triple excitations.

The accuracy of geometries and harmonic vibrational frequencies is evaluated for two equation-of-motion ionization potential coupled-cluster methods including CC3 and CCSDT-3 triples corrections. The first two Sigma states and first Pi state of the N2 +, CO+, CN, and BO diatomic radicals are studied. The calculations show a tendency for the CC3 variant to overestimate the bond lengths and to underestimate the vibrational frequencies, while the CCSDT-3 variant seems to be more reliable. It is also demonstrated that the accuracy of such methods is comparable to sophisticated traditional multireference approaches and the full configuration interaction method.

Improved centrifugal and hyperfine analysis of ND2H and NH2D and its application to the spectral line survey of L1544

Abstract Quantifying molecular abundances of astrochemical species is a key step towards the understanding of the chemistry occurring in the interstellar medium. This process requires a profound knowledge of the molecular energy levels, including their structure resulting from weak interactions between nuclear spins and the molecular rotation. With the aim of increasing the quality of spectral line catalogs for the singly- and doubly-deuterated ammonia (NH2D and ND2H), we have revised their rotational spectra by observing many hyperfine-resolved lines and more accurate high-frequency transitions. The measurements have been performed in the submillimeter-wave region (265–1565 GHz) using a fr…

High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification

The recently developed high-accuracy extrapolated ab initio thermochemistry method for theoretical thermochemistry, which is intimately related to other high-precision protocols such as the Weizmann-3 and focal-point approaches, is revisited. Some minor improvements in theoretical rigor are introduced which do not lead to any significant additional computational overhead, but are shown to have a negligible overall effect on the accuracy. In addition, the method is extended to completely treat electron correlation effects up to pentuple excitations. The use of an approximate treatment of quadruple and pentuple excitations is suggested; the former as a pragmatic approximation for standard cas…

Perturbative calculation of spin-orbit splittings using the equation-of-motion ionization-potential coupled-cluster ansatz.

Spin-orbit splittings for (2)Pi states are calculated within coupled-cluster (CC) theory via first-order degenerate perturbation theory. Using the equation-of-motion CC variant for ionization potentials (EOMIP-CC), the two components of the considered (2)Pi state are treated in a balanced way by generating both radical states via annihilation of one electron out of the CC wave function of the corresponding anion. We report on the implementation of the described approach within the CC singles and doubles approximation. To ensure computational efficiency, an atomic mean-field approximation for the spin-orbit integrals is used, resulting in a formulation in terms of one-electron transition-den…

Laboratory measurements and astronomical search for the HSO radical

[Context] Despite the fact that many sulfur-bearing molecules, ranging from simple diatomic species up to astronomical complex molecules, have been detected in the interstellar medium, the sulfur chemistry in space is largely unknown and a depletion in the abundance of S-containing species has been observed in the cold, dense interstellar medium. The chemical form of the missing sulfur has yet to be identified.

Parallel Calculation of CCSDT and Mk-MRCCSDT Energies.

A scheme for the parallel calculation of energies at the coupled-cluster singles, doubles, and triples (CCSDT) level of theory, several approximate iterative CCSDT schemes (CCSDT-1a, CCSDT-1b, CCSDT-2, CCSDT-3, and CC3), and for the state-specific multireference coupled-cluster ansatz suggested by Mukherjee with a full treatment of triple excitations (Mk-MRCCSDT) is presented. The proposed scheme is based on the adaptation of a highly efficient serial coupled-cluster code leading to a communication-minimized implementation by parallelizing the time-determining steps. The parallel algorithm is tailored for affordable cluster architectures connected by standard communication networks such as …

Insights into the orbital invariance problem in state-specific multireference coupled cluster theory.

In this communication we report the results of our studies on the orbital invariance properties of the state-specific multireference coupled cluster approach suggested by Mukherjee and co-workers (Mk-MRCC). In particular, we have gathered numerical evidence to show that even when the linear excitation manifold is modified in order to span the same space for each reference, the resulting method is not orbital invariant. In order to test this conjecture we have proposed a new truncation scheme (Mk-MRCCSDtq) which, in addition to full single and double excitations, contains partial triple and quadruple excitations. For a reference space generated by all possible combinations of two electrons i…

The hyperfine structure in the rotational spectra of bromofluoromethane: Lamb-dip technique and quantum-chemical calculations

International audience; The hyperfine structure in the rotational spectra of six isotopic species of bromofluoromethane, namely CH2{79}BrF, CH2{81}BrF, CDH{79}BrF, CDH{81}BrF, CD2{79}BrF, and CD2{81}BrF, has been investigated using the Lamb-dip technique in the submillimeter-wave frequency range. Measurements as well as assignment procedures have been supported by high-level quantum-chemical calculations of the hyperfine parameters at the coupled-cluster level. For all species, the accuracy of the determined rotational and centrifugal distortion constants as well as the bromine quadrupole-coupling constants have been improved with respect to available literature data, whereas the full bromi…

Importance of Triples Contributions to NMR Spin–Spin Coupling Constants Computed at the CC3 and CCSDT Levels

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin–spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1–3%, but much higher corrections were found for 1JCN in FCN, 15.7%, and 1JOF in OF2, 6.4%. The changes v…

Quantum-chemical calculation of spectroscopic parameter for rotational spectroscopy

This review provides a computational chemist’s perspective of rotational spectros- copy and discusses the theoretical background and application of state-of-the-art quantum-chemical methods for the accurate determination of the relevant spectroscopic parameters.

Benchmark Thermochemistry of the Hydroperoxyl Radical

A theoretical estimation of the enthalpy of formation for the hydroperoxyl radical is presented. These results are based on CCSD(T)/aug-cc-pCV5Z calculations extrapolated to the basis-set limit with additional corrections. Anharmonic vibrational zero-point energies, scalar relativistic, spin -orbit coupling, and diagonal BornOppenheimer corrections are further used to correct the extrapolated term energies, as well as various empirical corrections that account for correlation effects not treated at the CCSD(T) level. We estimate that ¢fH° ) 3.66 ( 0.10 kcal mol -1 (¢fH° ) 2.96 ( 0.10 kcal mol -1 ) using several reaction schemes. Significantly, it appears to be necessary to include effects o…

Why benchmark-quality computations are needed to reproduce 1-adamantyl cation NMR chemical shifts accurately.

While the experimental (1)H NMR chemical shiftsof the 1-adamantyl cation can be computed within reasonably small error bounds, the usual Hartree-Fock and density functional quantum-chemical computations, as well as those based on rather elaborate second-order Møller-Plesset perturbation theory, fail to reproduce its experimental (13)C NMR chemical shifts satisfactorily. This also is true even if the NMR shielding calculations treat electron correlation adequately by the coupled-cluster singles and doubles model augmented by a perturbative correction for triple excitations (i.e., at the CCSD(T) level) with quadruple-ζ basis sets. We demonstrate that good agreement can be achieved if highly a…

The Cotton-Mouton effect of Neon and Argon: a benchmark study using highly correlated coupled cluster wave functions

The Cotton-Mouton effect (magnetic field induced linear birefringence) has been studied for neon and argon using state-of-the-art coupled cluster techniques. The coupled cluster singles, doubles and triples (CCSDT) approach has been used to obtain static benchmark results and the CC3 model with an approximate treatment of triple excitations to obtain frequency-dependent results. In the case of neon the effect of excitations beyond triples has also been estimated via coupled cluster calculations including quadruple excitations (CCSDTQ), pentuple excitations (CCSDTQP), etc. up to the full configuration-interaction level. The results obtained for the anisotropy of the hypermagnetizability Delt…

Ground and Excited State First-Order Properties in Many-Body Expanded Full Configuration Interaction Theory

The recently proposed many-body expanded full configuration interaction (MBE-FCI) method is extended to excited states and static first-order properties different from total, ground state correlation energies. Results are presented for excitation energies and (transition) dipole moments of two prototypical, heteronuclear diatomics---LiH and MgO---in augmented correlation consistent basis sets of up to quadruple-$\zeta$ quality. Given that MBE-FCI properties are evaluated without recourse to a sampled wave function and the storage of corresponding reduced density matrices, the memory overhead associated with the calculation of general first-order properties only scales with the dimension of …

Quantum-chemical calculation of Born–Oppenheimer breakdown parameters to rotational constants

The paper describes how Born–Oppenheimer breakdown parameters for the rotational constants of diatomic molecules can be determined via quantum-chemical computations. The deviations from the Born–Oppenheimer equilibrium values are accounted for by considering the adiabatic correction to the equilibrium bond distances, the electronic contribution to the rotational constant via the rotational g tensor, and the so-called Dunham correction, which can be computed directly from a polynomial expansion of the potential curve around the equilibrium distance. Calculations for HCl, SiS, and HF demonstrate the accuracy that can be achieved in the theoretical treatment of the considered Born–Oppenheimer …

Coupled-cluster Theory

Calculation of frequency-dependent polarizabilities using general coupled-cluster models

Abstract An analytic scheme for the calculation of frequency-dependent polarizabilities within a response-theory approach has been implemented for the use within general coupled-cluster (CC) models with arbitrary excitations in the cluster operator. Calculations for CH + and CN demonstrate the fast convergence of the coupled-cluster approach when successively higher excitations are considered. Quadruple excitation effects on the frequency-dependent polarizabilities are found to be rather small except close to the poles.

Introduction to proceedings of Molecular Quantum Mechanics 2013: electron correlation: the many-body problem at the heart of chemistry

Spin-restricted coupled-cluster theory with triple excitations

Working equations for a spin-restricted coupled-cluster (SR-CC) ansatz with full inclusion of triple excitations are presented. The equations have been derived using a new formulation of the SR-CC theory that is equivalent to the original one but much easier processed and also provides a new interpretation of the underlying concepts of the SR-CC approach. Test calculations with a preliminary SR-CC singles, doubles, triples (SR-CCSDT) implementation indicate that spin-restriction has a rather small effect on the computed energies and that the effects are—as expected—less pronounced than in the case of the CC singles, doubles approximation. The corresponding partially spin-adapted scheme turn…

Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. II. Quadruples expansions

We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and lambda-CCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(…

Analytic energy gradients in closed-shell coupled-cluster theory with spin-orbit coupling

Gradients in closed-shell coupled-cluster (CC) theory with spin-orbit coupling included in the post Hartree-Fock treatment have been implemented at the CC singles and doubles (CCSD) level and at the CCSD level augmented by a perturbative treatment of triple excitations [CCSD(T)]. The additional computational effort required in analytic energy-gradient calculations is roughly the same as that for ground-state energy calculations in the case of CCSD, and it is about twice in the case of CCSD(T) calculations. The structures, harmonic frequencies, and dipole moments of some heavy-element compounds have been calculated using the present analytic energy-gradient techniques including spin-orbit co…

GERMANIUM DICARBIDE: EVIDENCE FOR A T−SHAPED GROUND STATE STRUCTURE

The equilibrium structure of germanium dicarbide GeC2 has been an open question since the late 1950s. Although most high-level quantum calculations predict an L-shaped geometry, a T-shaped or even a linear geometry cannot be ruled out because of the very flat potential energy surface. By recording the rotational spectrum of this dicarbide using sensitive microwave and millimeter techniques, we unambiguously establish that GeC2 adopts a vibrationally averaged T-shaped structure in its ground state. From analysis of 14 isotopologues, a precise r0 structure has been derived, yielding a Ge–C bond length of 1.952(1) A and an apex angle of 38.7(2)°.

Determining the Geometry of Hydrogen Bonds in Solids with Picometer Accuracy by Quantum-Chemical Calculations and NMR Spectroscopy

The structure of multiply hydrogen-bonded systems is determined with picometer accuracy by a combined solid-state NMR and quantum-chemical approach. On the experimental side, advanced 1H-15N dipolar recoupling NMR techniques are capable of providing proton-nitrogen distances of up to about 250 pm with an accuracy level of +/-1 pm for short distances (i.e., around 100 pm) and +/-5 pm for longer ones (i.e., 180 to 250 pm). The experiments were performed under fast magic-angle spinning, which ensures sufficient dipolar decoupling and spectral resolution of the 1H resonance lines. On the quantum-chemical side, the structures of the hydrogen-bonded systems were computationally optimised, yieldin…

Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order.

A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison …

The hyperfine structure in the rotational spectra of D2(17)O and HD(17)O: Confirmation of the absolute nuclear magnetic shielding scale for oxygen

Guided by theoretical predictions, the hyperfine structures of the rotational spectra of mono- and bideuterated-water containing (17)O have been experimentally investigated. To reach sub-Doppler resolution, required to resolve the hyperfine structure due to deuterium quadrupole coupling as well as to spin-rotation (SR) and dipolar spin-spin couplings, the Lamb-dip technique has been employed. The experimental investigation and in particular, the spectral analysis have been supported by high-level quantum-chemical computations employing coupled-cluster techniques and, for the first time, a complete experimental determination of the hyperfine parameters involved was possible. The experimental…

A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches

We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying co…

Coupled-cluster singles, doubles and triples (CCSDT) calculations of atomization energies

Atomization energies have been calculated for CO, H2O, F-2, HF, N-2 and CH2 (the (1)A(1) state) using the coupled-duster singles, doubles and triples (CCSDT) model as well as the coupled-cluster singles and doubles model with a perturbative correction for triples [CCSD(T)]. TheCCSD(T) model provides an excellent approximation to the CCSDT model; at the cc-pV5Z basis set level, the CCSDT valence triples contribution is underestimated by 9.1% (0.8 kJ/mol) for CH, and overestimated for the remaining molecules by as little as 4.3%(1.3 kJ/mol) for F-2,and as much as 8.4% (3.0 kJ/mol) for N-2. At the CCSDT level, the agreement with experiment is not improved, suggesting that some cancellation of …

Coupled-cluster techniques for computational chemistry: The CFOUR program package

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of …

Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory.

This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations …

Equilibrium structure of LiCCH

Optical Properties of Assemblies of Molecules and Nanoparticles

Organic dye molecules, colloidal semiconductor quantum dots, and light-harvesting complexes have been employed as optically active building blocks to create complex molecular assemblies via covalent and non-covalent interactions. Taking advantage of the chemical flexibility of the dye and quantum dot components, as well as recombinant protein expression and the ordering capability of cholesteric phases, specific optical function could be implemented. Photophysical phenomena that have been addressed include light-harvesting, electronic excitation energy transfer (EET), and lasing. Optical single-molecule experiments allow control of energy transfer processes in individual molecular dyads and…

NMR chemical shift calculations within local correlation methods: the GIAO-LMP2 approach

A scheme for the calculation of NMR chemical shifts using local second-order Moller–Plesset (LMP2) perturbation theory together with gauge-including atomic orbitals (GIAOs) is presented. Test calculations on the basis of a preliminary implementation within a conventional GIAO-MP2 code show that the deviations between GIAO-LMP2 and GIAO-MP2 are small, e.g., for 13C typically less than 1 ppm, and that the GIAO-LMP2 approach holds great promise for application to larger molecules.

Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules

Benchmark scalar-relativistic coupled-cluster calculations for dissociation energies of the 20 diatomic molecules containing 3d transition metals in the 3dMLBE20 database ( J. Chem. Theory Comput. 2015 , 11 , 2036 ) are reported. Electron correlation and basis set effects are systematically studied. The agreement between theory and experiment is in general satisfactory. For a subset of 16 molecules, the standard deviation between computational and experimental values is 9 kJ/mol with the maximum deviation being 15 kJ/mol. The discrepancies between theory and experiment remain substantial (more than 20 kJ/mol) for VH, CrH, CoH, and FeH. To explore the source of the latter discrepancies, the …

Analytical evaluation of first-order electrical properties based on the spin-free Dirac-Coulomb Hamiltonian.

We report an analytical scheme for the calculation of first-order electrical properties using the spin-free Dirac-Coulomb (SFDC) Hamiltonian, thereby exploiting the well-developed density-matrix formulations in nonrelativistic coupled-cluster (CC) derivative theory. Orbital relaxation effects are fully accounted for by including the relaxation of the correlated orbitals with respect to orbitals of all types, viz., frozen-core, occupied, virtual, and negative energy state orbitals. To demonstrate the applicability of the presented scheme, we report benchmark calculations for first-order electrical properties of the hydrogen halides, HX with X = F, Cl, Br, I, At, and a first application to th…

The magnetic hyperfine structure in the rotational spectrum of H2CNH

Abstract The hyperfine structure in the ground-state rotational spectrum of methanimine was studied in the frequency range of 64–172 GHz by means of the Lamb-dip technique. This allowed to resolve, in some hyperfine components due to the 14N nucleus, doublets separated by only some tenth of kHz. We explain the splittings as due to magnetic interactions of the three protons with their molecular environment. The analysis of the experimental spectrum has been guided by quantum-chemical calculations of the hyperfine parameters.

A comparison of excited state properties for iterative approximate triples linear response coupled cluster methods

Abstract A computational study of the potential energy curves of the 1 Π state of BH, 1 Π state of CH + , 1 Σ u and 1 Π u states of C 2 , 1 Π state of CO, and 1 Π g and 1 Σ − u states of N 2 is carried out with the CC3 and CCSDT-3 corrections to EOMEE-CCSD. Good agreement in structure, vibrational frequencies, and excitation energies of these iterative triples-corrected methods with respect to experiment is found for most of these examples. However, deficiencies in the approximate treatment of triples is evident for BH and CH + .

HEAT: High accuracy extrapolated ab initio thermochemistry.

A theoretical model chemistry designed to achieve high accuracy for enthalpies of formation of atoms and small molecules is described. This approach is entirely independent of experimental data and contains no empirical scaling factors, and includes a treatment of electron correlation up to the full coupled-cluster singles, doubles, triples and quadruples approach. Energies are further augmented by anharmonic zero-point vibrational energies, a scalar relativistic correction, first-order spin-orbit coupling, and the diagonal Born-Oppenheimer correction. The accuracy of the approach is assessed by several means. Enthalpies of formation (at 0 K) calculated for a test suite of 31 atoms and mole…

Rotational spectrum and equilibrium structure of silanethione, H2SiS

Unsubstituted silanethione, H(2)Si=S, has been characterized experimentally for the first time by means of rotational spectroscopy; the equilibrium structure of this fundamental molecule has been evaluated through a combination of experimental data from a total of ten isotopologues and results of high-level coupled-cluster calculations.

The effect of triple excitations in coupled cluster calculations of frequency-dependent polarizabilities

Abstract Frequency-dependent polarizabilities have been implemented within the CC3 model. Comparison with full configuration interaction results shows that the triple excitation effects included in CC3 lead to a significantly improved treatment for the dispersion of the polarizability of CH+. For the refractivity and polarizability anisotropy of N2, better agreement with experiment is found for the CC3 results than for those obtained with the coupled cluster singles and doubles model.

A mass-independent expanded Dunham analysis of aluminum monoxide and aluminum monosulfide

Abstract Pure rotational transitions of 27Al16O, 27Al18O, 27Al32S, and 27Al34S are recorded in the vibrational ground state and singly excited vibrational state using a mm-wavelength supersonic jet spectrometer in combination with a laser ablation source. In total 275 rotational transitions have been assigned. For the first time, mass-independent expanded Dunham analyses are performed using isotopologues of aluminum monoxide and aluminum monosulfide. The breakdown of the Born-Oppenheimer approximation is observed. Based on these mass-independent analyses, frequency positions of pure rotational transitions of the rare radioactive isotopologues 26AlO and 26AlS are predicted with uncertainties…

Synthesis, microwave spectrum, quantum chemical calculations, and conformational composition of a novel primary phosphine, cyclopropylethynylphosphine, (C3H5C≡CPH2).

International audience; The microwave spectrum of cyclopropylethynylphosphine, C3H5C≡CPH2, has been investigated in the 26-120 GHz spectral region. The spectrum is dominated by very rich and complex a-type R-branch pile-ups. There must be insignificant steric interaction between the phosphino group and the cyclopropyl ring due to the long distance between these two groups. However, the phosphino group does not undergo free or nearly free internal rotation. Instead, the spectra of two distinct conformers were assigned. Both these two forms have CS symmetry. The symmetry plane bisects the cyclopropyl ring and the phosphino group in both conformers, and the lone electron pair of the phosphino …

Perturbative triples corrections in state-specific multireference coupled cluster theory

We formulated and implemented a perturbative triples correction for the state-specific multireference coupled cluster approach with singles and doubles suggested by Mukherjee and co-workers, Mk-MRCCSD [Mol. Phys. 94, 157 (1998)]. Our derivation of the energy correction [Mk-MRCCSD(T)] is based on a constrained search for stationary points of the Mk-MRCC energy functional together with a perturbative expansion with respect to the appearing triples cluster operator. The Lambda-Mk-MRCCSD(T) approach derived in this way consists in (1) a correction to the off-diagonal matrix elements of the effective Hamiltonian which is unique to coupled cluster methods based on the Jeziorski-Monkhorst ansatz, …

Relativistic coupled-cluster calculations on XeF6: Delicate interplay between electron-correlation and basis-set effects

A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O(h), C(3v), and C(2v) conformers of XeF6, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O(h) and C(3v) structures are local minima on the potential energy surface, while the C(2v) structure is a transition state. Qualitative disagre…

The rotational spectrum of trans-DCOOD: Lamb-dip measurements, THz spectroscopy and quantum-chemical calculations

Abstract The rotational spectrum of the bi-deuterated isotopologue of trans-formic acid, trans-DCOOD, was recorded at sub-Doppler resolution in the millimeter- and sub-millimeter-wave region using the Lamb-dip technique. The hyperfine structure due to the deuterium nuclei could be resolved and accurate hyperfine constants were derived. The experimental determination of the deuterium quadrupole-coupling constants was supported by high-level quantum-chemical calculations at the coupled-cluster level using large atomic-orbital basis sets. The Lamb-dip measurements were also supplemented by THz Doppler-limited measurements in order to extend the predictive capability of the available spectrosco…

The Ground State Electronic Energy of Benzene.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$\zeta$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square devia…

Equilibrium Geometry of the Ethynyl (CCH) Radical

The equilibrium geometry of the ethynyl (CCH) radical has been obtained using the results of high-level quantum chemical calculations and the available experimental data. In a purely quantum chemical approach, the best theoretical estimates (1.208 A for r C C and 1.061-1.063 A for r C H ) have been obtained from CCSD-(T), CCSDT, MR-AQCC, and full CI calculations with basis sets up to core-polarized pentuple-zeta quality. In a mixed theoretical-experimental approach, empirical equilibrium geometrical parameters (1.207 A for r C C and 1.069 A for r C H ) have been obtained from a least-squares fit to the experimental rotational constants of four isotopomers of CCH which have been corrected fo…

Theoretische Chemie 2001

Mit Funktionalen, die nicht mehr nur von der Elektronendichte, sondern auch von den Orbitalen abhangen, scheinen einige Probleme, die Dichtefunktionalmethoden seit langem beeintrachtigen, gelost zu werden. Neue quantenchemische Ansatze und Techniken ermoglichen die detaillierte und routinemasige Untersuchung von Molekulen in elektronisch angeregten Zustanden. In der Clusterchemie erweisen sich theoretische Zugange unterschiedlicher Komplexitat als wertvolle Partner des Experiments.

On the approximation of the similarity-transformed Hamiltonian in single-reference and multireference coupled cluster theory

Abstract We consider the recursive single commutator (RSC) approximation of the Baker–Campbell–Hausdorff expansion introduced by Yanai and Chan [T. Yanai, G.K.-L. Chan, J. Chem. Phys. 124 (2006) 194106] and apply it in order to approximate the similarity transformation of the Hamiltonian in both traditional and unitary coupled cluster theory. The equilibrium bond distance, harmonic vibrational frequency, and anharmonic constant of H2, HF, N2, CuH, and Cu2 were computed using the coupled cluster approach with single and double excitations (CCSD) and CCSD with the RSC approximation of the similarity-transformed Hamiltonian (CCSD-RSC). Our results demonstrate that the RSC approximation introdu…

The rare isotopomers of HCN: HC15N and DC15N. Rotational spectrum and resolved nuclear hyperfine structures due to 15N and D.

In the present work the J + 1 ← J rotational transitions, with J = 0-7, of HC15N and the J + 1 ← J rotational transitions, with J = 0-7, 9, of DC15N have been investigated. The Lamb-dip technique has been employed in order to resolve the hyperfine structure due to deuterium and 15N. For HC15N, the hyperfine parameters have been determined for the first time. With respect to DC15N, only the spin rotation of 15N have been determined for the first time but a more reliable spin rotation of D has been obtained. The experimental evaluation of the hyperfine constants has been aided by highly accurate ab initio computations. Furthermore, the rotational transitions observed allowed us to provide the…

Bonding in the heavy analogue of hydrogen cyanide: the curious case of bridged HPSi.

The bonding of firstand second-row elements differ dramatically. The simplest unsaturated silicon hydrides Si2H2 and Si2H4 exhibit quite unusual geometries [1] compared to the analogous hydrocarbon molecules. For example, the most stable form of Si2H2 is nonplanar with C2v symmetry and two bridging H atoms, in sharp contrast to linear acetylene, HC! CH. Phosphorus and nitrogen share many of the same bonding characteristics, but P prefers single over multiple bonds. For these reasons, it may be difficult to predict the most stable isomeric arrangement, even for a small molecule with a single Por Si atom and especially when it contains both. Silicon–phosphorus bonds are important in materials…

Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

In this second part of our series on the recently proposed many-body expanded full configuration interaction (MBE-FCI) method, we introduce the concept of multideterminantal expansion references. Through theoretical arguments and numerical validations, the use of this class of starting points is shown to result in a focussed compression of the MBE decomposition of the FCI energy, thus allowing chemical problems dominated by strong correlation to be addressed by the method. The general applicability and performance enhancements of MBE-FCI are verified for standard stress tests such as the bond dissociations in H$_2$O, N$_2$, C$_2$, and a linear H$_{10}$ chain. Furthermore, the benefits of em…

PRECISE LABORATORY MEASUREMENTS OF TRANS-DCOOH AND TRANS-HCOOD FOR ASTROPHYSICAL OBSERVATIONS

The rotational spectra of the mono-deuterated isotopologues of trans-formic acid, trans-DCOOH and trans-HCOOD, were investigated. In the millimeter- and submillimeter-wave frequency regions the Lamb-dip technique was exploited to obtain sub-Doppler resolution and to resolve the hyperfine structure due to the deuterium and hydrogen nuclei, thus enabling the accurate determination of the corresponding hyperfine constants. The experimental determination was supported by high-level quantum-chemical calculations at the coupled-cluster level of theory using large atomic-orbital basis sets. The Lamb-dip measurements were also supplemented by THz Doppler- limited measurements in order to extend the…

Infrared Spectroscopy of Disilicon-Carbide, Si2C: The ν3 Fundamental Band

The ν3 antisymmetric stretching mode of disilicon-carbide, Si2C, was studied using a narrow line width infrared quantum cascade laser spectrometer operating at 8.3 μm. The Si2C molecules were produ...

Revised values for the nuclear quadrupole moments ofS33andS35

High-level quantum-chemical calculations are reported for the sulfur electric-field gradients of the CS and SiS molecules. Highly accurate values are obtained in these calculations by using coupled-cluster methods for the treatment of electron correlation together with large atomic-orbital basis sets and by taking into account relativistic effects. The computational results for the sulfur electric-field gradient are used to determine revised values for the $^{33}\mathrm{S}$ and $^{35}\mathrm{S}$ quadrupole moments, thereby taking advantage of available accurate values for the sulfur quadrupole couplings of CS and SiS from the analysis of rotational spectra. The derived values of $\ensuremat…

Electron correlation effects on the calculated 13C NMR spectra of vinyl cations

Abstract A study of calculated 13C NMR chemical shifts in vinyl cations is presented. The sensitivity of predicted isotropic shifts to correlation, basis set and geometry effects is explored. In order to obtain accurate estimates that are reasonably well converged with respect to further improvements in theory, it appears that the CCSD(T) method must be used with a basis of triple-zeta plus polarization quality on the carbon atoms. Second-order many-body perturbation theory performs adequately for all carbons except for that bearing the formal positive charge, while the self-consistent field approximation cannot be relied upon to predict even the correct qualitative ordering in the spectrum…

Communication: spin-orbit splittings in degenerate open-shell states via Mukherjee's multireference coupled-cluster theory: a measure for the coupling contribution.

We propose a generally applicable scheme for the computation of spin-orbit (SO) splittings in degenerate open-shell systems using multireference coupled-cluster (MRCC) theory. As a specific method, Mukherjee's version of MRCC (Mk-MRCC) in conjunction with an effective mean-field SO operator is adapted for this purpose. An expression for the SO splittings is derived and implemented using Mk-MRCC analytic derivative techniques. The computed SO splittings are found to be in satisfactory agreement with experimental data. Due to the symmetry properties of the SO operator, SO splittings can be considered a quality measure for the coupling between reference determinants in Jeziorski-Monkhorst base…

Coupled-cluster theory for atoms and molecules in strong magnetic fields

An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the depende…

Gas-phase detection of discharge-generated DSOD

Abstract We report the first spectroscopic detection of perdeuterated 1-oxadisulfane, DSOD, generated in a radio-frequency plasma of D2S and D2O. The chain molecule DSOD produces a perpendicular-type spectrum, with well-known spectral features encountered in previous studies of geometrically related molecules, such as compact Q-branches, which are clearly recognizable. The arrangement of the transitions shaping the Q-branches usually provides sufficient proof for a clear-cut detection of a chain molecule such as DSOD. Guided by quantum chemical calculations, we have located the band center of the r Q 2 -branch of DSOD in the frequency region near 466.5 GHz using the Cologne terahertz spectr…

Mechanical Properties of Single Molecules and Polymer Aggregates

This chapter deals with the mechanical properties of single polymer chains, aggregates, and supramolecular complexes. The topics discussed cover a broad range from fundamental statistical mechanics of the equilibrium elastic properties of single polymer chains to details of the behavior of binding pockets in biomolecular assemblies as observed by force spectroscopy. The first section treats the equilibrium mechanical properties of single polymer chains in various environments, investigated via extensive simulations employing coarse-grained models that have proven extremely successful in many branches of polymer physics, namely the bond-fluctuation model and the self-avoiding walk model. Apa…

The bromine nuclear quadrupole moment revisited

For the bromine atom and the hydrogen bromide molecule, we report results for the electric-field gradient at the bromine nucleus based on quantum-chemical calculations. Highly accurate values are obtained by using coupled-cluster methods for the treatment of electron correlation, by minimising remaining basis-set effects through the use of large atomic-orbital sets, and by taking into account relativistic effects. For hydrogen bromide, zero-point vibrational corrections are considered as well. The obtained results for the bromine electric-field gradients are used to derive values for the Br-79 quadrupole moment: 308.1 and 309.3 mb based on data for the bromine atom and hydrogen bromide, res…

Analytic second derivatives for general coupled-cluster and configuration-interaction models.

Analytic second derivatives of energy for general coupled-cluster (CC) and configuration-interaction (CI) methods have been implemented using string-based many-body algorithms. Wave functions truncated at an arbitrary excitation level are considered. The presented method is applied to the calculation of CC and CI harmonic frequencies and nuclear magnetic resonance chemical shifts up to the full CI level for some selected systems. The present benchmarks underline the importance of higher excitations in high-accuracy calculations.

Silicon Oxysulfide, OSiS: Rotational Spectrum, Quantum-Chemical Calculations, and Equilibrium Structure.

Silicon oxysulfide, OSiS, and seven of its minor isotopic species have been characterized for the first time in the gas phase at high spectral resolution by means of Fourier transform microwave spectroscopy. The equilibrium structure of OSiS has been determined from the experimental data using calculated vibration-rotation interaction constants. The structural parameters (rO-Si = 1.5064 A and rSi-S = 1.9133 A) are in very good agreement with values from high-level quantum chemical calculations using coupled-cluster techniques together with sophisticated additivity and extrapolation schemes. The bond distances in OSiS are very short in comparison with those in SiO and SiS. This unexpected fi…

Towards a spin-adapted coupled-cluster theory for high-spin open-shell states

A spin-adapted coupled-cluster (SA-CC) scheme based on the additional consideration of spin constraints is proposed for the quantum chemical treatment of high-spin open-shell cases. Its computational feasibility is demonstrated via a pilot implementation within the singles and doubles approximation. Test calculations indicate that the suggested SA-CC scheme provides results of similar accuracy as the more traditional schemes without spin adaptation.

Anharmonic force fields from analytic CCSD(T) second derivatives: HOF and F2O

The recent implementation of analytic second derivatives for CCSD(T) (coupled cluster theory with single and double excitations augmented by a perturbational treatment of connected triple excitations) has been combined with a numerical finite difference procedure to calculate cubic and semidiagonal quartic force fields. Computational details of this approach are outlined. Applications are reported for HOF and F2O. The CCSD(T) results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from MP2 (Mo/ller–Plesset second-order perturbation theory).

An orbital-invariant internally contracted multireference coupled cluster approach.

We have formulated and implemented an internally contracted multireference coupled cluster (ic-MRCC) approach aimed at solving two of the problems encountered in methods based on the Jeziorski-Monkhorst ansatz: (i) the scaling of the computational and memory costs with respect to the number of references, and (ii) the lack of invariance of the energy with respect to rotations among active orbitals. The ic-MRCC approach is based on a straightforward generalization of the single-reference coupled cluster ansatz in which an exponential operator is applied to a multiconfigurational wave function. The ic-MRCC method truncated to single and double excitations (ic-MRCCSD) yields very accurate pote…

THE HYPERFINE STRUCTURE of the ROTATIONAL SPECTRUM of HDO and ITS EXTENSION to the THz REGION: ACCURATE REST FREQUENCIES and SPECTROSCOPIC PARAMETERS for ASTROPHYSICAL OBSERVATIONS

The rotational spectrum of the mono-deuterated isotopologue of water, HD16O, has been investigated in the millimeter- and submillimeter-wave frequency regions, up to 1.6 THz. The Lamb-dip technique has been exploited to obtain sub-Doppler resolution and to resolve the hyperfine (hf) structure due to the deuterium and hydrogen nuclei, thus enabling the accurate determination of the corresponding hf parameters. Their experimental determination has been supported by high-level quantum-chemical calculations. The Lamb-dip measurements have been supplemented by Doppler-limited measurements (weak high-J and high-frequency transitions) in order to extend the predictive capability of the available s…

Rotational spectra and hyperfine structure of isotopic species of deuterated cyanoacetylene, DC3N

Abstract Cyanoacetylene enriched in deuterium was used to record pure rotational transitions of DC 3 N and its rare 13 C and 15 N isotopic species by employing Fourier transform microwave (FTMW) spectroscopy on a supersonic-jet expansion at centimeter wavelengths (8.2–25.4 GHz) and by using long-path absorption spectroscopy at millimeter and submillimeter wavelengths (82–900 GHz). In addition, submillimeter wave measurements (304–897 GHz) have been performed for DC 3 N in its v 7 = 1 lowest excited vibrational state. Hyperfine structure caused by the 14 N and D nuclei has been resolved in the FTMW spectra. Quantum-chemical calculations have been performed on the hyperfine structure paramete…

Linear-response theory for Mukherjee's multireference coupled-cluster method: Static and dynamic polarizabilities

The formalism of response theory is applied to derive expressions for static and dynamic polarizabilities within the state-specific multireference coupled-cluster theory suggested by Mukherjee and co-workers (Mk-MRCC) [J. Chem. Phys. 110, 6171 (1998)]. We show that the redundancy problem inherent to Mk-MRCC theory gives rise to spurious poles in the Mk-MRCC response functions, which hampers the reliable calculation of dynamic polarizabilities. Furthermore, we demonstrate that in the case of a symmetry-breaking perturbation a working response theory is obtained only if certain internal excitations are included in the responses of the cluster amplitudes. Exemplary calculations within the sing…

Spectroscopic Detection and Structure of Hydroxidooxidosulfur (HOSO) Radical, An Important Intermediate in the Chemistry of Sulfur-Bearing Compounds

The rotational spectrum of hydroxidooxidosulfur, HOSO, an intermediate of particular interest in the combustion of sulfur-rich fuels, has been determined to high accuracy from gas-phase measurements. Detection of specific isotopic species using isotopically enriched gases suggests that HOSO is formed in our discharge nozzle via the reaction H + SO2 (+M) → HOSO (+M). A precise experimental r0 geometry has also been derived from the isotopic analysis; HOSO has a cis configuration, but the subtle structural question of its planarity remains unresolved. From the derived spectroscopic constants, in situ and remote sensing for this fundamental radical can now be undertaken in a variety of environ…

Cost-Effective Treatment of Scalar Relativistic Effects for Multireference Systems: A CASSCF Implementation Based on the Spin-free Dirac-Coulomb Hamiltonian

We present an implementation of the complete active space-self-consistent field (CASSCF) method specifically designed to be used in four-component scalar relativistic calculations based on the spin-free Dirac-Coulomb (SFDC) Hamiltonian. Our implementation takes full advantage of the properties of the SFDC Hamiltonian that allow us to use real algebra and to exploit point-group and spin symmetry to their full extent while including in a rigorous way scalar relativistic effects in the treatment. The SFDC-CASSCF treatment is more expensive than its non-relativistic counterpart only in the orbital optimization step, while exhibiting the same computational cost for the rate-determining full conf…

Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks.

We present a general formulation of analytic nuclear gradients for the coupled-cluster with single and double substitution (CCSD) and equation-of-motion (EOM) CCSD energies computed using Cholesky decomposition (CD) representations of the electron repulsion integrals. By rewriting the correlated energy and response equations such that the storage of the largest four-index intermediates is eliminated, CD leads to a significant reduction in disk storage requirements, reduced I/O penalties, and an improved parallel performance. CD thus extends the scope of the systems that can be treated by (EOM-)CCSD methods, although analytic gradients in the framework of CD are needed to extend the applicab…

Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model

The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.

A worrisome failure of the CC2 coupled-cluster method when applied to ozone

Abstract The approximate coupled-cluster singles and doubles model CC2 is widely used for calculations of excited states in large molecules. We demonstrate a surprising failure of the CC2 geometry optimization of ozone, whereby the CC2 method predicts a barrierless, exothermic, and symmetric dissociation to three oxygen atoms. This is particularly astonishing since both second-order Moller–Plesset perturbation theory and coupled-cluster singles and doubles give reasonable equilibrium structures. We find that [ [ H , T 1 ] , T 1 ] leads to an unbalanced treatment of T 1 and T 2 in the CC2 equations. Results presented here suggest that considerable caution should be exercised when applying th…

Benchmark coupled-cluster g-tensor calculations with full inclusion of the two-particle spin-orbit contributions.

We present a parallel implementation to compute electron spin resonance g-tensors at the coupled-cluster singles and doubles (CCSD) level which employs the ACES III domain-specific software tools for scalable parallel programming, i.e., the super instruction architecture language and processor (SIAL and SIP), respectively. A unique feature of the present implementation is the exact (not approximated) inclusion of the five one- and two-particle contributions to the g-tensor [i.e., the mass correction, one- and two-particle paramagnetic spin-orbit, and one- and two-particle diamagnetic spin-orbit terms]. Like in a previous implementation with effective one-electron operators [J. Gauss et al.,…

Communication: The pole structure of the dynamical polarizability tensor in equation-of-motion coupled-cluster theory.

In this letter, we investigate the pole structure of dynamical polarizabilities computed within the equation-of-motion coupled-cluster (EOM-CC) theory. We show, both theoretically and numerically, that approximate EOM-CC schemes such as, for example, the EOM-CC singles and doubles model exhibit an incorrect pole structure in which the poles that reflect the excitations from the target state (i.e., the EOM-CC state) are supplemented by artificial poles due to excitations from the CC reference state. These artificial poles can be avoided by skipping the amplitude response and reverting to a sum-over-states formulation. While numerical results are generally in favor of such a solution, its maj…

On the photoelectron spectrum ofp-benzoquinone

A high-resolution photoelectron spectrum of p-benzoquinone in the low energy (9.5–11.5 eV) region is reported and analyzed with the aid of simulations based on high-level ab initio calculations. The results generally support the notion that the two prominent spectral features in this region are each due to a pair of final ion states. The lower energy feature beginning near 10 eV is due to oxygen lone-pair ionizations, while that beginning near 11 eV comes from π electron removal. Contrary to previous interpretations of the spectrum, however, the results of this study indicate that the two π states are nearly degenerate, with the strongest peak in the photoelectron spectrum representing a co…

The equilibrium structure and fundamental vibrational frequencies of dioxirane

Complete sets of quadratic and cubic force constants calculated for four isotopomers of dioxirane (CH2OO) are used to estimate vibration-rotation interaction contributions to observed values of rotational constants (B″), thereby yielding empirical estimates of the corresponding equilibrium values (Be). At the highest levels of theory, least-squares refinements of atomic coordinates to both the empirical Be values and the associated isotope shifts yield consistent sets of structural parameters. Recommended values are re(CO)=1.3846±0.0005 A; re(OO)=1.5133±0.0005 A; re(CH)=1.0853±0.0015 A and θe(HCH)=117.03±0.20°. Semidiagonal quartic force constants (in the normal coordinate representation) a…

Intramolecular structural parameters are key modulators of the gel-liquid transition in coarse grained simulations of DPPC and DOPC lipid bilayers

The capability of coarse-grained models based on the MARTINI mapping to reproduce the gel-liquid phase transition in saturated and unsaturated model lipids was investigated. We found that the model is able to reproduce a lower critical temperature for 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) with respect to 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). Nonetheless, the appearance of a gel phase for DOPC is strictly dependent on the intramolecular parameters chosen to model its molecular structure. In particular, we show that the bending angle at the coarse-grained bead corresponding to the unsaturated carbon-carbon bond acts as an order parameter determining the temperature of …

ChemInform Abstract: Electron-Correlated Approaches for the Calculation of NMR Chemical Shifts

A one-electron variant of direct perturbation theory for the treatment of scalar-relativistic effects

The different importance of scalar-relativistic two-electron contributions in second-order direct perturbation theory (DPT2) and the spin-free one-electron variant of exact two-component theory (SF...

The electronic spectrum of pyrrole

The electronic spectrum of pyrrole has been investigated by performing calculations using a hierarchy of coupled-cluster models consisting of CCS, CC2, CCSD, and CC3. Basis-set effects have been investigated by carrying out calculations using correlation-consistent basis sets augmented with functions especially designed for the description of Rydberg states. Oscillator strengths, excited state dipole moments, and second moments of the electronic charge distributions have been used to characterize the electronic transitions and final states. Structures and vibrational frequencies have been calculated for a few selected states, and the importance of distinguishing between vertical and adiabat…

Calculation of frequency-dependent hyperpolarizabilities using general coupled-cluster models.

By exploiting the similarities between response theory and analytic derivative theory, we present a scheme for calculating frequency-dependent hyperpolarizabilities at the coupled-cluster level within the framework for analytic third derivatives. This has been implemented for arbitrary levels of coupled-cluster theory up to the full-configuration-interaction limit. An investigation of some small molecules shows that the inclusion of triple excitations is essential for an accurate description of hyperpolarizabilities.

Perturbative treatment of spin-orbit-coupling within spin-free exact two-component theory using equation-of-motion coupled-cluster methods.

A scheme is reported for the perturbative calculation of spin-orbit coupling (SOC) within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) in combination with the equation-of-motion coupled-cluster singles and doubles method. Benchmark calculations of the spin-orbit splittings in 2Π and 2P radicals show that the accurate inclusion of scalar-relativistic effects using the SFX2C-1e scheme extends the applicability of the perturbative treatment of SOC to molecules that contain heavy elements. The contributions from relaxation of the coupled-cluster amplitudes are shown to be relatively small; significant contributions from correlating the inner-core orbitals are …

Triple excitation effects in coupled-cluster calculations of frequency-dependent hyperpolarizabilities

Abstract We describe an implementation of an analytic scheme for the calculation of static and dynamical first hyperpolarizabilities at the CC3 level in the framework of coupled-cluster response theory. Calculations are reported for the static, the second harmonic generation, and the optical rectification hyperpolarizabilities of FH. The results indicate the importance of triple excitation effects for accurate theoretical predictions of hyperpolarizabilities and lend further support to previous contentions that an experimental value for the second harmonic generation hyperpolarizabilities of FH should be reconsidered.

The rotational gas-phase spectrum of trans- and cis-HSSOH at 100GHz

Abstract We present the first pure rotational spectra of the two most stable conformers of oxatrisulfane, trans- and cis-HSSOH, in their vibrational ground state. For both conformers a-, b-, and c-type transitions have been recorded in the range from 75 to 120 GHz using an all solid-state spectrometer. More than 200 lines have been assigned for each conformer, most of them belonging to the r Q 2 - and the r Q 3 -branch of the perpendicular spectra. The least-squares fit analysis using a semirigid rotor Hamiltonian in S-reduction yields precise values for the ground-state rotational constants A 0 = 21 145.93422 ( 66 ) , B 0 = 4479.92301 ( 21 ) , C 0 = 3828.34269 ( 21 ) for cis-HSSOH, and A 0…

NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals.

We report on a formulation and implementation of a scheme to compute NMR shieldings at second-order Moller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed as well as perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field as well as for the computed NMR shieldings, before we illustrate the applicability of our CD based GIAO-MP2 scheme in calculations involving up to about one hundred atoms and more than one thousand basis functions.

State-specific multireference coupled-cluster theory

The multireference problem is considered one of the great challenges in coupled-cluster (CC) theory. Most recent developments are based on state-specific approaches, which focus on a single state and avoid some of the numerical problems of more general approaches. We review various state-of-the-art methods, including Mukherjee's state-specific multireference coupled-cluster (Mk-MRCC) theory, multireference Brillouin–Wigner coupled-cluster (MR-BWCC) theory, the MRexpT method, and internally contracted multireference coupled-cluster (ic-MRCC) theory. Related methods such as extended single-reference schemes [e.g., the complete active space coupled-cluster (CASCC) theory] and canonical transfo…

High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview

Effects of increased basis-set size as well as a correlated treatment of the diagonal Born-Oppenheimer approximation are studied within the context of the high-accuracy extrapolated ab initio thermochemistry (HEAT) theoretical model chemistry. It is found that the addition of these ostensible improvements does little to increase the overall accuracy of HEAT for the determination of molecular atomization energies. Fortuitous cancellation of high-level effects is shown to give the overall HEAT strategy an accuracy that is, in fact, higher than most of its individual components. In addition, the issue of core-valence electron correlation separation is explored; it is found that approximate add…

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models.

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-…

Force probe simulations using a hybrid scheme with virtual sites.

Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method an…

Theoretical investigation of electronic excitation energy transfer in bichromophoric assemblies.

Electronic excitation energy transfer (EET) rates in rylene diimide dyads are calculated using second-order approximate coupled-cluster theory and time-dependent density functional theory. We investigate the dependence of the EET rates on the interchromophoric distance and the relative orientation and show that Forster theory works quantitatively only for donor-acceptor separations larger than roughly 5 nm. For smaller distances the EET rates are over- or underestimated by Forster theory depending on the respective orientation of the transition dipole moments of the chromophores. In addition to the direct transfer rates we consider bridge-mediated transfer originating from oligophenylene un…

Communication: The absolute shielding scales of oxygen and sulfur revisited

Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics 2015, 142 and may be found at http://dx.doi.org/10.1063/1.4913634 We present an updated semi-experimental absolute shielding scale for the 17O and 33S nuclei. These new shielding scales are based on accurate rotational microwave data for the spin–rotation constants of H2 17O [Puzzarini et al., J. Chem. Phys. 131, 234304 (2009)], C17O [Cazzoli et al., Phys. Chem. Chem. Phys. 4, 3575 (2002)], and H2 33S [Helgaker et al., J. Chem. Phys. 139, 244308 (2013)] corrected both for v…

Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian.

We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of p…

Coupled-cluster methods including noniterative corrections for quadruple excitations

A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested fo…

On the vertical excitation energy of cyclopentadiene

The vertical excitation energy for the lowest valence pi--pi(*) transition of cyclopentadiene is investigated. Using a combination of high-level theoretical methods and spectroscopic simulations, the vertical separation at the ground state geometry is estimated to be 5.43+/-0.05 eV. This value is intermediate between those calculated with coupled-cluster and multireference perturbation theory methods and is about 0.13 eV higher than the observed maximum in the absorption profile.

First-principles calculation of electron spin-rotation tensors.

Using Curl's Hamiltonian (Curl, R. F. Mol. Phys. 1965, 9, 585) first-principles calculations at the Hartree-Fock and various coupled-cluster (CC) levels based on a perturbative scheme are reported. The effects of basis-set dependence and electron correlation have been investigated by performing benchmark calculations for a set of radicals comprising 12 species and 14 electronic states. In comparison to experimental results, the electron spin-rotation tensor is obtained with a 10-15% accuracy when using the CC singles and doubles approximation and a triple-zeta quality basis set. Some improvements are seen when triple excitations are considered via the CC singles, doubles, and triples model.

Analytic evaluation of first-order properties within the mean-field variant of spin-free exact two-component theory.

We present a scheme for the calculation of energies and analytic energy gradients within spin-free exact two-component (SFX2C) theory in its mean-field variant, which we refer to as SFX2C-mf. In the presented scheme, the Foldy-Wouthuysen transformation is carried out after the spin-free four-component Hartree-Fock treatment such that in electron-correlated calculations only the non-mean-field part of the two-electron interactions is handled in an untransformed manner. The formulation of analytic gradients requires some adjustments in comparison with the nonrelativistic case, i.e., the additional solution of the spin-free Dirac Coulomb coupled-perturbed Hartee-Fock equations together with a …

Rare isotopic species of hydrogen sulfide: the rotational spectrum of H236S

The rotational spectrum of the 36 S-bearing isotopologue of hydrogen sulfide (H2S) has been investigated for the first time in the 167 GHz−1.6 THz frequency range, thus providing an accurate and reliable set of spectroscopic parameters. The experimental investigation was backed up by state-of-the-art quantum-chemical calculations, which also allowed us to demonstrate the incorrectness of the previously reported spectroscopic constants. The present results are of suitable accuracy to attempt the astrophysical detection of the isotopic species under consideration. Finally, reliable predictions for the spectroscopic constants of other rare isotopologues of H2S, namely the mono- and bi-deuterat…

Determination of accurate rest frequencies and hyperfine structure parameters of cyanobutadiyne, HC5N

Very accurate transition frequencies of HC$_5$N were determined between 5.3 and 21.4 GHz with a Fourier transform microwave spectrometer. The molecules were generated by passing a mixture of HC$_3$N and C$_2$H$_2$ highly diluted in neon through a discharge valve followed by supersonic expansion into the Fabry-Perot cavity of the spectrometer. The accuracies of the data permitted us to improve the experimental $^{14}$N nuclear quadrupole coupling parameter considerably and the first experimental determination of the $^{14}$N nuclear spin-rotation parameter. The transition frequencies are also well suited to determine in astronomical observations the local speed of rest velocities in molecula…

State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve.

We study the nitrogen binding curve with the density matrix renormalization group (DMRG) and single-reference and multireference coupled cluster (CC) theory. Our DMRG calculations use up to 4000 states and our single-reference CC calculations include up to full connected hextuple excitations. Using the DMRG, we compute an all-electron benchmark nitrogen binding curve, at the polarized, valence double-zeta level (28 basis functions), with an estimated accuracy of 0.03mE_h. We also assess the performance of more approximate DMRG and CC theories across the nitrogen curve. We provide an analysis of the relative strengths and merits of the DMRG and CC theory under different correlation condition…

Accurate Nonlinear Optical Properties for Small Molecules

During the last decade it became possible to calculate by quantum chemical ab initio methods not only static but also frequency-dependent properties with high accuracy. Today, the most important tools for such calculations are coupled cluster response methods in combination with systematic hierarchies of correlation consistent basis sets. Coupled cluster response methods combine a computationally efficient treatment of electron correlation with a qualitatively correct pole structure and frequency dispersion of the response functions. Both are improved systematically within a hierarchy of coupled cluster models. The present contribution reviews recent advances in the highly accurate calculat…

Low-pressure pyrolysis of tBu2SO: synthesis and IR spectroscopic detection of HSOH.

Sulfenic acid (HSOH, 1) has been synthesized in the gas-phase by low-pressure high-temperature (1150 degrees C) pyrolysis of di-tert-butyl sulfoxide (tBu(2)SO, 2) and characterized by means of matrix isolation and gas-phase IR spectroscopy. High-level coupled-cluster (CC) calculations (CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ) support the first identification of the gas-phase IR spectrum of 1 and enable its spectral characterization. Five of the six vibrational fundamentals of matrix-isolated 1 have been assigned, and its rotational-resolved gas-phase IR spectrum provides additional information on the O-H and S-H stretching fundamentals. Investigations of the pyrolysis reaction by mass spectrome…

The accuracy of molecular dipole moments in standard electronic structure calculations

Abstract A systematic investigation has been carried out of the accuracy of calculated molecular equilibrium dipole moments of 11 polar closed-shell molecules, using the HF, MP2, CCSD and CCSD(T) models and correlation-consistent basis sets. Augmented basis sets are important for improving the basis-set convergence, but the quality of the results depends more on the correlation treatment than on the cardinal number of the basis set. Augmented triple-zeta basis sets are sufficient for most calculations. The mean absolute error of the HF calculations is 0.16 D, which is reduced at the MP2 and CCSD levels to 0.048 and 0.025 D, respectively. The CCSD(T) errors are small – typically

Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach.

A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin…

Ground and excited state geometries via Mukherjee’s multireference coupled-cluster method

Abstract A comprehensive study of molecular equilibrium structures is conducted to benchmark the multireference coupled-cluster (CC) method suggested by Mukherjee and coworkers (Mk-MRCC). We determine equilibrium structures and adiabatic excitation energies by applying the Mk-MRCC method within the singles and doubles (SD) approximation to ground and excited states of various small and medium-sized molecules. The results are compared to those obtained using other multireference or single-reference CC methods. For most molecules with a multireference ground state, it is found that equilibrium structures and excitation energies computed at the Mk-MRCCSD, equation-of-motion CCSD, multireferenc…

Rotational spectrum of silyl chloride: hyperfine structure and equilibrium geometry

The Lamb-dip technique was employed to record the rotational spectra of two isotopic species of silyl chloride, namely (28)SiH3Cl and (29)SiH3Cl, in order to investigate their hyperfine structure. High-accuracy quantum-chemical computations were employed to predict the hyperfine parameters involved and to support the experimental investigation. Analysis of the experimental spectra led to an improvement in the accuracy of the known spectroscopic constants as well as allowed us to determine additional spectroscopic parameters for the first time. Furthermore, the equilibrium structure of silyl chloride was reinvestigated using both theoretical and experimental data. The best theoretical and se…

Experimental and quantum-chemical characterization of heavy carbon subchalcogenides: Infrared detection of SeC3Se

Abstract High-resolution infrared studies of laser ablation products from carbon-selenium targets have revealed a new vibrational band at 2057 cm−1  that is identified as the ν 3 vibrational fundamental of the SeC3Se cluster. Because of the rich isotopic composition of selenium and the heavy nuclear masses involved, the vibrational band shows a relatively compact and complex structure despite the simple linear geometric arrangement. Overall, rotational-vibrational lines of six isotopologues could be assigned and fitted permitting the derivation of an accurate selenium-carbon bond length. Spectroscopic analysis has been greatly supported by high-level quantum-chemical calculations of the mol…

A Discussion of Some Problems Associated with the Quantum Mechanical Treatment of Open-Shell Molecules

The re Structure of Cyclopropane

A long-standing controversy regarding the re structure of cyclopropane is resolved by performing high-level quantum chemical calculations and analyzing the experimental rotational constants for C3H6 and C3H4D2 augmented by calculated vibrational corrections. For the latter, a least-squares fit yields the following set of parameters:  re (CC) = 1.5030(10) A, re(CH) = 1.0786(10) A, and αe(HCH) = 114.97(10)°, which compare favorably with both the pure computational result obtained at the CCSD(T)/cc-pVQZ level as well as an earlier estimate of the re structure of cyclopropane based on analysis of gas-phase electron diffraction data. Our results are in rather poor agreement with a structure base…

Zeeman effect in sulfur monoxide: A tool to probe magnetic fields in star forming regions

[Context] Magnetic fields play a fundamental role in star formation processes and the best method to evaluate their intensity is to measure the Zeeman effect of atomic and molecular lines. However, a direct measurement of the Zeeman spectral pattern from interstellar molecular species is challenging due to the high sensitivity and high spectral resolution required. So far, the Zeeman effect has been detected unambiguously in star forming regions for very few non-masing species, such as OH and CN.

Force probe simulations using an adaptive resolution scheme

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute a…

Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations

Using analytic gradient techniques and an additivity scheme for the various electron correlation contributions, i.e. core-correlation, contribution due to full treatment of triple excitations and contributions due to quadruple excitations calculated with different basis sets, the accuracy of computed geometrical parameters are analysed in comparison with experiment. For a test set of 12 closed-shell and 5 open-shell molecules, it is found that inclusion of quadruple excitations is essential to reach agreement with experiment. The mean error of 0.002 pm and the standard deviation of 0.040 pm of the present CCSD(T)/cc-pV6Z + core(CCSD(T)/cc-pCVQZ) + T/cc-pVTZ + Q/cc-pVDZ results for the close…

Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants

A detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from least-squares fits involving experimental rotational constants B(0) and sums of ab initio vibration-rotation interaction constants alpha(r)(B). The vibration-rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree-Fock vibration-rotation interaction constants have an accuracy similar to that obtained by a dir…

Nuclear magnetic shielding constants in the CC2 model

Abstract Test calculations of nuclear magnetic shielding constants in the CC2 model are performed using the gauge-including atomic orbital approach. Absolute shielding constants are reported for reprsentative first-row hydrides, a few multiply bonded molecules and some challenging cases. The performance of CC2 is analyzed by comparison with experimental data and results from calculations employing more sophisticated treatments of electron correlation. In most cases, CC2 shieldings and chemical shifts are close to those obtained at second-order perturbation theory, despite the fact that the CC2 model includes an approximate treatment of orbital relaxation effects at the correlated level.

A black-box, general purpose quadratic self-consistent field code with and without Cholesky Decomposition of the two-electron integrals

We present the implementation of a quadratically convergent self-consistent field (QCSCF) algorithm based on an adaptive trust-radius optimisation scheme for restricted open-shell Hartree���Fock (ROHF), restricted Hartree���Fock (RHF), and unrestricted Hartree���Fock (UHF) references. The algorithm can exploit Cholesky decomposition (CD) of the two-electron integrals to allow calculations on larger systems. The most important feature of the QCSCF code lies in its black-box nature ��� probably the most important quality desired by a generic user. As shown for pilot applications, it does not require one to tune the self-consistent field (SCF) parameters (damping, Pulay's DIIS, and other simil…

The equilibrium structure of trans-glyoxal from experimental rotational constants and calculated vibration–rotation interaction constants

A total of six high-resolution FT-IR spectra for trans-glyoxal-d2, trans-glyoxal-d1 and trans-glyoxal-13C2 were recorded with a resolution ranging from 0.003 to 0.004 cm−1. By means of a simultaneous ground state combination difference analysis for each of these isotopologues using the Watson Hamiltonian in A-reduction and Ir-representation the ground state rotational constants are obtained. An empirical equilibrium structure is determined for trans-glyoxal using these experimental ground state rotational constants and vibration–rotation interaction constants calculated at the CCSD(T)/cc-pVTZ level of theory. The least-squares fit yields the following structural parameters for trans-glyoxal…

Full configuration-interaction and coupled-cluster calculations of the indirect spin–spin coupling constant of BH

Abstract Full configuration-interaction calculations of the indirect spin–spin coupling constant of the BH molecule have been carried out in order to investigate the performance of various coupled-cluster (CC) methods in the treatment of electron-correlation effects, while the corresponding basis set convergence is analyzed in CC singles and doubles calculations. Assuming additivity of correlation and basis set effects, a theoretical estimate of 50.67 Hz is obtained for the 11 B 1 H spin–spin coupling constant.

Electron-Correlated Methods for the Calculation of NMR Chemical Shifts

The Ã 1Au state and the T2 potential surface of acetylene: Implications for triplet perturbations in the fluorescence spectra of the à state

The cis–trans isomerization reaction on the T2 surface of acetylene and the lowest excited singlet state of acetylene, A 1Au, are investigated by ab initio electronic structure theory. We report optimized geometries, dipole moments, and harmonic vibrational frequencies of stationary points and adiabatic energy differences between them using basis sets as large as triple‐ζ plus double polarization with higher angular momentum functions, TZ(2df,2pd), and theoretical methods up to coupled‐cluster singles and doubles with a perturbative triples correction [CCSD(T)] and the equation‐of‐motion coupled‐cluster method (EOM‐CCSD). Our theoretical predictions should aid the interpretation of observat…

Spin-restricted open-shell coupled-cluster theory for excited states

Using a linear-response approach, the recently introduced spin-restricted coupled-cluster (SR-CC) theory is extended to the treatment of excited states of high-spin open-shell molecules. Explicit equations are given within the usual singles and doubles approximation and our implementation (within an existing spin–orbital code) is described. It is shown that in SR-CC theory, due to spin constraints, the spin-expectation value for the excited states calculated as corresponding energy derivatives always corresponds to the exact value. In addition, the SR-CC singles and doubles (SR-CCSD) approach is extended to include also the so-called pseudotriple excitations (best described as double excita…

Equilibrium geometries of cyclic SiC3 isomers

Equilibrium geometries of two isomers of cyclic SiC3 are determined by both large scale ab initio calculation and a procedure involving the use of experimental data from microwave spectroscopy and calculated harmonic and cubic force fields. Internuclear distances corresponding to structures obtained by both procedures agree to better than 0.003 A in all cases, allowing for precise recommendations of equilibrium structures. Rather large residual inertial defects obtained from moments of inertia based on rotational constants adjusted for effects of vibration–rotation interaction were found to be reduced significantly by inclusion of electronic contributions as estimated from calculations of r…

Analytic evaluation of Raman intensities in coupled-cluster theory

We present the first implementation for the analytic calculation of polarizability derivatives using coupled-cluster theory. These derivatives are related to the intensity of bands seen in Raman spectroscopy, and are therefore important quantities that can also be measured experimentally. The required theory of analytic third derivatives is discussed and also connected to response theory to allow the calculation of frequency-dependent quantities. This work includes the use of a string-based general coupled-cluster/configuration-interaction program which makes the calculation of Raman intensities for arbitrary coupled-cluster or configuration-interaction methods up to the full configuration-…

Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants

A theory for the calculation of nuclear magnetic shielding constants at the coupled‐cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge‐including atomic orbital (GIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H2O,NH3, CH4, N2, CO, HCN, and F2. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the abil…

Perturbative treatment of scalar-relativistic effects in coupled-cluster calculations of equilibrium geometries and harmonic vibrational frequencies using analytic second-derivative techniques

An analytic scheme for the computation of scalar-relativistic corrections to nuclear forces is presented. Relativistic corrections are included via a perturbative treatment involving the mass-velocity and the one-electron and two-electron Darwin terms. Such a scheme requires mixed second derivatives of the nonrelativistic energy with respect to the relativistic perturbation and the nuclear coordinates and can be implemented using available second-derivative techniques. Our implementation for Hartree-Fock self-consistent field, second-order Moller-Plesset perturbation theory, as well as the coupled-cluster level is used to investigate the relativistic effects on the geometrical parameters an…

A coupled cluster study of the 1 1A1g and 1 1B2u states of benzene

A theoretical investigation of the equilibrium structures and harmonic frequencies of the 1 1A1g and 1 1B2u states of benzene is presented. The performance of coupled cluster singles (CCS), the recently proposed CC2 model, and coupled cluster singles and doubles (CCSD) is compared. The CC2 ground and excited states frequencies are a significant improvement of the CCS results and are relatively close to the CCSD results. A comparative analysis of the vibrations in the two electronic states of both C6H6 and C6D6 is presented. The reliability of predicted shifts in harmonic frequencies between the two states and isotopic shifts is estimated on the basis of the convergence in the CCS, CC2, and …

Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives.

In this paper we present a parallel adaptation of a highly efficient coupled-cluster algorithm for calculating coupled-cluster singles and doubles (CCSD) and coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations (CCSD(T)) energies, gradients, and, for the first time, analytic second derivatives. A minimal-effort strategy is outlined that leads to an amplitude-replicated, communication-minimized implementation by parallelizing the time-determining steps for CCSD and CCSD(T). The resulting algorithm is aimed at affordable cluster architectures consisting of compute nodes with sufficient memory and local disk space and that are connected by standard co…

Theoretical study of electronically excited cis- and trans-glyoxal

Abstract The equation-of-motion coupled cluster method for excitation energies in the singles and doubles approximation (EOMEE-CCSD) is applied to an investigation of the structure and harmonic frequencies of planar conformers of glyoxal in their first excited singlet states. For the trans-isomer, agreement between calculated harmonic frequencies and observed fundamentals is generally satisfactory, although the theoretical values are slightly more than 10% too high for the carbonyl stretching modes. Parallel calculations of the corresponding ground state properties allow for an empirical prediction of the excited state frequencies in which calculated differences in normal-mode frequencies a…

DLPNO-MP2 second derivatives for the computation of polarizabilities and NMR shieldings

We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller–Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole …

Papers accepted for publication in The Analyst