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…
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…
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…
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…
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…
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…
Equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields.
A program for the direct calculation of excitation energies of atoms and molecules in strong magnetic fields is presented. The implementation includes the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) method for electronically excited states as well as its spin-flip variant. Differences to regular EOM-CCSD implementations are due to the appearance of the canonical angular-momentum operator in the Hamiltonian causing the wave function to become complex. The gauge-origin problem is treated by the use of gauge-including atomic orbitals. Therefore, a modified Davidson method for diagonalizing complex non-Hermitian matrices is used. Excitation energies for selected atoms and mole…
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-…
Foreword: Prof. Gauss Festschrift
As guest editors, we are excited to present the Molecular Physics Festschrift in honour of Jurgen Gauss, professor of theoretical chemistry at the Johannes Gutenberg-Universitat Mainz, Germany, on ...
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…
Kohn–Sham energy decomposition for molecules in a magnetic field
We study the total molecular electronic energy and its Kohn–Sham components within the framework of magnetic-field density-functional theory (BDFT), an alternative to current-dependent density-functional theory (CDFT) for molecules in the presence of magnetic fields. For a selection of closed-shell dia- and paramagnetic molecules, we investigate the dependence of the total electronic energy and its Kohn–Sham components on the magnetic field. Results obtained from commonly used density-functional approximations are compared with those obtained from Lieb optimizations based on magnetic-field dependent relaxed coupled-cluster singles-and-doubles (CCSD) and second-order Moller–Plesset (MP2) den…
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 …
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 …
Erratum: “GW quasiparticle energies of atoms in strong magnetic fields” [J. Chem. Phys. 150, 214112 (2019)]
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…
Full triples contribution in coupled-cluster and equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields
Coupled-cluster as well as equation-of-motion coupled-cluster methods play an important role whenever high accuracy is warranted. Concerning excitation energies, consideration of triple excitations is typically required to reach an accuracy better than 0.1–0.3 eV. In the context of strong magnetic fields such accuracy is needed for the prediction of spectra of strongly magnetized White Dwarfs. In addition it turns out that in order to correctly model the behavior of energies with respect to the magnetic field strength, triple excitations are required. Due to avoided crossings which are extremely often encountered in the context of strong magnetic fields, double-excitation character can be t…
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…
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…
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…
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…
GW quasiparticle energies of atoms in strong magnetic fields
Quasiparticle energies of the atoms H–Ne have been computed in the GW approximation in the presence of strong magnetic fields with field strengths varying from 0 to 0.25 atomic units (0.25 B 0 =0.25 ℏe −1 a −2 0 ≈58 763 0.25 B0=0.25 ℏe−1a0−2≈58 763 T). The GW quasiparticle energies are compared with equation-of-motion ionization-potential (EOM-IP) coupled-cluster singles-and-doubles (CCSD) calculations of the first ionization energies. The best results are obtained with the evGW@PBE0 method, which agrees with the EOM-IP-CCSD model to within about 0.20 eV. Ionization potentials have been calculated for all atoms in the series, representing the first systematic study of ionization potentials …
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...
Transition-Dipole Moments for Electronic Excitations in Strong Magnetic Fields Using Equation-of-Motion and Linear Response Coupled-Cluster Theory
An implementation of transition-dipole moments at the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) and CCSD linear response (LR) levels of theory for the treatment of atoms and molecules in strong magnetic fields is presented. The presence of a finite magnetic field leads, in general, to a complex wave function and a gauge-origin dependence, necessitating a complex computer code together with the use of gauge-including atomic orbitals. As in the field-free case, for EOM-CC, the evaluation of transition-dipole moments consists of setting up the one-electron transition-density matrix (TDM) which is then contracted with dipole-moment integrals. In the case of CC-LR, the evalua…
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.