Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly.

The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory. The authors show that the method can lose its orbital invariance and size consistency when no special care is taken in the elimination of redundant excitations. Using the BeH(2) model system, four schemes are compared which differ in their treatment of linear dependencies between excitations of different rank (such as between singles and doubles). While the energy curves agree within tens of μE(h) when truncating the cluster operator at double excitations (icMRCCSD…

A modified ansatz for explicitly correlated coupled-cluster wave functions that is suitable for response theory

A modified ansatz for explicitly correlated coupled-cluster wave functions with a single correlation factor is set forward. It is based on the fixed amplitude ansatz of Ten-no [Chem. Phys. Lett. 398, 56 (2004)] to which an extra term is added that allows for the explicitly correlated description of singly excited configurations. The new approach has been implemented for coupled-cluster singles and doubles with the aid of automated techniques. Numerical results are presented for vertical excitation energies, and ground and excited state equilibrium distances and harmonic frequencies of diatomics. The new approach is shown to provide a nearly unbiased description of ground and predominantly s…

Excited states with internally contracted multireference coupled-cluster linear response theory.

In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Kohn [J. Chem. Phys. 134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linear-response formalism to the time-averaged ic-MRCC Lagrangian leads to unphysical second-order poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical impleme…

Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations.

The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Köhn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducin…

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…

Explicitly correlated connected triple excitations in coupled-cluster theory.

A way to incorporate explicit electron correlation into connected triple excitations in coupled-cluster theory is proposed. The new ansatz is applied to the coupled-cluster singles and doubles model with noniterative triple excitations [CCSD(T)] and does not introduce any further sets of equations to be solved. A first implementation using automated generation and string-based evaluation of the explicit expressions is reported. The results demonstrate that the ansatz significantly enhances the basis set convergence of the noniterative triple excitation correction and thus improves upon previous approaches to explicitly correlated CCSD(T).

Meaning and magnitude of the reduced density matrix cumulants

Abstract Within the framework of a generalized normal ordering (GNO), invented by Mukherjee [1] , the reduced density matrix cumulants of the (multiconfigurational) reference wave function play a central role, as they arise directly from the contraction rules. The extended Wick theorem allows contractions of an arbitrary number of active annihilators and creators through a cumulant of corresponding rank. Because the cumulant rank truncates naturally only at the number of active spin orbitals, practical applications of the GNO concept seem to rely on a fast convergence of the cumulant series, allowing one to neglect cumulants with high rank. By computing cumulant norms for selected systems (…

Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence.

An implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 using a single Slater-type geminal has been obtained with the aid of automated term generation and evaluation techniques. In contrast to a previously reported computer code [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], our implementation features a reduced dependence on the auxiliary basis set due to the use of a reformulated evaluation of the so-called Z-intermediate rather than straight forward insertion of an auxiliary basis expansion, which allows an unambiguous comparison to more approximate CCSD-F12 models. First benchmark results for total correlation energies and reactio…

Excited states of [3.3](4,4')biphenylophane: the role of charge-transfer excitations in dimers with pi-pi interaction.

The singlet and triplet electronic excitation manifold of [3.3](4,4')biphenylophane (BPP), an intramolecular dimer, and 4,4'-dimethylbiphenyl (DMBP), the corresponding monomer, has been analyzed by employing the approximate coupled-cluster singles and doubles model (CC2). The calculated triplet-triplet and singlet-singlet transient absorption spectra show good agreement with recent experimental results. The calculations suggest a strong interaction of the two biphenyl moieties of BPP in the first singlet and triplet excited states due to the overlapping pi-electron systems, and Forster-Dexter theory for weak coupling cannot be applied. Both the first excited singlet and triplet states of BP…

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…

Explicitly correlated internally contracted multireference coupled-cluster singles and doubles theory: ic-MRCCSD(F12∗)

Abstract An explicitly correlated ansatz employing Slater-type geminals and cusp conditions is developed for the internally contracted multireference coupled-cluster singles and doubles method. Only the most important geminal terms are retained in the spirit of earlier work for single-reference theory. Throughout all our test calculations, the new ic-MRCCSD(F12∗) method improves the basis set convergence of many properties, e.g., spectroscopic constants or singlet–triplet splittings, with only little extra computational cost. If a perturbative correction for connected triples is included (the ic-MRCCSD(F12∗)+(T) method), very accurate results can be obtained even with minimal active spaces.

Surface Hopping Dynamics Including Intersystem Crossing using the Algebraic Diagrammatic Construction Method

We report an implementation for employing the algebraic diagrammatic construction to second order [ADC(2)] ab initio electronic structure level of theory in nonadiabatic dynamics simulations in the framework of the SHARC (surface hopping including arbitrary couplings) dynamics method. The implementation is intended to enable computationally efficient, reliable, and easy-to-use nonadiabatic dynamics simulations of intersystem crossing in organic molecules. The methodology is evaluated for the 2-thiouracil molecule. It is shown that ADC(2) yields reliable excited-state energies, wave functions, and spin-orbit coupling terms for this molecule. Dynamics simulations are compared to previously re…

Towards the Hartree-Fock and coupled-cluster singles and doubles basis set limit: A study of various models that employ single excitations into a complementary auxiliary basis set.

In explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] calculations, the basis set incompleteness error in the double excitations is reduced to such an extent that the error in the Hartree–Fock energy and the error in the single excitations become important. Using arguments from perturbation theory to systematically truncate the coupled-cluster singles and CCSD(F12) Lagrangians, a series of coupled-cluster models are proposed and studied that reduce these basis set incompleteness errors through additional single excitations into a complementary auxiliary basis. Convergence with model and size of complementary basis is rapid and there appears to be no need to go beyond seco…

Perturbative treatment of triple excitations in internally contracted multireference coupled cluster theory.

Internally contracted multireference coupled cluster (ic-MRCC) methods with perturbative treatment of triple excitations are formulated based on Dyall's definition of a zeroth-order Hamiltonian. The iterative models ic-MRCCSDT-1, ic-MRCC3, and their variants ic-MRCCSD(T), ic-MRCC(3) which determine the energy correction from triples by a non-iterative step are consistent in the single-reference limit with CCSDT-1a, CC3, CCSD(T), and CC(3), respectively. Numerical tests on the potential energy surfaces of BeH(2), H(2)O, and N(2) as well as on the structure and harmonic vibrational frequencies of the ozone molecule show that these methods account very well for higher order correlation effects…

Infrared study of the MoO3 doping efficiency in 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP)

AbstractElectrochemical doping produces clear changes in the vibrational spectra of organic semiconductors as we show here for the system molybdenum oxide (MoO3) doped into the charge transport material 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP). Based on density-functional theory (DFT) calculations of vibrational spectra, the new spectral features can be attributed to the CBP cation that forms as a result of electron transfer from CBP to MoO3. The intensity of the new vibrational lines is a direct measure for the probability of charge transfer. MoO3 agglomerating within the CBP matrix limits the active interface area between the two species. The appearance of a broad electronic transition …

Can coupled-cluster theory treat conical intersections?

Conical intersections between electronic states are of great importance for the understanding of radiationless ultrafast relaxation processes. In particular, accidental degeneracies of hypersurfaces, i.e., between states of the same symmetry, become increasingly relevant for larger molecular systems. Coupled-cluster theory, including both single and multireference based schemes, offers a size-extensive description of the electronic wave function, but it sacrifices the Hermitian character of the theory. In this contribution, we examine the consequences of anti-Hermitian contributions to the coupling matrix element between near-degenerate states such as linear dependent eigenvectors and compl…

Solvent Effects on Electronically Excited States Using the Conductor-Like Screening Model and the Second-Order Correlated Method ADC(2).

The conductor-like screening model (COSMO) is used to treat solvent effects on excited states within a correlated method based on the algebraic-diagrammatic construction through second-order ADC(2). The origin of solvent effects is revisited, and it is pointed out that two types of contributions have to be considered. One effect is due to the change of the solute's charge distribution after excitation, which triggers a reorganization of the solvent. Initially, only the electronic degrees of freedom adapt to the new charge distribution (nonequilibrium case); for sufficiently long-lived states, the reorientation of the solvent molecules contributes, as well (equilibrium case). The second effe…

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…

Implementation of transition moments between excited states in the approximate coupled-cluster singles and doubles model

An implementation of transition moments between excited states for the approximate coupled-cluster singles and doubles model (CC2) using the resolution of the identity (RI) approximation is reported. The accuracy of the RI approximation is analyzed for a testset of 7 molecules and 76 transitions. The RI error is found to be very small for both transition moments and oscillator strengths. Furthermore, the performance of the CC2 model in comparison with coupled-cluster singles and doubles (CCSD) is studied for 40 transitions of the same testset, yielding deviations of about 12% for the transition moments and 24% for the oscillator strengths. In addition, for 13 transitions of the testset the …

The Triplet Excimer of Naphthalene: A Model System for Triplet−Triplet Interactions and Its Spectral Properties

Basic concepts of triplet excimer formation and triplet−triplet interactions between molecules with conjugated π-systems are investigated by means of ab initio quantum chemical calculations, employing the second-order coupled-cluster method CC2 and the second-order propagator method ADC(2). The naphthalene dimer turns out to be a very fruitful model system for which weak and strong electronic coupling can be identified depending on the mutual arrangement of the monomer moieties. From geometry optimizations in the excited state, we determine binding energies, including solvent effects, and transient absorption spectra. The most stable T1 conformation turns out to be a face-to-face arrangemen…

A Series of MIICuII3 Stars (M = Mn, Ni, Cu, Zn) Exhibiting Unusual Magnetic Properties

The work in this report describes the syntheses, electrospray ionization mass spectromtery, structures, and experimental and density functional theoretical (DFT) magnetic properties of four tetrametallic stars of composition [M(II)(Cu(II)L)3](ClO4)2 (1, M = Mn; 2, M = Ni; 3, M = Cu; 4, M = Zn) derived from a single-compartment Schiff base ligand, N,N'-bis(salicylidene)-1,4-butanediamine (H2L), which is the [2 + 1] condensation product of salicylaldehyde and 1,4-diaminobutane. The central metal ion (Mn(II), Ni(II), Cu(II), or Zn(II)) is linked with two μ2-phenoxo bridges of each of the three [Cu(II)L] moieties, and thus the central metal ion is encapsulated in between three [Cu(II)L] units. …

Ab initio modeling of excitonic and charge-transfer states in organic semiconductors: the PTB1/PCBM low band gap system.

A detailed quantum chemical simulation of the excitonic and charge-transfer (CT) states of a bulk heterojunction model containing poly(thieno[3,4-b]thiophene benzodithiophene) (PTB1)/[6,6]-phenyl-C61-butyric acid methyl ester (PCBM) is reported. The largest molecular model contains two stacked PTB1 trimer chains interacting with C60 positioned on top of and lateral to the (PTB1)3 stack. The calculations were performed using the algebraic diagrammatic construction method to second order (ADC(2)). One main result of the calculations is that the CT states are located below the bright inter-chain excitonic state, directly accessible via internal conversion processes. The other important aspects…

Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)

Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help ration…

Emergence of Coherence through Variation of Intermolecular Distances in a Series of Molecular Dimers

Quantum coherences between electronically excited molecules are a signature of entanglement and play an important role for energy transport in molecular assemblies. Here we monitor and analyze for a homologous series of molecular dimers embedded in a solid host the emergence of coherence with decreasing intermolecular distance by single-molecule spectroscopy and quantum chemistry. Coherent signatures appear as an enhancement of the purely electronic transitions in the dimers which is reflected by changes of fluorescence spectra and lifetimes. Effects that destroy the coherence are the coupling to the surroundings and to vibrational excitations. Complementary information is provided by excit…

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…

Kommentar zu: H. Mustroph, S. Ernst “Das Franck-Condon-Prinzip”

Die Zeitschrift “Chemie in unserer Zeit” wendet sich an ein breites Leserspektrum. Sie will zuverlassig uber neue Entwicklungen in der Chemie und verwandten Gebieten berichten sowie komplexe Sachverhalte auch fur den Nichtfachmann verstandlich aufbereiten. Mit grosem Bedauern kommen wir jedoch zu der Einschatzung, dass der Beitrag “Wer kennt es noch? Das Franck-Condon-Prinzip” von H. Mustroph und S. Ernst (im Folgenden als Ref. 1 bezeichnet) nach unserem Ermessen diesem Anspruch nicht gerecht wird. Der Beitrag enthalt einige erhebliche fachliche Fehler sowie sachlich unbegrundete und zum Teil irrefuhrende Kritik an Lehrbuchinhalten und wissenschaftlichen Arbeiten. Wir sehen es daher geboten…

Response properties with explicitly correlated coupled-cluster methods using a Slater-type correlation factor and cusp conditions

The recently proposed extension of the explicitly correlated coupled-cluster ansatz using cusp conditions [A. Kohn, J. Chem. Phys. 130, 104104 (2009)] is tested for suitability in the calculation of response properties. For this purpose, static and dynamic electrical properties up to ESHG hyperpolarizabilities as well as optical rotations have been computed within the CCSD(F12) model. It is shown that effectively converged correlation contributions can reliably be obtained using augmented quadruple zeta basis sets already. The ansatz is optionally equipped with an extension capable of reducing the one-electron basis set error. A further simplification of the method specific Lagrangian aimed…

Ab Initio Studies of Triplet-State Properties for Organic Semiconductor Molecules

Triplet–triplet annihilation (TTA) leads to a reduced efficiency of organic light-emitting diodes (OLEDs) at high current densities. Spacial confinement of the triplet excitons, which is mainly dependent on triplet energy differences, can reduce the TTA rate. Therefore, a deliberate choice of the organic semiconductor materials with particular attention to their triplet energies can help to considerably increase the device efficiency. Organic solid-state lasers are, on the other hand, efficiently quenched by singlet–triplet annihilation (STA), which is closely related to the triplet–triplet absorption of the organic semiconductors. To establish a useful set of parameters related to the proc…

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…

Communication: Restoring full size extensivity in internally contracted multireference coupled cluster theory.

The reason for the lack of size extensivity in the valence space in current implementations of internally contracted multireference coupled cluster theories is the procedure used to eliminate redundant components from the cluster operator. We present a simple way to restore full size extensivity by performing this critical step in a basis of excitation operators that are normal ordered with respect to the multiconfigurational reference function.

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…

Explicitly Correlated Electrons in Molecules

Quantum Chemical Parametrization and Spectroscopic Characterization of the Frenkel Exciton Hamiltonian for a J-Aggregate Forming Perylene Bisimide Dye

Quantum chemical and quantum dynamical calculations are performed for a bay-substituted perylene bisimide dye up to its hexameric aggregate. The aggregate structure is determined by employing the self-consistent charge density functional tight-binding (SCC-DFTB) approach including dispersion corrections. It is characterized by a stabilization via two chains of hydrogen bonds facilitated by amide functionalities. Focusing on the central embedded dimer, the Coulomb coupling for this J-aggregate is determined by means of the time-dependent density functional theory (TDDFT) to be -514 cm(-1). Exciton vibrational coupling is treated within the shifted oscillator model from which five strongly co…

CCDC 1048420: Experimental Crystal Structure Determination

Related Article: Suraj Mondal, Shuvankar Mandal, Luca Carrella, Arpita Jana, Michel Fleck, Andreas Köhn, Eva Rentschler, and Sasankasekhar Mohanta|2015|Inorg.Chem.|54|117|doi:10.1021/ic501900d

CCDC 1048423: Experimental Crystal Structure Determination

Related Article: Suraj Mondal, Shuvankar Mandal, Luca Carrella, Arpita Jana, Michel Fleck, Andreas Köhn, Eva Rentschler, and Sasankasekhar Mohanta|2015|Inorg.Chem.|54|117|doi:10.1021/ic501900d

CCDC 1048421: Experimental Crystal Structure Determination

Related Article: Suraj Mondal, Shuvankar Mandal, Luca Carrella, Arpita Jana, Michel Fleck, Andreas Köhn, Eva Rentschler, and Sasankasekhar Mohanta|2015|Inorg.Chem.|54|117|doi:10.1021/ic501900d

CCDC 1048422: Experimental Crystal Structure Determination

Related Article: Suraj Mondal, Shuvankar Mandal, Luca Carrella, Arpita Jana, Michel Fleck, Andreas Köhn, Eva Rentschler, and Sasankasekhar Mohanta|2015|Inorg.Chem.|54|117|doi:10.1021/ic501900d