Coupled Cluster Response Theory Research Articles

Recent Advances in Explicitly Correlated Coupled-Cluster Response Theory for Excited States and Optical Properties

Abstract The derivation of coupled-cluster response theory for explicitly correlated wavefunctions with terms linear in the interelectronic distance r 12 (CC-R12) or a function f 12 thereof (CC-F12) is reviewed and an implementation at the CCSD(R12) and CCSD(F12) for excitation energies and the linear, quadratic and cubic reponse functions is reported for ansätze 1 and 2. We discuss the results of first applications for vertical excitation energies, excited state equilibrium structures and vibrational frequencies, polarizabilities and first and second hyperpolarizabilities with focus on present limitations and future prospects of the approach. We show in particular that the standard choice of the geminal functions and wavefunction expansion can in certain cases lead to a bias towards the unperturbed ground state and how this can be avoided by extending the geminal space. If taken care of this, in particular CCSD(F12)/ansatz 2 shows for the potential energy curves of excited states and for optical properties a similar enhanced basis set convergence of the correlation contribution due to connected double excitations as for ground state energies. For diffuse excited states and hyperpolarizbilities the correlation contribution converges with CCSD(F12)/ansatz 2 often faster than orbital relaxation contributions. The convergence of the latter can be improved by allowing single excitations into a space spanned by a complementary auxiliary basis set.

A QM/MM study on the fast photocycle of blue light using flavin photoreceptors in their light-adapted/active form

Based on QM/MM calculations using a combination of time-dependent Hartree-Fock and coupled cluster response theory a mechanism is proposed for the photocycle of blue light using flavin (BLUF) domains in the signaling/light adapted conformation. In analogy to the dark-adapted form, a charge transfer state drives proton transfer from the highly conserved tyrosine residue to the flavin chromophore. The latter step is mediated by the adjacent glutamine residue, which, in the light adapted conformation, exists as its imidic tautomer. However, before the proton transfer is even halfway completed, a conical intersection seam between the charge transfer and ground state is reached. Two channels for the decay back to the initial light-adapted conformation are open, a rapid one leading directly through the funnel of the conical intersection, bypassing the formation of the biradical intermediate, and a slower one via the biradical intermediate. The mechanism as proposed here: (i) explains the very rapid photocycle; and (ii) confirms the concept of photoirreversibility, both of which have been experimentally observed for BLUF domains in their light-adapted conformations.

Highly accurate CCSD(R12) and CCSD(F12) optical response properties using standard triple-ζ basis sets

Coupled-cluster response theory for frequency-dependent optical properties within the coupled-cluster singles-and-doubles model (CCSD) has been derived and implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package DALTON. The basis set convergence of static dipole moments, polarizabilities, and parallel averages of first and second hyperpolarizabilities has been investigated for Ne, BH, N(2), CO, and BF. The frequency-dependent results are presented for the electronic second-harmonic generation of N(2). With triple-zeta basis sets, the CCSD(F12) correlation contributions using ansatz 2 are close to the basis set limits for dipole moments and second hyperpolarizabilities; the CCSD(R12) results are better than the CCSD results obtained with at least quintuple-zeta basis sets for polarizabilities and first hyperpolarizabilities. The exponent of Slater-type correlation factor for CCSD(F12) ground state energy may not be optimal and has to be re-examined for response properties. We also suggest that the remaining one-electron basis set errors arising within the coupled-cluster singles should be reduced by allowing excitations into the auxiliary orbital space.

Solving the eigenvalue equations of correlated vibrational structure methods: Preconditioning and targeting strategies

Various preconditioners and eigenvector targeting strategies in combination with the Davidson and Olsen methods are presented for solving eigenvalue equations encountered in vibrational configuration interaction, its response generalization, and vibrational coupled cluster response theory. The targeting methods allow significant flexibility and robustness in computing selected vibrational states, which are particularly important in the often occurring but nontrivial cases of near degeneracies. We have investigated the effect of a mode-excitation level-based generally applicable preconditioning scheme aiming to improve the robustness of the more standard diagonal preconditioning method. Although increasing convergence rates may be achieved in general through a hierarchy of these preconditioners, the strategy is not always beneficial in terms of CPU time. Features of the methods are demonstrated in calculations of the overtone vibrational states of formaldehyde and the fundamental states of vinyl fluoride, vinyl chloride, vinyl bromide, and naphthalene.

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO(4), in the experimentally accessible energy range of 3-11 eV, have been captured by time-dependent relativistic density functional linear response theory based on an exact two-component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled-cluster linear response theory in conjunction with relativistic effective core potentials. The simulated-excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of (3)T(1) and (3)T(2) symmetries are split significantly by the spin-orbit coupling. The possible source for the substantial spin-orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO(4).

Parallel computation of coupled-cluster hyperpolarizabilities

Static hyperpolarizabilities of molecules (water, acetonitrile, chloroform, and para-nitroaniline) are calculated with large basis sets using coupled-cluster response theory and compared to four common density functional theory methods. These results reveal which methods and basis sets are appropriate for nonlinear optical studies for different types of molecules and provide a means for estimating errors from the quantum chemical approximation when including vibrational contributions or solvent effects at the QM/MM level. The largest calculation reported, which was for 72 electrons in 812 functions at C(2v) symmetry, took only a few hours on 256 nodes demonstrating that even larger calculations are quite feasible using modern supercomputers.

Excited states of [formula omitted]: A comprehensive time-dependent relativistic density functional theory study

The perrhenate anion, ReO4-, is taken as a showcase of heavy transition metal complexes, to examine the performance of time-dependent relativistic density functional linear response theory for electronic excitations, which is based on a newly proposed exact two-component Hamiltonian resulting from the symmetrized elimination of the small component. In total 30 scalar and 63 spinor excited states are investigated and the results are grossly in good agreement with those by the singles and doubles coupled-cluster linear response theory. It is found that only a few scalar states of 3T1 and 3T2 symmetries are split significantly by the spin–orbit coupling, whereas only those excited states involving the Rydberg-type virtual orbital are affected by the solvent effects. The nature of the optical absorption spectra is also highlighted.

Coupled cluster response theory in parameter subspaces

AbstractWe introduce a response function formalism that enables smaller number of parameters than that defined in standard coupled cluster response theory. This is essential in the development of reduced scaling methods. The formalism is general and it applies to all parameterizations at all levels of the coupled cluster hierarchy. We show that to achieve physically reasonable results the parameterization must fulfill certain criteria. The linear response functions are derived and discussed in the context of optimized virtual orbitals and Cholesky decomposition of the cluster amplitudes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

A Conclusive Mechanism of the Photoinduced Reaction Cascade in Blue Light Using Flavin Photoreceptors

On the basis of extensive first-principle calculations within the framework of quantum mechanics/molecular mechanics (QM/MM), a conclusive mechanism for the formation of the signaling state of blue light using flavin (BLUF) domain proteins is proposed which is compatible with the experimental data presently available. Time-dependent density functional, as well as advanced coupled cluster response theory was employed for the QM part in order to describe the relevant excited states. One of the key residues involved in the mechanism is the glutamine adjacent to the flavin chromophore. The reaction cascade, triggered by the initial photoexcitation of the flavin chromophore, involves isomerization of this residue but no rotation as assumed previously. The fact that only the environment, but not the flavin chromophore by itself, is chemically transformed along the individual steps of the mechanism is unique for biological photoreceptors. The final isomer of the glutamine tautomer, i.e., the imidic acid, is further stabilized by the interchange of a methionine residue in the binding pocket with a tryptophan residue. The flip of these two residues might be the trigger for the large conformational change of this protein which is consequently transmitted as the signal to the biological environment.

Coupled-cluster dynamic polarizabilities including triple excitations

Dynamic polarizabilities for open- and closed-shell molecules were obtained by using coupled-cluster (CC) linear response theory with full treatment of singles, doubles, and triples (CCSDT-LR) with large basis sets utilizing the NWChem software suite. By using four approximate CC methods in conjunction with augmented cc-pVNZ basis sets, we are able to evaluate the convergence in both many-electron and one-electron spaces. For systems with primarily dynamic correlation, the results for CC3 and CCSDT are almost indistinguishable. For systems with significant static correlation, the CC3 tends to overestimate the triples contribution, while the PS(T) approximation [J. Chem. Phys. 127, 164105 (2007)] produces mixed results that are heavily dependent on the accuracies provided by noniterative approaches used to correct the equation-of-motion CCSD excitation energies. Our results for open-shell systems show that the choice of reference (restricted open-shell Hartree-Fock versus unrestricted Hartree-Fock) can have a significant impact on the accuracy of polarizabilities. A simple extrapolation based on pentuple-zeta CCSD calculations and triple-zeta CCSDT calculations reproduces experimental results with good precision in most cases.

Phenol-water1⩽n⩽3 revisited: An ab initio study on the photophysics of these clusters at the level of coupled cluster response theory

The S1(pi*<--pi) state surfaces of the phenol-water(1<or=n<or=3) clusters are reexplored at the level of coupled cluster response theory. The global minima for n=2 and n=3 so obtained are qualitatively different from those reported so far, which were obtained with methods such as configuration interaction singles or complete active space self-consistent field lacking dynamical electron correlation effects. Furthermore, the minimum-energy points on the conical intersection seams were located in this work. The results of these calculations offer a qualitative explanation for the anomalous photophysical behavior (broad congested absorption band structure, low quantum yield, short lifetime) of n=2 and the observed predissociation of n=3 at excess energies beyond approximately 100 cm(-1), resolving a disagreement between theory and experiment which persisted for almost a decade.

Transition strengths and first-order properties of excited states from local coupled cluster CC2 response theory with density fitting

A new ab initio method for calculating transition strengths and orbital-unrelaxed first-order properties of singlet ground and excited states of extended molecular systems is presented. It is based on coupled cluster response theory at the level of the CC2 model with local approximations introduced to the doubles-excitation part of the wave function. Density fitting is employed for the calculation of the electron repulsion integrals, so that--with the exception of doubles amplitudes--only three-indexed objects do occur in the formalism. The new method was tested by performing calculations for a set of various molecules and excited states and by comparing the results with corresponding canonical (nonlocal) calculations. It turned out that for calculating transition strengths and properties of excited states the ordinary Boughton-Pulay domains are insufficient in numerous cases. To circumvent this problem a new scheme for extending domains is proposed, which is based on the solution of the coupled perturbed localization and Hartree-Fock equations. When such extended domains are used, a satisfactory agreement between canonical and local results is achieved.

Vibrational excitation energies from vibrational coupled cluster response theory

Response theory in the context of vibrational coupled cluster (VCC) theory is introduced and used to obtain vibrational excitation energies. The relation to the vibrational configuration interaction (VCI) approach is described, and the increase in accuracy of VCC response energies relative to VCI energies is discussed theoretically in terms of a perturbational order expansion and demonstrated numerically. To illustrate the theory, a pilot implementation is used to obtain anharmonic vibrational frequencies for fundamental, first overtone and combination excitations of formaldehyde as well as for the fundamental transitions of ethylene.

Frequency-dependent nonlinear optical properties with explicitly correlated coupled-cluster response theory using the CCSD(R12) model

Response theory up to infinite order is combined with the explicitly correlated coupled-cluster singles and doubles model including linear-r(12) corrections, CCSD(R12). The additional terms introduced by the linear-r(12) contributions, not present in the conventional CCSD calculation, are derived and discussed with respect to the extra costs required for their evaluation. An implementation is presented up to the cubic response function for one-electron perturbations, i.e., up to frequency-dependent second hyperpolarizabilities. As first applications the authors computed the electronic polarizabilities and second hyperpolarizabilities of BH, N(2), and formaldehyde and show that the improvement in the one-electron basis set convergence known from the R12 method for ground state energies is retained for higher-order optical properties. Frequency-dependent results are presented for the second hyperpolarizability of N(2).

On the Photophysics of Artificial Blue-Light Photoreceptors: An Ab Initio Study on a Flavin-Based Dye Dyad at the Level of Coupled-Cluster Response Theory

The photophysical behavior of a phenothiazine-phenyl-isoalloxazine dye dyad, a model system for blue-light photoreceptors functioning on the basis of photoinduced electron transfer, was investigated by employing a combination of time-dependent density functional and coupled-cluster response theory. A conical intersection between a "bright" locally excited and a "dark" charge-transfer state was found in the low-energy region of the corresponding potential energy surfaces. We propose that, for the solvated dyad, this conical intersection is responsible for the experimentally observed fast fluorescence quenching in that system.

Extensions of r12 corrections to CC2-R12 for excited states

As known since about two decades, R12 methods, which include terms linear in the interelectronic distance r(12) in the wave function, improve substantially the basis set convergence of the ground state correlation energy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the r(12) pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states.

Coupled-cluster response theory with linear-r12 corrections: The CC2-R12 model for excitation energies

Coupled-cluster response theory for vertical excitation energies within the second-order approximate coupled-cluster singles-and-doubles model CC2, including linear-r(12) corrections, is derived and implemented for Ansatze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation in order to calculate the three- and four-electron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground- and excited-state wave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory.

Coupled Cluster Theory with Emphasis on Selected New Developments

Coupled cluster (CC) methods for the description of the correlated motion of electrons and nuclei are reviewed with emphasis on selected new initiatives. The basic aspects of standard electronic CC theory are described including the rationale behind the most widely used methods like coupled cluster singles and doubles (CCSD) and the CCSD(T) approach. The hierarchy of coupled cluster models consisting of coupled cluster singles (CCS), CC2, CCSD and CC3 is also described. A brief account of the theory behind the calculation of molecular properties using CC methods, and the description of response properties and excited states using CC response theory is followed by a discussion of the use of CC theory in the context of effective models for describing molecules in solution. In another part of the review we consider recent initiatives aimed at the development of coupled cluster methods for describing the correlated motion of the atomic nuclei. A recently developed second quantization formulation of many-mode dynamics for distinguishable degrees of freedom forms the basis for developing new quantum dynamical methods in particular vibrational coupled cluster (VCC) methods. The VCC theory is reviewed and discussed in comparison with vibrational configuration interaction (VCI), and vibrational Moller–Plesset (VMP) perturbation theory. The review concludes with a discussion of some important future research topics

A coupled cluster response study of the electric dipole polarizability, first and second hyperpolarizabilities of HCl

The electric dipole polarizability and first and second hyperpolarizabilities of HCl are computed within coupled cluster response theory. A systematic basis set convergence study with Dunning's correlation consistent basis sets is first performed. Correlation effects are studied using the coupled cluster singles and doubles and CC3 models. The latter takes iteratively into account the effect of connected triple excitations. Emphasis is given to the accurate prediction of the frequency dependence and the appropriate inclusion of the effect of molecular vibrations. The results should provide the most accurate theoretical estimates to-date for the electric dipole (hyper)polarizabilities of HCl. The agreement with experiment is excellent.

Vibronic transitions from coupled-cluster response theory: Theory and application to HSiF and H2O

A scheme for calculating the vibrational structure of electronic spectra using coupled-cluster response theory is proposed. To calculate the vibrational structure of electronic transitions, the optimized geometries of the two electronic states, the molecular Hessians, the dipole transition moment and (for vibrationally induced transitions) the geometrical gradient of the dipole transition moment are used in conjunction with a recently developed method for the evaluation of Franck–Condon factors of multidimensional harmonic oscillators. Allowed and vibrationally induced transitions are both described. In this pilot implementation, the required geometrical derivatives are calculated by an automated finite-difference method. The scheme is applied to the 1 1A″←1 1A′ transition of monofluorosilylene (HSiF) and the vibrationally induced 1 1A2←1 1A1 transition of water.