The orbital-specific-virtual local coupled cluster singles and doubles method

We extend the orbital-specific-virtual tensor factorization, introduced for local M?ller-Plesset perturbation theory in Ref. [J. Yang, Y. Kurashige, F. R. Manby and G. K. L. Chan, J. Chem. Phys. 134, 044123 (2011)], to local coupled cluster singles and doubles theory (OSV-LCCSD). The method is implemented by modifying an efficient projected-atomic-orbital local coupled cluster program (PAO-LCCSD) described recently, [H.-J. Werner and M. Schu?tz, J. Chem. Phys. 135, 144116 (2011)]. By comparison of both methods we find that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold. Overall, the OSV-LCCSD approach together with an MP2 correction yields small domain errors in practical calculations. The applicability of the OSV-LCCSD is demonstrated for molecules with up to 73 atoms and realistic basis sets (up to 2334 basis functions).     

Hybrid coupled cluster methods: combining active space coupled cluster methods with coupled cluster singles, doubles, and perturbative triples

Based on the coupled-cluster singles, doubles, and a hybrid treatment of triples (CCSD(T)-h) method developed by us [J. Shen, E. Xu, Z. Kou, and S. Li, J. Chem. Phys. 132, 114115 (2010); and ibid. 133, 234106 (2010); and ibid. 134, 044134 (2011)], we developed and implemented a new hybrid coupled cluster (CC) method, named CCSD(T)q-h, by combining CC singles and doubles, and active triples and quadruples (CCSDtq) with CCSD(T) to deal with the electronic structures of molecules with significant multireference character. These two hybrid CC methods can be solved with non-canonical and canonical MOs. With canonical MOs, the CCSD(T)-like equations in these two methods can be solved directly without iteration so that the storage of all triple excitation amplitudes can be avoided. A practical procedure to divide canonical MOs into active and inactive subsets is proposed. Numerical calculations demonstrated that CCSD(T)-h with canonical MOs can well reproduce the corresponding results obtained with non-canonical MOs. For three atom exchange reactions, we found that CCSD(T)-h can offer a significant improvement over the popular CCSD(T) method in describing the reaction barriers. For the bond-breaking processes in F(2) and H(2)O, our calculations demonstrated that CCSD(T)q-h is a good approximation to CCSDTQ over the entire bond dissociation processes.     

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.     

Reduced multireference coupled cluster method with singles and doubles: Perturbative corrections for triples

The reduced multireference coupled-cluster method with singles and doubles (RMR CCSD) that employs multireference configuration interaction wave function as an external source for a small subset of approximate connected triples and quadruples, is perturbatively corrected for the remaining triples along the same lines as in the standard CCSD(T) method. The performance of the resulting RMR CCSD(T) method is tested on four molecular systems, namely, the HF and F(2) molecules, the NO radical, and the F(2) (+) cation, representing distinct types of molecular structure, using up to and including a cc-pVQZ basis set. The results are compared with those obtained with the standard CCSD(T), UCCSD(T), CCSD(2), and CR CCSD(T) methods, wherever applicable or available. An emphasis is made on the quality of the computed potentials in a broad range of internuclear separations and on the computed equilibrium spectroscopic properties, in particular, harmonic frequencies omega(e). It is shown that RMR CCSD(T) outperforms other triply corrected methods and is widely applicable.     

Dispersion energy from density-fitted density susceptibilities of singles and doubles coupled cluster theory

A new method of calculation of the second-order dispersion energy is proposed. It is based on the Longuet-Higgins formula [Faraday Discuss. Chem. Soc. 40, 7 (1965)], which describes the dispersion interaction in terms of frequency-dependent density susceptibilities of monomers. In this study, the density susceptibilities are obtained from the coupled cluster theory at the singles and doubles level. Density fitting is applied in order to reduce the computational effort for the evaluation of density susceptibilities. It is shown that density fitting improves the scaling of the computational resources with molecular size by one order of magnitude without affecting the accuracy of the resulting dispersion energy. Numerical results are presented for several van der Waals molecules to illustrate the performance of the new approach.     

Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations

This paper describes the extension of the linear-scaling divide-and-conquer (DC)-based correlation method to the coupled cluster with singles and doubles excitations (CCSD) theory. In this DC-CCSD method, the CCSD equations are solved for all subsystems including their buffer regions with the use of the subsystem orbitals, which are obtained by the DC-Hartree-Fock method. Then, the correlation energy of the total system is evaluated by summing up the subsystem contributions other than the buffer regions by the energy density analysis technique. Numerical applications demonstrate that the present DC-CCSD gives highly accurate results with drastically less computational costs with regard to the required computer memory, scratch-disk capacity, and calculation time.     

Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions

A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model using Cholesky decomposition of the two-electron integrals is presented. Significantly reducing storage demands and computational effort without sacrificing accuracy compared to the conventional model, the algorithm is well suited for large-scale applications. Extensive basis set convergence studies are presented for the static and frequency-dependent electric dipole polarizability of benzene and C60, and for the optical rotation of CNOFH2 and (-)-trans-cyclooctene (TCO). The origin-dependence of the optical rotation is calculated and shown to persist for CC2 even at basis set convergence.     

Calculation of two-photon absorption strengths with the approximate coupled cluster singles and doubles model CC2 using the resolution-of-identity approximation

An implementation of two-photon absorption matrix elements using the approximate second-order coupled-cluster singles and doubles model CC2 is presented. In this implementation we use the resolution-of-the-identity approximation for the two-electron repulsion integrals to reduce the computational cost. To avoid storage of large arrays we introduce in addition a numerical Laplace transformation of orbital energy denominators for the response of the doubles amplitudes. The error due to the numerical Laplace transformation is found to be negligible. Using this new implementation, we performed a series of benchmark calculations on substituted benzene and azobenzene derivatives to get reference values for TD-DFT results. We show that results obtained with the Coulomb-attenuated B3LYP functional are in reasonable agreement with the coupled-cluster results, whereas other density functionals which do not have a long-range correction give considerably less accurate results. Applications to the AF240 dye molecule and a weakly bound molecular tweezer complex demonstrate that this new RI-CC2 implementation allows for the first time to compute two-photon absorption cross sections with a correlated wave function method for molecules with more than 70 atoms and to apply this method for benchmarking TD-DFT calculations on molecules which are of particular relevance for experimental studies of two-photon absorption.     

Calculation of X‐ray scattering intensities by means of the coupled cluster singles and doubles model

Total X‐ray scattering intensity σ_ee(q) is very sensitive to electron correlation effects. In this study σ_ee(q) of N₂, CO, and N₂O have been computed by the coupled cluster singles and doubles (CCSD) method and compared with configuration interaction singles and doubles (CISD) calculations as well as experimental observations. σ_ee(q) curves by CCSD calculations are rather close to those by CISD, but although small, there still exist some discrepancies between calculated and observed values. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1315–1320, 2001     

Multireference Brillouin-Wigner coupled cluster method with singles, doubles, and triples: efficient implementation and comparison with approximate approaches

We have developed an efficient implementation of the multireference Brillouin-Wigner coupled cluster method with full iterative treatment of connected singles, doubles, and triples. Its computational costs are too high for applications to larger molecules; however, it can be used as a useful tool for benchmarking approximate methods. Performance of the method has been tested on the ground and low-lying excited states of the oxygen molecule and on the singlet-triplet gap in methylene; the results are in good agreement with experimental data.     

Gauge-origin-independent coupled cluster singles and doubles calculation of magnetic circular dichroism of azabenzenes and phosphabenzene using London orbitals

A computational study of the Faraday B term of magnetic circular dichroism at the coupled cluster singles and doubles level is presented for pyridine, pyrazine, pyrimidine, and phosphabenzene. Gauge-origin independence is obtained by expressing the B term as a total derivative of the one-photon dipole transition strength and using London orbitals. The high quality of the coupled cluster singles and doubles (CCSD) B terms makes these useful for the assignment of experimental spectra. Previous assignments of the experimental spectra based on the qualitative perimeter model are confirmed by the CCSD results for the three azines, while a reassignment is proposed for phosphabenzene. For non-overlapping bands, the B terms calculated at the equilibrium geometries are in good agreement with the experimental values. For overlapping bands, large deviations occur. Attributing a line width to the calculated equilibrium B terms leads to a large cancellation of positive and negative contributions. This cancellation may result in a large displacement of the band center maximum, leading to a large uncertainty in the assignments of "vertical experimental excitation energies" (pyridine). Bands may also completely vanish due to such cancellation (phosphabenzene). Explicit consideration of the cancellation yields simulated theoretical spectra that are in good agreement with experiment once the theoretical spectra are parallel displaced. A major contribution for this parallel displacement is the shift in the excitation energies due to correlation beyond CCSD, as seen when comparing vertical CCSD and CC3 equilibrium-geometry excitation energies.     

Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω⁻¹ HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH⁺ and N₂ molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI. Received: 2 July 1998 / Accepted: 28 August 1998 / Published online: 11 November 1998     

Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone

To assess the separation of dynamic and nondynamic correlations and orbital choice, we calculate the molecular structure and harmonic vibrational frequencies of ozone with the recently developed tailored coupled cluster singles and doubles method (TCCSD). We employ the Hartree-Fock and complete active space (CAS) self-consistent field (SCF) orbitals to perform TCCSD calculations. When using the Hartree-Fock orbitals, it is difficult to reproduce the experimental vibrational frequency of the asymmetric stretching mode. On the other hand, the TCCSD based on the CASSCF orbitals in a correlation consistent polarized valence triple zeta basis yields excellent results with the two symmetric vibrations differing from the experimental harmonic values by 2 cm(-1) and the asymmetric vibration differing by 9 cm(-1).     

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).     

One-electron properties and electrostatic interaction energies from the expectation value expression and wave function of singles and doubles coupled cluster theory

One-electron density matrices resulting from the explicitly connected commutator expansion of the expectation value were implemented at the singles and doubles coupled cluster (CCSD) level. In the proposed approach the one-electron density matrix is obtained at a little extra cost in comparison to the calculation of the CCSD correlation energy. Therefore, in terms of the computational time the new method is significantly less demanding than the conventional linear-response CCSD theory which requires additionally an expensive calculation of the left-hand solution of the CCSD equations. The quality of the new density matrices was investigated by computing a set of one-electron properties for a series of molecules of varying sizes and comparing the results with data obtained using the full configuration interaction method or higher level coupled cluster theory. It has been found that the results obtained using the new approach are of the same quality as those predicted by the linear-response CCSD method. The novel one-electron density matrices have also been applied to study the energy of the electrostatic interaction for a number of van der Waals complexes, including the benzene and azulene dimers.     

A truncation hierarchy of coupled cluster models of strongly correlated systems based on perfect-pairing references: the singles+doubles models

Paired, active-space treatments of static correlation are augmented with additional amplitudes to produce a hierarchy of parsimonious and efficient cluster truncations that approximate the total energy. The number of parameters introduced in these models grow with system size in a tractable way: two powers larger than the static correlation model it is built upon: for instance cubic for the models built on perfect pairing, fourth order for a perfect quadruples (PQ) reference, and fifth order for the models built on perfect hextuples. These methods are called singles+doubles (SD) corrections to perfect pairing, PQ, perfect hextuples, and two variants are explored. An implementation of the SD methods is compared to benchmark results for F(2) and H(2)O dissociation problems, the H(4) and H(8) model systems, and the insertion of beryllium into hydrogen. In the cases examined even the quartic number of parameters associated with PQSD is able to provide results which meaningfully improve on coupled-cluster singles doubles (CCSD) (which also has quartic amplitudes) and compete with existing multi-reference alternatives.     

A simple correction to final state energies of doublet radicals described by equation-of-motion coupled cluster theory in the singles and doubles approximation

A computationally inexpensive energy correction is suggested for radicals described by the equation-of-motion coupled cluster method for ionized states in the singles and doubles approximation (EOMIP-CCSD). The approach is primarily intended for doublet states that are qualitatively described by Koopmans' approximation. Following a strategy similar to those used in multireference coupled cluster theory, the proposed correction accounts for all correlation effects through third order in perturbation theory and also includes selected contributions to higher-order energies. As an initial test of the numerical performance of the method, total energies and energy splittings are calculated for some small prototype radicals.     

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution.     

Dissociation of ground and nsigma* states of CF3Cl using multireference configuration interaction with singles and doubles and with multireference average quadratic coupled cluster extensivity corrections

Extended complete active space self-consistent field (CASSCF), multireference configuration interaction with singles and doubles (MR-CISD), and multireference average quadratic coupled cluster (MR-AQCC) calculations have been performed on the ground (S(0)) and first excited (nsigma(*),S(1)) states of the CF(3)Cl molecule. Full geometry optimizations have been carried out for S(0) as well as "relaxed" potential energy calculations for both states, along the C-Cl bond distance. Vertical excitation energies (DeltaE(vertical)), dissociation energies (DeltaE(diss)), dissociation enthalpies (DeltaH(diss)), and the oscillator strength (f) have also been computed. Basis set effects, basis set superposition error (BSSE), and spin-orbit and size-extensivity corrections have also been considered. The general agreement between theoretical and available experimental results is very good. The best results for the equilibrium geometrical parameters of S(0) (at MR-AQCCaug-cc-pVTZ+d level) are 1.762 and 1.323 A, for the C-Cl and C-F bond distances, respectively, while the corresponding experimental values are 1.751 and 1.328 A. The [angle](ClCF) and [angle](FCF) bond angles are in excellent agreement with the corresponding experimental values (110.3 degrees and 108.6 degrees ). The best calculated values for DeltaE(vertical), DeltaH(diss), and f are 7.63 eV [at the MR-AQCCaug-cc-pV(T+d)Z level], 3.59 eV[MR-AQCCaug-cc-pV(T+d)Z level+spin-orbit and BSSE corrections], and 2.74x10(-3) (MR-CISD/cc-pVTZ), in comparison with the corresponding experimental values of 7.7+/-0.1 eV, 3.68 eV, and 3.12 x 10(-3)+/-2.50 x 10(-4). The results concerning the potential energy curves for S(0) and S(1) show a tendency toward the nonoccurrence of crossing between these two states (in the intermediate region along the C-Cl coordinate), as the basis set size increases. Such tendency is accompanied by a decreasing well depth for the S(1) state. Dynamic electronic correlation (especially at the MR-AQCC level) is also an important factor toward an absence of crossing along the C-Cl coordinate. Further investigations of a possible crossing using gradient driven techniques (at CASSCF and MR-CISD levels) seem to confirm its absence.