Ondřej Demel

Multireference Brillouin-Wigner coupled clusters method with noniterative perturbative connected triples

We developed and implemented the state-specific Brillouin-Wigner coupled cluster method with singles, doubles, and noniterative perturbative triples, called MR BWCCSD(T), for a general number of closed- and open-shell reference configurations. To assess the accuracy of the method, we performed calculations of the three lowest electronic states of the oxygen molecule and of the automerization barrier of cyclobutadiene. For the oxygen molecule, the results were in a good agreement in comparison with those of the iterative MR BWCCSDTalpha method. For cyclobutadiene, the effect of connected triples was found to be minor, which is in agreement with the previous study by and Balková and Bartlett [J. Chem. Phys. 101, 8972 (1994)].

Application of Double Ionization State-Specific Equation of Motion Coupled Cluster Method to Organic Diradicals

The state-specific equation of motion coupled cluster method is applied to three systems of diradical character: automerization of cyclobutadiene, singlet-triplet gaps of trimethylmethylene, and Bergman reaction. The aim of the paper is to assess the performance of the method and test numerically the importance of orbital optimization, three-body terms in transformed Hamiltonian, and the choice of cluster equations.

Towards the multireference Brillouin–Wigner coupled-clusters method with iterative connected triples: MR BWCCSDT-α approximation

We developed and implemented an approximation of the state-specific Brillouin-Wigner coupled-cluster method with singles, doubles, and triples, called MRBWCCSDT-alpha, for a general number of closed- and open-shell reference configurations. The accuracy of the method is assessed on the calculation of the oxygen molecule in the X3sigma(g-), a1delta(g), and b1sigma(g+) states and the results of this multireference treatment are compared with previous MRBWCCSD results and with those obtained by the doubly ionized similarity transformed equation-of-motion CCSD and multireference configuration interaction methods and with experimental spectroscopic data. Explicit tests of the size-extensivity of the MRBWCCSDT-alpha method with iterative size-extensivity correction are also performed.

Multireference Mukherjee’s coupled cluster method with triexcitations in the linked formulation: Efficient implementation and applications

We have formulated the multireference Mukherjees coupled clusters method with triexcitations (MR MkCCSDT) in the linked version and implemented it in the ACES II program package. The assessment of the new method has been performed on the first three electronic states of the oxygen molecule, on studies of singlet-triplet gap in methylene and twisted ethylene, where a comparison with other multireference CC treatments and with experimental data is available. The MR MkCCSDT results show accuracy comparable to which can be achieved with CCSDT in single reference cases. Comparison of the previously developed MkCCSD(T) method with MkCCSDT as a reference suggests, that MkCCSD(T) might be a promising candidate for an accurate treatment of systems where the static correlation plays an important role, at least for situations where small model spaces are sufficient.

Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation

A new version of the multireference Mukherjees coupled cluster method with perturbative triexcitations has been formulated, which is based on the uncoupled approximation applied to the triples equation. In contrast to the method developed by Evangelista et al. [J. Chem. Phys. 132, 074107 (2010)], the proposed approach does not require to solve the equation for T(3) amplitudes iteratively, yet yields results of essentially the same quality. The method, abbreviated as MR MkCCSD(Tu), has been implemented in the ACES II program package and its assessment has been performed on the BeH(2) model and on the tetramethyleneethane molecule.

Communication: Multireference equation of motion coupled cluster: A transform and diagonalize approach to electronic structure

The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective subspaces (inactive, active, external). Applications to first row transition metal atoms (Cr, Mn, and Fe) are presented yielding results for up to 524 electronic states (for Cr) with an rms error compared to experiment of about 0.05 eV. The accuracy of the MREOM family of methods is closely related to its favorable extensivity properties as illustrated by calculations on the O2-O2 dimer. The computational costs of the transformation steps in MREOM are comparable to those of closed-shell Coupled Cluster Singles and Doubles (CCSD) approach.

Uncoupled multireference state-specific Mukherjee’s coupled cluster method with triexcitations

We have developed the uncoupled version of multireference Mukherjees coupled cluster method with connected triexcitations. The method has been implemented in ACES II program package. The agreement between the uncoupled and the standard version of Mukherjees multireference coupled cluster method has been reported previously at the singles and doubles level by Das et al. [J. Mol. Struct.: THEOCHEM 79, 771 (2006); Chem. Phys. 349, 115 (2008)]. The aim of this article is to investigate this method further, in order to establish how its performance changes with the size of the basis set, size of the model space, multireference character of different molecules, and inclusion of connected triple excitations. Assessment of the new method has been performed on the singlet methylene, potential energy curve of fluorine molecule, and third b (1)Σ(g)(+) electronic state of oxygen molecule.

A Local Pair Natural Orbital-Based Multireference Mukherjee's Coupled Cluster Method.

This paper reports the development of a local variant of Mukherjees state-specific multireference coupled cluster method based on the pair natural orbital approach (LPNO-MkCC). The current implementation is restricted to single and double excitations. The performance of the LPNO-MkCCSD method was tested on calculations of naphthyne isomers, tetramethyleneethane, and β-carotene molecules. The results show that 99.7-99.8% of correlation energy was recovered with respect to the MkCC method based on canonical orbitals. Moreover, the errors of relative energies between different isomers or along a potential energy curve (with respect to the canonical method) are below 0.4 kcal/mol, safely within the chemical accuracy. The computational efficiency of our implementation of LPNO-MkCCSD in the ORCA program allows calculation of the β-carotene molecule (96 atoms and 1984 basis functions) on a single CPU core.

Additional global internal contraction in variations of multireference equation of motion coupled cluster theory

Extensions of multireference equation of motion coupled cluster theory (MR-EOMCC) [D. Datta and M. Nooijen, J. Chem. Phys. 137, 204107 (2012)] are presented that include additional correlation effects into the global, internally contracted similarity transformation, induced by the cluster operators. As a result the final uncontracted diagonalization space can be more compact than in the parent MR-EOMCC approach. A wide range of applications, including transition metal atomic excitation spectra, a large set of valence excited states of organic compounds, and potential energy surfaces of ground and excited states of butadiene, is presented to benchmark the applicability of the parent MR-EOMCC methodology and its new variations.

Benchmark Applications of Variations of Multireference Equation of Motion Coupled-Cluster Theory

In this work, several variations of the multireference equation of motion (MR-EOM) methodology are investigated for the calculation of excitation spectra. These variants of MR-EOM are characterized by the following aspects: (1) the operators included in the sequence of similarity transformations of the molecular electronic Hamiltonian, (2) whether permutational symmetries (i.e., hermitization, vertex symmetry) are imposed on the final elements of the similarity-transformed Hamiltonian, (3) the size of the manifold over which the similarity-transformed Hamiltonian is diagonalized, (4) whether the two-body cumulant is included in the expressions defining the amplitudes and the elements of the transformed Hamiltonian. The MR-EOM methods are benchmarked for the calculation of the excitation energies of a test set of organic molecules. With the availability of reliable benchmark data for this test set, it is possible to gauge the relative accuracy of these approaches. We also further examine a subset of the MR-EOM methods for the calculation of the excitation energies of some transition-metal complexes. These systems prove to be particularly difficult for single-reference coupled-cluster methods.