Stanislav Kedžuch

Second order explicitly correlated R12 theory revisited: a second quantization framework for treatment of the operators' partitionings.

Second order R12 theory is presented and derived alternatively using the second quantized hole-particle formalism. We have shown that in order to ensure the strong orthogonality between the R12 and the conventional part of the wave function, the explicit use of projection operators can be easily avoided by an appropriate partitioning of the involved operators to parts which are fully describable within the computational orbital basis and complementary parts that involve imaginary orbitals from the complete orbital basis. Various Hamiltonian splittings are discussed and computationally investigated for a set of nine molecules and their atomization energies. If no generalized Brillouin condition is assumed, with all relevant partitionings the one-particle contribution arising in the explicitly correlated part of the first order wave function has to be considered and has a significant role when smaller atomic orbital basis sets are used. The most appropriate Hamiltonian splitting results if one follows the conventional perturbation theory for a general non-Hartree-Fock reference. Then, no couplings between the R12 part and the conventional part arise within the first order wave function. The computationally most favorable splitting when the whole complementary part of the Hamiltonian is treated as a perturbation fails badly. These conclusions also apply to MP2-F12 approaches with different correlation factors.

Avoiding numerical instabilities in R12 calculations through universal R12 consistent basis sets

Abstract We show that the incidental numerical instabilities in explicitly correlated coupled cluster R12 (CC-R12) calculations can be a priori removed by using systematically developed R12 suited basis sets. Those are quite different from basis sets developed for conventional calculations mainly in polarization functions. Using even tempered polarization sets for carbon and oxygen we were able to define compromise R12 suited bases which describe equally well atomic ground states, positive and negative ions and electric field polarized atoms. Corresponding energies obtained with such ‘R12 universal’ sets remain accurate to within a few μ E h with respect to the ‘R12 optimal’ bases of individual systems.

Perturbative triples correction for explicitly correlated Mukherjee’s state-specific coupled cluster method

This paper reports incorporation of the perturbative triples correction within the explicitly correlated Mukherjee’s multireference coupled cluster method using the SP ansatz. In accord with the standard approximation, these corrections are not directly entered by the correlation factor amplitudes, but the explicitly correlated part of the effective Hamiltonian is included in full. The performance of the new method is tested on singlet methylene, potential curve of fluorine molecule and automerisation barrier of cyclobutadiene. It has been found that the convergence pattern of the MkCCSD(T)-F12 results with increasing basis set is improved by approximately one cardinal number, as compared to conventional MkCCSD(T). This improvement appears at the level of single and double excitations, whereas no significant impact of the explicit treatment of the electron correlation on the (T) correction has been observed, in analogy to a single-reference approach.

Multireference R12 Coupled Cluster Theory

In order to account for static electron correlation, the explicitly correlated coupled cluster (CC) theory based on the R12 Ansatz is formulated with respect to a multi-determinantal reference using the Brillouin – Wigner (BW) approach. Though the latter avoids appearance of the intruder states, one pays for this desired feature by the loss of size extensivity. However, to some extent this can be remedied by an a posteriori correction. Since the BW-CC method offers simplest form of amplitude equations among Hilbert space MR CC ones, we have chosen it as the first step when developing MR CC-R12 approaches. It is shown that introducing of the basis set incompleteness correction via an explicit inclusion of the correlation factor into the wave function, separately for each reference, is easily realizable. Test calculations for the H4 model using the R12 optimized 9s6p4d3f basis and its subsets with increasing highest angular momentum show the potential of the MR CC-R12 approach. R12 results with meresp functions are very close to values obtained by using a conventional approach and the full 9s6p4d3f basis set. We stress, however, that care must be taken to treat the R12 corrections with comparable accuracy for all the reference determinants.

A MRCC study of the isomerisation of cyclopropane

ABSTRACT Mukherjees and Brillouin-Wigner multi-reference coupled cluster methods with universal state selective (USS) corrections were used to study the isomerisation of cyclopropane to propene through a trimethylene/propylidene diradicals. Main aim was to obtain high quality ab-initio data using advanced methods that treat both static and dynamic correlation in the involved species, however, we also report implementation of the diagonal USS correction in the LPNO-MRCC code and its performance assessment. The MkCCSD(T)/cc-pV5Z lower bound of interaction energy of cyclopropane isomerisation via trimethylene is 65.6 kcal/mol (59.9 kcal/mol with ZPVE correction), in a good agreement with experimental values in the range 60–65 kcal/mol. The MkCCSD(T)/cc-pV5Z adiabatic singlet-triplet gap in trimethylene is 0.6 kcal/mol, slightly higher than previous CASPT2 result −0.7 kcal/mol by Skancke et al.