Karol Kowalski

Efficient computer implementation of the renormalized coupled-cluster methods: The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) approaches

Abstract The recently proposed renormalized (R) and completely renormalized (CR) coupled-cluster (CC) methods of the CCSD[T] and CCSD(T) types have been implemented using recursively generated intermediates and fast matrix multiplication routines. The details of this implementation, including the complete set of equations that have been used in writing efficient computer codes, memory requirements, and typical CPU timings, are discussed. The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) computer codes and similar codes for the standard CC methods, including the LCCD, CCD, CCSD, CCSD[T], and CCSD(T) approaches, have been incorporated into the gamess package. Information about the main features of this new set of CC programs is provided.

The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches

This paper is the first in a series of papers on the new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC). A hierarchy of MMCC approximations, including the renormalized and completely renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) methods, which can be viewed as generalizations of the well-known perturbative coupled-cluster CCSD[T], CCSD(T), CCSD(TQf), and CCSDT(Qf) schemes, is introduced. In this initial study, an emphasis is placed on the ability of the MMCC approach to describe bond breaking and large effects due to connected triples and quadruples by modifying the standard noniterative CC approaches, such as the popular CCSD(T) method. The performance of selected MMCC approaches, including the renormalized and completely renormalized CCSD[T], CCSD(T), and CCSD(TQ) schemes, is illustrated by the results of pilot calculations for the HF and H2O molecules.

New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states.

The single-reference ab initio methods for high accuracy calculations of potential energy surfaces (PESs) of excited electronic states, termed the completely renormalized equation-of-motion coupled-cluster approaches with singles, doubles, and noniterative triples [CR-EOMCCSD(T)], are developed. In the CR-EOMCCSD(T) methods, which are based on the formalism of the method of moments of coupled-cluster equations, the suitably designed corrections due to triple excitations are added, in a state-selective manner, to the excited-state energies obtained in the standard equation-of-motion coupled-cluster calculations with singles and doubles (EOMCCSD). It is demonstrated that the CR-EOMCCSD(T) approaches, which can be regarded as the excited-state analogs of the ground-state CR-CCSD(T) theory, provide a highly accurate description of excited states dominated by double excitations, excited states displaying a manifestly multireference character, and PESs of excited states along bond breaking coordinates with the ease of the ground-state CCSD(T) or CR-CCSD(T) calculations. The performance of the CR-EOMCCSD(T) methods is illustrated by the results of calculations for the excited states of CH+, HF, N2, C2, and ozone.

The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt

The full version of the equation-of-motion coupled-cluster (EOMCC) method with all singles and doubles, and a selected set of triples defined through active orbitals (EOMCCSDt) has been implemented and tested using the H8, H2O, N2, C2, and CH+ systems. It is demonstrated that the full EOMCCSDt method provides the results of the full EOMCCSDT (EOMCC singles, doubles, and triples) quality at the fraction of the computer effort associated with the EOMCCSDT calculations. This includes excited states that are dominated by doubles and states that have large triexcited components. The excellent performance of the EOMCCSDt approach is observed even when the ground electronic state has a quasidegenerate character, which means that we can apply the EOMCCSDt formalism to excited states that cannot be adequately described by the perturbative triples models. The EOMCCSDt method is equivalent to the EOMCCSDT approach if all orbitals used in the EOMCCSDt calculations are active.

Renormalized CCSD(T) and CCSD(TQ) approaches: Dissociation of the N2 triple bond

The recently proposed renormalized and completely renormalized CCSD(T) and CCSD(TQ) methods, which can be viewed as generalizations of the noniterative perturbative CCSD(T) and CCSD(TQf) schemes and which result from the more general method of moments of coupled-cluster equations, are applied to the dissociation of the ground-state N2 molecule. It is shown that the renormalized and completely renormalized CCSD(T) and CCSD(TQ) methods provide significantly better results for large N–N separations than their unrenormalized CCSD(T) and CCSD(TQf) counterparts.

A comparison of the renormalized and active-space coupled-cluster methods: Potential energy curves of BH and F2

Abstract The renormalized noniterative CCSD(T) and CCSD(TQ) methods, which are the examples of the method of moments of coupled-cluster (CC) equations, and the active-space CC approach with internal and semi-internal triexcited clusters (CCSDt) are applied to the potential energy curves of BH and F 2 . It is shown that the renormalized CCSD(T) and CCSD(TQ) methods are practically as effective in removing the failing of the standard noniterative CC approaches at larger internuclear separations as the CCSDt method. The results of the CCSDt and renormalized CCSD(T) and CCSD(TQ) calculations are also compared with those obtained with other perturbative CC approaches that focus on bond breaking.

The active-space equation-of-motion coupled-cluster methods for excited electronic states: The EOMCCSDt approach

The idea of selecting the most important higher-than-doubly excited configurations in single-reference coupled-cluster (CC) calculations for quasidegenerate ground states of molecular systems through the use of active orbitals is extended to excited electronic states via the equation-of-motion (EOM) CC formalism. The resulting EOMCCSDt method, in which triexcited clusters T3 and the corresponding three-body components of the EOMCC excitation operator R are restricted to internal and semiinternal components defined through active orbitals, is capable of significantly improving the vertical excitation energies obtained with the conventional EOMCCSD (EOMCC singles and doubles) approach at a fraction of the computer cost associated with the full EOMCCSDT (EOMCC singles, doubles, and triples) calculations. The results of pilot calculations for the H8, CH2, and CH+ molecules indicate that the EOMCCSDt method using small active spaces is as accurate as the EOMCCSDT approach. In particular, the EOMCCSDt method is...

New type of noniterative energy corrections for excited electronic states: Extension of the method of moments of coupled-cluster equations to the equation-of-motion coupled-cluster formalism

The recently proposed method of moments of coupled-cluster equations (MMCC) is extended to excited states via the equation-of-motion coupled-cluster (EOMCC) formalism. The main idea of the new MMCC theory is that of the noniterative energy corrections which, when added to the excited-state energies obtained in standard approximate EOMCC calculations, recover the exact energies. The MMCC corrections are expressed in terms of the generalized moments of the EOMCC equations. Approximate variants of the excited-state MMCC formalism, including the MMCC(2,3) approach, are introduced. In the MMCC(2,3) method, very simple energy corrections, expressed in terms of matrix elements of the triples-reference, triples-singles, and triples-doubles blocks of the EOMCCSD (EOMCC singles and doubles) similarity-transformed Hamiltonian, are added to the excited-state energies obtained in EOMCCSD calculations. The performance of the MMCC(2,3) approach is illustrated by the results of pilot calculations for the potential energy...

Excited-state potential energy curves of CH+: a comparison of the EOMCCSDt and full EOMCCSDT results

The recently developed equation-of-motion coupled-cluster (EOMCC) method with singles, doubles, and a selected set of triples defined through active orbitals (EOMCCSDt) is applied to the excited-state potential energy curves of the CH+ ion. The results are compared with the EOMCCSD (EOMCC singles and doubles), EOMCCSDT (EOMCC singles, doubles, and triples), and full configuration interaction results. It is demonstrated that the EOMCCSDt method provides the excited-state potentials of the EOMCCSDT quality and that the EOMCCSDt and EOMCCSDT methods restore the asymptotic degeneracy of excited states, which is broken by the EOMCCSD and other EOMCC doubles models.

Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules

The general-purpose open-shell implementation of the completely renormalized equation-of-motion coupled-cluster approach with singles, doubles, and noniterative triples [CR-EOMCCSD(T)] is reported. Benchmark calculations for the low-lying doublet and quartet states of the CH radical show that the CR-EOMCCSD(T) method is capable of providing a highly accurate description of ground and excited states of open-shell molecules. This includes states with strong double excitation character, for which the conventional EOMCCSD approach fails.