Method of Moments of Coupled-Cluster Equations: Externally Corrected Approaches Employing Configuration Interaction Wave Functions

Piecuch, Piotr; Kowalski, Karol; Pimienta, Ian S. O.

doi:10.3390/i3050475

Cited by 28 publications

(37 citation statements)

References 79 publications

(208 reference statements)

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“…We have recently introduced a new, nonstandard method of correcting the results of various CC calculations, termed the method of moments of coupled-cluster equations (MMCC) [7,[117][118][119][120][121][122][123]. The main idea of the MMCC formalism is that of the noniterative energy corrections which, when added to the energies obtained in approximate CC or equation-of-motion CC (EOMCC) [128][129][130] calculations, such as CCSD or EOMCCSD, recover the exact (full configuration interaction or full CI) energies of ground or excited states.…”

Section: (P)mentioning

confidence: 99%

“…The main idea of the MMCC formalism is that of the noniterative energy corrections which, when added to the energies obtained in approximate CC or equation-of-motion CC (EOMCC) [128][129][130] calculations, such as CCSD or EOMCCSD, recover the exact (full configuration interaction or full CI) energies of ground or excited states. It has been demonstrated that the MMCC formalism allows us to renormalize the existing noniterative single-reference CC approximations, such as CCSD(T) [115], CCSD(TQ f ) [116], and CCSDT(Q f ) [116], so that they can correctly describe entire ground-state PESs in situations where the standard arguments based on MBPT, on which the CCSD(T), CCSD(TQ f ), and similar approximations are based, completely fail [7,26,[117][118][119][120][121][131][132][133] (cf., also, Ref. 134 for a rederivation of the renormalized CCSD(T) expressions, published one year earlier in Refs.…”

Section: (P)mentioning

confidence: 99%

“…Independent of the approximate form of |Ψ µ chosen for such calculations, corrections δ µ can be calculated in a state-specific manner. Our belief that simple estimates of wave functions |Ψ µ may be sufficient to obtain accurate δ µ values is based on the success of the single-reference MMCC methods and their renormalized CC analogs [7,26,[117][118][119][120][121][122][123][131][132][133][134], in which simple perturbative or CI wave functions are used to construct the relevant energy corrections.…”

Section: (P)mentioning

confidence: 99%

“…We can also think of using the CISDt or CISDtq [7,120,122,123] approaches, in which triply and quadruply excited configurations of the single-reference CI method are selected via active orbitals, to construct wave functions |Ψ µ in Eq. (33).…”

Section: (P)mentioning

confidence: 99%

“…In the standard multi-reference methods, we can only hope that by adding sufficiently many higher-order terms to the equations representing low-order approaches, one obtains better results; the control over the choice of higher-order terms is limited by the fact that we use the MRMBPT or similar arguments, which may not be sufficiently transparent in situations where the MRMBPT approach suffers from intruder states. The MM-SUMRCC theory, which is a multireference analog of the recently developed method of moments of the single-reference [7,[118][119][120][121] and equation-of-motion [121][122][123] CC equations, is overviewed in this paper.…”

Section: Introductionmentioning

confidence: 99%

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The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

Piecuch

Kowalski

2002

IJMS

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Some recent advances in the area of multi-reference coupled-cluster theory of the state-universal type are overviewed. An emphasis is placed on the following new developments: (i) the idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUMRCCSD) with the multi-reference many-body perturbation theory (MRMBPT), in which cluster amplitudes of the SUM-RCCSD formalism that carry only core and virtual orbital indices are replaced by their first-order MRMBPT estimates; and (ii) the idea of combining the recently proposed method of moments of coupled-cluster equations with the SUMRCC formalism. It is demonstrated that the new SUMRCCSD(1) method, obtained by approximating the SUMRCCSD cluster amplitudes carrying only core and virtual orbital indices by their first-order MRMBPT values, provides the results that are comparable to those obtained with the complete SUMRCCSD approach.

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Section: (P)mentioning

confidence: 99%

Section: (P)mentioning

confidence: 99%

Section: (P)mentioning

confidence: 99%

Section: (P)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

Piecuch

Kowalski

2002

IJMS

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Efficient singular‐value decomposition of the coupled‐cluster triple excitation amplitudes

Lesiuk

2019

J Comput Chem

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We demonstrate a novel technique to obtain singular‐value decomposition (SVD) of the coupled‐cluster triple excitations amplitudes, tijkabc. The presented method is based on the Golub‐Kahan bidiagonalization strategy and does not require tijkabc to be stored. The computational cost of the method is comparable to several coupled cluster singles and doubles (CCSD) iterations. Moreover, the number of singular vectors to be found can be predetermined by the user and only those singular vectors which correspond to the largest singular values are obtained at convergence. We show how the subspace of the most important singular vectors obtained from an approximate triple amplitudes tensor can be used to solve equations of the CC3 method. The new method is tested for a set of small and medium‐sized molecular systems in basis sets ranging in quality from double‐ to quintuple‐zeta. It is found that to reach the chemical accuracy (≈1 kJ/mol) in the total CC3 energies as little as 5 − 15% of SVD vectors are required. This corresponds to the compression of the tijkabc amplitudes by a factor of about 0.0001 − 0.005. Significant savings are obtained also in calculation of interaction energies or rotational barriers, as well as in bond‐breaking processes. © 2019 Wiley Periodicals, Inc.

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Biorthogonal method of moments of coupled‐cluster equations: Alternative derivation, further considerations, and application to a model magnetic system

Piecuch

Gour

Włoch

2008

Int J of Quantum Chemistry

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ABSTRACT:The energy expansion defining the biorthogonal method of moments of coupled-cluster equations (MMCC) Włoch, J Chem Phys, 2005, 123, 224105 and Piecuch et al., Chem Phys Lett 2006, 418, 467], which leads to the size extensive completely renormalized (CR) coupled-cluster (CC) approach with singles, doubles, and noniterative triples employing the left eigenstates of the similarity-transformed Hamiltonian, termed CR-CC(2,3), is overviewed and rederived. The rederivation of the biorthogonal MMCC expansion presented in this work is based on a direct resummation and subsequent elimination of the many-body components of the exponential wave operator of CC theory that appear at individual moment contributions in the original MMCC energy expansion [Kowalski and Piecuch, J Chem Phys, 2000, 113, 18; Piecuch, J Chem Phys 2001, 115, 2966], enabling one to understand why the CR-CC(2,3) method using the biorthogonal MMCC theory is more accurate than the earlier CR-CCSD(T) approach. The superiority of the CR-CC(2,3) method over the CR-CCSD(T) and other previously developed single-reference CC methods with a noniterative treatment of triply excited clusters, including the widely used CCSD(T) approach BIORTHOGONAL METHOD OF MOMENTS OF COUPLED-CLUSTER EQUATIONSand the triples corrections defining the CCSD(2) schemes, is illustrated by examining the singlet-triplet gap of the (HFH) − magnetic system in which two paramagnetic centers are linked via a polarizable diamagnetic bridge.

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Method of Moments of Coupled-Cluster Equations: Externally Corrected Approaches Employing Configuration Interaction Wave Functions

Cited by 28 publications

References 79 publications

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

Efficient singular‐value decomposition of the coupled‐cluster triple excitation amplitudes

Biorthogonal method of moments of coupled‐cluster equations: Alternative derivation, further considerations, and application to a model magnetic system

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