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Title: Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

Abstract

Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM–CCSD) and linear-response coupled cluster singles and doubles (LR–CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM–MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM–MBPT2 method was rarely more than a tenth of an eV from EOM–CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P–EOM–MBPT2, which is an order of magnitude faster than EOM–CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P–EOM–MBPT2 does not. The difference between the CC2 and P–EOM–MBPT2 can ultimately be traced back to how each method approximates EOM–CCSD and LR–CCSD. The results suggest that CC2 and P–EOM–MBPT2 are complementary: CC2 is best suited for the description of valence states while P–EOM–MBPT2 proves tomore » be a superior O(N{sup 5}) method for the description of Rydberg states.« less

Authors:
;  [1];  [2];  [3]
  1. Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States)
  2. Department of Chemistry, University of Kansas, Lawrence, Kansas 66045 (United States)
  3. Gaussian, Inc., 340 Quinnipiac St, Bldg 40, Wallingford, Connecticut 06492 (United States)
Publication Date:
OSTI Identifier:
22310733
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 16; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; COMPARATIVE EVALUATIONS; EQUATIONS OF MOTION; EXCITATION; MANY-BODY PROBLEM; MOLECULES; PERTURBATION THEORY; RYDBERG STATES

Citation Formats

Goings, Joshua J., Li, Xiaosong, E-mail: xsli@uw.edu, Caricato, Marco, and Frisch, Michael J.. Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations. United States: N. p., 2014. Web. doi:10.1063/1.4898709.
Goings, Joshua J., Li, Xiaosong, E-mail: xsli@uw.edu, Caricato, Marco, & Frisch, Michael J.. Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations. United States. doi:10.1063/1.4898709.
Goings, Joshua J., Li, Xiaosong, E-mail: xsli@uw.edu, Caricato, Marco, and Frisch, Michael J.. Tue . "Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations". United States. doi:10.1063/1.4898709.
@article{osti_22310733,
title = {Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations},
author = {Goings, Joshua J. and Li, Xiaosong, E-mail: xsli@uw.edu and Caricato, Marco and Frisch, Michael J.},
abstractNote = {Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM–CCSD) and linear-response coupled cluster singles and doubles (LR–CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM–MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM–MBPT2 method was rarely more than a tenth of an eV from EOM–CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P–EOM–MBPT2, which is an order of magnitude faster than EOM–CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P–EOM–MBPT2 does not. The difference between the CC2 and P–EOM–MBPT2 can ultimately be traced back to how each method approximates EOM–CCSD and LR–CCSD. The results suggest that CC2 and P–EOM–MBPT2 are complementary: CC2 is best suited for the description of valence states while P–EOM–MBPT2 proves to be a superior O(N{sup 5}) method for the description of Rydberg states.},
doi = {10.1063/1.4898709},
journal = {Journal of Chemical Physics},
number = 16,
volume = 141,
place = {United States},
year = {Tue Oct 28 00:00:00 EDT 2014},
month = {Tue Oct 28 00:00:00 EDT 2014}
}
  • Cited by 8
  • No abstract prepared.
  • We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-cluster wave function is used to define a similarity-transformed Hamiltonian, which is partitioned into a zeroth-order part that the reference problem solves exactly plus a first-order perturbation. Standard perturbation theory through second-order provides the leading correction. Applied to the valence optimized doubles (VOD) approximation to the full-valence complete active space self-consistent field method, the second-order correction, which we call (2), captures dynamical correlation effects through external single, double, and semi-internal triple and quadruple substitutions. A factorization approximation reduces the cost of the quadruple substitutions tomore » only sixth order in the size of the molecule. A series of numerical tests are presented showing that VOD(2) is stable and well-behaved provided that the VOD reference is also stable. The second-order correction is also general to standard unwindowed coupled-cluster energies such as the coupled-cluster singles and doubles (CCSD) method itself, and the equations presented here fully define the corresponding CCSD(2) energy. (c) 2000 American Institute of Physics.« less
  • A new, efficient approximation for coupled cluster singles and doubles (CCSD) is proposed in which CCSD calculation is performed in a valence active space followed by a second-order perturbative correction to account for the inactive singles and doubles cluster amplitudes. This method, denoted VCCSD(SD), satisfactorily reproduces CCSD results in a variety of test cases, including spectroscopic constants of diatomic molecules, reaction energies, the Cope rearrangement, and other relative energies. Use of VCCSD alone is significantly less satisfactory. Formally, the O2V4 scaling of CCSD is reduced to o2v2V2, where o is the number of active occupied orbitals, v is the numbermore » of active virtual orbitals, and V is the total number of virtual orbitals. We also investigate the role of orbital optimizations and the appropriate choice of an active space in such methods.« less
  • This paper discusses practical scheme of correcting the linear response coupled cluster with singles and doubles (LR-CCSD) equations by shifting their poles, corresponding to the equation-of-motion CCSD (EOMCCSD) excitation energies, through adding the no-iterative corrections due to triples to the EOMCCSD excitation energies. A simple criterion is derived for the excited states to be corrected in the spectral resolution of similarity transformed Hamiltonian on the CCSD level. Benchmark calculations were performed to compare the accuracies of static and dynamic polarizabilities obtained in the way with the CC3 and CCSDT counterparts.