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Title: Similarity-transformed equation-of-motion vibrational coupled-cluster theory

Abstract

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green’s function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in amore » quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicit« less

Authors:
ORCiD logo [1];  [2]; ORCiD logo [1]
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  1. Univ. of Illinois, Urbana-Champaign, IL (United States)
  2. Univ. of Waterloo, ON (Canada)
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1512936
Alternate Identifier(s):
OSTI ID: 1419608
Grant/Contract Number:  
SC0006028; FG02-11ER16211
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 5; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Faucheaux, Jacob A., Nooijen, Marcel, and Hirata, So. Similarity-transformed equation-of-motion vibrational coupled-cluster theory. United States: N. p., 2018. Web. doi:10.1063/1.5004151.
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Faucheaux, Jacob A., Nooijen, Marcel, & Hirata, So. Similarity-transformed equation-of-motion vibrational coupled-cluster theory. United States. https://doi.org/10.1063/1.5004151
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Faucheaux, Jacob A., Nooijen, Marcel, and Hirata, So. Mon . "Similarity-transformed equation-of-motion vibrational coupled-cluster theory". United States. https://doi.org/10.1063/1.5004151. https://www.osti.gov/servlets/purl/1512936.
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@article{osti_1512936,
title = {Similarity-transformed equation-of-motion vibrational coupled-cluster theory},
author = {Faucheaux, Jacob A. and Nooijen, Marcel and Hirata, So},
abstractNote = {A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green’s function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicit},
doi = {10.1063/1.5004151},
journal = {Journal of Chemical Physics},
number = 5,
volume = 148,
place = {United States},
year = {Mon Feb 05 00:00:00 EST 2018},
month = {Mon Feb 05 00:00:00 EST 2018}
}
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https://doi.org/10.1063/1.5004151
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Cited by: 9 works
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Figures / Tables:

FIG. 1 FIG. 1: Structure of the bare ($\hat{H}$), singly ($\bar{H}$), and doubly ( $\bar{\bar{H}}$) similarity-transformed Hamiltonian of electronic CCSD in the excited, ionized, and electron-attached sectors. The blocks whose elements are zero and approximately zero are represented by 0 and ≈0, respectively, while the others are represented by $X$, $\bar{X}$, andmore » $\bar{\bar{X}}$. The blue-colored blocks are the ones expressly made to vanish by the similarity transformation. $E$HF and $E$$CC$ denote the HF and CCSD energy, respectively, for the ground state. The dashed-boxed areas are the formal diagonalization spaces of equation-of-motion (EOM)-CCSD ($\bar{H}$(EE)), ionization potential (IP)-EOM-CCSD ($\bar{H}$(IP)), electron affinity (EA)-EOM-CCSD ($\bar{H}$(EA)), and similarity-transformed equation-of-motion (STEOM)-CCSD ( $\bar{\bar{H}}$ (EE) ). Diagonalization in the dashed-boxed area of $\bar{\bar{H}}$ (IP) ( $\bar{\bar{H}}$ (EA) ) is equivalent to IP-EOM-CCSD (EA-EOM-CCSD) for principal IPs (EAs).« less
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    Green’s function coupled cluster formulations utilizing extended inner excitations
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    • The Journal of Chemical Physics, Vol. 149, Issue 21
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