## 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 »

- Authors:

- Univ. of Illinois, Urbana-Champaign, IL (United States)
- Univ. of Waterloo, ON (Canada)

- Publication Date:

- Research Org.:
- Univ. of Illinois, Urbana-Champaign, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- 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.
```

```
Faucheaux, Jacob A., Nooijen, Marcel, & Hirata, So. Similarity-transformed equation-of-motion vibrational coupled-cluster theory. United States. doi:10.1063/1.5004151.
```

```
Faucheaux, Jacob A., Nooijen, Marcel, and Hirata, So. Mon .
"Similarity-transformed equation-of-motion vibrational coupled-cluster theory". United States. doi:10.1063/1.5004151. https://www.osti.gov/servlets/purl/1512936.
```

```
@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 = {2018},

month = {2}

}

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Works referenced in this record:

##
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