### A time-dependent formulation of multi-reference perturbation theory

Here, we discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting time-dependent n-electron valence second-order perturbation theory (t-NEVPT2) method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics.We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules and outline directions for the future.

- Publication Date:

- Grant/Contract Number:
- SC0008624; SC0010530

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 144; Journal Issue: 6; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Research Org:
- Princeton Univ., NJ (United States)

- Sponsoring Org:
- USDOE Office of Science (SC)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

- OSTI Identifier:
- 1469673

- Alternate Identifier(s):
- OSTI ID: 1237776

```
Sokolov, Alexander Yu., and Chan, Garnet Kin-Lic.
```*A time-dependent formulation of multi-reference perturbation theory*. United States: N. p.,
Web. doi:10.1063/1.4941606.

```
Sokolov, Alexander Yu., & Chan, Garnet Kin-Lic.
```*A time-dependent formulation of multi-reference perturbation theory*. United States. doi:10.1063/1.4941606.

```
Sokolov, Alexander Yu., and Chan, Garnet Kin-Lic. 2016.
"A time-dependent formulation of multi-reference perturbation theory". United States.
doi:10.1063/1.4941606. https://www.osti.gov/servlets/purl/1469673.
```

```
@article{osti_1469673,
```

title = {A time-dependent formulation of multi-reference perturbation theory},

author = {Sokolov, Alexander Yu. and Chan, Garnet Kin-Lic},

abstractNote = {Here, we discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting time-dependent n-electron valence second-order perturbation theory (t-NEVPT2) method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics.We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules and outline directions for the future.},

doi = {10.1063/1.4941606},

journal = {Journal of Chemical Physics},

number = 6,

volume = 144,

place = {United States},

year = {2016},

month = {2}

}