# Time-dependent *N*-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and *all-trans* polyenes

## Abstract

In earlier work [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order *N*-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally contracted perturbation formulation and (ii) yielded the fully uncontracted NEVPT2 energy. We present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows us to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group algorithm. In addition, we report a low-scaling MPS-based implementation of strongly contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in *all-trans* polyenes (C _{4}H _{6} to C _{24}H _{26}), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals

- Authors:

- California Inst. of Technology (CalTech), Pasadena, CA (United States). Division of Chemistry and Chemical Engineering

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)

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

- Contributing Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- OSTI Identifier:
- 1474039

- Alternate Identifier(s):
- OSTI ID: 1365432

- Grant/Contract Number:
- SC0008624; SC0010530; AC02-05CH11231

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 146; Journal Issue: 24; 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; 74 ATOMIC AND MOLECULAR PHYSICS; polymers; correlation energy; transition metals; chemical elements; excitation energies; matrix product state; time dependent formulation; dissociation energy; perturbation theory; density matrix renormalization group

### Citation Formats

```
Sokolov, Alexander Yu., Guo, Sheng, Ronca, Enrico, and Chan, Garnet Kin-Lic.
```*Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes*. United States: N. p., 2017.
Web. doi:10.1063/1.4986975.

```
Sokolov, Alexander Yu., Guo, Sheng, Ronca, Enrico, & Chan, Garnet Kin-Lic.
```*Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes*. United States. doi:10.1063/1.4986975.

```
Sokolov, Alexander Yu., Guo, Sheng, Ronca, Enrico, and Chan, Garnet Kin-Lic. Thu .
"Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes". United States.
doi:10.1063/1.4986975. https://www.osti.gov/servlets/purl/1474039.
```

```
@article{osti_1474039,
```

title = {Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes},

author = {Sokolov, Alexander Yu. and Guo, Sheng and Ronca, Enrico and Chan, Garnet Kin-Lic},

abstractNote = {In earlier work [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally contracted perturbation formulation and (ii) yielded the fully uncontracted NEVPT2 energy. We present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows us to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group algorithm. In addition, we report a low-scaling MPS-based implementation of strongly contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C4H6 to C24H26), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals},

doi = {10.1063/1.4986975},

journal = {Journal of Chemical Physics},

number = 24,

volume = 146,

place = {United States},

year = {Thu Jun 22 00:00:00 EDT 2017},

month = {Thu Jun 22 00:00:00 EDT 2017}

}

*Citation information provided by*

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Web of Science

Works referenced in this record:

##
Density‐functional thermochemistry. III. The role of exact exchange

journal, April 1993

- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652