# DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes

## Abstract

We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. Internally contracted CASPT2 requires to contract the generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of the reference wavefunction. The required 4-RDM elements can be obtained from 3-particle reduced density matrices (3-RDM) of different wavefunctions, formed by symmetry-conserving single-particle excitations op top of the reference wavefunction. In our spin-adapted DMRG code CHEMPS2https://github.com/sebwouters/chemps2, we decompose these excited wavefunctions as spin-adapted matrix product states and calculate their 3-RDM in order to obtain the required contraction of the generalized Fock matrix with the 4-RDM of the reference wavefunction. In this work, we study the longitudinal static second hyperpolarizability of all-trans polyenes C{sub 2n}H{sub 2n+2} [n = 4–12] in the cc-pVDZ basis set. DMRG-SCF and DMRG-CASPT2 yield substantially lower values and scaling with system size compared to RHF and MP2, respectively.

- Authors:

- Center for Molecular Modelling, Ghent University, Technologiepark 903, 9052 Zwijnaarde (Belgium)

- Publication Date:

- OSTI Identifier:
- 22678969

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DENSITY MATRIX; PERTURBATION THEORY; POLYENES; WAVE FUNCTIONS

### Citation Formats

```
Wouters, Sebastian, Van Speybroeck, Veronique, and Van Neck, Dimitri.
```*DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes*. United States: N. p., 2016.
Web. doi:10.1063/1.4959817.

```
Wouters, Sebastian, Van Speybroeck, Veronique, & Van Neck, Dimitri.
```*DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes*. United States. doi:10.1063/1.4959817.

```
Wouters, Sebastian, Van Speybroeck, Veronique, and Van Neck, Dimitri. Sun .
"DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes". United States.
doi:10.1063/1.4959817.
```

```
@article{osti_22678969,
```

title = {DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes},

author = {Wouters, Sebastian and Van Speybroeck, Veronique and Van Neck, Dimitri},

abstractNote = {We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. Internally contracted CASPT2 requires to contract the generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of the reference wavefunction. The required 4-RDM elements can be obtained from 3-particle reduced density matrices (3-RDM) of different wavefunctions, formed by symmetry-conserving single-particle excitations op top of the reference wavefunction. In our spin-adapted DMRG code CHEMPS2https://github.com/sebwouters/chemps2, we decompose these excited wavefunctions as spin-adapted matrix product states and calculate their 3-RDM in order to obtain the required contraction of the generalized Fock matrix with the 4-RDM of the reference wavefunction. In this work, we study the longitudinal static second hyperpolarizability of all-trans polyenes C{sub 2n}H{sub 2n+2} [n = 4–12] in the cc-pVDZ basis set. DMRG-SCF and DMRG-CASPT2 yield substantially lower values and scaling with system size compared to RHF and MP2, respectively.},

doi = {10.1063/1.4959817},

journal = {Journal of Chemical Physics},

number = 5,

volume = 145,

place = {United States},

year = {Sun Aug 07 00:00:00 EDT 2016},

month = {Sun Aug 07 00:00:00 EDT 2016}

}