# A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model

## Abstract

We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.

- Authors:

- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada)
- (Canada)

- Publication Date:

- OSTI Identifier:
- 22419876

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; CATIONS; COUPLINGS; ELECTRONIC STRUCTURE; HAMILTONIANS; POTENTIAL ENERGY; SURFACES

### Citation Formats

```
Endicott, Julia S., Joubert-Doriol, Loïc, Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6.
```*A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model*. United States: N. p., 2014.
Web. doi:10.1063/1.4887258.

```
Endicott, Julia S., Joubert-Doriol, Loïc, Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca, & Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6.
```*A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model*. United States. doi:10.1063/1.4887258.

```
Endicott, Julia S., Joubert-Doriol, Loïc, Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Mon .
"A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model". United States.
doi:10.1063/1.4887258.
```

```
@article{osti_22419876,
```

title = {A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model},

author = {Endicott, Julia S. and Joubert-Doriol, Loïc and Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6},

abstractNote = {We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.},

doi = {10.1063/1.4887258},

journal = {Journal of Chemical Physics},

number = 3,

volume = 141,

place = {United States},

year = {Mon Jul 21 00:00:00 EDT 2014},

month = {Mon Jul 21 00:00:00 EDT 2014}

}