# Relaxation dynamics in quantum dissipative systems: The microscopic effect of intramolecular vibrational energy redistribution

## Abstract

We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much moremore »

- Authors:

- Facultad de Física, Universidad de la Habana, San Lázaro y L, Vedado, 10400 Havana (Cuba)
- (Germany)
- Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin (Germany)

- Publication Date:

- OSTI Identifier:
- 22420048

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPARATIVE EVALUATIONS; COUPLING; DENSITY MATRIX; DIATOMS; HAMILTONIANS; INTERACTIONS; MARKOV PROCESS; MOLECULES; RELAXATION; SIMULATION; WAVE PACKETS

### Citation Formats

```
Uranga-Piña, L., Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin, and Tremblay, J. C., E-mail: jean.c.tremblay@gmail.com.
```*Relaxation dynamics in quantum dissipative systems: The microscopic effect of intramolecular vibrational energy redistribution*. United States: N. p., 2014.
Web. doi:10.1063/1.4892376.

```
Uranga-Piña, L., Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin, & Tremblay, J. C., E-mail: jean.c.tremblay@gmail.com.
```*Relaxation dynamics in quantum dissipative systems: The microscopic effect of intramolecular vibrational energy redistribution*. United States. doi:10.1063/1.4892376.

```
Uranga-Piña, L., Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin, and Tremblay, J. C., E-mail: jean.c.tremblay@gmail.com. Thu .
"Relaxation dynamics in quantum dissipative systems: The microscopic effect of intramolecular vibrational energy redistribution". United States.
doi:10.1063/1.4892376.
```

```
@article{osti_22420048,
```

title = {Relaxation dynamics in quantum dissipative systems: The microscopic effect of intramolecular vibrational energy redistribution},

author = {Uranga-Piña, L. and Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin and Tremblay, J. C., E-mail: jean.c.tremblay@gmail.com},

abstractNote = {We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It demontrates that most of the mode mixing during relaxation is due to the potential part of the Hamiltonian and not to the coupling among relaxation operators.},

doi = {10.1063/1.4892376},

journal = {Journal of Chemical Physics},

number = 7,

volume = 141,

place = {United States},

year = {Thu Aug 21 00:00:00 EDT 2014},

month = {Thu Aug 21 00:00:00 EDT 2014}

}