Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials

TL;DR

This paper investigates the extension of the Caldeira-Leggett model to anharmonic potentials in vibrational spectroscopy, demonstrating its applicability to certain systems like solids and surfaces through a Fourier-based parameterization and error analysis.

Contribution

It extends the Fourier method for generalized Langevin dynamics to nonlinear cases based on the CL model and provides empirical criteria for its applicability.

Findings

The CL model can describe systems with anharmonic potentials under certain conditions.

The Fourier method effectively parameterizes nonlinear generalized Langevin dynamics.

Empirical criteria help determine when the CL model is applicable.

Abstract

The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy owing to its utmost simplicity. However, the applicability of the model to cases with anharmonic system potentials, as it is required for the description of realistic systems in solution, is questionable due to the presence of the invertibility problem [J. Phys. Chem. Lett., \textbf{6}, 2722 (2015)] unless the system itself resembles the CL model form. This might well be the case at surfaces or in the solid regime, which we here confirm for a particular example of an iodine molecule in the atomic argon environment under high pressure. For this purpose we extend the recently proposed Fourier method for parameterizing linear generalized Langevin dynamics[J. Chem. Phys., \textbf{142}, 244110 (2015)] to the non-linear case based on the CL model and perform an extensive error analysis. In order to judge on the applicability of this model in advance, we give handy empirical criteria and discuss the effect of the potential renormalization term. The obtained results provide evidence that the CL model can be used for describing a potentially broad class of systems.