Gas phase infrared spectra from quasi-classical Kubo time correlation functions

Abstract

We generalise the recently developed phase integration method (PIM) to obtain a computable approximation of the Kubo expression for quantum time correlation functions. Our scheme combines exact sampling of the quantum thermal density with classical dynamics to provide a quasi-classical approximation for the correlation function. The method will be specialised to the evaluation of the momentum autocorrelation function, with the goal to compute infrared spectra of simple molecules in the gas phase. Application to two simple but interesting benchmark systems shows that the approach is accurate and stable over a broad range of temperatures.

Keywords:

• quasi-classical dynamics
• infrared spectra
• Wigner density
• linearised dynamics
• phase integration method

Acknowledgements

We are delighted to have the opportunity to dedicate this work to Jean-Pierre Hansen. His interests and impact on the community of simulations stretches beyond his own scientific contributions: indeed, he has been the true ‘pope’ of our community for many years. Thus, although he has never directly contributed to quantum-classical simulations, we hope that he will have fun with this unusual reading. The authors wish to acknowledge funding from the ANR grant number ANR-12-BS08-0010-03 QUANTEAU and the SFI/HEA Irish Centre for High-End Computing (ICHEC) for proving generous computational resources.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In actual calculations, the cumulant expansion in Equation (31(31) $$\begin{array}{c}\hfill \int d\Delta \mathbf{r}{\rho }_c\left(\Delta \mathbf{r}\right|\mathbf{r})e^{-\frac{i}{\hslash }\mathbf{p}.\Delta {\mathbf{r}}^{(\nu -1)}}=e^{-E(\mathbf{r},\mathbf{p})}\end{array}$$(31) ) is truncated at a finite order that ensures convergence of the series.

Additional information

Funding

The ANR [grant number ANR-12-BS08-0010-03 QUANTEAU.