Proton-transfer spectroscopy beyond the normal-mode scenario

TL;DR

This paper develops a stochastic theory to analyze proton-transfer spectral signatures beyond normal-mode analysis, applying it to ab initio simulations of H$_5$O$_2{}^{+}$, revealing distinct spectral contributions linked to transfer kinetics.

Contribution

It introduces a novel stochastic framework that captures proton transfer dynamics and spectral features beyond traditional normal-mode analysis, applicable to variable barrier heights.

Findings

Identified three spectral contributions: harmonic, transfer path, and stochastic transfer-waiting.

Transfer-waiting frequency depends exponentially on barrier height.

Transfer-path frequency is insensitive to barrier height.

Abstract

A stochastic theory is developed to predict the spectral signature of proton-transfer processes and applied to infrared spectra computed from ab initio molecular-dynamics simulations of a single H$_5$O$_2{}^{+}$ cation. By constraining the oxygen atoms to a fixed distance, this system serves as a tunable model for general proton-transfer processes with variable barrier height. Three spectral contributions at distinct frequencies are identified and analytically predicted: the quasi-harmonic motion around the most probable configuration, amenable to normal-mode analysis, the contribution due to transfer paths when the proton moves over the barrier and a shoulder for low frequencies stemming from the stochastic transfer-waiting-time distribution; the latter two contributions are not captured by normal-mode analysis but exclusively report on the proton-transfer kinetics. In accordance with reaction kinetic theory, the transfer-waiting-contribution frequency depends inverse exponentially on the barrier height, whereas the transfer-path-contribution frequency is rather insensitive to the barrier height.