A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds I: The Symmetric Case

TL;DR

This paper introduces a new mathematical framework for analyzing vibrational energy levels in molecules with symmetric hydrogen bonds, accounting for anharmonic effects and differing nuclear masses, with applications to bihalide ions.

Contribution

It develops an alternative to the Born--Oppenheimer approximation tailored for symmetric hydrogen-bonded molecules, incorporating anharmonic effects at leading order.

Findings

The theory applies to symmetric bihalide ions like FHF- and ClHCl-

It provides detailed analysis for the FHF- ion

Shows anharmonic effects are significant in vibrational level calculations

Abstract

We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with symmetrical Hydrogen bonds. In our approach, the masses of the Hydrogen nuclei are scaled differently from those of the heavier nuclei, and we employ a specialized form for the electron energy level surface. Consequently, anharmonic effects play a role in the leading order calculations of vibrational levels. Although we develop a general theory, our analysis is motivated by an examination of symmetric bihalide ions, such as FHF- or ClHCl-. We describe our approach for the FHF- ion in detail.