# A global potential energy surface for H$_3^+$

## TL;DR

This paper presents a highly accurate, globally correct potential energy surface for H₃⁺, combining advanced computational methods to improve predictions of rovibrational levels and dissociation energy.

## Contribution

The authors developed BOPES75K+ by refitting existing data and incorporating relativistic and QED effects, achieving unprecedented accuracy for H₃⁺ PES.

## Key findings

- Root mean square deviation of 0.05 cm⁻¹ below dissociation.
- Predictions of rovibrational levels with ~0.1 cm⁻¹ accuracy.
- Improved dissociation energy estimate of 35,076 ± 2 cm⁻¹.

## Abstract

A globally correct potential energy surface (PES) for the \hp\ molecular ion is presented. The Born-Oppenheimer (BO) \ai\ grid points of Pavanello et. al. [\textit{J. Chem. Phys.} {\bf 136}, 184303 (2012)] are refitted as BOPES75K, which reproduces the energies below dissociation with a root mean square deviation of 0.05~\cm; points between dissociation and 75\,000 \cm\ are reproduced with the average accuracy of a few wavenumbers. The new PES75K+ potential combines BOPES75K with adiabatic, relativistic and quantum electrodynamics (QED) surfaces to provide the most accurate representation of the \hp\ global potential to date, overcoming the limitations on previous high accuracy H$_3^+$ PESs near and above dissociation. PES75K+ can be used to provide predictions of bound rovibrational energy levels with an accuracy of approaching 0.1~\cm. Calculation of rovibrational energy levels within PES75K+ suggests that the non-adiabatic correction remains a limiting factor. The PES is also constructed to give the correct asymptotic limit making it suitable for use in studies of the H$^+$\,+\,H$_2$ prototypical chemical reaction. An improved dissociation energy for H$_3^+$ is derived as $D_0\,=\,$35\,076\,$\pm\,2\,$cm$^{-1}$.