State of the art for ab initio vs empirical potentials for predicting 6e$^{-}$ excited state molecular energies: Application to Li$_{2}\left(b,1^{3}\Pi_{u}\right)$

TL;DR

This paper develops the first empirical potential for the Li₂ b(1³Πᵤ) state using experimental and theoretical data, achieving high accuracy predictions that could resolve longstanding discrepancies in molecular energy measurements.

Contribution

The paper introduces a novel empirical potential for Li₂'s b(1³Πᵤ) state, combining experimental data and high-precision theoretical constants, enabling accurate energy predictions up to v=100.

Findings

Empirical potential matches ab initio vibrational spacings within 0.8 cm⁻¹.

Potential covers vibrational levels v=0-34 with predictions up to v=100.

Results facilitate high-precision measurements and resolve longstanding experimental-theoretical discrepancies.

Abstract

We build the first analytic empirical potential for the most deeply bound $\mbox{Li}_{2}$ state: $b\left(1^{3}\Pi_{u}\right)$. Our potential is based on experimental energy transitions covering $v=0-34$, and very high precision theoretical long-range constants. It provides high accuracy predictions up to $v=100$ which pave the way for high-precision long-range measurements, and hopefully an eventual resolution of the age old discrepancy between experiment and theory for the $\mbox{Li}\left(2^{2}S\right)+\mbox{Li}\left(2^{2}P\right)$ $C_{3}$ value. State of the art ab initio calculations predict vibrational energy spacings that are all in at most 0.8 cm$^{-1}$ disagreement with the empirical potential.