Global empirical potentials from purely rotational measurements

TL;DR

This paper presents a method to construct empirical potential energy surfaces for molecules using only pure rotational spectra, achieving high accuracy without vibrational data, exemplified on ZnO.

Contribution

The authors demonstrate a technique to derive global empirical potentials solely from rotational measurements, surpassing previous accuracy levels and matching ab initio calculations without vibrational data.

Findings

Achieved sub-kHz precision in rotational transition measurements.

Determined vibrational spacings and bond lengths with unprecedented accuracy.

Produced a globally accurate potential matching ab initio calculations without vibrational spectra.

Abstract

The recent advent of chirped-pulse FTMW technology has created a plethora of pure rotational spectra for molecules for which no vibrational information is known. The growing number of such spectra demands a way to build empirical potential energy surfaces for molecules, without relying on any vibrational measurements. Using ZnO as an example, we demonstrate a powerful technique for efficiently accomplishing this. We first measure eight new ultra-high precision ($\pm2$ kHz) pure rotational transitions in the $X$-state of ZnO. Combining them with previous high-precision ($\pm50$ kHz) pure rotational measurements of different transitions in the same system, we have data that spans the bottom 10\% of the well. Despite not using any vibrational information, our empirical potentials are able to determine the size of the vibrational spacings and bond lengths, with precisions that are more than three and two orders of magnitude greater, respectively, than the most precise empirical values previously known, and the most accurate \emph{ab initio} calculations in today's reach. By calculating the $C_{6},$ $C_{8},$ and $C_{10}$ long-range constants and using them to anchor the top of the well, our potential is \emph{globally} in excellent agreement with \emph{ab initio} calculations, without the need for vibrational spectra and without the need for \emph{any} data in the top 90\% of the well.