From PECs to Spectrum and From Spectrum to PECs: A Morse Protocol for Diatomic X‑ray Absorption

A central pursuit in molecular science is to bridge molecular
potential
energy surfaces (PESs) with spectroscopic observables, both predicting
spectra from potentials and inferring potentials from spectra. Here,
we present a unified framework for diatomic systems by establishing
and validating a bidirectional bridge between Morse potential parameters
and vibrationally resolved X-ray absorption spectra. Using quantum
wavepacket simulations, we first decode the forward relationship by
linking specific potential parameters to distinct spectral features:
the equilibrium bond displacement (ΔR) dictates
Franck–Condon progressions, the anharmonicity parameter (α)
modulates intensity ratios, and the well depth (De) governs the absolute energy scaling. These systematic
parameter-sensitivity scans vividly illustrate Franck–Condon
progressions and produce a trusted library to assess the physical
plausibility of fitted parameters in the reverse procedure. Further
quantitative analysis of spectral descriptors transforms these intuitive
trends into explicit scaling laws within the scanned ranges. Conversely,
we then validate this correspondence in reverse by inverting high-resolution
experimental spectra of prototypical CO and CO+ systems,
directly extracting both ground and core-excited state potential energy
curves (PECs) with quantitative accuracy. Furthermore, two complementary
diagnostic methodsspectral root-mean-square error (RMSE) and
parameter-space deviationsare employed to comprehensively
analyze the performance of different electronic-structure methods.
The resulting physics-informed framework decodes explicit structure–spectrum
relationships, providing both a powerful tool for spectral analysis
and a valuable diagnostic for assessing novel electronic structure
methods across broad regions of the PES.