Twins in rotational spectroscopy: Does a rotational spectrum uniquely identify a molecule?

TL;DR

This work investigates whether a pure rotational spectrum uniquely identifies a molecule by framing structure identification as an inverse problem and testing for isospectral twins. It introduces constrained and unconstrained construction environments and a funnel-based approach to prune candidate twin pairs across large datasets using criteria on rotational constants $(A,B,C)$ and dipole ratios, with typical experimental tolerances around $\sim 10\, \text{kHz}$ for line frequencies and $\lesssim 1\%$ for constants. The study finds that constrained structures yield no isospectral collisions, while unconstrained geometries admit collisions; across real molecule datasets, twin pairs exist but can generally be resolved with higher-accuracy theory or additional experiments (e.g., isotopic substitution, dipole-aware measurements). These results imply that the spectrum-to-structure map is ill-posed under common computational accuracies but can become well-posed with richer data and measurements, affecting practical spectral fingerprinting and database-assisted identification.

Abstract

Rotational spectroscopy is the most accurate method for determining structures of molecules in the gas phase. It is often assumed that a rotational spectrum is a unique "fingerprint" of a molecule. The availability of large molecular databases and the development of artificial intelligence methods for spectroscopy makes the testing of this assumption timely. In this paper, we pose the determination of molecular structures from rotational spectra as an inverse problem. Within this framework, we adopt a funnel-based approach to search for molecular twins, which are two or more molecules, which have similar rotational spectra but distinctly different molecular structures. We demonstrate that there are twins within standard levels of computational accuracy by generating rotational constants for many molecules from several large molecular databases, indicating the inverse problem is ill-posed. However, some twins can be distinguished by increasing the accuracy of the theoretical methods or by performing additional experiments.

Figures (9)

• Figure 1: Diagram showing forward and inverse mapping in rotational spectroscopy.
• Figure 2: Funnel diagram for evaluating possible spectral twins in a dataset of molecule geometries.
• Figure 3: Cumulative distribution of Ray's $\kappa$ across constrained (blue) and unconstrained (orange) environments with a varying number of point masses (10,25,50). Silbey's cumulative probability distribution on $\kappa$ is also shown (black), along with the cumulative distribution of $\kappa$ within GEOM (Drug) and QM9 datasets (green and red, respectively).
• Figure 4: Box-and-whisker distribution of Ray's $\kappa$ for all molecules in the PubChem dataset, for binned masses in Daltons (Da). The counts of PubChem molecules falling into each mass range is also listed. Silbey and Kinsey's probability distribution on $\kappa$ is also shown silbey1988preponderance, with black lines representing corresponding quartiles.
• Figure 5: The remaining number of twin pairs in QM9 based on the overall rotational inertia $R$ as well as rotational constants $(A,B,C)$. The number of remaining twin pairs becomes progressively smaller as tolerance decreases from 1% to 0.01%.