From bridges to cycles in spectroscopic networks

Abstract

Spectroscopic networks provide a particularly useful representation of observed rovibronic transitions of molecules, as well as of related quantum states, whereby the states form a set of vertices connected by the measured transitions forming a set of edges. Among their several uses, SNs offer a practical framework to assess data in line-by-line spectroscopic databases. They can be utilized to help detect flawed transition entries. Methods which achieve this validation work for transitions taking part in at least one cycle in a measured spectroscopic network but they do not work for bridges. The concept of two-edge-connectivity of graph theory, introduced here to high-resolution spectroscopy, offers an elegant approach that facilitates putting the maximum number of bridges, if not all, into at least one cycle. An algorithmic solution is shown how to augment an existing spectroscopic network with a minimum number of new spectroscopic measurements selected according to well-defined guidelines. In relation to this, two metrics are introduced, ranking measurements based on their utility toward achieving the goal of two-edge-connectivity. Utility of the new concepts are demonstrated on spectroscopic data of $$^{14} {\text {NH}}_3$$ 14 NH 3 .

Verification labels for rovibronic quantum-state energy uncertainties

“…A cycle is a path if and . If the edge does not participate in any cycles in the graph, then it is called a bridge 9 .…”

A network approach to atomic spectra

“…Here, we investigate the potential of network science to make predictions about atomic spectra as prototypical complex physical systems, which are closely related to the underlying quantum mechanical structure [21]. This reverses the reasoning as compared to prior works [36][37][38][39], which drew conclusions about spectroscopic networks based on knowledge about the molecular structure. Using a stochastic blockmodel approach, we find that communities reveal the underlying quantum mechanical properties of the atom.…”

“…The structural information gained from network science has been applied to the analysis of spectroscopic data by mapping molecular spectra to networks [36]. Such mappings can be used to improve data accuracy and assignment [36,37], identify errors [38,39], and design efficient measurements [37,38]. However, previous applications of network modeling to molecular spectroscopic data have focused on efficiently analyzing the data, rather than making predictions about the underlying molecular structure.…”

A Network Approach to Atomic Spectra

“…This spectroscopic data can be naturally viewed as a network by identifying energy levels with the nodes (vertices) of the network, and transitions with the links (edges) between nodes. Such a mapping has been used previously to describe molecular spectroscopic data [24], improve their accuracy and assignment [24,25], identify errors [26,27], and design efficient measurements [25,26]. Spectroscopic data can be obtained either from a solution of the Schrödinger equation for small systems such as hydrogen or helium, or from the empirical observation of transitions, as compiled, e.g., in the NIST atomic spectra database [28].…”