The role of intensities in determining characteristics of spectroscopic networks

Spectroscopic networks (SNs) are large, finite, weighted, undirected, rooted graphs, where the vertices are discrete energy levels, the edges are transitions, and the weights are transition intensities. While first-principles SNs are “deterministic” by definition, if a realistic transition intensity cut-off is employed during the construction of these SNs, a certain randomness (“stochasticity”) is introduced. Experiments naturally build random graphs. It is shown on the example of the HD16O isotopologue of the water molecule how intensities, in the present case one-photon absorption intensities, determine the structure as well as the degree distribution and edge density of SNs. The degree distribution of realistic computed SNs can be described as scale free, with the usual and well known consequences. Experimental SNs, based on measured and assigned transitions, also turn out to be scale free. The graph-theoretical view of high-resolution molecular spectra offers several new ideas for improving the accuracy and robustness of information systems containing spectroscopic data. For example, it is shown that most all rotational–vibrational energy levels are involved in at least a few relatively strong transitions suggesting that an almost complete coverage of experimental quality energy levels can be deduced from measurements.