Spectroscopic networks

The concept of spectroscopic networks (SNs) is a new paradigm of high-resolution molecular spectroscopy which we proposed a few years ago. SNs are large, finite, weighted, undirected, rooted graphs, where the vertices are discrete energy levels, the edges are transitions, and the weights are provided by transition intensities. While first-principles SNs are ‘‘deterministic’’ by definition, if a realistic transition intensity cut-off is employed during the construction of the SN, a certain randomness (‘‘stochasticity’’) is introduced. High-resolution spectroscopic experiments naturally build random graphs. The degree distribution of realistic computed SNs can be described as scale free, with usual and well-known consequences. Experimental SNs, based on measured and assigned (labeled) 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. Just as an example, almost all of the 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 carefully designed and executed measurements.

Related publications:

A. G. Császár and T. Furtenbacher, Spectroscopic Networks, J. Mol. Spectrosc. 2011, 266, 99-103.

T. Furtenbacher and A. G. Császár, The role of intensities in determining characteristics of spectroscopic networks, J. Mol. Struct. (Boris Galabov Special Issue) 2012, 1009, 123-129.

MARVEL: Measured Active Rotational-Vibrational Energy Levels

When determining energy levels from several, in cases many, measured and assigned high-resolution molecular spectra according to the Ritz principle, it is advantageous to investigate the spectra via the concept of spectroscopic networks (SNs). Experimental SNs are finite, weighted, undirected, multiedge, and rooted graphs. A considerable practical problem arises from the fact that SNs can be very large for isotopologues of molecules widely studied; for example, the experimental dataset for the H₂¹⁶O molecule contains some 200,000 measured transitions and 20,000 energy levels. In order to treat such large SNs and extract the maximum amount of information from them, sophisticated algorithms related to the inversion of the transition data are needed. Our algorithm and code called measured active rotational-vibrational energy levels (MARVEL) is aimed to perform these tasks as efficiently as possible. The Hamiltonian-independent MARVEL procedure starts with collecting, critically evaluating, selecting, and compiling all available measured transitions, including assignments and uncertainties, into a single database. Then, spectroscopic networks (SN) are determined which contain all interconnecting rotational-vibrational energy levels supported by the grand database of the selected transitions. Adjustment of the uncertainties of the lines is performed next, presently with the help of a robust reweighting strategy, until a self-consistent set of lines and uncertainties is achieved. Inversion of the transitions through a weighted least-squares-type procedure results in MARVEL energy levels and associated uncertainties. The resulting set of MARVEL energy levels is called active since when new experimental measurements become available the same evaluation, adjustment, and inversion procedure should be repeated in order to obtain more dependable energy levels and uncertainties. To achieve numerical efficiency, we found the following algorithms applicable to very large SNs: reading the input data employs hash codes, building the components of the SN utilizes a recursive depth-first search algorithm, solving the linear least-squares problem is via the conjugate gradient method, and determination of the uncertainties of the energy levels takes advantage of the robust reweighting algorithm. The MARVEL technique has already been used to determine accurate energy levels for several isotopologues of small molecules: H₂¹⁶O, H₂¹⁷O, H₂¹⁸O, HD¹⁶O, HD¹⁷O, HD¹⁸O, H₂D⁺, HD₂⁺, and H₂¹²C¹²C¹⁶O. The MARVEL energy levels and the transitions they determine, according to approximate and exact selection rules, can be used, for example, in determining accurate partition functions and the temperature-dependent thermochemistry of ideal gases.

Related publications:

T. Furtenbacher, A. G. Császár, and J. Tennyson, MARVEL: Measured Active Rotational-Vibrational Energy Levels, J. Mol. Spectry. 2007, 245, 115-125.

T. Furtenbacher and A. G. Császár, MARVEL: Measured Active Rotational-Vibrational Energy Levels. II. Algorithmic Improvements, J. Quant. Spectr. Rad. Transfer (Flaud, Camy-Peyret, Barbe Special Issue) 2012, 113, 929-935.