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 H_{2}^{16}O
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: H_{2}^{16}O, H_{2}^{17}O, H_{2}^{18}O,
HD^{16}O, HD^{17}O, HD^{18}O, H_{2}D^{+},
HD_{2}^{+}, and H_{2}^{12}C^{12}C^{16}O.
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.