Small Molecules—Big Data

Abstract

Quantum mechanics builds large-scale graphs (networks): the vertices are the discrete energy levels the quantum system possesses, and the edges are the (quantum-mechanically allowed) transitions. Parts of the complete quantum mechanical networks can be probed experimentally via high-resolution, energy-resolved spectroscopic techniques. The complete rovibronic line list information for a given molecule can only be obtained through sophisticated quantum-chemical computations. Experiments as well as computations yield what we call spectroscopic networks (SN). First-principles SNs of even small, three to five atomic molecules can be huge, qualifying for the big data description. Besides helping to interpret high-resolution spectra, the network-theoretical view offers several ideas for improving the accuracy and robustness of the increasingly important information systems containing line-by-line spectroscopic data. For example, the smallest number of measurements necessary to perform to obtain the complete list of energy levels is given by the minimum-weight spanning tree of the SN and network clustering studies may call attention to "weakest links" of a spectroscopic database. A present-day application of spectroscopic networks is within the MARVEL (Measured Active Rotational-Vibrational Energy Levels) approach, whereby the transitions information on a measured SN is turned into experimental energy levels via a weighted linear least-squares refinement. MARVEL has been used successfully for 15 molecules and allowed to validate most of the transitions measured and come up with energy levels with well-defined and realistic uncertainties. Accurate knowledge of the energy levels with computed transition intensities allows the realistic prediction of spectra under many different circumstances, e.g., for widely different temperatures. Detailed knowledge of the energy level structure of a molecule coming from a MARVEL analysis is important for a considerable number of modeling efforts in chemistry, physics, and engineering.

Accurate empirical rovibrational energies and transitions of H216O

“…Sets of rovibrational transitions, whether they are measured or computed, can be treated as building blocks of spectroscopic networks (SN, see Refs. [8][9][10][11][12][13], whereby (a) the vertices are the energy levels, (b) the edges correspond to the transitions, oriented from the lower energy level to the upper one (independently whether the transition was recorded in absorption, emission, or by means of an action spectroscopy), and (c) the (positive) edge weights are the wavenumbers of the transitions. Note that many other weighting schemes (e.g., weighting by line intensities) can be utilized in practical applications of SNs.…”

“…Previously, such experimental accuracy was reserved to pure rotational transitions measured in the microwave (MW) region of the electromagnetic spectrum but nowadays there is growing evidence that this accuracy can be extended all the way from the MW to the near infrared (NIR) region [3][4][5] and beyond. 6,7 A related relevant development in theoretical high-resolution molecular spectroscopy has been the introduction of spectroscopic networks, [8][9][10] and the Measured Active Rotational- 16,17,18). 33,34 Similarly, the most recent edition of the HITRAN database, HITRAN2016, 30 makes use of MARVEL energy levels for H 2 n O (n = 16, 17, 18), 35,36 as well as for the deuterated isotopologues.…”

“…As of today no ortho-para rovibrational transitions have been observed in water vapor. 66 This has the consequence that water spectra are related to two principal components 10 of the spectroscopic network of H 2 16 O, those of orthoand para-H 2 16 O. Note that the number q = v 3 +K a +K c is even for para and odd for ortho rovibrational states, where v 3 is the vibrational quantum number corresponding to the antisymmetric stretch motion, while K a and K c are the usual rigid-rotor quantum numbers of an asymmetrictop molecule.…”

Ab initio spectroscopic characterization of the radical CH3OCH2 at low temperatures

“…V ZPVE (θ, α) represents the zero point vibrational energy correction, which was determined at the MP2 level of theory within the harmonic approximation. Previous works show the relevance of this correction for obtaining reliable results [48]. The kinetic parameters, the pseudopotential and the vibrational correction of the potential energy surface are supplied as supplementary material (see Supplementary Material Document No.…”

Spectroscopic-network-assisted precision spectroscopy and its application to water

“…Building the list of target lines, forming accurate paths and cycles after the measurements, necessitates the use of elements of network theory 15 and the concept of spectroscopic networks 16,17 , the most general extension of the Ritz principle. In spectroscopic networks, energy levels are the vertices (nodes) and transitions are the edges (links).…”