Over the past years there have been a rapid improvement in nuclear motion approaches to solving spectroscopic problems, which has been described as the fourth age of quantum chemistry.A. G. Császár, C. Fabri, T. Szidarovszky, E. Mátyus, T. Furtenbacher, and G. Czakó, Phys. Chem. Chem. Phys. 14, 1085 (2012).he methodology which is commonly attributed to the spectroscopy from first principles is in fact a combination of high level ab initio (electronic structure) calculations, high level nuclear motion (variational) calculations and empirical refinement to the highly accurate experimental data (e.g. line positions).J. Tennyson and S.N. Yurchenko , Int. J. Quant. Chem. 117, 92, (2017).n this talk, I will discuss the current state-of-the-art of the theoretical molecular spectroscopy, which shows that this methodology is increasingly competitive with experiment and allows in many cases a more reliable determination of various molecular data.J. Tennyson, J. Chem. Phys. 145, 120901 (2016).ur variational program TROVES.N. Yurchenko, W. Thiel, P. Jensen, J. Mol. Spectrosc. 245, 126–140 (2007).s one of the modern computational tools successfully used to generate huge lists of transitions which provide the input for models of atmospheric absorption. I will review the methodology used by TROVE and other variational programs for accurate solution of the nuclear motion Schrödinger equation for general medium size polyatomic molecules, show examples of successful applications and discuss cases, which are still challenging for the modern ab initio methods.

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A. G. Császár, C. Fabri, T. Szidarovszky, E. Mátyus, T. Furtenbacher, and G. Czakó, Phys. Chem. Chem. Phys. 14, 1085 (2012).T J. Tennyson and S.N. Yurchenko , Int. J. Quant. Chem. 117, 92, (2017).I J. Tennyson, J. Chem. Phys. 145, 120901 (2016).O S.N. Yurchenko, W. Thiel, P. Jensen, J. Mol. Spectrosc. 245, 126–140 (2007).i

Infrared absorption spectra of hot methane up to 1000 K were recorded with a high-resolution Fourier transform spectrometer in the 5200-9300 cm⁻¹ spectral region. The experimental observations were compared to the predictions of variational calculations. Preliminary quantum number assignments were made for the observed features. Generally good agreement was found between observations and calculations particularly in the Tetradecad region, from 2.1 to 1.6 μm. Spectra in the Icosad (1.6-1.3 μm) and Triacontad (1.25-1.1 μm) regions suffered from some interference from a hot water impurity.

Many methods have been proposed for fitting potential energy surfaces. Unfortunately, there are few comparative studies. In this paper, we compare neural networks (NN) with Gaussian process (GP) regression. We re-fit an accurate PES of formaldehyde and compare PES errors on the entire point set used to solve the vibrational Schrödinger equation, i.e. the only error that matters in quantum dynamics calculations. We also compare the vibrational spectra computed on the underlying reference PES and the NN and GP potential surfaces. The NN and GP surfaces are constructed with exactly the same points and the corresponding spectra are computed with the same points and the same basis. The GP fitting error is lower and the GP spectrum is more accurate. The best NN fits to 625/1250/2500 symmetry unique potential energy points have global PES root mean square errors (RMSE) of 6.53/2.54/0.86 cm-1, whereas the best GP surfaces have RMSE values of 3.87/1.13/0.62 cm-1, respectively. When fitting 625 symmetry unique points, the error the first 100 vibrational levels is only 0.06 cm-1 with the best GP fit, whereas the spectrum on the best NN PES has an error of 0.22 cm-1, with respect to the spectrum computed on the reference PES. This error is reduced to about 0.01 cm-1 when fitting 2,500 points with either NN or GP. We also find that the GP surface produces a relatively accurate spectrum when obtained based on as few as 313 points.

One has to calculate thousands or millions of ab initio points for potential energy surfaces even for molecules with only a few atoms. For diatomics, the MLR (Morse/long-range)Dattani N. S., Le Roy R. J., Ross A., Linton C. (2008) Proceedings of the 63rd Annual International Symposium on Molecular Spectroscopy. p301Le Roy R. J., Dattani N. S., Coxon J. A., Ross A. J., Crozet P., Linton C. (2009) J. Chem Phys. 131, 204309 model has been very successful, making it possible to represent the entire curve accurately with just a few ab initio points, or a few spectral lines. With the MLR model it is also possible to extrapolate and interpolate in a way that allows successful predictions of energy level locations several thousand cm⁻¹ away from the data regionDattani N. S., Le Roy R. J. (2011) J. Mol. Spec.. 268, 199-210.; Semczuk M., et al. (2013) Phys. Rev. A 87, 052505 However no analogous model has existed yet for the intramolecular potentials of polyatomic molecules. A simple model is presented which accurately describes some small molecules with far fewer parameters than previous models, and can be extended to larger molecules too. The benefit of having a good model function is orders of magnitude greater for polyatomics than for diatomics since the amount of data needed for an accurate potential is reduced in each dimension. For example if the calculation of 100 ab initio points is reduced to 10 in a diatomic molecule, we may estimate that this factor of 10 reduction in cost becomes at least 10¹⁰ for a molecule whose potential depends on 10 radial coordinates. As an example, an analytic potential for CO₂ is built, which requires fewer parameters than the previous state-of-the-art analytic potential, and obeys the theoretical long-range behavior more closely than all previous potentials, including inclusion of the Axelrod-Teller three-body interaction. The model is based on accurate diatomic potentials representing all atom-atom pairwise interactions, and for CO₂, a three-body correction representing the rest of the energy. This emphasizes the value of accurate molecular spectroscopy for simple diatomics, which is sometimes considered to be less interesting than research involving large molecules. Diatomic potentials are valuable as building blocks for large-molecule potentials. An open-source computer program for building PolyMLR potentials for polyatomic molecules is introduced.

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Dattani N. S., Le Roy R. J., Ross A., Linton C. (2008) Proceedings of the 63rd Annual International Symposium on Molecular Spectroscopy. p301

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Dattani N. S., Le Roy R. J. (2011) J. Mol. Spec.. 268, 199-210.; Semczuk M., et al. (2013) Phys. Rev. A 87, 052505.

The Virtual Multifrequency Spectrometer (VMS) is a tool that aims at integrating a wide range of computational and experimental spectroscopic techniques with the final goal of disclosing the static and dynamic physical-chemical properties "hidden" in molecular spectra. VMS is composed of two parts, namely, VMS-Comp, which provides access to the latest developments in the field of computational spectroscopy, and VMS-Draw, which provides a powerful graphical user interface (GUI) for an intuitive interpretation of theoretical outcomes and a direct comparison to experiment. In the present work, we introduce VMS-ROT, a new module of VMS that has been specifically designed to deal with rotational spectroscopy. This module offers an integrated environment for the analysis of rotational spectra: from the assignment of spectral transitions to the refinement of spectroscopic parameters and the simulation of the spectrum. While bridging theoretical and experimental rotational spectroscopy, VMS-ROT is strongly integrated with quantum-chemical calculations, and it is composed of four independent, yet interacting units: (1) the computational engine for the calculation of the spectroscopic parameters that are employed as a starting point for guiding experiments and for the spectral interpretation, (2) the fitting-prediction engine for the refinement of the molecular parameters on the basis of the assigned transitions and the prediction of the rotational spectrum of the target molecule, (3) the GUI module that offers a powerful set of tools for a vis-a-vis comparison between experimental and simulated spectra, and (4) the new assignment tool for the assignment of experimental transitions in terms of quantum numbers upon comparison with the simulated ones. The implementation and the main features of VMS-ROT are presented, and the software is validated by means of selected test cases ranging from isolated molecules of different sizes to molecular complexes. VMS-ROT offers an integrated environment for the analysis of the rotational spectra, with the innovative perspective of an intimate connection to quantum-chemical calculations that can be exploited at different levels of refinement, as an invaluable support and complement for experimental studies.

The methylene cation is spectroscopically poorly characterized as it is difficult to produce in large amounts. It is subject to the Renner-Teller effect giving rise to ground X̃^+ 2A₁ and excited Ã^+ 2B₁ electronic states. Photoelectron spectroscopy of the methylene radical allows us to gain information about both and its cation. The former is also theoretically challenging as it is a very non-rigid species characterized by a barrier to linearity of less than 2000 cm⁻¹ in its ground X̃ ³B₁ electronic state. The first photoelectron spectra of were investigated using pulsed-field-ionization zero-kinetic-energy spectroscopy.Willitsch et al., J. Chem. Phys. 117 (2002) 1939; and Willitsch & Merkt, ibid. 118 (2003) 2235 rotationally resolved spectrum containing X̃^+ 2A₁ ←X̃ ³B₁ transitions was recorded from 83600 to 84070 cm⁻¹ and analyzed in terms of rotational constants. The threshold photoelectron spectrum of has been recorded from 9.8 to 12 eV (79040 to 96800 cm⁻¹) using a recently developed flow tube reactorGarcia et al., J. Chem. Phys. 142 (2015) 164201nd VUV synchrotron radiation. This new spectrum spans a larger energy range than the previous ones, but with less resolution. It displays narrow and broad features due respectively to the X̃^+ 2A₁ ← X̃ ³B₁ and Ã^+ 2B₁ ← X̃ ³B₁ ionizing transitions. Using new ab initio potential energy surfaces and available ones,Jensen & Bunker, J. Chem. Phys.  89 (1988) 1327; and Jensen, Brumm, Kraemer & Bunker, J.\ Molec. Spectrsoc. 172 (1995) 194he photoelectron spectrum is currently being computed using two models. The first one accounts for the large amplitude bending mode and the rotation only; the second one, also accounts for the stretching modes. The experimental and theoretical spectra will be discussed in the paper.

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Willitsch et al., J. Chem. Phys. 117 (2002) 1939; and Willitsch & Merkt, ibid. 118 (2003) 2235A Garcia et al., J. Chem. Phys. 142 (2015) 164201a Jensen & Bunker, J. Chem. Phys.  89 (1988) 1327; and Jensen, Brumm, Kraemer & Bunker, J.\ Molec. Spectrsoc. 172 (1995) 194t

The energy at the empirical bond length of Li₂(1³Σ_u⁺) of 4.1700Å Dattani N. S., Le Roy R. J. (2011) J. Mol. Spec.. 268, 199-210.; Semczuk M., et al. (2013) Phys. Rev. A 87, 052505as obtained at all-electron FCI level with an aug-cc-pCV5Z-NR basis set, all-electron CCSDT(Q) with aug-cc-pCV7Z-NR, and all-electron CCSD(T) with aug-cc-pCV8Z-NR; along with corrections due to special relativity converged with respect to electron correlation and basis set size using the spin-free Dirac-Coulomb Hamiltonian, and further such corrections at the Hartree-Fock level using the Breit and Gaunt Hamiltonians. Corrections to the point-size nucleus approximation were calculated but found to be negligible. The result was compared to the lowest energy of the best empirical potentials^b with the empirical Born-Oppenheimer breakdown corrections removed, making it essentially an infinite-mass to infinite-mass comparison. The discrepancy between the energy obtained from laboratory spectroscopy and the energy obtained completely by the computer was only 0.06 cm⁻¹, which is of the same order of magnitude as the uncertainty on the empirical value, which is ±0.007 cm⁻¹ before including the added uncertainty coming from the Born-Oppenheimer breakdown parameter u₀ which itself has an uncertainty of 0.01 cm⁻¹. It is discussed what is necessary for the computer spectrometer to outperform the laboratory spectrometer. The ionization energy of the carbon atom was calculated at all-electron FCI level with aug-cc-pCV8Z-NR and aug-cc-pCV7Z-NR basis sets (the latter only for basis set extrapolation); along with corrections due to special relativity converged with respect to electron correlation and basis set size using the 1e⁻ X2C Hamiltonian, further corrections using state-averaged Dirac-Fock for the contribution from the Breit Hamiltonian and some QED contributions; along with DBOC corrections to the clamped nucleus approximation converged with respect to electron correlation and basis set size. Again, corrections to the point-size nucleus approximation were calcualted but found to be negligible. The final energy was compared to the very recent experimental value published by NISTHaris K., Krimada A. E., (2017) arXiv:1704.07474.ith the experimental spin-orbit lowering of 12.672508 cm⁻¹ removed. The discrepancy was 0.994 cm⁻¹ compared to the ±0.009 cm⁻¹ uncertainty in the laboratory value.

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Dattani N. S., Le Roy R. J. (2011) J. Mol. Spec.. 268, 199-210.; Semczuk M., et al. (2013) Phys. Rev. A 87, 052505w Haris K., Krimada A. E., (2017) arXiv:1704.07474.w