Analysis of measured high-resolution doublet rovibronic spectra and related line lists of 12CH and 16OH

Detailed understanding of the energy-level structure of the quantum states as well as of the rovibronic spectra of the ethylidyne (CH) and the hydroxyl (OH) radicals is mandatory for a multitude of modelling efforts within multiple chemical, combustion, astrophysical, and atmospheric environments. Accurate empirical rovibronic energy levels, with associated uncertainties, are reported for the low-lying doublet electronic states of 12CH and 16OH, using the Measured Active Rotational-Vibrational Energy Levels (Marvel) algorithm. For 12CH, a total of 1521 empirical energy levels are determined in the primary spectroscopic network (SN) of the radical, corresponding to the following seven electronic states: X 2Π, A 2Δ, B 2Σ−, C2 Σ+, D 2Π, E 2Σ+, and F 2Σ+. The energy levels are derived from 6348 experimentally measured and validated transitions, collected from 29 sources. For 16OH, the lowest four doublet electronic states, X 2Π, A 2Σ+, B 2Σ+, and C 2Σ+, are considered, and a careful analysis and validation of 15 938 rovibronic transitions, collected from 45 sources, results in 1624 empirical rovibronic energy levels. The large set of spectroscopic data presented should facilitate the refinement of line lists for the 12CH and 16OH radicals. For both molecules hyperfine-resolved experimental transitions have also been considered, forming SNs independent from the primary SNs

An update to the MARVEL data set and ExoMol line list for ¹²C₂

The spectrum of dicarbon (C_{2}) is important in astrophysics and for spectroscopic studies of plasmas and flames. The C_{2} spectrum is characterized by many band systems with new ones still being actively identified; astronomical observations involve eight of these bands. Recently, Furtenbacher et al. presented a set of 5699 empirical energy levels for {12}^C_{2}, distributed among 11 electronic states and 98 vibronic bands, derived from 42 experimental studies and obtained using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. Here, we add data from 13 new sources and update data from 5 sources. Many of these data sources characterize high-lying electronic states, including the newly detected 3 {3}^Π_{g} state. Older studies have been included following improvements in the MARVEL procedure that allow their uncertainties to be estimated. These older works in particular determine levels in the C {1}^Π_{g} state, the upper state of the insufficiently characterized Deslandres–d’Azambuja (C {1}^Π_{g}–A {1}^Π_{u}) band. The new compilation considers a total of 31 323 transitions and derives 7047 empirical (MARVEL) energy levels spanning 20 electronic and 142 vibronic states. These new empirical energy levels are used here to update the 8states C_{2} ExoMol line list This updated line list is highly suitable for high-resolution cross-correlation studies in astronomical spectroscopy of, for example, exoplanets, as 99.4 per cent of the transitions with intensities over 10^{−18} cm molecule^{−1} at 1000 K have frequencies determined by empirical energy levels

MARVEL Analysis of the Measured High-resolution Rovibronic Spectra of 48 Ti 16 O

Accurate, experimental rovibronic energy levels, with associated labels and uncertainties, are reported for 11 low-lying electronic states of the diatomic ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ molecule, determined using the Marvel (Measured Active Rotational-Vibrational Energy Levels) algorithm. All levels are based on lines corresponding to critically reviewed and validated high-resolution experimental spectra taken from 24 literature sources. The transition data are in the 2–22,160 cm−1 region. Out of the 49,679 measured transitions, 43,885 are triplet–triplet, 5710 are singlet–singlet, and 84 are triplet–singlet transitions. A careful analysis of the resulting experimental spectroscopic network (SN) allows 48,590 transitions to be validated. The transitions determine 93 vibrational band origins of ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$, including 71 triplet and 22 singlet ones. There are 276 (73) triplet–triplet (singlet–singlet) band-heads derived from Marvel experimental energies, 123(38) of which have never been assigned in low- or high-resolution experiments. The highest J value, where J stands for the total angular momentum, for which an energy level is validated is 163. The number of experimentally derived triplet and singlet ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ rovibrational energy levels is 8682 and 1882, respectively. The lists of validated lines and levels for ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ are deposited in the supporting information to this paper

An improved rovibrational linelist of formaldehyde, H₂¹²C¹⁶O

Published high-resolution rotation-vibration transitions of H₂¹²C¹⁶O the principal isotopologue of methanal, are analyzed using the MARVEL (Measured Active Rotation-Vibration Energy Levels) procedure. The literature results are augmented by new, high-accuracy measurements of pure rotational transitions within the ground, ν_{3}, ν_{4}, and ν_{6} vibrational states. Of the 16 596 non-redundant transitions processed, which come from 43 sources including the present work, 16 403 could be validated, providing 5029 empirical energy levels of H₂¹²C¹⁶O with statistically well-defined uncertainties. All the empirical rotational-vibrational energy levels determined are used to improve the accuracy of ExoMol’s AYTY line list for hot formaldehyde. The complete list of collated experimental transitions, the empirical energy levels determined, as well as the extended and improved line list are provided as Supplementary Material

Definitive Ideal-Gas Thermochemical Functions of the H216O Molecule

A much improved temperature-dependent ideal-gas internal partition function, Qint(T), of the H216O molecule is reported for temperatures between 0 and 6000 K. Determination of Qint(T) is principally based on the direct summation technique involving all accurate experimental energy levels known for H216O (almost 20 000 rovibrational energies including an almost complete list up to a relative energy of 7500 cm−1), augmented with a less accurate but complete list of first-principles computed rovibrational energy levels up to the first dissociation limit, about 41 000 cm−1 (the latter list includes close to one million bound rovibrational energy levels up to J = 69, where J is the rotational quantum number). Partition functions are developed for ortho- and para-H216O as well as for their equilibrium mixture. Unbound rovibrational states of H216O above the first dissociation limit are considered using an approximate model treatment. The effect of the excited electronic states on the thermochemical functions is neglected, as their contribution to the thermochemical functions is negligible even at the highest temperatures considered. Based on the high-accuracy Qint(T) and its first two moments, definitive results, in 1 K increments, are obtained for the following thermochemical functions: Gibbs energy, enthalpy, entropy, and isobaric heat capacity. Reliable uncertainties (approximately two standard deviations) are estimated as a function of temperature for each quantity determined. These uncertainties emphasize that the present results are the most accurate ideal-gas thermochemical functions ever produced for H216O. It is recommended that the new value determined for the standard molar enthalpy increment at 298.15 K, 9.904 04 ± 0.000 01 kJ mol−1, should replace the old CODATA datum, 9.905 ± 0.005 kJ mol−1

Saddle point localization of molecular wavefunctions

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN???HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, l) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states

Marvel analysis of the measured high-resolution rovibrational spectra of H232S

44325 measured and assigned transitions of H232S, the parent isotopologue of the hydrogen sulfide molecule, are collated from 33 publications into a single database and reviewed critically. Based on this information, rotation-vibration energy levels are determined for the ground electronic state using the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The ortho and para principal components of the measured spectroscopic network of H232S are considered separately. The verified set of 25 293 ortho- and 18 778 para- H232S transitions determine 3969 ortho and 3467 para energy levels. The MARVEL results are compared with alternative data compilations, including a theoretical variational linelist

IUPAC critical evaluation of the rotational-vibrational spectra of water vapor, Part III: Energy levels and transition wavenumbers for H2 16O

This is the third of a series of articles reporting critically evaluated rotational–vibrational line positions, transition intensities, and energy levels, with associated critically reviewed labels and uncertainties, for all the main isotopologues of water. This paper presents experimental line positions, experimental-quality energy levels, and validated labels for rotational–vibrational transitions of the most abundant isotopologue of water, H216O. The latest version of the MARVEL (Measured Active Rotational–Vibrational Energy Levels) line-inversion procedure is used to determine the rovibrational energy levels of the electronic ground state of H216O from experimentally measured lines, together with their self-consistent uncertainties, for the spectral region up to the first dissociation limit. The spectroscopic network of H216O containstwo components, an ortho (o) and a para (p) one. For o-H216O and p-H216O, experimentally measured, assigned, and labeled transitions were analyzed from more than 100 sources. The measured lines come from one-photon spectra recorded at room temperature in absorption, from hot samples with temperatures up to 3000 K recorded in emission, and from multiresonance excitation spectra which sample levels up to dissociation. The total number of transitions considered is 184 667 of which 182 156 are validated: 68 027 between para states and 114 129 ortho ones. These transitions give rise to 18 486 validated energy levels, of which 10 446 and 8040 belong to o-H216O and p-H216O, respectively. The energy levels, including their labeling with approximate normal-mode and rigid-rotor quantum numbers, have been checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators as well as against previous compilations of energy levels. The extensive list of MARVEL lines and levels obtained are deposited in the supplementary data of this paper, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package