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Jonathan Tennyson - One of the best experts on this subject based on the ideXlab platform.
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hybrid variational perturbation method for calculating ro vibrational Energy Levels of polyatomic molecules
Molecular Physics, 2015Co-Authors: A I Pavlyuchko, Sergei N Yurchenko, Jonathan TennysonAbstract:A procedure for calculation of rotational–vibrational states of medium-sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalising a Hamiltonian matrix, which is partitioned into two sub-blocks. The first, smaller sub-block includes matrix elements with the largest contribution to the Energy Levels targeted in the calculations. The second, larger sub-block comprises those basis states which have little effect on these Energy Levels. Numerical perturbation theory, implemented as a Jacobi rotation, is used to compute the contributions from the matrix elements of the second sub-block. Only the first sub-block needs to be stored in memory and diagonalised. Calculations of the vibrational–rotational Energy Levels also employ a partitioning of the Hamiltonian matrix into sub-blocks, each of which corresponds either to a single vibrational state or a set of resonating vibrational states, with all associated rotat...
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iupac critical evaluation of the rotational vibrational spectra of water vapor part iii Energy Levels and transition wavenumbers for h216o
Journal of Quantitative Spectroscopy & Radiative Transfer, 2013Co-Authors: Jonathan Tennyson, Attila G Csaszar, P F Bernath, L R Brown, A Campargue, Ludovic Daumont, Robert R Gamache, Joseph T Hodges, O V Naumenko, Oleg L PolyanskyAbstract: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.
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marvel measured active rotational vibrational Energy Levels
Journal of Molecular Spectroscopy, 2007Co-Authors: Tibor Furtenbacher, Attila G Csaszar, Jonathan TennysonAbstract:An algorithm is proposed, based principally on an earlier proposition of Flaud and co-workers [Mol. Phys. 32 (1976) 499], that inverts the information contained in uniquely assigned experimental rotational–vibrational transitions in order to obtain measured active rotational–vibrational Energy Levels (MARVEL). The 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, with the help of a robust weighting 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. Local sensitivity coefficients could be computed for each Energy level. The resulting set of MARVEL Levels is called active as 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. MARVEL is tested on the example of the H2 17 O isotopologue of water and a list of 2736 depend
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experimental Energy Levels of the water molecule
Journal of Physical and Chemical Reference Data, 2001Co-Authors: Jonathan Tennyson, Nikolai F Zobov, Ross Williamson, Oleg L Polyansky, P F BernathAbstract:Experimentally derived Energy Levels are presented for 12 248 vibration–rotation states of the H2 16O isotopomer of water, more than doubling the number in previous, disparate, compilations. For each level an error and reference to source data is given. The Levels have been checked using Energy Levels derived from sophisticated variational calculations. These Levels span 107 vibrational states including members of all polyads up to and including 8v. Band origins, in some cases estimates, are presented for 101 vibrational modes.
Attila G Csaszar - One of the best experts on this subject based on the ideXlab platform.
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iupac critical evaluation of the rotational vibrational spectra of water vapor part iii Energy Levels and transition wavenumbers for h216o
Journal of Quantitative Spectroscopy & Radiative Transfer, 2013Co-Authors: Jonathan Tennyson, Attila G Csaszar, P F Bernath, L R Brown, A Campargue, Ludovic Daumont, Robert R Gamache, Joseph T Hodges, O V Naumenko, Oleg L PolyanskyAbstract: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.
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marvel measured active rotational vibrational Energy Levels ii algorithmic improvements
Journal of Quantitative Spectroscopy & Radiative Transfer, 2012Co-Authors: Tibor Furtenbacher, Attila G CsaszarAbstract:Abstract 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, rooted graphs, whereby the vertices are the Energy Levels, the edges are the transitions, and the weights are provided by transition intensities. 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 H2 16O molecule contains some 160,000 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 are needed when inverting the transition data. To achieve numerical effectiveness, we found the following efficient 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.
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marvel measured active rotational vibrational Energy Levels
Journal of Molecular Spectroscopy, 2007Co-Authors: Tibor Furtenbacher, Attila G Csaszar, Jonathan TennysonAbstract:An algorithm is proposed, based principally on an earlier proposition of Flaud and co-workers [Mol. Phys. 32 (1976) 499], that inverts the information contained in uniquely assigned experimental rotational–vibrational transitions in order to obtain measured active rotational–vibrational Energy Levels (MARVEL). The 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, with the help of a robust weighting 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. Local sensitivity coefficients could be computed for each Energy level. The resulting set of MARVEL Levels is called active as 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. MARVEL is tested on the example of the H2 17 O isotopologue of water and a list of 2736 depend
Tucker Carrington - One of the best experts on this subject based on the ideXlab platform.
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vibrational Energy Levels of ch5
Journal of Chemical Physics, 2008Co-Authors: Xiaogang Wang, Tucker CarringtonAbstract:We present a parallelized contracted basis-iterative method for calculating numerically exact vibrational Energy Levels of CH(5)(+) (a 12-dimensional calculation). We use Radau polyspherical coordinates and basis functions that are products of eigenfunctions of bend and stretch Hamiltonians. The bend eigenfunctions are computed in a nondirect product basis with more than 200x10(6) functions and the stretch functions are computed in a product potential optimized discrete variable basis. The basis functions have amplitude in all of the 120 equivalent minima. Many low-lying Levels are well converged. We find that the Energy level pattern is determined in part by the curvature and width of the valley connecting the minima and in part by the slope of the walls of this valley but does not depend on the height or shape of the barriers separating the minima.
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a comparison of filter diagonalisation methods with the lanczos method for calculating vibrational Energy Levels
Chemical Physics Letters, 1999Co-Authors: Shiwei Huang, Tucker CarringtonAbstract:Abstract In this Letter we compare two low-storage filter diagonalisation methods for calculating Energy Levels and compare both to the Lanczos algorithm. We are able to calculate Energy Levels in a high-lying window in the vibrational spectrum of H 2 O with fewer matrix–vector products using the Lanczos algorithm than using the filter diagonalisation methods. We find that the Lanczos calculation is less costly and that the cost of building the Hamiltonian and overlap matrices in the filtered basis is excessive if one uses a non-Chebyshev discrete variable representation filter.
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calculating rovibrational Energy Levels of a triatomic molecule with a simple lanczos method
Journal of Chemical Physics, 1999Co-Authors: Pranab Sarkar, Nicolas Poulin, Tucker CarringtonAbstract:We present a simple Lanczos method for calculating rovibrational Energy Levels of a triatomic molecule from a kinetic Energy operator (KEO) with the z axis perpendicular to the molecular plane. We use rotational basis functions which are linear combinations of symmetric top functions so that all matrix elements are real. For some molecules, coupling between rotation and vibration is less important if the z axis is chosen perpendicular to the molecular plane, but the singularities of the z-axis operator are more difficult to deal with than those of the commonly used y-axis operator. The KEO with z axis perpendicular to the plane also reduces the number of sums over vibrational indices required to evaluate Hamiltonian matrix-vector products. Using a new symmetry-adapted basis and the z-axis KEO we calculate rovibrational Energy Levels of H2O for high J values. Even at J=40 we do not observe the formation of fourfold clusters.
Wei Cheng - One of the best experts on this subject based on the ideXlab platform.
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frontier electronic Energy Levels of tetrahedral td fullerenes
Journal of Electron Spectroscopy and Related Phenomena, 2000Co-Authors: Wei Cheng, Au Chin TangAbstract:Abstract The electronic structure of the tetrahedral (T d ) fullerenes C n with n ≤3600 have been calculated in the Huckel approximation by means of group theoretical method, and the frontier electronic Energy Levels have been reported. Therefore their electronic spectra have been discussed by use of the value of frontier Energy Levels.
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FRONTIER ELECTRONIC Energy Levels OF ICOSAHEDRAL FULLERENES
Chemical Physics Letters, 1997Co-Authors: Au Chin Tang, Wei ChengAbstract:Abstract In this Letter, we have calculated the electronic structures of 161 icosahedral fullerenes of which the frontier electronic Energy Levels have been examined in detail. On the analysis of the electronic Energy Levels, their corelation rules have been obtained. By use of the corelation rules, we can predict the frontier electronic Energy Levels of all the icosahedral fullerenes and discuss their electronic spectra in a more convenient way.
P F Bernath - One of the best experts on this subject based on the ideXlab platform.
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Experimental Energy Levels and partition function of the 12C2 molecule
2016Co-Authors: Furtenbacher T, P F Bernath, Ag Csaszar, Sn Yurchenko, Tennyson JAbstract:The carbon dimer, the 12C2 molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic Energy Levels are reported for 12C2, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic Energy Levels, 1,325, 4,309, and 65 Levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable Energy level of the a 3Πu state, corresponding to the J = 2 total angular momentum quantum number and the F1 spin-multiplet component, is 603.817(5) cm−1. This well-determined Energy difference should facilitate observations of singlet–triplet intercombination lines which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL Energy Levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic Energy Levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin-orbit coupled potential Energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for 12C2 up to 4,000 K
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iupac critical evaluation of the rotational vibrational spectra of water vapor part iii Energy Levels and transition wavenumbers for h216o
Journal of Quantitative Spectroscopy & Radiative Transfer, 2013Co-Authors: Jonathan Tennyson, Attila G Csaszar, P F Bernath, L R Brown, A Campargue, Ludovic Daumont, Robert R Gamache, Joseph T Hodges, O V Naumenko, Oleg L PolyanskyAbstract: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.
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experimental Energy Levels of the water molecule
Journal of Physical and Chemical Reference Data, 2001Co-Authors: Jonathan Tennyson, Nikolai F Zobov, Ross Williamson, Oleg L Polyansky, P F BernathAbstract:Experimentally derived Energy Levels are presented for 12 248 vibration–rotation states of the H2 16O isotopomer of water, more than doubling the number in previous, disparate, compilations. For each level an error and reference to source data is given. The Levels have been checked using Energy Levels derived from sophisticated variational calculations. These Levels span 107 vibrational states including members of all polyads up to and including 8v. Band origins, in some cases estimates, are presented for 101 vibrational modes.
