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Wodraszka R, Carrington T. Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate MCTDH calculations with general potential energy surfaces. J Chem Phys 2024; 160:214121. [PMID: 38836450 DOI: 10.1063/5.0214557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2024] [Accepted: 05/14/2024] [Indexed: 06/06/2024] Open
Abstract
We propose a new collocation multi-configuration time-dependent Hartree (MCTDH) method. It reduces point-set error by using more points than basis functions. Collocation makes it possible to use MCTDH with a general potential energy surface without computing any integrals. The collocation points are associated with a basis larger than the basis used to represent wavefunctions. Both bases are obtained from a direct product basis built from single-particle functions by imposing a pruning condition. The collocation points are those on a sparse grid. Heretofore, collocation MCTDH calculations with more points than basis functions have only been possible if both the collocation grid and the basis set are direct products. In this paper, we exploit a new pseudo-inverse to use both more points than basis functions and a pruned basis and grid. We demonstrate that, for a calculation of the lowest 50 vibrational states (energy levels and wavefunctions) of CH2NH, errors can be reduced by two orders of magnitude by increasing the number of points, without increasing the basis size. This is true also when unrefined time-independent points are used.
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Affiliation(s)
- Robert Wodraszka
- Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada
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Xie C, Guan Y, Yarkony DR, Guo H. Vibrational energy levels of the S0 and S1 states of formaldehyde using an accurate ab initio based global diabatic potential energy matrix. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1918775] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Changjian Xie
- Institute of Modern Physics, Northwest University, Xi’an, Shaanxi, People’s Republic of China
| | - Yafu Guan
- Department of Chemistry, Johns Hopkins University, Baltimore, MD, USA
| | - David R. Yarkony
- Department of Chemistry, Johns Hopkins University, Baltimore, MD, USA
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM, USA
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Yurchenko SN, Mellor TM. Treating linear molecules in calculations of rotation-vibration spectra. J Chem Phys 2020; 153:154106. [PMID: 33092364 DOI: 10.1063/5.0019546] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, a numerical implementation of the exact kinetic energy operator (KEO) for triatomic molecules (symmetric of XY2-type and asymmetric of YXZ-type) is presented. The implementation is based on the valence coordinates with the bisecting (XY2-type molecules) and bond-vector (YXZ) embeddings and includes the treatment of the singularity at linear geometry. The KEO is represented in a sum-of-product form. The singularity caused by the undetermined angle at the linear configuration is resolved with the help of the associated Legendre and Laguerre polynomials used as parameterized bending basis functions in the finite basis set representation. The exact KEO implementation is combined with the variational solver theoretical rovibrational energies, equipped with a general automatic symmetry-adaptation procedure and efficient basis step contraction schemes, providing a powerful computational solver of triatomic molecules for accurate computations of highly excited ro-vibrational spectra. The advantages of different basis set choices are discussed. Examples of specific applications for computing hot spectra of linear molecules are given.
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Affiliation(s)
- Sergei N Yurchenko
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Thomas M Mellor
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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Avila G, Mátyus E. Toward breaking the curse of dimensionality in (ro)vibrational computations of molecular systems with multiple large-amplitude motions. J Chem Phys 2019; 150:174107. [PMID: 31067897 DOI: 10.1063/1.5090846] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schrödinger equation applicable to floppy, polyatomic systems with multiple large-amplitude motions. This progress is achieved through the combination of (i) the numerical kinetic-energy operator (KEO) approach of Mátyus et al. [J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak nonproduct grid method of Avila and Carrington, Jr. [J. Chem. Phys. 131, 174103 (2009)]. The numerical representation of the KEO makes it possible to choose internal coordinates and a body-fixed frame best suited for the molecular system. The Smolyak scheme reduces the size of the direct-product grid representation by orders of magnitude, while retaining some of the useful features of it. As a result, multidimensional (ro)vibrational states are computed with system-adapted coordinates, a compact basis- and grid-representation, and an iterative eigensolver. Details of the methodological developments and the first numerical applications are presented for the CH4·Ar complex treated in full (12D) vibrational dimensionality.
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Affiliation(s)
- Gustavo Avila
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest 1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest 1117, Hungary
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Šmydke J, Császár AG. On the use of reduced-density matrices for the semi-automatic assignment of vibrational states. Mol Phys 2019. [DOI: 10.1080/00268976.2018.1562124] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Jan Šmydke
- MTA-ELTE Complex Chemical Systems Research Group and Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Attila G. Császár
- MTA-ELTE Complex Chemical Systems Research Group and Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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Nauts A, Lauvergnat D. Numerical on-the-fly implementation of the action of the kinetic energy operator on a vibrational wave function: application to methanol. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1473652] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- André Nauts
- Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, Louvain-la-Neuve, Belgium
- Laboratoire de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay, France
| | - David Lauvergnat
- Laboratoire de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay, France
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Wodraszka R, Carrington T. A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2018; 148:044115. [DOI: 10.1063/1.5018793] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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Fábri C, Quack M, Császár AG. On the use of nonrigid-molecular symmetry in nuclear motion computations employing a discrete variable representation: A case study of the bending energy levels of C H 5 +. J Chem Phys 2017; 147:134101. [DOI: 10.1063/1.4990297] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Csaba Fábri
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Martin Quack
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Attila G. Császár
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
- MTA-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
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Wang XG, Carrington T. Using monomer vibrational wavefunctions as contracted basis functions to compute rovibrational levels of an H2O-atom complex in full dimensionality. J Chem Phys 2017; 146:104105. [DOI: 10.1063/1.4977179] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Xiao-Gang Wang
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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Yu DQ, Huang H, Nyman G, Sun ZG. Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates. CHINESE J CHEM PHYS 2016. [DOI: 10.1063/1674-0068/29/cjcp1507141] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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Avila G, Carrington T. A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra. J Chem Phys 2015; 143:214108. [DOI: 10.1063/1.4936294] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gustavo Avila
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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Brown J, Carrington T. Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions. J Chem Phys 2015; 143:044104. [DOI: 10.1063/1.4926805] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James Brown
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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Piserchia A, Barone V. Discrete variable representation of the Smoluchowski equation using a sinc basis set. Phys Chem Chem Phys 2015; 17:17362-74. [PMID: 26078048 DOI: 10.1039/c5cp02060c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a new general framework for solving the monodimensional Smoluchowski equation using a discrete variable representation (DVR) based on the so called sinc basis set. The reliability of our implementation is assessed by comparing the convergence of diffusive operator eigenvalues calculated using our method and using a simple finite difference scheme for some model diffusive problems. The results here presented open encouraging possibilities for dealing with more complicated systems, where additional coordinate dependent terms in the equation or multidimensional treatments are needed and traditional methods often become unfeasible.
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Affiliation(s)
- Andrea Piserchia
- Scuola Normale Superiore, piazza dei Cavalieri 7, I-56126 Pisa, Italy.
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Partanen L, Pesonen J, Sjöholm E, Halonen L. A rotamer energy level study of sulfuric acid. J Chem Phys 2013; 139:144311. [DOI: 10.1063/1.4823836] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
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Baraban JH, Beck AR, Steeves AH, Stanton JF, Field RW. Reduced dimension discrete variable representation study of cis–trans isomerization in the S1 state of C2H2. J Chem Phys 2011; 134:244311. [DOI: 10.1063/1.3570823] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Toffoli D, Sparta M, Christiansen O. Accurate multimode vibrational calculations using a B-spline basis: theory, tests and application to dioxirane and diazirinone. Mol Phys 2011. [DOI: 10.1080/00268976.2010.547522] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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19
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Avila G, Carrington T. Nonproduct quadrature grids for solving the vibrational Schrödinger equation. J Chem Phys 2009; 131:174103. [DOI: 10.1063/1.3246593] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cooper J, Carrington T. Computing vibrational energy levels by using mappings to fully exploit the structure of a pruned product basis. J Chem Phys 2009; 130:214110. [DOI: 10.1063/1.3140272] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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Salmi T, Hänninen V, Garden AL, Kjaergaard HG, Tennyson J, Halonen L. Calculation of the O−H Stretching Vibrational Overtone Spectrum of the Water Dimer. J Phys Chem A 2008; 112:6305-12. [DOI: 10.1021/jp800754y] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Teemu Salmi
- Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland, Department of Chemistry, University of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Vesa Hänninen
- Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland, Department of Chemistry, University of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Anna L. Garden
- Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland, Department of Chemistry, University of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Henrik G. Kjaergaard
- Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland, Department of Chemistry, University of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Jonathan Tennyson
- Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland, Department of Chemistry, University of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Lauri Halonen
- Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland, Department of Chemistry, University of Otago, P.O. Box 56, 9054 Dunedin, New Zealand, and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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Domcke W, Stock G. Theory of Ultrafast Nonadiabatic Excited-State Processes and their Spectroscopic Detection in Real Time. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141595.ch1] [Citation(s) in RCA: 250] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Light JC, Carrington T. Discrete-Variable Representations and their Utilization. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141731.ch4] [Citation(s) in RCA: 419] [Impact Index Per Article: 24.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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Lo J, Shizgal BD. Spectral convergence of the quadrature discretization method in the solution of the Schrödinger and Fokker-Planck equations: Comparison with sinc methods. J Chem Phys 2006; 125:194108. [PMID: 17129090 DOI: 10.1063/1.2378622] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I2 with a Morse potential is also considered.
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Affiliation(s)
- Joseph Lo
- Institute of Applied Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada.
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Nightingale MP, Roy PN. Excited States of Weakly Bound Bosonic Clusters: Discrete Variable Representation and Quantum Monte Carlo. J Phys Chem A 2006; 110:5391-4. [PMID: 16623467 DOI: 10.1021/jp056577q] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
We compare two approaches for the accurate calculation of the energy levels of weakly bound boson trimers. The first approach is based on correlation function Monte Carlo employing optimized trial functions, while the second approach is based on the discrete variable representation. A trimer with atoms of half the mass of neon is used as a test problem for benchmark calculations. The two approaches yield identical results, within error bars, for all the J = 0 energy levels below the dissociation threshold. The relative merits of the two techniques are discussed, and a perspective is given for extension to larger clusters.
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Affiliation(s)
- M P Nightingale
- Department of Physics, East Hall, University of Rhode Island, Kingston, Rhode Island 02881, USA.
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Yuan KJ, Sun Z, Wang SM, Cong SL. On using Fourier series and Legendre polynomials as angular basis sets for nonrotating triatomic molecules. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.08.066] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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28
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Czakó G, Szalay V, Császár AG, Furtenbacher T. Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates. J Chem Phys 2005; 122:024101. [PMID: 15638566 DOI: 10.1063/1.1827594] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Two methods are developed, when solving the related time-independent Schrodinger equation (TISE), to cope with the singular terms of the vibrational kinetic energy operator of a triatomic molecule given in orthogonal internal coordinates. The first method provides a mathematically correct treatment of all singular terms. The vibrational eigenfunctions are approximated by linear combinations of functions of a three-dimensional nondirect-product basis, where basis functions are formed by coupling Bessel-DVR functions, where DVR stands for discrete variable representation, depending on distance-type coordinates and Legendre polynomials depending on angle bending. In the second method one of the singular terms related to a distance-type coordinate, deemed to be unimportant for spectroscopic applications, is given no special treatment. Here the basis set is obtained by taking the direct product of a one-dimensional DVR basis with a two-dimensional nondirect-product basis, the latter formed by coupling Bessel-DVR functions and Legendre polynomials. With the basis functions defined, matrix representations of the TISE are set up and solved numerically to obtain the vibrational energy levels of H3+. The numerical calculations show that the first method treating all singularities is computationally inefficient, while the second method treating properly only the singularities having physical importance is quite efficient.
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Affiliation(s)
- Gábor Czakó
- Department of Theoretical Chemistry, Eötvös University, H-1518 Budapest 112, PO Box 32, Hungary
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Liu YD, Roy PN. Energy levels and wave functions of weakly-bound 4Hex 20NeyH (x+y=2) systems using Pekeris coordinates and a symmetry-adapted Lanczos approach. J Chem Phys 2004; 121:6282-9. [PMID: 15446922 DOI: 10.1063/1.1787488] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
Energy levels and wave functions of floppy triatomic rare gas hydrides are calculated using a Pekeris coordinate system and the importance of various triangular configurations is assessed through the calculation of reduced distribution functions and relative weights. The calculations are performed using a symmetry-adapted Lanczos recursion within the discrete variable representation. For the 4He2H- anion, the present results are compared with those obtained from calculations based on other methods, and the accuracy of the present method is discussed. Calculations are also performed for the case of 4He2H and 20Ne2H, as well as for the mixed 4He 20NeH neutrals. Our results show that no bound states are found for 4He2H while only one bound state is found for both the 20Ne2H and 4He 20NeH complexes. Interestingly, a very important and common property of these systems is that there is a significant contribution from linear configurations to their bound states.
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Affiliation(s)
- Yong Dong Liu
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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Hazra A, Chang HH, Nooijen M. First principles simulation of the UV absorption spectrum of ethylene using the vertical Franck-Condon approach. J Chem Phys 2004; 121:2125-36. [PMID: 15260766 DOI: 10.1063/1.1768173] [Citation(s) in RCA: 85] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.
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Affiliation(s)
- Anirban Hazra
- Department of Chemistry, Princeton University, New Jersey 08544, USA
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Roy PN. Energy levels and wave functions of weakly bound bosonic trimers using Pekeris coordinates and a symmetry-adapted Lanczos approach. J Chem Phys 2003. [DOI: 10.1063/1.1599348] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
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Schwenke DW. New rovibrational kinetic energy operators using polyspherical coordinates for polyatomic molecules. J Chem Phys 2003. [DOI: 10.1063/1.1574013] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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Harland BB, Roy PN. An initial value representation semiclassical approach for the study of molecular systems with geometric constraints. J Chem Phys 2003. [DOI: 10.1063/1.1545772] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Wei H. An Eckart-frame kinetic energy operator for tetra-atomic planar molecules. J Chem Phys 2003. [DOI: 10.1063/1.1562625] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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Yu HG. An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach. J Chem Phys 2002. [DOI: 10.1063/1.1488575] [Citation(s) in RCA: 69] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kostin MA, Polyansky OL, Tennyson J. Calculations of rotation–vibration states with thezaxis perpendicular to the plane: High accuracy results for H3+. J Chem Phys 2002. [DOI: 10.1063/1.1464540] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
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Katz G, Yamashita K, Zeiri Y, Kosloff R. The Fourier method for tri-atomic systems in the search for the optimal coordinate system. J Chem Phys 2002. [DOI: 10.1063/1.1448285] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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Leforestier C, Viel A, Gatti F, Muñoz C, Iung C. The Jacobi–Wilson method: A new approach to the description of polyatomic molecules. J Chem Phys 2001. [DOI: 10.1063/1.1337048] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wormer PE, van Der Avoird A. Intermolecular potentials, internal motions, and spectra of van der waals and hydrogen-bonded complexes. Chem Rev 2000; 100:4109-44. [PMID: 11749342 DOI: 10.1021/cr990046e] [Citation(s) in RCA: 117] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- P E Wormer
- Institute of Theoretical Chemistry, NSR Center, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
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Nela M, Permogorov D, Miani A, Halonen L. Vibration–rotation fluorescence spectra of water in the ground electronic state. J Chem Phys 2000. [DOI: 10.1063/1.481983] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Luckhaus D. 6D vibrational quantum dynamics: Generalized coordinate discrete variable representation and (a)diabatic contraction. J Chem Phys 2000. [DOI: 10.1063/1.481924] [Citation(s) in RCA: 181] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Carrington T. The advantage of writing kinetic energy operators in polyspherical curvilinear coordinates in terms of zi=cos φi. J Chem Phys 2000. [DOI: 10.1063/1.480987] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yu HG, Nyman G. Quantum dynamics of the O(3P)+CH4→OH+CH3 reaction: An application of the rotating bond umbrella model and spectral transform subspace iteration. J Chem Phys 2000. [DOI: 10.1063/1.480576] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zúñiga J, Alacid M, Bastida A, Carvajal FJ, Requena A. Determination of highly excited rovibrational states for N2O using generalized internal coordinates. J Chem Phys 1999. [DOI: 10.1063/1.478538] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wei H, Carrington Jr. T. An exact Eckart-embedded kinetic energy operator in Radau coordinates for triatomic molecules. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)00186-9] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Wei H. Ghost levels and near-variational forms of the discrete variable representation: Application to H2O. J Chem Phys 1997. [DOI: 10.1063/1.473714] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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Nakajima T, Kato S. An ab initio study of the internal conversion rate from the first singlet excited state to the ground state in formaldehyde. J Chem Phys 1996. [DOI: 10.1063/1.472433] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wei H, Carrington T. A time‐dependent calculation of the alignment and orientation of the CN fragment of the photodissociation of ICN. J Chem Phys 1996. [DOI: 10.1063/1.471860] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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A time-dependent approach to the nonradiative decay of polyatomic molecule: S1 to S0 transition of H2CO. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(96)00034-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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