메뉴 건너뛰기




Volumn 180, Issue 11, 2009, Pages 2025-2033

A method for solving the molecular Schrödinger equation in Cartesian coordinates via angular momentum projection operators

Author keywords

Finite difference methods; Grid computing; Molecular dynamics; Projection operators; Schr dinger equation

Indexed keywords

ANGULAR MOMENTUM; DEGREES OF FREEDOM (MECHANICS); FINITE DIFFERENCE METHOD; HAMILTONIANS; KINETIC ENERGY; KINETICS; MATHEMATICAL OPERATORS; MOLECULAR DYNAMICS; MOLECULES; PROGRAM PROCESSORS;

EID: 70149087091     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2009.06.004     Document Type: Article
Times cited : (26)

References (54)
  • 1
    • 41049118534 scopus 로고    scopus 로고
    • A time-dependent quantum dynamics investigation of the guanine-cytosine system: A six-dimensional model
    • Villani G. A time-dependent quantum dynamics investigation of the guanine-cytosine system: A six-dimensional model. J. Chem. Phys. 128 11 (2008) 114306
    • (2008) J. Chem. Phys. , vol.128 , Issue.11 , pp. 114306
    • Villani, G.1
  • 3
    • 0035810449 scopus 로고    scopus 로고
    • The semiclassical initial value representation: A potentially practical way for adding quantum effects to classical molecular dynamics simulations
    • Miller W.H. The semiclassical initial value representation: A potentially practical way for adding quantum effects to classical molecular dynamics simulations. J. Phys. Chem. A 105 (2001) 2942-2955
    • (2001) J. Phys. Chem. A , vol.105 , pp. 2942-2955
    • Miller, W.H.1
  • 4
    • 0001438439 scopus 로고    scopus 로고
    • Quantum molecular dynamics on grids
    • Wyatt R.E., and Zhang J. (Eds), Marcel Dekker, Inc.
    • Kosloff R. Quantum molecular dynamics on grids. In: Wyatt R.E., and Zhang J. (Eds). Dynamics of Molecules and Chemical Reactions (1996), Marcel Dekker, Inc. 185-230
    • (1996) Dynamics of Molecules and Chemical Reactions , pp. 185-230
    • Kosloff, R.1
  • 5
    • 54249124024 scopus 로고    scopus 로고
    • Accurate numerical computation of rovibrational G matrices in molecules of arbitrary size
    • Gervasi O. (Ed), Springer, Berlin
    • Castro M.E., Nino A., and Munoz-Caro C. Accurate numerical computation of rovibrational G matrices in molecules of arbitrary size. In: Gervasi O. (Ed). Computational Science and its Applications - ICCSA 2008 vol. 5072 (2008), Springer, Berlin 1011-1025
    • (2008) Computational Science and its Applications - ICCSA 2008 , vol.5072 , pp. 1011-1025
    • Castro, M.E.1    Nino, A.2    Munoz-Caro, C.3
  • 7
    • 70149092581 scopus 로고    scopus 로고
    • ENACTS, European network for advanced computing technology for science
    • ENACTS, European network for advanced computing technology for science. http://www.epcc.ed.ac.uk/enacts/
  • 8
    • 34848821006 scopus 로고    scopus 로고
    • Quantum dynamics of chemical reactions
    • Goldfield E.M., and Gray S.K. Quantum dynamics of chemical reactions. Adv. Chem. Phys. 136 (2007) 1-37
    • (2007) Adv. Chem. Phys. , vol.136 , pp. 1-37
    • Goldfield, E.M.1    Gray, S.K.2
  • 9
    • 0000980511 scopus 로고    scopus 로고
    • High order finite difference algorithms for solving the Schrödinger equation in molecular dynamics
    • Guantes R., and Farantos S.C. High order finite difference algorithms for solving the Schrödinger equation in molecular dynamics. J. Chem. Phys. 111 (1999) 10827-10835
    • (1999) J. Chem. Phys. , vol.111 , pp. 10827-10835
    • Guantes, R.1    Farantos, S.C.2
  • 10
    • 0034511472 scopus 로고    scopus 로고
    • High order finite difference algorithms for solving the Schrödinger equation in molecular dynamics. II. Periodic variables
    • Guantes R., and Farantos S.C. High order finite difference algorithms for solving the Schrödinger equation in molecular dynamics. II. Periodic variables. J. Chem. Phys. 113 (2000) 10429-10437
    • (2000) J. Chem. Phys. , vol.113 , pp. 10429-10437
    • Guantes, R.1    Farantos, S.C.2
  • 12
    • 0001765826 scopus 로고
    • Efficient calculation of rovibrational eigenstates of sequentially bonded four-atom molecules
    • Bramley M.J., and Handy N.C. Efficient calculation of rovibrational eigenstates of sequentially bonded four-atom molecules. J. Chem. Phys. 98 2 (1981) 1378-1397
    • (1981) J. Chem. Phys. , vol.98 , Issue.2 , pp. 1378-1397
    • Bramley, M.J.1    Handy, N.C.2
  • 16
    • 0035829697 scopus 로고    scopus 로고
    • Dispersion fitted finite difference method with applications to molecular quantum mechanics
    • Gray S.K., and Goldfield E.M. Dispersion fitted finite difference method with applications to molecular quantum mechanics. J. Chem. Phys. 115 18 (2001) 8331-8344
    • (2001) J. Chem. Phys. , vol.115 , Issue.18 , pp. 8331-8344
    • Gray, S.K.1    Goldfield, E.M.2
  • 17
    • 0000690504 scopus 로고
    • Theoretical methods for rovibrational states of floppy molecules
    • Bačić Z., and Light J.C. Theoretical methods for rovibrational states of floppy molecules. Annu. Rev. Phys. Chem. 40 (1989) 469-498
    • (1989) Annu. Rev. Phys. Chem. , vol.40 , pp. 469-498
    • Bačić, Z.1    Light, J.C.2
  • 20
    • 49649159681 scopus 로고
    • A note on angular momentum projection operators
    • Corbett J.O. A note on angular momentum projection operators. Nucl. Phys. A 169 (1971) 426-428
    • (1971) Nucl. Phys. A , vol.169 , pp. 426-428
    • Corbett, J.O.1
  • 21
    • 36449006911 scopus 로고
    • Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. I. Theory and application to a quantum-dynamics model
    • Wall M.R., and Neuhauser D. Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. I. Theory and application to a quantum-dynamics model. J. Chem. Phys. 102 20 (1995) 8011-8022
    • (1995) J. Chem. Phys. , vol.102 , Issue.20 , pp. 8011-8022
    • Wall, M.R.1    Neuhauser, D.2
  • 22
    • 0013489388 scopus 로고
    • Spectral projection approach to the quantum scattering calculations
    • Mandelshtam V.A., and Taylor H.S. Spectral projection approach to the quantum scattering calculations. J. Chem. Phys. 102 19 (1995) 7390-7399
    • (1995) J. Chem. Phys. , vol.102 , Issue.19 , pp. 7390-7399
    • Mandelshtam, V.A.1    Taylor, H.S.2
  • 23
    • 0000472233 scopus 로고    scopus 로고
    • A general and efficient filter-diagonalization method without time propagation
    • Chen R., and Guo H. A general and efficient filter-diagonalization method without time propagation. J. Chem. Phys. 105 4 (1996) 1311-1317
    • (1996) J. Chem. Phys. , vol.105 , Issue.4 , pp. 1311-1317
    • Chen, R.1    Guo, H.2
  • 24
    • 36449009501 scopus 로고
    • 2: An accurate quantum mechanical calculation using filter-diagonalization
    • 2: An accurate quantum mechanical calculation using filter-diagonalization. J. Chem. Phys. 103 23 (1995) 10074-10084
    • (1995) J. Chem. Phys. , vol.103 , Issue.23 , pp. 10074-10084
    • Mandelshtam, V.A.1    Grozdanov, T.P.2    Taylor, H.S.3
  • 25
    • 33748607211 scopus 로고    scopus 로고
    • 3+ molecular ion for J = 0. An accurate calculation using filter-diagonalization
    • 3+ molecular ion for J = 0. An accurate calculation using filter-diagonalization. J. Chem. Soc., Faraday Trans. 93 (1997) 847-860
    • (1997) J. Chem. Soc., Faraday Trans. , vol.93 , pp. 847-860
    • Mandelshtam, V.A.1    Taylor, H.S.2
  • 27
    • 9944236731 scopus 로고    scopus 로고
    • Methods for calculating vibrational energy levels
    • Carrington Jr. T. Methods for calculating vibrational energy levels. Can. J. Chem. 82 (2004) 900-914
    • (2004) Can. J. Chem. , vol.82 , pp. 900-914
    • Carrington Jr., T.1
  • 28
    • 45149101350 scopus 로고    scopus 로고
    • Recursive solutions to large eigenproblems in molecular spectroscopy and reaction dynamics
    • Guo H. Recursive solutions to large eigenproblems in molecular spectroscopy and reaction dynamics. Rev. Comput. Chem. 25 (2007) 285-347
    • (2007) Rev. Comput. Chem. , vol.25 , pp. 285-347
    • Guo, H.1
  • 31
    • 0002515487 scopus 로고    scopus 로고
    • Efficient management of parallelism in object oriented numerical software libraries
    • Arge E., Bruaset A.M., and Langtangen H.P. (Eds), Birkhäuser Press
    • Balay S., Gropp W.D., McInnes L.C., and Smith B.F. Efficient management of parallelism in object oriented numerical software libraries. In: Arge E., Bruaset A.M., and Langtangen H.P. (Eds). Modern Software Tools in Scientific Computing (1997), Birkhäuser Press 163-202
    • (1997) Modern Software Tools in Scientific Computing , pp. 163-202
    • Balay, S.1    Gropp, W.D.2    McInnes, L.C.3    Smith, B.F.4
  • 32
    • 0000689432 scopus 로고    scopus 로고
    • Time-dependent quantum dynamics for gas-phase and gas-surface reactions
    • Wyatt R.E., and Zhang J. (Eds), Marcel Dekker, Inc.
    • Zhang D.H., and Zhang J.Z.H. Time-dependent quantum dynamics for gas-phase and gas-surface reactions. In: Wyatt R.E., and Zhang J. (Eds). Dynamics of Molecules and Chemical Reactions (1996), Marcel Dekker, Inc. 231-276
    • (1996) Dynamics of Molecules and Chemical Reactions , pp. 231-276
    • Zhang, D.H.1    Zhang, J.Z.H.2
  • 33
    • 0000018266 scopus 로고
    • Propagation methods for quantum molecular dynamics
    • Kosloff R. Propagation methods for quantum molecular dynamics. Annu. Rev. Phys. Chem. 45 (1994) 145-178
    • (1994) Annu. Rev. Phys. Chem. , vol.45 , pp. 145-178
    • Kosloff, R.1
  • 35
    • 0001550062 scopus 로고    scopus 로고
    • Numerical methods with high order of accuracy applied in the quantum system
    • Zhu W., Zhao X., and Tang Y. Numerical methods with high order of accuracy applied in the quantum system. J. Chem. Phys. 104 6 (1996) 2275-2286
    • (1996) J. Chem. Phys. , vol.104 , Issue.6 , pp. 2275-2286
    • Zhu, W.1    Zhao, X.2    Tang, Y.3
  • 36
    • 0242510121 scopus 로고
    • An accurate and efficient scheme for propagating the time dependent Schrödinger equation
    • Tal-Ezer H., and Kosloff R. An accurate and efficient scheme for propagating the time dependent Schrödinger equation. J. Chem. Phys. 81 9 (1984) 3967-3971
    • (1984) J. Chem. Phys. , vol.81 , Issue.9 , pp. 3967-3971
    • Tal-Ezer, H.1    Kosloff, R.2
  • 37
  • 38
    • 3843087197 scopus 로고    scopus 로고
    • Supersymmetric improvement of the Pekeris approximation for the rotating Morse potential
    • Morales D.A. Supersymmetric improvement of the Pekeris approximation for the rotating Morse potential. Chem. Phys. Lett. 394 (2004) 68-75
    • (2004) Chem. Phys. Lett. , vol.394 , pp. 68-75
    • Morales, D.A.1
  • 39
    • 0041867565 scopus 로고
    • Single-centre expansion of Gaussian basis functions and the angular decomposition of their overlap integrals
    • Kaufmann K., and Baumeister W. Single-centre expansion of Gaussian basis functions and the angular decomposition of their overlap integrals. J. Phys. B: At. Mol. Opt. Phys. 22 (1989) 1-12
    • (1989) J. Phys. B: At. Mol. Opt. Phys. , vol.22 , pp. 1-12
    • Kaufmann, K.1    Baumeister, W.2
  • 40
    • 0000577219 scopus 로고
    • Analysis of the rotational levels of water
    • Coudert L.H. Analysis of the rotational levels of water. J. Mol. Spec. 154 (1992) 427-442
    • (1992) J. Mol. Spec. , vol.154 , pp. 427-442
    • Coudert, L.H.1
  • 45
    • 0031094323 scopus 로고    scopus 로고
    • The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data
    • Partridge H., and Schwenke D.W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data. J. Chem. Phys. 106 11 (1997) 4618-4639
    • (1997) J. Chem. Phys. , vol.106 , Issue.11 , pp. 4618-4639
    • Partridge, H.1    Schwenke, D.W.2
  • 46
    • 33646987904 scopus 로고
    • 2O classical and semiclassical considerations
    • 2O classical and semiclassical considerations. Mol. Phys. 44 3 (1981) 709-723
    • (1981) Mol. Phys. , vol.44 , Issue.3 , pp. 709-723
    • Lawton, R.T.1    Child, M.S.2
  • 47
    • 36149038529 scopus 로고
    • Collective rotations of asymmetrically deformed many-body systems
    • Lathouwers L.F., and Deumens E. Collective rotations of asymmetrically deformed many-body systems. J. Phys. A: Math. Gen. 15 (1982) 2785-2799
    • (1982) J. Phys. A: Math. Gen. , vol.15 , pp. 2785-2799
    • Lathouwers, L.F.1    Deumens, E.2
  • 49
    • 0142052927 scopus 로고    scopus 로고
    • Eigenspectra calculations using Cartesian coordinates and a rotational symmetry adapted Lanczos method
    • Montgomery J., and Poirier B. Eigenspectra calculations using Cartesian coordinates and a rotational symmetry adapted Lanczos method. J. Chem. Phys. 119 13 (2003) 6609-6619
    • (2003) J. Chem. Phys. , vol.119 , Issue.13 , pp. 6609-6619
    • Montgomery, J.1    Poirier, B.2
  • 50
    • 64549128661 scopus 로고    scopus 로고
    • Towards black-box-type full- and reduced-dimensional variational rovibrational computations
    • Mátyus E., Czakó G., and Császár A.G. Towards black-box-type full- and reduced-dimensional variational rovibrational computations. J. Chem. Phys. 130 6 (2009) 134112-134116
    • (2009) J. Chem. Phys. , vol.130 , Issue.6 , pp. 134112-134116
    • Mátyus, E.1    Czakó, G.2    Császár, A.G.3
  • 51
    • 58049219748 scopus 로고    scopus 로고
    • Resolution of large symmetric eigenproblems on a world wide grid
    • Choy L., Petiton S.G., and Sato M. Resolution of large symmetric eigenproblems on a world wide grid. Int. J. Grid Util. Comput. 1 2 (2009) 71-85
    • (2009) Int. J. Grid Util. Comput. , vol.1 , Issue.2 , pp. 71-85
    • Choy, L.1    Petiton, S.G.2    Sato, M.3
  • 52
    • 0000291562 scopus 로고
    • Potential optimized discrete variable representation
    • Echave J., and Clary D. Potential optimized discrete variable representation. Chem. Phys. Lett. 190 3-4 (1992) 225-230
    • (1992) Chem. Phys. Lett. , vol.190 , Issue.3-4 , pp. 225-230
    • Echave, J.1    Clary, D.2
  • 53
    • 12144262727 scopus 로고
    • The discrete variable representation of a triatomic Hamiltonian in bond length-bond angle coordinates
    • Wei H., and Carrington Jr. T. The discrete variable representation of a triatomic Hamiltonian in bond length-bond angle coordinates. J. Chem. Phys. 97 5 (1992) 3029-3037
    • (1992) J. Chem. Phys. , vol.97 , Issue.5 , pp. 3029-3037
    • Wei, H.1    Carrington Jr., T.2
  • 54
    • 33645362471 scopus 로고    scopus 로고
    • High-lying rotational levels of water: Comparison of calculated and experimental energy levels for (000) and (010) up to J = 25 and 21
    • Lanquetin R., Coudert L.H., and Camy-Peyret C. High-lying rotational levels of water: Comparison of calculated and experimental energy levels for (000) and (010) up to J = 25 and 21. J. Mol. Spec. 195 (1999) 54-67
    • (1999) J. Mol. Spec. , vol.195 , pp. 54-67
    • Lanquetin, R.1    Coudert, L.H.2    Camy-Peyret, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.