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Automatic computer procedure for generating exact and analytical kinetic energy operators based on the plyspherical approach

Bibliographic reference Ndong, Manadou ; Joubert-Doriol, Loïc ; Meyer, Hans-Dieter ; Nauts, André ; Gatti, Fabien ; et. al. Automatic computer procedure for generating exact and analytical kinetic energy operators based on the plyspherical approach. In: Journal of Chemical Physics, Vol. 136, no. 3, p. 16 pages (17 January 2012)
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  1. Podolsky Boris, Quantum-Mechanically Correct Form of Hamiltonian Function for Conservative Systems, 10.1103/physrev.32.812
  2. Wilson J. E. B., Molecular Vibrations (1955)
  3. Nauts André, Chapuisat Xavier, Momentum, quasi-momentum and hamiltonian operators in terms of arbitrary curvilinear coordinates, with special emphasis on molecular hamiltonians, 10.1080/00268978500102031
  4. Pesonen Janne, Vibrational coordinates and their gradients: A geometric algebra approach, 10.1063/1.480897
  5. Tennyson Jonathan, Sutcliffe Brian T., Theabinitiocalculation of the vibrational‐rotational spectrum of triatomic systems in the close‐coupling approach, with KCN and H2Ne as examples, 10.1063/1.444316
  6. Brocks G., van der Avoird A., Sutcliffe B.T., Tennyson J., Quantum dynamics of non-rigid systems comprising two polyatomic fragments, 10.1080/00268978300102831
  7. Sutcliffe Brian T., Tennyson Jonathan, A generalized approach to the calculation of ro-vibrational spectra of triatomic molecules, 10.1080/00268978600101801
  8. Handy N.C., The derivation of vibration-rotation kinetic energy operators, in internal coordinates, 10.1080/00268978700101081
  9. Chapuisat Xavier, Nauts André, Brunet Jean-Phillippe, Exact quantum molecular Hamiltonians : Part I. Application to the dynamics of three particles, 10.1080/00268979100100011
  10. Bramley Matthew J., Handy Nicholas C., Efficient calculation of rovibrational eigenstates of sequentially bonded four‐atom molecules, 10.1063/1.464305
  11. Bramley Matthew J., Carrington Tucker, A general discrete variable method to calculate vibrational energy levels of three‐ and four‐atom molecules, 10.1063/1.465576
  12. Wei Hua, Carrington Jr. Tucker, An exact Eckart-embedded kinetic energy operator in Radau coordinates for triatomic molecules, 10.1016/s0009-2614(98)00186-9
  13. Smeyers Yves G., Meléndez F. J., Senent M. Luisa, Ab initio theoretical study of the methyl and phosphine torsion modes in ethylphosphine, 10.1063/1.473975
  14. Muñoz-Caro C., QCPE Bull., 13, 4 (1993)
  15. Senent M.L, Determination of the kinetic energy parameters of non-rigid molecules, 10.1016/s0009-2614(98)01052-5
  16. Rush Daniel J., Wiberg Kenneth B., Ab Initio CBS-QCI Calculations of the Inversion Mode of Ammonia, 10.1021/jp9624358
  17. Luckhaus David, 6D vibrational quantum dynamics: Generalized coordinate discrete variable representation and (a)diabatic contraction, 10.1063/1.481924
  18. Lauvergnat David, Nauts André, Exact numerical computation of a kinetic energy operator in curvilinear coordinates, 10.1063/1.1469019
  19. Mátyus Edit, Czakó Gábor, Császár Attila G., Toward black-box-type full- and reduced-dimensional variational (ro)vibrational computations, 10.1063/1.3076742
  20. Laane J., Harthcock M.A., Killough P.M., Bauman L.E., Cooke J.M., Vector representation of large-amplitude vibrations for the determination of kinetic energy functions, 10.1016/0022-2852(82)90146-1
  21. Harthcock M.A., Laane J., Calculation of kinetic energy terms for the vibrational Hamiltonian: Application to large-amplitude vibrations using one-, two-, and three-dimensional models, 10.1016/0022-2852(82)90147-3
  22. Frederick John H., Woywod Clemens, General formulation of the vibrational kinetic energy operator in internal bond-angle coordinates, 10.1063/1.480101
  23. Wang Xiao-Gang, Carrington Tucker, A simple method for deriving kinetic energy operators, 10.1063/1.1313544
  24. Chapuisat Xavier, Iung Christophe, Vector parametrization of theN-body problem in quantum mechanics: Polyspherical coordinates, 10.1103/physreva.45.6217
  25. Gatti Fabien, Muñoz Claudio, Iung Christophe, A general expression of the exact kinetic energy operator in polyspherical coordinates, 10.1063/1.1361069
  26. Gatti Fabien, Iung Christophe, Exact and constrained kinetic energy operators for polyatomic molecules: The polyspherical approach, 10.1016/j.physrep.2009.05.003
  27. Wang X -G, Carrington Jr. T, An exact kinetic energy operator for (HF)3in terms of local polar and azimuthal angles, 10.1139/p01-012
  28. Mladenović Mirjana, Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. II. Nonorthogonal descriptions of internal molecular geometry, 10.1063/1.480663
  29. Gatti Fabien, Iung Christophe, Menou Michel, Chapuisat Xavier, Vector parametrization of the N-atom problem in quantum mechanics. II. Coupled-angular-momentum spectral representations for four-atom systems, 10.1063/1.476328
  30. Iung Christophe, Gatti Fabien, Polyspherical parametrization of an N-atom system: Principles and applications, 10.1002/qua.20728
  31. Gatti Fabien, Vector parametrization of the N-atom problem in quantum mechanics. III. Separation into two subsystems: Application to NH3, 10.1063/1.480051
  33. Carrington Tucker, Wang Xiao-Gang, Computing ro-vibrational spectra of van der Waals molecules, 10.1002/wcms.73
  34. Gatti Fabien, Iung Christophe, Menou Michel, Justum Yves, Nauts André, Chapuisat Xavier, Vector parametrization of the N-atom problem in quantum mechanics. I. Jacobi vectors, 10.1063/1.476327
  35. Iung Christophe, Gatti Fabien, Viel Alexandra, Chapuisat Xavier, Vector parametrization of the N-atom problem in quantum mechanics with non-orthogonal coordinates, 10.1039/a903466h
  36. Meyer H.-D., Manthe U., Cederbaum L.S., The multi-configurational time-dependent Hartree approach, 10.1016/0009-2614(90)87014-i
  37. Beck M. H., Meyer H.-D., Efficiently computing bound-state spectra: A hybrid approach of the multi-configuration time-dependent Hartree and filter-diagonalization methods, 10.1063/1.1334618
  38. Multidimensional Quantum Dynamics, ISBN:9783527627400, 10.1002/9783527627400
  39. Gatti Fabien, Nauts André, Vector parametrization, partial angular momenta and unusual commutation relations in physics, 10.1016/j.chemphys.2003.08.014
  40. Gatti F., Iung C., Leforestier C., Menou M., Justum Y., Nauts A., Chapuisat X., Vector parametrization of the three-atom problem in quantum mechanics, 10.1016/s0166-1280(97)00240-6
  41. Zare R. N., Angular Momentum (2003)
  42. Nauts André, Gatti Fabien, Unusual commutation relations in physics, 10.1119/1.3482257
  43. Brocks G., van der Avoird A., Sutcliffe B.T., Tennyson J., Quantum dynamics of non-rigid systems comprising two polyatomic fragments, 10.1080/00268978300102831
  44. Qiu Yanhui, Bačić Zlatko, Exact six-dimensional quantum calculations of the rovibrational levels of (HCl)2, 10.1063/1.473139
  45. Fellers R. S., Braly L. B., Saykally R. J., Leforestier C., Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with split Wigner pseudospectral approach. II. Improvements and tests of additional potentials, 10.1063/1.478535
  46. Zou Shengli, Bowman Joel M., Reduced dimensionality quantum calculations of acetylene↔vinylidene isomerization, 10.1063/1.1462580
  47. Richter Falk, Hochlaf Majdi, Rosmus Pavel, Gatti Fabien, Meyer Hans-Dieter, A study of the mode-selective trans–cis isomerization in HONO using ab initio methodology, 10.1063/1.1632471
  48. Richter Falk, Rosmus Pavel, Gatti Fabien, Meyer Hans-Dieter, Time-dependent wave packet study on trans-cis isomerization of HONO, 10.1063/1.1651051
  49. Richter Falk, Gatti Fabien, Léonard Céline, Le Quéré Frédéric, Meyer Hans-Dieter, Time-dependent wave packet study ontrans-cisisomerization of HONO driven by an external field, 10.1063/1.2784553
  50. Vendrell Oriol, Brill Michael, Gatti Fabien, Lauvergnat David, Meyer Hans-Dieter, Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water-dimer III: Mixed Jacobi-valence parametrization and benchmark results for the zero point energy, vibrationally excited states, and infrared spectrum, 10.1063/1.3152488
  51. Biedenham L. C., Angular Momentum in Quantum Mechanics (1981)