User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations

Primary tabs

Czako, Gabor Furtenbacher, Tibor Barletta, Paolo Csaszar, Attila G. Szalay, Viktor Sutcliffe, Brian T.

A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R, embedding. The singular term related to the diatom-type coordinate, R-1, deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R1, with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H-3(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2007
Language Anglais
Journal information "Physical Chemistry Chemical Physics" - Vol. 9, no. 26, p. 3407-3415 (2007)
Peer reviewed yes
Publisher Royal Soc Chemistry (Cambridge)
issn 1463-9076
e-issn 1463-9084
Publication status Publié
Affiliation UCL
Links
  1. Bramley, J. Chem. Phys., 99, 8519 (1993)
  2. Kozin, J. Chem. Phys., 118, 4896 (2002)
  3. Bramley, J. Chem. Phys., 98, 1378 (1993)
  4. Carter, Chem. Phys. Lett., 240, 400 (1995)
  5. Luckhaus, J. Chem. Phys., 118, 8797 (2003)
  6. Mladenović Mirjana, Discrete variable approaches to tetratomic molecules, 10.1016/s1386-1425(01)00669-2
  7. Yu, J. Chem. Phys., 117, 2030 (2002)
  8. Yu, J. Chem. Phys., 120, 2270 (2003)
  9. Polyansky, Science, 299, 539 (2003)
  10. Tennyson, J. Phys. Chem., Ref. Data, 30, 735 (2001)
  11. Furtenbacher, J. Mol. Spectrosc. (2007)
  12. Sutcliffe, J. Chem. Soc., Faraday Trans., 89, 2321 (1993)
  13. Last, J. Chem. Phys., 107, 1451 (1997)
  14. Baer, J. Chem. Phys., 91, 4169 (1989)
  15. Baer, Chem. Phys. Lett., 167, 269 (1990)
  16. Watson James K. G., Erratum: Vibration–rotation calculations for using a Morse-based discrete variable representation, 10.1139/p94-092
  17. Watson, Chem. Phys., 190, 291 (1995)
  18. Henderson, J. Chem. Phys., 98, 7191 (1993)
  19. Carter, J. Chem. Phys., 93, 8902 (1990)
  20. Spirko, J. Mol. Spectrosc., 134, 430 (1987)
  21. Henderson, Chem. Phys. Lett., 173, 133 (1990)
  22. Henderson, Mol. Phys., 89, 953 (1996)
  23. Munro, Mol. Phys., 104, 115 (2006)
  24. Barletta, Mol. Phys., 104, 2801 (2006)
  25. Zhang, J. Chem. Phys., 123, 014308 (2005)
  26. Bramley, J. Chem. Phys., 100, 6175 (1994)
  27. Bramley, J. Chem. Phys., 103, 9705 (1995)
  28. Mandelshtam, J. Chem. Soc., Faraday Trans., 93, 847 (1997)
  29. Wu, J. Chem. Phys., 107, 2705 (1997)
  30. Light, J. Chem. Phys., 82, 1400 (1985)
  31. Harris, J. Chem. Phys., 43, 1515 (1965)
  32. Dickinson, J. Chem. Phys., 49, 4209 (1968)
  33. Szalay, J. Chem. Phys., 119, 10512 (2003)
  34. Szalay, J. Chem. Phys., 105, 6940 (1996)
  35. Henderson, Comput. Phys. Commun., 75, 365 (1993)
  36. Tennyson, Comput. Phys. Commun., 163, 85 (2004)
  37. Sutcliffe, Int. J. Quantum Chem., 39, 183 (1991)
  38. Czakó, Mol. Phys., 102, 2411 (2004)
  39. Furtenbacher, J. Mol. Struct., 780–781, 283 (2006)
  40. Tennyson, J. Mol. Spectrosc., 101, 71 (1983)
  41. Johnson, J. Chem. Phys., 73, 5051 (1980)
  42. Vincke, J. Phys. B: At. Mol. Opt. Phys., 26, 811 (1993)
  43. Hesse, Phys. Rev. E, 65, 046703 (2002)
  44. Czakó, J. Chem. Phys., 122, 024101 (2005)
  45. Littlejohn, J. Chem. Phys., 116, 8691 (2002)
  46. Littlejohn, J. Chem. Phys., 117, 27 (2002)
  47. Czakó, J. Chem. Phys., 124, 014110 (2006)
  48. Sorensen, SIAM J. Matr. Anal. Appl., 13, 357 (1992)
  49. Radau, Ann. Sci. Ec. Normale Super., 5, 311 (1868)
  50. Smith, Phys. Rev. Lett., 45, 1157 (1980)
  51. Leforestier, J. Chem. Phys., 94, 6388 (1991)
  52. Szalay, J. Chem. Phys., 99, 1978 (1993)
  53. Baye, J. Phys. A: Math. Gen., 19, 2041 (1986)
  54. Lanczos C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, 10.6028/jres.045.026
  55. Polyansky, Mol. Phys., 98, 261 (2000)
  56. Tennyson, Philos. Trans. Royal Soc. London, Ser. A, 358, 2419 (2000)
Bibliographic reference Czako, Gabor ; Furtenbacher, Tibor ; Barletta, Paolo ; Csaszar, Attila G. ; Szalay, Viktor ; et. al. Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations. In: Physical Chemistry Chemical Physics, Vol. 9, no. 26, p. 3407-3415 (2007)
Permanent URL http://hdl.handle.net/2078.1/37506