Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates

Journal of Chemical Physics

Volumn 122, Issue 2, 2005, Pages

  Czakó, Gábor ^a,b   Szalay, Viktor ^a,b   Császár, Attila G ^a   Furtenbacher, Tibor ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

COORDINATES; LINEAR COMBINATIONS; SINGULARITIES; VIBRATIONAL ENERGY;

ATOMS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; HAMILTONIANS; KINETIC ENERGY; MOLECULES; POLYNOMIALS; SPECTROSCOPIC ANALYSIS;

VIBRATION MEASUREMENT;

EID: 22944443941     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1827594     Document Type: Article

References (47)

1. See, for example, Special Issue of Spectrochim. Acta, Part A 58A, (2002).
2. J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985).
3. D. O. Harris, G. G. Engerholm, and W. D. Gwinn, J. Chem. Phys. 43, 1515 (1965).
4. A. S. Dickinson and P. R. Certain, J. Chem. Phys. 49, 4209 (1968).
5. V. Szalay, G. Czakó, Á. Nagy, T. Furtenbacher, and A. G. Császár, J. Chem. Phys. 119, 10512 (2003).
6. J. C. Light and T. Carrington, Jr., Adv. Chem. Phys. 114, 263 (2000).
7. V. Szalay, J. Chem. Phys. 105, 6940 (1996).
8. J. R. Henderson and J. Tennyson, Comput. Phys. Commun. 75, 365 (1993).
9. J. Tennyson, M. A. Kostin, P. Barletta, G. J. Harris, O. L. Polyansky, J. Ramanlal, and N. F. Zobov, Comp. Phys. Comm. (to be published).
10. B. T. Sutcliffe and J. Tennyson, Int. J. Quantum Chem. 39, 183 (1991).
11. G. Czakó, T. Furtenbacher, A. G. Császár, and V. Szalay, Mol. Phys. 102, 2411 (2004).
12. M. J. Bramley and T. Carrington, Jr., J. Chem. Phys. 99, 8519 (1993).
13. I. N. Kozin, M. N. Law, J. M. Hutson, and J. Tennyson, J. Chem. Phys. 118, 4896 (2002).
14. M. J. Bramley and N. C. Handy, J. Chem. Phys. 98, 1378 (1993);
15. S. Carter, N. Pinnavaia, and N. C. Handy, Chem. Phys. Lett. 240, 400 (1995).
16. D. Luckhaus, J. Chem. Phys. 118, 8797 (2003).
17. M. Mladenović, Spectrochim. Acta, Part A 58A, 795 (2002).
18. H.-G. Yu, J. Chem. Phys. 117, 2030 (2002).
19. X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 119, 101 (2003).
20. X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 121, 2937 (2004).
21. H.-G. Yu, J. Chem. Phys. 120, 2270 (2003).
22. B. T. Sutcliffe, J. Chem. Soc., Faraday Trans. 89, 2321 (1993).
23. J. L. Gottfried, B. J. McCall, and T. Oka, J. Chem. Phys. 118, 10890 (2003).
24. A. V. Meremianin and J. S. Briggs, Phys. Rep. 384, 121 (2003).
25. For example, for triatomic vibrational calculations in hyperspherical coordinates, used by S. Carter and W. Meyer, J. Chem. Phys. 93, 8902 (1990) and others, no radial singularity is present in the Hamiltonian.
26. Recently the approach using hyperspherical coordinates has been extended to obtain eigenstates beyond the barrier to linearity by P. Schiffels, A. Alijah, and J. Hinze, Mol. Phys. 101, 189 (2003).
27. H. Wei and T. Carrington, Jr., J. Chem. Phys. 101, 1343 (1994).
28. V. Spirko, A. Cejhan, and P. Jensen, J. Mol. Spectrosc. 134, 430 (1987).
29. J. R. Henderson, J. Tennyson, and B. T. Sutcliffe, J. Chem. Phys. 98, 7191 (1993).
30. J. Tennyson and B. T. Sutcliffe, J. Mol. Spectrosc. 101, 71 (1983).
31. J. K. G. Watson, Can. J. Phys. 72, 702 (1994);
32. J. K. G. Watson, Chem. Phys. 190, 291 (1995).
33. M. J. Bramley, J. W. Tromp, T. Carrington, Jr., and G. C. Corey, J. Chem. Phys. 100, 6175 (1994).
34. For vibration-only calculations the spherical oscillator and the spherical harmonic oscillator functions are identical.
35. V. A. Mandelshtam and H. S. Taylor, J. Chem. Soc., Faraday Trans. 93, 847 (1997).
36. M. Vincke, L. Malegat, and D. Baye, J. Phys. B 26, 811 (1993).
37. M. Hesse, Phys. Rev. E 65, 046703 (2002).
38. R. G. Littlejohn and M. Cargo, J. Chem. Phys. 117, 27 (2002).
39. D. Lemoine, J. Chem. Phys. 118, 6697 (2003).
40. C. G. J. Jacobi, Cr. Hebd. Acad. Sci. 15, 236 (1842).
41. R. Radau, Ann. Sci. Ec. Normale Super. 5, 311 (1868).
42. V. Szalay, J. Chem. Phys. 99, 1978 (1993).
43. O. L. Polyansky, R. Prosmiti, W. Klopper, and J. Tennyson, Mol. Phys. 98, 261 (2000).
44. The imaginary part of the vibrational eigenenergies obtained from the AS-FBR representation turned out to be zero for all the eigenvalues investigated.
45. Almost all of the CPU time is spent in building a matrix representation of the potential energy operator, explicit diagonalization of the final Hamiltonian took a trivial amount of computer time.
46. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations (SIAM, Philadelphia, 2002).
47. J. Tennyson (private communication).