Rayleigh-schrödinger perturbation theory: Practical implementation of matrix and vector formalisms and description of an heuristic sufficiency convergence criterion

Journal of Mathematical Chemistry

Volumn 22, Issue 1, 1997, Pages 85-95

  Besalú, Emili ^a   Carbó‐Dorca, Ramon ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006402566     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019107410723     Document Type: Article

References (47)

1. J.P. Ader, Phys. Lett. A 97 (1983) 178.
2. V.C. Aguilera-Navarro, F.M. Fernández, R. Guardiola and J. Ros, J. Phys. A 25 (1992) 6379-6392.
3. G.A. Arteca, F.M. Fernández and E.A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics (Springer, Berlin, 1990).
4. E. Besalú and R. Carbó, J. Math. Chem. 15 (1994) 397-106.
5. E. Besalú and R. Carbó, J. Math. Chem. 18 (1995) 37-72.
6. R. Carbó and E. Besalú, J. Math. Chem. 13 (1993) 331-342.
7. R. Carbó and E. Besalú, Comput. Chem. 18(2) (1994) 117-126.
8. R. Carbó-Dorca and E. Besalú, J. Math. Chem. 20 (1996) 263-271.
9. R. Carbó, L. Molino and B. Calabuig, J. Comput. Chem. 13 (1992) 155.
10. M. Dunn, T.C. Germann, D.Z. Goodson, C.A. Traynor, J.D. Morgan III, D.K. Watson and D.R. Herschbach, J. Chem. Phys. 101(7) (1994) 5987.
11. M. Dunn, D.K. Watson, J.R. Walkup and T.C. Germann, J. Chem. Phys. 104(24) (1996) 9870.
12. E. Durand, Solutions Numériques des Équations Algébriques, Vol. II (Massen & Cie, Paris, 1961).
13. F.M. Fernández, Phys. Rev. A 48(1) (1993) 189.
14. F.M. Fernández, Phys. Lett. A 194 (1994) 343-347.
15. F.M. Fernández, Phys. Rev. 50(4) (1994) 2953.
16. F.M. Fernández, J. Chem. Phys. 103(15) (1995) 6581.
17. F.M. Fernández, J. Math. Phys. 36(8) (1995) 3922.
18. F.M. Fernández and E.A. Castro, J. Chem. Phys. 98(8) (1993) 6392.
19. F.M. Fernández and E.A. Castro, J. Math. Phys. 34(8) (1993) 3670.
20. F.M. Fernández and R. Guardiola, J. Phys. A 26 (1993) 7169-7180.
21. F.M. Fernández and J.F. Ogilvie, Phys. Lett. A 178 (1993) 11-16.
22. G.H. Golub and Ch.F. van Loan, Matrix Computations (The Johns Hopkins University Press, London, 1993).
23. R. Guida, K. Konishi and H. Suzuki, Ann. Phys. 241 (1995) 152-184.
24. W. Janke and H. Kleinert, Phys. Lett. 199 (1995) 287-290.
25. W. Janke and H. Kleinert, Phys. Rev. Lett. 75(15) (1995) 2787.
26. G. Jolicard, A. Grosjean and J.P. Killingbeck, J. Chem. Phys. 105(14) (1996) 5359.
27. G. Jolicard and J.P. Killingbeck, J. Chem. Phys. 103(5) (1995) 1846.
28. T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, 1966).
29. J.P. Killingbeck and G. Jolicard, Chem. Phys. Lett. 255 (1996) 79-82.
30. T. Koga, H. Tatewaki and A.J. Thakkar, Theor. Chim. Acta 88 (1994) 273.
31. C. Møller and M.S. Plesset, Phys. Rev. 46 (1934) 618.
32. F. Rellich, Perturbation Theory of Eigenvalue Problems (Gordon and Breach, New York, 1969).
33. B.O. Roos and P.E.M. Siegbahn, in: Methods of Electronic Structure Theory, Vol. 3, ed. H.F. Shaefer (Plenum Press, New York, 1977).
34. I. Shavitt, in: Methods of Electronic Structure Theory, Vol. 3, ed. H.F. Shaefer (Plenum Press, New York, 1977).
35. E.L. Sibert III, J. Chem. Phys. 88(7) (1988) 4378.
36. L. Skála, J. Čížek, J. Dvořák and V. Špirko, Phys. Rev. A 53(4) (1996) 2009.
37. A.A. Suvernev and D.Z. Goodson, J. Chem. Phys. 106(7) (1997) 2681.
38. TWOEL-96 program. Institute of Computational Chemistry, University of Girona, Girona, Spain (1996).
39. F. Vinette and J. Čížek, Comput. Phys. Comm. 52 (1988) 35-41.
40. E.J. Weniger, Ann. Phys. 246 (1996) 133-165.
41. E.J. Weniger, Int. J. Quant. Chem. 57 (1996) 265-280.
42. E.J. Weniger, Phys. Rev. Lett. 77(14) (1996) 2859.
43. E.J. Weniger, J. Čížek and F. Vinette, J. Math. Phys. 34(2) (1993) 571.
44. J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965).
45. J.H. Wilkinson and C. Reinsch, Linear Algebra (Springer, Berlin, 1971).
46. C.H. Wilsox, ed., Perturbation Theory and Its Applications in Quantum Mechanics (Wiley, New York, 1966).
47. M.R.M. Witwit and J.P. Killingbeck, J. Phys. A 26 (1993) 3659-3662.