Power series expansion of the roots of a secular equation containing symbolic elements: Computer algebra and Moseley's law

Journal of Chemical Physics

Volumn 114, Issue 23, 2001, Pages 10265-

  Barnett, Michael P ^a   Decker, Thomas ^b   Krandick, Werner ^c  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF PADERBORN   (Germany)

^c DREXEL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035875426     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1371260     Document Type: Article

References (46)

1. E. A. Hylleraas, Z. Phys. 65, 209 (1930).
2. C. W. Scherr and R. E. Knight, Rev. Mod. Phys. 35, 436 (1963).
3. L. W. Manning and F. C. Sanders, J. Chem. Phys. 113, 9419 (2000).
4. H. M. Schmidt and J. Linderberg, Phys. Rev. A 49, 4404 (1994).
5. H. E. Montgomery, Jr., Chem. Phys. Lett. 294, 468 (1998).
6. J. N. Silverman, Chem. Phys. Lett. 160, 514 (1998).
7. J. R. Dias, Molecular Orbital Calculations Using Chemical Graph Theory (Springer, Berlin, 1993).
8. P. Raghunathan, Proc.-Indian Acad. Sci., Chem. Sci. 90, 467 (1981).
9. C. L. Pekeris, Phys. Rev. 112, 1649 (1958).
10. T. Helgaker, in The Encyclopedia of Computational Chemistry, edited by P. v. R. Schleyer (Wiley, New York, 1998), pp. 1157-1163.
11. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, Reading, MA, 1950).
12. W. Magnus and S. Winkler, Hill's Equation (Dover, Mineola, NY, 1979).
13. C. L. Pekeris, Phys. Rev. 115, 1649 (1959).
14. T. Kinoshita, Phys. Rev. 115, 366 (1959).
15. F. Weinhold, Proc. R. Soc. London, Ser. A 327, 209 (1972).
16. S. Wolfram, The Mathematica Book, 4th ed. (Cambridge University Press, Reading, MA, 1999).
17. J. H. Wilkinson, Numer. Math. 1, 150 (1959).
18. F. S. Acton, Numerical Methods that Work (Mathematical Association of America, Washington, DC, 1990).
19. Y. Accad, C. L. Pekeris, and B. Schiff, Phys. Rev. A 4, 516 (1972).
20. W. Kutzelnigg and P. von Herigonte, Adv. Quantum Chem. 36, 185 (2000).
21. H. G. J. Moseley, Philos. Mag. 26, 1024 (1913); 27, 703 (1914).
22. H. G. J. Moseley, Philos. Mag. 26, 1024 (1913); 27, 703 (1914).
23. A. E. Ruark and H. C. Urey, Atoms, Molecules and Quanta (McGraw-Hill, New York, 1930).
24. G. Tanner, K. Richter, and J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000).
25. M. P. Barnett, http://www.princeton.edu/̃allengrp/ms/radialDensities (2000).
26. M. P. Barnett, Comput. Math. Appl. 26, 35 (1993).
27. M. P. Barnett and K. R. Perry, Comput. Math. Appl. 28, 17 (1994).
28. M. P. Barnett and K. R. Perry, TUGBoat 15, 285 (1994).
29. M. P. Barnett, TUGboat 19, 147 (1998).
30. M. P. Barnett, http://vvww.princeton.edu/̃allengrp/ms/ctpall.ps (1996).
31. G. Collins et al., SACLIB User's Guide, Technical Report 93-19, RISC-Linz, Johannes Kepler University, Linz, Austria, 1993.
32. B. L. Hicks, J. Chem. Phys. 8, 569 (1940).
33. H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (van Nostrand, New York, 1943).
34. D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, translated by R. C. Williams (Freeman, San Francisco, 1963).
35. K. O. Geddes, S. R. Czapor, and G. Labahn, Algorithms for Computer Algebra (Kluwer, Boston, 1992).
36. J. von zur Gathen and J. Gerhard, Modern Computer Algebra (Cambridge University Press, Cambridge, MA, 1998).
37. F. Calogero and J.-P. Françoise, J. Phys. A 30, 211 (1997).
38. H. Cox, P. E. Sinclair, S. J. Smith, and B. T. Sutcliffe, Mol. Phys. 87, 399 (1996).
39. P. Bracken and J. Čížek, Int. J. Quantum Chem. 53, 467 (1994).
40. E. J. Weniger, J. Čížek, and F. Vinette, J. Math. Phys. 34, 571 (1993).
41. H. H. Homeier, J. Mol. Struct.: THEOCHEM 419, 29 (1997).
42. J. Čížek and P. Bracken, Phys. Rev. Lett. 77, 211 (1996).
43. I. Shavitt, in Methods of Computational Physics, Vol. 2, edited by B. Alder (Academic, New York, 1963), pp. 1-46.
44. M. P. Barnett, Int. J. Quantum Chem. 76, 464 (2000).
45. M. P. Barnett, J. Chem. Phys. 113, 9419 (2000).
46. M. P. Barnett, htlp://www.princeton.edu/̃allengrp/ms/axcat.ps (1998).