Computational method for general multicenter electronic structure calculations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 6 B, 2000, Pages 7169-7183

  Batcho, P F ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ELECTRONIC STRUCTURE; ELECTRONS; FINITE ELEMENT METHOD; ITERATIVE METHODS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; COMPUTATION THEORY; DENSITY FUNCTIONAL THEORY; DIFFERENTIAL EQUATIONS; HAMILTONIANS; MOLECULES; WAVE FUNCTIONS;

DENSITY FUNCTIONAL THEORY; LOCAL DENSITY APPROXIMATIONS; PIECEWISE VARIATIONAL SPECTRAL APPROXIMATION; QUANTUM MECHANICAL PROPERTIES; SPECTRAL ELEMENT METHOD;

MOLECULES; CONVERGENCE OF NUMERICAL METHODS;

OZONE;

CHEMICAL STRUCTURE; CHEMISTRY; COMPUTER SIMULATION; ELECTRON; QUANTUM THEORY;

COMPUTER SIMULATION; ELECTRONS; MODELS, MOLECULAR; MOLECULAR STRUCTURE; OZONE; QUANTUM THEORY;

CO-ORDINATE TRANSFORMATION; CONVERGENCE RATES; DIATOMIC MOLECULES; ELECTRONIC STRUCTURE CALCULATIONS; HAMILTONIAN SYSTEMS; POINT SINGULARITIES; SPECTRAL APPROXIMATIONS; SPECTRAL ELEMENT METHOD;

EID: 0034195179     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.7169     Document Type: Article

References (76)

1. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry; Introduction to Advanced Electronic Structure Theory (McGraw-Hill, New York, 1989).
2. W. Jones and N. M. March, Theoretical Solid State Physics (Wiley, New York, 1973), Vol. 1.
3. M. Head-Gordon, J. Phys. Chem. 100, 13 213 (1996).
4. P. F. Batcho, Phys. Rev. A 57, 4246 (1998).
5. J. D. Morgan, in Numerical Determination of the Electronic Structure of Atoms, Diatomics, and Polyatomic Molecules, edited by M. Defranceschi and J. Delhalle (Kluwer, Dordrecht, 1988).
6. J. Kobus, Chem. Phys. Lett. 202, 7 (1993).
7. L. Laaksonen, P. Pyykko, and D. Sundholm, Comput. Phys. Rep. 4, 313 (1986).
8. P. Pyykko, in Numerical Determination of the Electronic Structure of Atoms, Diatomics, and Polyatomic Molecules (Ref. [5]).
9. D. Moncrieff and S. Wilson, J. Phys. B 27, (1994).
10. D. Gottlieb and C. W. Shu, SIAM Rev. 39, 4 (1997); 39, 644 (1997).
11. D. Gottlieb and C. W. Shu, SIAM Rev. 39, 4 (1997); 39, 644 (1997).
12. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (SIAM, Philadelphia, 1977).
13. A. T. Patera, J. Comput. Phys. 54, 468 (1984).
14. Y. Maday and A. T. Patera, in State of the Art Surveys in Computational Mechanics, edited by A. Noor (American Society of Mechanical Engineers, New York, 1987).
15. E. M. Ronquist, Ph. D. Thesis, Massachusetts Institute of Technology, 1988 (unpublished).
16. P. Honenberg and W. Kohn, Phys. Rev. B 136, 864 (1964).
17. W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133 (1965).
18. Density Functional Theory of Molecules, Clusters, and Solids, edited by D. E. Ellis (Academic, New York, 1995).
19. Chemical Applications of Density Functional Theory, edited by B. B. Laird, R. B. Ross, and T. Ziegler, ACS Symposium, 1996 (American Chemical Society, Washington D.C., 1996), Series 629.
20. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989); W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12 974 (1996).
21. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989); W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12 974 (1996).
22. B. I. Dunlap, Int. J. Quantum Chem. 64, 193 (1997).
23. D. Heinemann, B. Fricke, and D. Kolb, Phys. Rev. A 38, 4994 (1988).
24. S. R. White, J. W. Wilkins, and M. P. Teter, Phys. Rev. B 39, 5819 (1989).
25. F. S. Levin and J. Shertzer, Phys. Rev. A 32, 3285 (1985).
26. E. Tsuchida and M. Tsukada, Solid State Commun. 94, 5 (1995).
27. J. Ackermann, B. Erdmann, and R. Roitzsch, J. Chem. Phys. 101, 7643 (1994).
28. H. Murakami, V. Sonnad, and E. Clementi, Int. J. Quantum Chem. 42, 785 (1992).
29. H. Yu and A. D. Bandrauk, J. Chem. Phys. 102, 1257 (1995).
30. S. Goedecker, Rev. Mod. Phys. 71, 1085 (1999).
31. P. E. Maslen, C. Ochsenfeld, C. A. White, M. S. Lee, and M. Head-Gordon, J. Phys. Chem. A 102, 2215 (1998).
32. E. Hernandez and M. J. Gillan, Phys. Rev. B 53, 7147 (1996).
33. X. P. Li, R. W. Nunes, and D. Vanderbilt, Phys. Rev. B 47, 16 (1993); 47, 10 891 (1993).
34. X. P. Li, R. W. Nunes, and D. Vanderbilt, Phys. Rev. B 47, 16 (1993); 47, 10 891 (1993).
35. T. A. Arias, Rev. Mod. Phys. 71, 269 (1999).
36. N. A. Modine, G. Zumbach, and E. Kaxiras, Phys. Rev. B 55, 10 289 (1997).
37. R. A. Friesner, Annu. Rev. Phys. Chem. 42, 1341 (1991).
38. A. D. Becke and R. M. Dickson, J. Chem. Phys. 92, 3610 (1991); A. D. Becke, ibid. 107, 8554 (1997).
39. A. D. Becke and R. M. Dickson, J. Chem. Phys. 92, 3610 (1991); A. D. Becke, ibid. 107, 8554 (1997).
40. P. F. Batcho, G. E. Karniadakis, and S. A. Orszag, J. Fluids Struct. 5, 681 (1991).
41. P. F. Batcho and G. E. Karniadikis, Phys. Fluids A 3, 1051 (1991).
42. P. F. Batcho, Ph.D. Thesis, Princeton University, 1994 (unpublished).
43. P. F. Batcho and G. E. Karniadakis, J. Comput. Phys. 115, 121 (1994).
44. A. Ghizzetti and A. Ossicini, Quadrature Formulae (Academic, New York, 1970).
45. S. Sherwin, Ph.D. thesis, Princeton University, 1995 (unpublished); S. J. Sherwin and G. E. Karniadakis, J. Comput. Phys. 124, 14 (1996).
46. S. Sherwin, Ph.D. thesis, Princeton University, 1995 (unpublished); S. J. Sherwin and G. E. Karniadakis, J. Comput. Phys. 124, 14 (1996).
47. Y. Maday and R. Munoz, J. Sci. Comput. 3, 323 (1988).
48. I. Stich, R. Car, M. Parinello, and S. Baroni, Phys. Rev. B 8, 4997 (1989).
49. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 4 (1992).
50. M. P. Teter, M. C. Payne, and D. C. Allan, Phys. Rev. B 40, 18 (1989).
51. S. Costiner and S. Ta'asan, ICASE Report 94-91 (ICASE, Virginia, 1994); Phys. Rev. E 51, 3704 (1995); 52, 1181 (1995).
52. S. Costiner and S. Ta'asan, ICASE Report 94-91 (ICASE, Virginia, 1994); Phys. Rev. E 51, 3704 (1995); 52, 1181 (1995).
53. S. Costiner and S. Ta'asan, ICASE Report 94-91 (ICASE, Virginia, 1994); Phys. Rev. E 51, 3704 (1995); 52, 1181 (1995).
54. E. L. Briggs, D. J. Sullivan, and J. Bernholc, Phys. Rev. B 52, 5471 (1995); F. F. Grinstein, H. Rabitz, and A. Askar, J. Comput. Phys. 51, 423 (1983).
55. E. L. Briggs, D. J. Sullivan, and J. Bernholc, Phys. Rev. B 52, 5471 (1995); F. F. Grinstein, H. Rabitz, and A. Askar, J. Comput. Phys. 51, 423 (1983).
56. K. Davstad, J. Comput. Phys. 99, 33 (1992).
57. Linear and Nonlinear Conjugate Gradient Related Methods, edited by L. Adams and J. L. Nazareth (SIAM, Philadelphia, 1996).
58. R. B. Lehoucq, D. C. Sorensen, and C. Vang, Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, 1998).
59. L. F. Pavariono and O. B. Widlund, Int. J. Comput. Math. Appl. 33, 193 (1997).
60. P. M. Morse and H. Feshbach, Methods of Mathematical Physics I (McGraw Hill, New York, 1953).
61. L. Greengard and V. Roklin, Acta Numerica 6, 2298 (1997).
62. O. Gunnarsoon and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
63. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980); G. S. Painter, Phys. Rev. B 24, 4264 (1981).
64. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980); G. S. Painter, Phys. Rev. B 24, 4264 (1981).
65. P. J. Hay and T. H. Dunning, Jr., J. Chem. Phys. 67, 2290 (1977).
66. M. Morin, A. E. Foti, and D. R. Salahub, Can J. Chem. 63, 1982 (1985).
67. B. S. Jursic, J. Mol. Struct.: THEOCHEM 389, 251 (1997).
68. W. D. Laidig and H. F. Schaefer, J. Chem. Phys. 74, 3411 (1981).
69. R. P. Messmer and D. R. Salahub, J. Chem. Phys. 65, 779 (1976).
70. R. Newmann, R. H. Nobes, and N. C. Handy, Mol. Phys. 97, 1 (1996).
71. G. Hunter, Int. J. Quantum Chem. XXIX, 197 (1986).
72. D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998).
73. M. Levy and H. O. Yang, Phys. Rev. A 38, 2 (1988).
74. N. H. March, Int. J. Quant. Chem., Quantum Bio. Symp. 13, 003 (1986).
75. L. I. Schiff, Quantum Mechanics, 3rd ed (McGraw-Hill, New York, 1968).
76. P. Pyykko, Chem. Rev. 88, 563 (1988).