Linear scaling computation of the Fock matrix

Journal of Chemical Physics

Volumn 106, Issue 13, 1997, Pages 5526-5536

  Challacombe, Matt ^a   Schwegler, Eric ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010259404     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.473575     Document Type: Article

References (96)

1. D. K. W. Mok, R. Neumann, and N. C. Handy, J. Phys. Chem. 100, 6225 (1996).
2. A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
3. A. D. Becke, J. Chem. Phys. 104, 1040 (1996).
4. B. Johnson, P. Gill, and J. Pople, J. Chem. Phys. 98, 5612 (1993).
5. C. W. Bauschlicher, Chem. Phys. Lett. 246, 40 (1995).
6. G. S. Tschumper, J. T. Fermann, and H. F. Schaefer III, J. Chem. Phys. 104, 3676 (1996).
7. V. Barone, C. Adamo, and F. Mele, Chem. Phys. Lett. 249, 290 (1996).
8. J. R. Chelikowsky, N. Troullier, and Y. Saad, Phys. Rev. Lett. 72, 1240 (1994).
9. J. R. Chelikowsky, N. Troullier, K. Wu, and Y. Saad, Phys. Rev. B 50, 11 355 (1994).
10. E. L. Briggs, D. J. Sulivan, and J. Bernholc, Phys. Rev. B 52, R5471 (1995).
11. K. Cho, T. A. Arias, J. D. Joannopoulos, and P. K. Lam, Phys. Rev. Lett. 71, 1808 (1993).
12. S. Q. Wei and M. Y. Chou, Phys. Rev. Lett. 76, 2650 (1996).
13. C. A. White, B. Johnson, P. Gill, and M. Head-Gordon, Chem. Phys. Lett. 230, 8 (1994).
14. C. A. White, B. G. Johnson, P. M. W. Gill, and M. Head-Gordon, Chem. Phys. Lett. 253, 268 (1996).
15. R. Kutteh and J. B. Nicholas, Chem. Phys. Lett. 238, 173 (1995).
16. M. Challacombe, E. Schwegler, and J. Almlöf, in Computational Chemistry: Review of Current Trends, edited by J. Leczszynski (World Scientific, Singapore, 1996), pp. 53-107.
17. M. Challacombe, E. Schwegler, and J. Almlöf, J. Chem. Phys. 104, 4685 (1996).
18. M. C. Strain, G. E. Scuseria, and M. J. Frisch, Science 271, 51 (1996).
19. S. Wilson, Int. J. Quantum Chem. 60, 47 (1996).
20. P. O. Löwdin, Annu. Rev. Phys. Chem. 11, 107 (1960).
21. S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1985).
22. M. Head-Gordon and J. A. Pople, J. Chem. Phys. 89, 5777 (1988).
23. P. M. W. Gill, M. Head-Gordon, and J. A. Pople, Int. J. Quantum Chem. Symp. 23, 269 (1989).
24. T. P. Hamilton and H. F. Schaefer, Chem. Phys. 150, 163 (1991).
25. T. P. Hamilton and H. F. Schaefer, Can. J. Chem. 70, 416 (1992).
26. P. M. W. Gill and J. A. Pople, Int. J. Quantum Chem. 40, 753 (1991).
27. I. Panas, Chem. Phys. Lett. 184, 86 (1991).
28. U. Ryu, Y. S. Lee, and R. Lindh, Chem. Phys. Lett. 185, 562 (1991).
29. R. Lindh, Theor. Chim. Acta 85, 423 (1993).
30. S. Ten-no and S. Iwata, Chem. Phys. Lett. 211, 259 (1993).
31. B. Johnson, P. Gill, and J. Pople, Chem. Phys. Lett. 206, 229 (1993).
32. P. M. W. Gill, Adv. Quantum Chem. 25, 141 (1994).
33. C. Roothaan, Rev. Mod. Phys. 23, 69 (1951).
34. G. G. Hall, Proc. R. Soc. 208 A, 328 (1951).
35. J. A. Pople and R. K. Nesbet, J. Chem. Phys. 22, 571 (1954).
36. P. O. Löwdin, Phys. Rev. 97, 1490 (1955).
37. R. McWeeny, Rev. Mod. Phys. 126, 1028 (1962).
38. L. Cohen and C. Frishberg, J. Chem. Phys. 65, 4234 (1976).
39. X. P. Li, R. W. Nunes, and D. Vanderbilt, Phys. Rev. B 47, 10 891 (1993).
40. E. Hernández, M. J. Gillan, and C. M. Goringe, 1995, available at http:// www.chem.brown.edu/chem-ph.html.
41. E. Hernández and M. J. Gillan, Phys. Rev. B 51, 10 157 (1995).
42. X. Chen, J. M. Langlois, and W. A. Goddard III, Phys. Rev. B 54, 2348 (1995).
43. V. Dyczmons, Theor. Chim. Acta 28, 307 (1973).
44. R. Ahlrichs, Theor. Chim. Acta 33, 157 (1974).
45. J. Barnes and P. Hut, Nature 324, 446 (1986).
46. L. Hernquist, Appl. J. Suppl. 64, 715 (1987).
47. J. E. Barnes and P. Hut. Appl. J. Suppl. 70, 389 (1989).
48. M. S. Warren and J. K. Salmon, in Proceedings SUPERCOMPUTING '93 (IEEE Computer Society, Los Alamitos, 1993), pp. 12-21.
49. S. Pfalzner and P. Gibbon, Comp. Phys. Commun. 79, 24 (1994).
50. J. K. Salmon, Int. J. Super. Appl. 8, 129 (1994).
51. M. S. Warren and J. K. Salmon, Comp. Phys. Commun. 87, 266 (1995).
52. L. Greengard and V. Rokhlin, J. Comp. Phys. 73, 325 (1987).
53. K. E. Schmidt and M. A. Lee, J. Stat. Phys. 63, 1223 (1991).
54. H. Petersen, D. Soelvason, J. W. Perram, and E. R. Smith, J. Chem. Phys. 101, 8870 (1994).
55. H. Petersen, E. R. Smith, and D. Soelvason, Proc. R. Soc. A 448, 401 (1994).
56. C. A. White and M. Head-Gordon, J. Chem. Phys. 101, 6593 (1994).
57. C. A. White, B. G. Johnson, P. M. W. Gill, and M. Head-Gordon, Chem. Phys. Lett. 257, 647 (1996).
58. C. A. White and M. Head-Gordon, J. Chem. Phys. 105, 5061 (1996).
59. W. D. Elliot and J. A. Board Jr., Technical Report No. 94-001, Duke University Department of Electrical Engineering, (unpublished), available at http://www.ee.duke.edu/Research/SciComp/papers.html.
60. J. A. Board Jr., Z. S. Hakura, W. D. Elliot, and W. T. Rankin, Technical Report No. 94-006, Duke University Department of Electrical Engineering (unpublished), available at http://www.ee.duke.edu/Research/SciComp/ papers.html.
61. E. Schwegler and M. Challacombe, J. Chem. Phys. 105, 2726 (1996).
62. G. R. Ahmadi and J. Almlof, Chem. Phys. Lett. 246, 364 (1995).
63. L. McMurchie, Ph.D. thesis, University of Seattle, 1977.
64. L. McMurchie and E. R. Davidson, J. Comp. Phys. 26, 218 (1978).
65. V. R. Saunders, in Methods in Computational Molecular Physics, edited by G. H. F. Diercksen and S. Wilson (Reidel, Boston, 1983), pp. 1-36.
66. I. Shavitt, Methods Comp. Phys. 2, 1 (1963).
67. P. J. Davis, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1987), pp. 260-2.
68. S. Aluru, G. M. Prabhu, and J. Gustafson, in Proceedings SUPERCOMPUTING '94 (IEEE Computer Society, Los Alamitos, 1995), pp. 420-6.
69. S. Aluru, J. Sci. Comp. 17, 773 (1996).
70. K. Esselink, Inf. Proc. Lett. 41, 141 (1992).
71. K. Esselink, Comput. Phys. Commun. 87, 375 (1995).
72. B. C. Carlson and G. S. Rushbrooke, Proc. Cambridge Philos. Soc. 46, 626 (1950).
73. H. Y. Wang and R. LeSar, J. Chem. Phys. 104, 4173 (1996).
74. J. M. Pérez-Jordá and W. Yang, J. Chem. Phys. 104, 8003 (1996).
75. S. Wolfram, Mathematica, A System for Doing Mathematics by Computer, 2nd ed. (Addison-Wesley, Redwood City, 1991).
76. M. Sofroniou, Math. J. 3, 74 (1993).
77. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977), Vol. II, see Appendix II for a useful discussion of the Dirac delta function and its derivatives.
78. J. Applequist, J. Phys. A 22, 4303 (1989).
79. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Prodacts, 2nd ed. (Academic, San Diego, 1980).
80. Handbook of Mathematical Functions, 9 ed., edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1987).
81. M. Dupuis, A. Marquez, and E. R. Davidson, HONDO 95.3 from CHEMStation, IBM Corporation, Neighborhood Road, Kingston, New York 12401, 1995.
82. H. Michels and F. Prosser, QCPE 11, 62 (1965).
83. M. J. Frisch et al., GAUSSIAN 94, Revision D.1, Gaussian Inc., Pittsburgh, Pennsylvania, 1995.
84. N. H. Andersen et al., Biochemistry 31, 1280 (1992).
85. F. Bontems et al., Biochemistry 31, 7756 (1992).
86. G. M. Clore et al., Nat. Struct. Biol. 2, 321 (1995).
87. S. Lustig, S. Rastogi, and N. Wagner, J. Comp. Phys. 122, 317 (1995).
88. J. R. Pilkington and S. B. Baden, IEEE Trans. Parallel and Distributed Systems. 7, 288 (1996).
89. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies in FORTRAN (Cambridge University, Port Chester, 1992), p. 463.
90. B. Honig and A. Nicholls, Science 268, 1144 (1995).
91. IBM Visualization Data Explorer Version 3.1, IBM Corporation, New York (1995), DX chemistry extensions were used and are freely available from the Cornell Theory Center DX repository.
92. S. A. Goldstein, D. J. Pheasant, and C. Miller, Neuron 12, 1377 (1994).
93. C. Miller, Neuron 1, 1003 (1988).
94. C. Van Alsenoy, A. Peeters, and J. Martin (personal communication, 1996).
95. C. Van Alsenoy, J. Comp. Chem. 9, 620 (1988).
96. C. Van Alsenoy and A. Peeters, J. Mol. Struct. (Theochem) 286, 19 (1993).