Distance-dependent Schwarz-based integral estimates for two-electron integrals: Reliable tightness vs. Rigorous upper bounds

Journal of Chemical Physics

Volumn 136, Issue 14, 2012, Pages

  Maurer, Simon A ^a   Lambrecht, Daniel S ^a,b   Flaig, Denis ^a   Ochsenfeld, Christian ^a  

^a UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISTANCE INFORMATION; ELECTRON CORRELATION EFFECT; EXCHANGE INTEGRALS; INTEGRAL ESTIMATE; MULTIPOLE-BASED INTEGRAL ESTIMATES; SCREENING PERFORMANCE; TWO-ELECTRON INTEGRALS; UPPER BOUND;

BENCHMARKING; CHARGE DISTRIBUTION; ELECTRONS;

ESTIMATION;

EID: 84859928932     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3693908     Document Type: Article

References (50)

1. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Macmillan, New York, 1982).
2. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1994).
3. T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic-Structure Theory (Wiley-VCH, Weinheim, 2000).
4. R. Ahlrichs, Theor. Chim. Acta 33, 157 (1974).
5. J. Almlöf, K. Faegri, and K. Korsell, J. Comput. Chem. 3, 385 (1982).
6. D. Cremer and J. Gauss, J. Comput. Chem. 7, 274 (1986).
7. J. L. Whitten, J. Chem. Phys. 58, 4496 (1973).
8. M. Häser and R. Ahlrichs, J. Comput. Chem. 10, 104 (1989).
9. P. M. W. Gill, B. G. Johnson, and J. A. Pople, Chem. Phys. Lett. 217, 65 (1994).
10. C. A. White, B. G. Johnson, P. M. W. Gill, and M. Head-Gordon, Chem. Phys. Lett. 230, 8 (1994).
11. M. Challacombe, E. Schwegler, and J. Almlöf, J. Chem. Phys. 104, 4685 (1996).
12. M. C. Strain, G. E. Scuseria, and M. J. Frisch, Science 271, 51 (1996).
13. E. Schwegler, M. Challacombe, and M. Head-Gordon, J. Chem. Phys. 106, 9708 (1997).
14. C. Ochsenfeld, C. A. White, and M. Head-Gordon, J. Chem. Phys. 109, 1663 (1998).
15. E. Schwegler and M. Challacombe, J. Chem. Phys. 111, 6223 (1999).
16. C. Ochsenfeld, J. Kussmann, and D. S. Lambrecht, in Reviews in Computational Chemistry, edited by K. B. Lipkowitz and T. R. Cundari (Wiley- VCH, 2007), Vol. 23, pp. 1-81.
17. C. A. White, B. G. Johnson, P. M. W. Gill, and M. Head-Gordon, Chem. Phys. Lett. 253, 268 (1996).
18. C. Ochsenfeld, Chem. Phys. Lett. 327, 216 (2000).
19. B. G. Johnson, C. A. White, Q. Zhang, B. Chen, R. L. Graham, P. M. W. Gill, and M. Head-Gordon, in Recent Developments and Applications of Modern Density Functional Theory, edited by J. Seminario (Elsevier, Amsterdam, 1996), pp. 441-464.
20. P. Sałek, S. Høst, L. Thøgersen, P. Jørgensen, P.Manninen, J. Olsen, B. Jansík, S. Reine, F. Pawłowski, E. Tellgren, T. Helgaker, and S. Coriani, J. Chem. Phys. 126, 114110 (2007).
21. E. Rudberg, E. H. Rubensson, and P. Sałek, J. Chem. Theory Comput. 7, 340 (2011).
22. C. Ochsenfeld, J. Kussmann, and F. Koziol, Angew. Chem., Int. Ed. 43, 4485 (2004).
23. J. Zienau, J. Kussmann, and C. Ochsenfeld, Mol. Phys. 108, 333 (2010).
24. C. Ochsenfeld and M. Head-Gordon, Chem. Phys. Lett. 270, 399 (1997).
25. J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 127, 054103 (2007).
26. M. Beer, J. Kussmann, and C. Ochsenfeld, J. Chem. Phys. 134, 74102 (2011).
27. D. S. Lambrecht and C. Ochsenfeld, J. Chem. Phys. 123, 184101 (2005).
28. J. Almlöf, Chem. Phys. Lett. 181, 319 (1991).
29. M. Häser and J. Almlöf, J. Chem. Phys. 96, 489 (1992).
30. M. Häser, Theor. Chim. Acta 87, 147 (1993).
31. A. K. Wilson and J. Almlöf, Theor. Chim. Acta 95, 49 (1997).
32. P. Y. Ayala and G. E. Scuseria, J. Chem. Phys. 110, 3660 (1999).
33. D. S. Lambrecht, B. Doser, and C. Ochsenfeld, J. Chem. Phys. 123, 184102 (2005).
34. B. Doser, D. S. Lambrecht, J. Kussmann, and C. Ochsenfeld, J. Chem. Phys. 130, 64107 (2009).
35. B. Doser, J. Zienau, L. Clin, D. S. Lambrecht, and C. Ochsenfeld, Z. Phys. Chem. 224, 397 (2010).
36. P. Jurecka, J. Sponer, J. Cerný, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006).
37. See http://www.cup.uni-muenchen.de/pc/ochsenfeld/download.html for structure files.
38. S. A. Maurer, D. S. Lambrecht, and C. Ochsenfeld, "Efficient integral screening in linear-scaling Møller-Plesset perturbation theory" (unpublished).
39. J. Almlöf, in Lecture Notes in Quantum Chemistry II, Lecture Notes in Chemistry, Vol. 64, edited by B. Roos (Springer, Berlin, 1994).
40. Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown, A. T. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O'Neill, R. A. DiStasio, Jr., R. C. Lochan, T. Wang, G. J. Beran, N. A. Besley, J. M. Herbert, C. Yeh Lin, T. Van Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G. Kedziora, R. Z. Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee, W. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock III, W. Zhang, A. T. Bell, A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel, W. J. Hehre, H. F. Schaefer III, J. Kong, A. I. Krylov, P. M. W. Gill, and M. Head- Gordon, Phys. Chem. Chem. Phys. 8, 3172 (2006).
41. M. Head-Gordon and J. A. Pople, J. Chem. Phys. 89, 5777 (1988).
42. P. Pulay, Chem. Phys. Lett. 73, 393 (1980).
43. T. Van Voorhis and M. Head-Gordon, Mol. Phys. 100, 1713 (2002).
44. W. J. Hehre, R. Ditchfield, and J. A. Pople, J. Chem. Phys. 56, 2257 (1972).
45. P. C. Hariharan and J. A. Pople, Theor. Chim. Acta 28, 213 (1973).
46. A. Schäfer, H. Horn, and R. Ahlrichs, J. Chem. Phys. 97, 2571 (1992).
47. T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).
48. R. A. Kendall, T. H. Dunning, and R. J. Harrison, J. Chem. Phys. 96, 6796 (1992).
49. P. M. W. Gill, B. G. Johnson, and J. A. Pople, Chem. Phys. Lett. 209, 506 (1993).
50. See supplementary material at http://dx.doi.org/10.1063/1.3693908 for remaining figures and data tables.