Discrete variable representation in electronic structure theory: Quadrature grids for least-squares tensor hypercontraction

Journal of Chemical Physics

Volumn 138, Issue 19, 2013, Pages

  Parrish, Robert M ^a   Hohenstein, Edward G ^b,c   Martínez, Todd J ^b,c   Sherrill, C David ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; EFFICIENCY; ELECTRONIC STRUCTURE;

DISCRETE VARIABLE REPRESENTATION; ELECTRON REPULSION INTEGRALS; ELECTRONIC STRUCTURE THEORY; LEAST SQUARES FITTING; QUALITATIVE FEATURES; REASONABLE ACCURACY; RELATIVE EFFICIENCY; SIMULTANEOUS DIAGONALIZATION;

TENSORS;

EID: 84878347415     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4802773     Document Type: Article

References (83)

1. W. Koch and M. C. Holthausen, A Chemist's Guide to Density Functional Theory (Wiley-VCH, New York, 2001).
2. A. D. Becke, J. Chem. Phys. 88, 2547 (1988). 10.1063/1.454033
3. P. M. W. Gill, B. G. Johnson, and J. A. Pople, Chem. Phys. Lett. 209, 506 (1993). 10.1016/0009-2614(93)80125-9
4. C. W. Murray, N. C. Handy, and G. J. Lamming, Mol. Phys. 78, 997 (1993). 10.1080/00268979300100651
5. O. Treutler and R. Ahlrichs, J. Chem. Phys. 102, 346 (1995). 10.1063/1.469408
6. M. M. Mura and P. J. Knowles, J. Chem. Phys. 104, 9848 (1996). 10.1063/1.471749
7. R. Lindh, P.-A. Malmqvist, and L. Gagliardi, Theor. Chem. Acc. 106, 178 (2001). 10.1007/s002140100263
8. P. M. W. Gill and S.-H. Chien, J. Comput. Chem. 24, 732 (2003). 10.1002/jcc.10211
9. A. El-Sherbiny and R. A. Poirier, J. Comput. Chem. 25, 1378 (2004). 10.1002/jcc.20063
10. S.-H. Chien and P. M. W. Gill, J. Comput. Chem. 27, 730 (2006). 10.1002/jcc.20383
11. R. A. Friesner, J. Phys. Chem. 92, 3091 (1988). 10.1021/j100322a017
12. J. A. Pople, P. M. Gill, and B. G. Johnson, Chem. Phys. Lett. 199, 557 (1992). 10.1016/0009-2614(92)85009-Y
13. A. D. Becke and E. R. Johnson, J. Chem. Phys. 122, 154104 (2005). 10.1063/1.1884601
14. Q. Wu and T. Van Voorhis, Phys. Rev. A 72, 024502 (2005). 10.1103/PhysRevA.72.024502
15. Q. Wu and T. Van Voorhis, J. Chem. Theory Comput. 2, 765 (2006). 10.1021/ct0503163
16. M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004). 10.1103/PhysRevLett.92.246401
17. O. A. Vydrov and T. V. Voorhis, J. Chem. Phys. 130, 104105 (2009). 10.1063/1.3079684
18. O. A. Vydrov and T. V. Voorhis, J. Chem. Phys. 132, 164113 (2010). 10.1063/1.3398840
19. A. Heßelmann, G. Jansen, and M. Schütz, J. Chem. Phys. 122, 014103 (2005). 10.1063/1.1824898
20. A. J. Misquitta and K. Szalewicz, J. Chem. Phys. 122, 214109 (2005). 10.1063/1.1924593
21. R. A. Friesner, Chem. Phys. Lett. 116, 39 (1985). 10.1016/0009-2614(85) 80121-4
22. R. A. Friesner, J. Chem. Phys. 85, 1462 (1986). 10.1063/1.451237
23. R. A. Friesner, J. Chem. Phys. 86, 3522 (1987). 10.1063/1.451955
24. M. N. Ringnalda, Y. Won, and R. A. Friesner, J. Chem. Phys. 92, 1163 (1990). 10.1063/1.458178
25. M. N. Ringnalda, M. Belhadj, and R. A. Friesner, J. Chem. Phys. 93, 3397 (1990). 10.1063/1.458819
26. B. H. Greeley, J. Chem. Phys. 101, 4028 (1994). 10.1063/1.467520
27. T. J. Martínez, A. Mehta, and E. A. Carter, J. Chem. Phys. 97, 1876 (1992). 10.1063/1.463176
28. T. J. Martínez and E. A. Carter, J. Chem. Phys. 100, 3631 (1994). 10.1063/1.466350
29. T. J. Martínez and E. A. Carter, J. Chem. Phys. 102, 7564 (1995). 10.1063/1.469088
30. T. J. Martínez and E. A. Carter, " Pseudospectral methods applied to the electron correlation problem.," in Modern Electronic Structure Theory, edited by, D. R. Yarkony, Advanced Series in Physical Chemistry Vol. 2 (World Scientific, Singapore, 1995), pp. 1132-1165.
31. G. Reynolds, T. J. Martínez, and E. A. Carter, J. Chem. Phys. 105, 6455 (1996). 10.1063/1.472495
32. R. A. Friesner, J. Phys. Chem. A 103, 1913 (1999). 10.1021/jp9825157
33. C. Ko, D. K. Malick, D. A. Braden, R. A. Friesner, and T. J. Martínez, J. Chem. Phys. 128, 104103 (2008). 10.1063/1.2834222
34. F. Neese, F. Wennmohs, A. Hansen, and U. Becker, Chem. Phys. 356, 98 (2009). 10.1016/j.chemphys.2008.10.036
35. S. Kossmann and F. Neese, J. Chem. Theory Comput. 6, 2325 (2010). 10.1021/ct100199k
36. R. M. Parrish, E. G. Hohenstein, T. J. Martínez, and C. D. Sherrill, J. Chem. Phys. 137, 224106 (2012). 10.1063/1.4768233
37. S. Boys and P. Rajagopal, " Quantum calculations: Which are accumulative in accuracy, unrestricted in expansion functions, and economical in computation.," Advances in Quantum Chemistry (Academic Press, 1966), Vol. 2, pp. 1-24.
38. E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012). 10.1063/1.4732310
39. E. G. Hohenstein, R. M. Parrish, C. D. Sherrill, and T. J. Martínez, J. Chem. Phys. 137, 221101 (2012). 10.1063/1.4768241
40. J. L. Whitten, J. Chem. Phys. 58, 4496 (1973). 10.1063/1.1679012
41. B. I. Dunlap, J. W. D. Connolly, and J. R. Sabin, Int. J. Quantum Chem. 12, 81 (1977). 10.1002/qua.560120813
42. B. I. Dunlap, J. W. D. Connolly, and J. R. Sabin, J. Chem. Phys. 71, 3396 (1979). 10.1063/1.438728
43. O. Vahtras, J. Almlöf, and M. W. Feyereisen, Chem. Phys. Lett. 213, 514 (1993). 10.1016/0009-2614(93)89151-7
44. A. P. Rendell and T. J. Lee, J. Chem. Phys. 101, 400 (1994). 10.1063/1.468148
45. R. A. Kendall and H. A. Fruchtl, Theor. Chem. Acc. 97, 158 (1997). 10.1007/s002140050249
46. F. Weigend, Phys. Chem. Chem. Phys. 4, 4285 (2002). 10.1039/b204199p
47. N. H. F. Beebe and J. Linderberg, Int. J. Quantum Chem. 12, 683 (1977). 10.1002/qua.560120408
48. I. Roeggen and E. Wisloff-Nilssen, Chem. Phys. Lett. 132, 154 (1986). 10.1016/0009-2614(86)80099-9
49. H. Koch, A. S. de Meras, and T. B. Pedersen, J. Chem. Phys. 118, 9481 (2003). 10.1063/1.1578621
50. F. Aquilante, T. B. Pedersen, and R. Lindh, J. Chem. Phys. 126, 194106 (2007). 10.1063/1.2736701
51. F. Aquilante, L. Gagliardi, T. B. Pedersen, and R. Lindh, J. Chem. Phys. 130, 154107 (2009). 10.1063/1.3116784
52. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry (McGraw Hill, New York, 1982).
53. E. G. Hohenstein, S. I. L. Kokkila, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 138, 124111 (2013). 10.1063/1.4795514
54. Z. Bačić and J. C. Light, Annu. Rev. Phys. Chem. 40, 469 (1989). 10.1146/annurev.pc.40.100189.002345
55. J. C. Light and T. Carrington, Adv. Chem. Phys. 114, 263 (2000). 10.1002/9780470141731.ch4
56. D. O. Harris, G. G. Engerholm, and W. D. Gwinn, J. Chem. Phys. 43, 1515 (1965). 10.1063/1.1696963
57. A. S. Dickinson and P. R. Certain, J. Chem. Phys. 49, 4209 (1968). 10.1063/1.1670738
58. J. Lill, G. Parker, and J. Light, Chem. Phys. Lett. 89, 483 (1982). 10.1016/0009-2614(82)83051-0
59. R. W. Heather and J. C. Light, J. Chem. Phys. 79, 147 (1983). 10.1063/1.445574
60. J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985). 10.1063/1.448462
61. D. T. Colbert and W. H. Miller, J. Chem. Phys. 96, 1982 (1992). 10.1063/1.462100
62. R. Dawes and T. Carrington, J. Chem. Phys. 121, 726 (2004). 10.1063/1.1758941
63. M. R. Wall, T. Dieckmann, J. Feigon, and D. Neuhauser, Chem. Phys. Lett. 291, 465 (1998). 10.1016/S0009-2614(98)00613-7
64. B. Poirier, Phys. Rev. A 56, 120 (1997). 10.1103/PhysRevA.56.120
65. B. Poirier and W. H. Miller, Chem. Phys. Lett. 265, 77 (1997). 10.1016/S0009-2614(96)01408-X
66. B. Poirier, J. Chem. Phys. 108, 5216 (1998). 10.1063/1.475958
67. F. Gygi, J.-L. Fattebert, and E. Schwegler, Comput. Phys. Commun. 155, 1 (2003). 10.1016/S0010-4655(03)00315-1
68. R. Dawes and T. Carrington, J. Chem. Phys. 122, 134101 (2005). 10.1063/1.1863935
69. R. Dawes and T. Carrington, J. Chem. Phys. 124, 054102 (2006). 10.1063/1.2162168
70. G. Avila and J. Tucker Carrington, J. Chem. Phys. 131, 174103 (2009). 10.1063/1.3246593
71. G. H. Golub and J. H. Welsch, Math. Comput. 23, 221 (1969). 10.1090/S0025-5718-69-99647-1
72. D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson, Upper Saddle River, NJ, 2005).
73. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York, 1964).
74. V. I. Lebedev and D. N. Laikov, Dokl. Math. 59, 477 (1999).
75. R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, Chem. Phys. Lett. 257, 213 (1996). 10.1016/0009-2614(96)00600-8
76. F. Weigend, A. Köhn, and C. Hättig, J. Chem. Phys. 116, 3175 (2002). 10.1063/1.1445115
77. C. G. J. Jacobi, J. Reine Angew. Math. 1846, 51 (1846). 10.1515/crll.1846.30.51
78. A. Bunse-Gerstner, R. Byers, and V. Mehrmann, SIAM J. Matrix Anal. Appl. 14, 927 (1993). 10.1137/0614062
79. J.-F. Cardoso and A. Souloumiac, SIAM J. Matrix Anal. Appl. 17, 161 (1996). 10.1137/S0895479893259546
80. J. M. Turney, A. C. Simmonett, R. M. Parrish, E. G. Hohenstein, F. A. Evangelista, J. T. Fermann, B. J. Mintz, L. A. Burns, J. J. Wilke, M. L. Abrams, N. J. Russ, M. L. Leininger, C. L. Janssen, E. T. Seidl, W. D. Allen, H. F. Schaefer, R. A. King, E. F. Valeev, C. D. Sherrill, and T. D. Crawford, WIREs Comput. Mol. Sci. 2, 556-565 (2012). 10.1002/wcms.93
81. B. G. Johnson, P. M. Gill, and J. A. Pople, Chem. Phys. Lett. 220, 377 (1994). 10.1016/0009-2614(94)00199-5
82. See supplementary material at http://dx.doi.org/10.1063/1.4802773 E-JCPSA6-138-023317 for detailed energies, grids, and geometries of benchmark molecules, as well as multiple views of grids discussed in the text.
83. T. H. Dunning, J. Chem. Phys. 90, 1007 (1989). 10.1063/1.456153