A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

Journal of Chemical Physics

Volumn 139, Issue 23, 2013, Pages

  West, Aaron C ^a   Schmidt, Michael W ^a   Gordon, Mark S ^a   Ruedenberg, Klaus ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; MOLECULAR ORBITALS; MOLECULAR PHYSICS; MOLECULES; QUANTUM CHEMISTRY;

ATOMIC POPULATION; COMPREHENSIVE ANALYSIS; ELECTRONIC WAVE FUNCTIONS; HARTREE-FOCK WAVE FUNCTION; INTER-ATOMIC BONDING; LOCALIZATION METHOD; LOCALIZED MOLECULAR ORBITALS; LOCALIZED ORBITALS;

WAVE FUNCTIONS;

EID: 84901783324     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4840776     Document Type: Article

References (94)

1. See, e.g., K. Ruedenberg and W. H. E. Schwarz, " Three millennia of atoms and molecules," Pioneers of Quantum Chemistry, ACS Symposium Series Vol. 1122, edited by E. T. Strom, A. K. Wilson (ACS, Washington DC, 2013).
2. C. A. Coulson, Rev. Mod. Phys. 32, 170 (1960). 10.1103/RevModPhys.32.170
3. K. Ruedenberg, Rev. Mod. Phys. 34, 326 (1962). 10.1103/RevModPhys.34.326
4. K. Fukui, T. Yonezawa, and H. Shingu, J. Chem. Phys. 20, 722 (1952). 10.1063/1.1700523
5. R. B. Woodward and R. Hoffmann, J. Am. Chem. Soc. 87, 395 (1965). 10.1021/ja01080a054
6. R. S. Mulliken, J. Chem. Phys. 36, 3428 (1962). 10.1063/1.1732476
7. W. H. Adams, J. Chem. Phys. 37, 2009 (1962). 10.1063/1.1733420
8. E. R. Davidson, J. Chem. Phys. 46, 3320 (1967). 10.1063/1.1841219
9. P. W. Anderson, Phys. Rev. Lett. 21, 13 (1968); 10.1103/PhysRevLett.21.13
10. J. D. Weeks, P. W. Anderson, and A. G. H. Davidson, J. Chem. Phys. 58, 1388 (1973). 10.1063/1.1679371
11. K. R. Roby, Mol. Phys. 27, 81 (1974). 10.1080/00268977400100071
12. R. Heinzmann and R. Ahlrichs, Theor. Chim. Acta 42, 33 (1976); 10.1007/BF00548289
13. C. Ehrhardt and R. Ahlrichs, Theor. Chim. Acta 68, 231 (1985). 10.1007/BF00526774
14. J. P. Foster and F. Weinhold, J. Am. Chem. Soc. 102, 7211 (1980); 10.1021/ja00544a007
15. A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. 83, 735 (1985); 10.1063/1.449486
16. A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev. 88, 899 (1988). 10.1021/cr00088a005
17. D. Sanchez-Portal, E. Artacho, and J. M. Soler, Phys. Condens. Matter 8, 3859 (1996). 10.1088/0953-8984/8/21/012
18. I. Mayer, Chem. Phys. Lett. 242, 499 (1995); 10.1016/0009-2614(95)00748-S
19. I. Mayer, J. Phys. Chem. 100, 6249 (1996). 10.1021/jp952779i
20. J. Cioslowski and A. Liashenko, J. Chem. Phys. 108, 4405 (1998). 10.1063/1.475853
21. K. Ruedenberg, M. W. Schmidt, M. M. Gilbert, and S. T. Elbert, Chem. Phys. 71, 41 (1982); 10.1016/0301-0104(82)87004-3
22. K. Ruedenberg, M. W. Schmidt, and M. Gilbert, Chem. Phys. 71, 51 (1982); 10.1016/0301-0104(82)87005-5
23. K. Ruedenberg, M. W. Schmidt, M. Gilbert, and S. T. Elbert, Chem. Phys. 71, 65 (1982). 10.1016/0301-0104(82)87006-7
24. T. R. Cundari and M. S. Gordon, J. Am. Chem. Soc. 113, 5231 (1991); 10.1021/ja00014a015
25. T. R. Cundari and M. S. Gordon, J. Am. Chem. Soc. 114, 539 (1992); 10.1021/ja00028a022
26. T. R. Cundari and M. S. Gordon, J. Phys. Chem. 96, 631 (1992); 10.1021/j100181a023
27. N. Matsunaga, T. R. Cundari, M. W. Schmidt, and M. S. Gordon, Theor. Chim. Acta 83, 57 (1992); 10.1007/BF01113243
28. T. L. Windus and M. S. Gordon, J. Am. Chem. Soc. 114, 9559 (1992); 10.1021/ja00050a040
29. M. S. Gordon and M. W. Schmidt, J. Am. Chem. Soc. 115, 7486 (1993); 10.1021/ja00069a056
30. M. S. Gordon and T. R. Cundari, Coord. Chem. Rev. 147, 87 (1996); 10.1016/0010-8545(95)01133-1
31. N. Takagi, M. W. Schmidt, and S. Nagase, Organometallics 20, 1646 (2001); 10.1021/om0009841
32. M. W. Schmidt, J. A. Boatz, and M. S. Gordon, J. Chem. Phys. A 109, 7285 (2005); 10.1021/jp058149q
33. D. D. Zorn, J. A. Boatz, and M. S. Gordon, J. Phys. Chem. B 110, 11110 (2006); 10.1021/jp060854r
34. T. Zeng, D. G. Fedorov, M. W. Schmidt, and M. Klobukowski, J. Chem. Theory Comput. 7, 2864 (2011). 10.1021/ct200457q
35. J. Ivanic, G. J. Atchity, and K. Ruedenberg, Theor. Chem. Acc. 120, 281 (2008); 10.1007/s00214-007-0308-4
36. J. Ivanic and K. Ruedenberg, Theor. Chem. Acc. 120, 295 (2008). 10.1007/s00214-007-0313-7
37. M. S. Lee and M. Head-Gordon, J. Chem. Phys. 107, 9085 (1997); 10.1063/1.475199
38. M. S. Lee and M. Head-Gordon, Int. J. Quantum Chem. 76, 169 (2000). 10.1002/(SICI)1097-461X(2000)76:2<169::AID-QUA7>3.0.CO;2-G
39. W. C. Lu, C. Z. Wang, M. W. Schmidt, L. Bytautas, K. M. Ho, and K. Ruedenberg, J. Chem. Phys. 120, 2629 (2004); 10.1063/1.1638731
40. W. C. Lu, C. Z. Wang, M. W. Schmidt, L. Bytautas, K. M. Ho, and K. Ruedenberg, J. Chem. Phys. 120, 2638 (2004); 10.1063/1.1638732
41. W. C. Lu, C. Z. Wang, K. Ruedenberg, and K. M. Ho, Phys. Rev. B 72, 205123 (2005). In these papers the quasi-atomic orbitals were called quasi-atomic minimal-basis-set orbitals (QUAMBOs). 10.1103/PhysRevB.72.205123
42. M. W. Schmidt, T. Windus, and E. Hull, " Hartree-Fock valence virtual orbitals: An unambiguous quantification of the LUMO concept," (unpublished).
43. S. Iwata, Chem. Phys. Lett. 83, 134 (1981). 10.1016/0009-2614(81)80305-3
44. G. Knizia, J. Chem. Theory Comput. 9 (11), 4834-4843 (2013). 10.1021/ct400687b
45. D. N. Laikov, Int. J. Quantum Chem. 111, 2851 (2011). 10.1002/qua.22767
46. J. E. Subotnik, A. D. Dutoi, and M. Head-Gordon, J. Chem. Phys. 123, 114108 (2005). 10.1063/1.2033687
47. The word "stock" is being used with the meaning it has in horticulture, notably in arboriculture and viticulture. See, e.g., K. Mudge, J. Janick, S. Scofield, and E. E. Goldschmidt, " A History of Grafting," Horticult. Rev. 35, 9 (2009). 10.1002/9780470593776.ch9
48. See, e.g., K. Ruedenberg, M. W. Schmidt, and J. Ivanic, The Chemical Bond, Chap. 1 edited by G. Frenking and S. Shaik (Wiley and Sons, in press).
49. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, J. Comput. Chem. 14, 1347 (1993); 10.1002/jcc.540141112
50. M. S. Gordon and M. W. Schmidt, Theory and Applications of Computational Chemistry, the first forty years, edited by C. E. Dykstra, G. Frenking, K. S. Kim, and G. E. Scuseria (Elsevier, Amsterdam, 2005), pp. 1167-1189.
51. The GAMESS program is available from http://www.msg.chem.iastate.edu/GAMESS/GAMESS.html.
52. W. C. Lu, C. Z. Wang, T. L. Chan, K. Ruedenberg, and K. M. Ho, Phys. Rev. B 70, 041101 (R) (2004). 10.1103/PhysRevB.70.041101
53. In the current implementation, atomic open-shell SCF orbitals are used instead, see Ref. 22.
54. K. Andersson, P. A. Malmqvist, B. O. Roos, A. J. Sadlej, and K. Wolinski, J. Phys. Chem. 94, 5483 (1990). 10.1021/j100377a012
55. For H, C, N, O: T. H. Dunning, J. Chem. Phys. 90, 1007 (1989); 10.1063/1.456153
56. R. A. Kendall, T. H. Dunning, and R. J. Harrison, J. Chem. Phys. 96, 6796 (1992); 10.1063/1.462569
57. For Na: B. P. Prascher, D. E. Woon, K. A. Peterson, and T. H. Dunning, Theor. Chem. Acc. 128, 69 (2011); 10.1007/s00214-010-0764-0
58. For Si, S, Cl: K. A. Peterson, and T. H. Dunning, J. Chem. Phys. 117, 10548 (2002); 10.1063/1.1520138
59. For As: A. K. Wilson, D. E. Woon, K. A. Peterson, T. H. Dunning, J. Chem. Phys. 110, 7667 (1999); 10.1063/1.478678
60. For Mn: N. B. Balabanov, K. A. Peterson, J. Chem. Phys. 123, 064107 (2005). 10.1063/1.1998907
61. C. A. Coulson, H. C. Longuet-Higgins, Proc. Roy. Soc. London, Ser. A 191, 39 (1947); 10.1098/rspa.1947.0102
62. B. H. Chirgwin, Phys. Rev. 107, 1013 (1957). We consider the name "population bond order matrix" more appropriate than the name "charge bond order matrix." 10.1103/PhysRev.107.1013
63. F. Hund, Z. Phys. 73, 1 (1932);
64. F. Hund, Z. Phys. 73, 565 (1932). 10.1007/BF01342005
65. C. A. Coulson, Trans. Faraday Soc. 38, 433 (1942). 10.1039/tf9423800433
66. J. E. Lennard-Jones, Proc. R. Soc. London, Ser. A 198 (1), 14 (1949). 10.1098/rspa.1949.0084
67. G. G. Hall and J. E. Lennard-Jones, Proc. R. Soc. London, Ser. A 202, 155 (1950); 10.1098/rspa.1950.0091
68. G. G. Hall and J. E. Lennard-Jones, Proc. R. Soc. London, Ser. A 205, 357 (1951); 10.1098/rspa.1951.0034
69. G. G. Hall, Rep. Prog. Phys. 22, 1 (1959). 10.1088/0034-4885/22/1/301
70. J. E. Lennard-Jones and J. A. Pople, Proc. R. Soc. London, Ser. A 202, 166 (1950); 10.1098/rspa.1950.0092
71. J. E. Lennard-Jones and J. A. Pople, Proc. R. Soc. London, Ser. A 210, 190 (1951) 10.1098/rspa.1951.0240
72. C. Edmiston and K. Ruedenberg, Rev. Mod. Phys. 35, 457 (1963); 10.1103/RevModPhys.35.457
73. (b) K. Ruedenberg in Istanbul Lectures on Quantum Chemistry, edited by O. Sinanoglu (Academic Press, 1965), Vol. 1, p. 85;
74. C. Edmiston and K. Ruedenberg, J. Chem. Phys. 43, S97-S115 (1965). 10.1063/1.1701520
75. L. Bytautas, J. Ivanic, and K. Ruedenberg, J. Chem. Phys. 119, 8217 (2003). In this investigation, the localized occupied and valence-virtual were determined by the Edmiston-Ruedenberg localization. 10.1063/1.1610434
76. J. Pipek and P. G. Mezey, J. Chem. Phys. 90, 4916 (1989). 10.1063/1.456588
77. S. F. Boys, in Quantum Theory of Atoms, Solids and the Solid State, edited by P. O. Löwdin (Academic Press, New York, 1966), p. 253.
78. W. von Niessen, J. Chem. Phys. 56, 4290 (1972). 10.1063/1.1677859
79. 2 criterion introduced in Ref. 41(a) is incorrectly attributed to Ref. 49. 10.1063/1.1681683
80. R. C. Raffenetti, K. Ruedenberg, C. L. Janssen, and H. F. Schaefer, Theor. Chim. Acta 86, 149 (1993). 10.1007/BF01113521
81. J. E. Subotnik, Y. Shao, W. Z. Liang, and M. Head-Gordon, J. Chem. Phys. 121, 9220 (2004). 10.1063/1.1790971
82. J. M. Foster and S. F. Boys, Rev. Mod. Phys. 32, 300 (1960). 10.1103/RevModPhys.32.300
83. B. Jansik, S. Host, K. Kristensen, and P. Jørgensen, J. Chem. Phys. 134, 194104 (2011); 10.1063/1.3590361
84. I. M. Hoyvik, B. Jansik, and P. Jørgensen, J. Comput. Chem. 34, 1456 (2013). This paper also contains many further references regarding work on external orbitals. 10.1002/jcc.23281
85. S. Saebo and P. Pulay, Ann. Rev. Phys. Chem. 44, 213 (1993). 10.1146/annurev.pc.44.100193.001241
86. M. Schütz, G. Hetzer, and H. J. Werner, J. Chem. Phys. 111, 5691 (1999); 10.1063/1.479957
87. M. Schütz and H. J. Werner, J. Chem. Phys. 114, 661 (2001). 10.1063/1.1330207
88. G. Das and A. C. Wahl, J. Chem. Phys. 56, 1769 (1972). 10.1063/1.1677438
89. J. L. Whitten, J. Chem. Phys. 56, 5458 (1972). 10.1063/1.1677062
90. B. C. Carlson and J. M. Keller, Phys. Rev. 105, 102 (1957). 10.1103/PhysRev.105.102
91. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins Univ. Press, Baltimore, 2012);
92. Regarding the history of the SVD, see G. W. Stewart, SIAM Rev. 35, 551 (1993). 10.1137/1035134
93. A. T. Amos and G. G. Hall, Proc. R. Soc. London Ser. A 263, 483 (1961). 10.1098/rspa.1961.0175
94. H. F. King, R. E. Stanton, H. Kim, R. E. Wyatt, and R. G. Parr, J. Chem. Phys. 47, 1936 (1967). 10.1063/1.1712221