Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations

Journal of Chemical Physics

Volumn 122, Issue 3, 2005, Pages

  Neese, Frank ^a  

^a MAX PLANCK INSTITUTE FOR CHEMICAL ENERGY CONVERSION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COULOMB TERMS; NUCLEAR CHARGE MODEL; SPIN-ORBIT COUPLING; SPIN-ORBIT MEAN-FIELD (SOMF) METHOD;

APPROXIMATION THEORY; CORRELATION METHODS; ELECTRONS; PROBABILITY DENSITY FUNCTION; TENSORS;

QUANTUM THEORY;

EID: 22944473686     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1829047     Document Type: Article

References (113)

1. M. Kaupp, V. G. Malkin, and O. L. Malkina, in Encyclopedia of Computational Chemistry, edited by P. v. R. Schleyer, N. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer III, and P. R. Schreiner (Wiley, Chichester, 1998).
2. A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions (Clarendon, Oxford, 1970).
3. J. S. Griffith, The Theory of Transition Metal Ions (Cambridge University Press, Cambridge, 1964).
4. F. Neese and E. I. Solomon, in Magnetoscience-From Molecules to Materials edited by M. Drillon and J. S. Miller (Wiley, New York, 2003), Vol. 4, p. 345.
5. S. D. Peyerimhoff, in Encyclopedia Computation Chemistry, edited by P. v. R. Schleyer, N. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer III, and P. R. Schreiner (Wiley, Chichester, 1998), p. 2646.
6. F. Neese and E. I. Solomon, Inorg. Chem. 38, 1847 (1999).
7. O. Kahn, Molecular Magnetism (VCH, New York, 1993).
8. H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 1957).
9. G. Breit, Phys. Rev. 34, 553 (1929);
10. 36, 363 (1930);
11. 39, 616 (1932).
12. J. C. Slater, The Quantum Theory of Atomic Structure (McGraw-Hill, New York, 1960), Vol. 2.
13. M. Blume and R. E. Watson, Proc. R. Soc. London, Ser. A 270, 127 (1962).
14. M. Blume and R. E. Watson, Proc. R. Soc. London, Ser. A 271, 565 (1963);
15. M. Blume, A. J. Freeman, and R. E. Watson, Phys. Rev. A 134, 320 (1964).
16. H. Horie, Prog. Theor. Phys. 10, 296 (1953).
17. J. P. Elliot, Proc. R. Soc. London, Ser. A 218, 345 (1953).
18. E. U. Condon and G. H. Shortly, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1963).
19. R. Pasternak and G. Wagniere, J. Comput. Chem. 2, 347 (1981);
20. R. Manne and M. C. Zerner, Int. J. Quantum Chem., Symp. 19, 165 (1986);
21. M. Kotzian, N. Rösch, and M. C. Zerner, 25, 545 (1991);
22. M. Böckmann, M. Klessinger, and M. C. Zerner, J. Phys. Chem. 100, 10570 (1996);
23. F. Neese and E. I. Solomon, Inorg. Chem. 37, 6568 (1998);
24. Y. H. Hsiao and M. C. Zerner, Int. J. Quantum Chem. 75, 577 (1999);
25. J. Mählmann and M. Klessinger, 77, 446 (2000);
26. F. Neese, 83, 104 (2001).
27. S. Koseki, M. S. Gordon, M. W. Schmidt, and N. Matsunaga, J. Phys. Chem. 99, 12764 (1995);
28. S. Koseki, M. W. Schmidt, and M. S. Gordon, 96, 10768 (1992);
29. J. Phys. Chem. A 102, 10430 (1998).
30. B. A. Hess and C. M. Marian, in Computational Molecular Spectroscopy, edited by P. Jensen and P. R. Bunker (Wiley, New York, 2000), p. 169ff.
31. Y. S. Lee, W. C. Ermler, and K. S. Pitzer, J. Chem. Phys. 67, 5861 (1977);
32. R. M. Pitzer and N. W. Winter, 89, 446 (1988);
33. L. Pacios and J. Christiansen, 82, 2664 (1985);
34. P. Hafner and W. H. E. Schwarz, J. Phys. B 11, 217 (1977);
35. D. G. Fedorov and M. Klobukowski, Chem. Phys. Lett. 360, 223 (2002).
36. T. E. H. Walker and W. G. Richards, J. Chem. Phys. 52, 1311 (1970);
37. P. W. Abegg and T.-K. Ha, Mol. Phys. 27, 763 (1974);
38. J. Breulet, J. Comput. Chem. 2, 244 (1981).
39. D. G. Fedorov and M. S. Gordon, J. Chem. Phys. 112, 5611 (1999).
40. O. Vahtras, H. Ågren, P. Jørgensen, H. J. A. Jensen, T. Helgaker, and J. Olsen, J. Chem. Phys. 96, 2118 (1992).
41. O. Vahtras, H. Ågren, P. Jørgensen, H. J. A. Jensen, S. B. Padkjaer, and T. Helgaker, J. Chem. Phys. 96, 6120 (1992);
42. H. Ågren, O. Vahtras, and B. Minaev, Adv. Quantum Chem. 27, 71 (1996);
43. J. Vaara, K. Ruud, O. Vahtras, H. Ågren, and J. Jokisaari, J. Chem. Phys. 109, 1212 (1998);
44. J. Vaara, K. Ruud, and O. Vahtras, 111, 2900 (1999).
45. M. Engström, B. Minaev, O. Vahtras, and H. Ågren, Chem. Phys. 237, 149 (1998).
46. B. A. Hess, C. M. Marian, and S. D. Peyerimhoff, in Modern Electronic Structure Theory, edited by D. Yarkony (World Scientific, Singapore, 1995).
47. M. Peric, B. Engels, and S. D. Peyerimhoff, in Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, edited by S. R. Langhoff (Kluwer Academic, Amsterdam, 1995), p. 261.
48. C. M. Marian, in Reviews in Computational Chemistry edited by K. B. Lipkowitz and D. B. Boyd (Wiley-VCH, New York, 2001), Vol. 17.
49. F. Rakowitz and C. M. Marian, Chem. Phys. Lett. 257, 157 (1996);
50. R. J. Buenker, A. B. Alekseyev, H.-P. Liebermann, R. Lingott, and G. Hirsch, J. Chem. Phys. 108, 3400 (1998).
51. B. A. Hess, C. M. Marian, U. Wahlgren, and O. Gropen, Chem. Phys. Lett. 251, 365 (1996).
52. C. M. Marian and U. Wahlgren, Chem. Phys. Lett. 251, 357 (1996).
53. B. Schimmelpfennig, L. Maron, U. Wahlgren, C. Teichteil, H. Fagerli, and O. Gropen, Chem. Phys. Lett. 286, 261 (1998);
54. 286, 267 (1998);
55. O. Launilla, B. Schimmelpfennig, H. Fagerli, O. Gropen, A. G. Taklif, and U. Wahlgren, J. Mol. Spectrosc. 186, 131 (1997);
56. U. Wahlgren, M. Sjøvoll, H. Fagerli, O. Gropen, and B. Schimmelpfennig, Theor. Chem. Acc. 97, 324 (1997).
57. A. Berning, M. Schweizer, H. J. Werner, P. J. Knowles, and P. Palmieri, Mol. Phys. 98, 1823 (2000).
58. B. Schimmelpfennig, AMFI-An Atomic Mean Field Integral Program (University of Stockholm, Stockholm, Sweden, 1996).
59. O. L. Malkina, B. Schimmelpfennig, M. Kaupp, B. A. Hess, P. Chandra, U. Wahlgren, and V. G. Malkin, Chem. Phys. Lett. 296, 93 (1998);
60. K. Ruud, B. Schimmelpfennig, and H. Ågren, 310, 215 (1999);
61. L. Gagliardi, B. Schimmelpfennig, L. Maron, U. Wahlgren, and A. Willets, 344, 207 (2001);
62. P. Å. Malmquvist, B. O. Roos, and B. Schimmelpfennig, 357, 230 (2002);
63. M. Kleinschmidt, J. Tatchen, and C. M. Marian, J. Comput. Chem. 23, 824 (2002);
64. A. V. Arbuznikov, J. Vaara, and M. Kaupp, J. Chem. Phys. 120, 2127 (2002).
65. O. L. Malkina, J. Vaara, B. Schimmelpfenning, M. Munzarová, V. Malkin, and M. Kaupp, J. Am. Chem. Soc. 122, 9206 (2000).
66. Z. Rinkevicius, L. Telyatnyk, P. Salek, O. Vahtras, and H. Ågren, J. Chem. Phys. 119, 10489 (2003).
67. T. Nakajima, T. Yanai, and K. Hirao, J. Comput. Chem. 25, 847 (2002);
68. F. Wang and L. Li, 23, 920 (2002);
69. M. Barysz and A. J. Sadlej, J. Chem. Phys. 116, 2696 (2002);
70. W. Klopper, J. van Lenthe, and A. C. Hennum, 113, 9957 (2000);
71. S. Faas, J. van Lenthe, A. C. Hennum, and J. G. Snijders, 113, 4052 (2000);
72. M. Mayer, S. Kröger, and N. Rösch, 115, 4411 (2001);
73. C. van Wüllen, J. Comput. Chem. 23, 779 (2002).
74. E. van Lenthe, J. G. Snijders, and E. J. Baerends, J. Chem. Phys. 105, 6505 (1996).
75. W. Pauli, Z. Phys. 43, 601 (1927).
76. G. Schreckenbach and T. Ziegler, J. Phys. Chem. A 101, 3388 (1997).
77. M. R. Pederson and S. N. Khanna, Phys. Rev. B 60, 9566 (1999).
78. S. Patchkovskii and G. Schreckenbach, in Calculation of NMR and EPR Parameters, edited by M. Kaupp, M. Bühl, and V. Malkin (Wiley-VCH, Weinheim, 2004), p. 505.
79. C. J. Pickard and F. Mauri, Phys. Rev. Lett. 88, 086403 (2002).
80. F. Neese, ORCA-An ab initio, Density Functional and Semiempirical Program Package, Version 2.4, Revision 10 (Max Planck Institut für Bioanorganische Chemie, Mülheim, 2004).
81. T. Helgaker and P. R. Taylor, in Modern Electronic Structure Theory, edited by D. R. Yarkony (World Scientific, Singapore, 1995), p. 725.
82. B. Schimmelpfennig (private communication).
83. J. Tatchen, Diploma thesis, Universität Bonn, 1999.
84. J. Tatchen and C. M. Marian, Chem. Phys. Lett. 313, 351 (1999).
85. J. L. Whitten, J. Chem. Phys. 58, 4496 (1973);
86. B. I. Dunlap, J. W. D. Connolly, and J. R. Sabin, 71, 3396 (1979);
87. O. Vahtras, J. Almlüf, and M. W. Feyereisen, Chem. Phys. Lett. 213, 514 (1993).
88. K. Eichkorn, F. Weigend, O. Treutler, and R. Ahlrichs, Theor. Chem. Acc. 97, 119 (1997);
89. K. Eichkorn, O. Treutler, H. Öhm, M. Häser, and R. Ahlrichs, Chem. Phys. Lett. 240, 283 (1995).
90. C. A. White and M. Head-Gordon, J. Chem. Phys. 104, 2620 (1996);
91. Y. Shao and M. Head-Gordon, Chem. Phys. Lett. 323, 415 (2000);
92. F. Neese, J. Comput. Chem. 24, 1740 (2003).
93. F. Neese and G. Olbrich, Chem. Phys. Lett. 362, 170 (2002).
94. F. Neese, J. Chem. Phys. 115, 11080 (2001).
95. A. D. Becke, Phys. Rev. A 38, 3098 (1988);
96. J. P. Perdew, Phys. Rev. B 33, 8822 (1986).
97. F. Weigend, M. Häser, H. Patzelt, and R. Ahlrichs, Chem. Phys. Lett. 294, 143 (1998);
98. F. Weigend, A. Köhn, and C. Hättig, J. Chem. Phys. 116, 3175 (2002).
99. K. K. Stavrev and M. C. Zerner, Int. J. Quantum Chem. 65, 877 (1997).
100. E. Schwegler and M. Challacombe, J. Chem. Phys. 106, 5526 (1997);
101. C. Ochsenfeld, 109, 1663 (1998).
102. F. Neese, J. Phys. Chem. A 105, 4290 (2001);
103. F. Neese, J. Chem. Phys. 118, 3939 (2003);
104. F. Neese, Mag. Res. Chem. 42, S187 (2004).
105. F. Neese, Chem. Phys. Lett. 380, 721 (2003).
106. S. Brownridge, F. Grein, J. Tatchen, M. Kleinschmidt, and C. M. Marian, J. Chem. Phys. 118, 9552 (2003).
107. J. Gauss and F. Neese (unpublished).
108. J. Bendix, M. Brorson, and C. E. Schäffer, Inorg. Chem. 32, 2838 (1993).
109. The exponents of the s-type Gaussians in the fit set were determined as described in the DeMon2k users manual http://www.deMon-software.com/. One steeper s function was added by doubling the exponent of the steepest s function in the original fit set.
110. K. G. Dyall and E. van Lenthe, J. Chem. Phys. 111, 1366 (1999).
111. R. Ditchfield, Mol. Phys. 27, 789 (1974).
112. A. Schäfer, H. Horn, and R. Ahlrichs, J. Chem. Phys. 97, 2571 (1992).
113. S. Patchkovskii and T. Ziegler, J. Phys. Chem. A 105, 5490 (2001).