Density functional calculations of electronic g-tensors using spin-orbit pseudopotentials and mean-field all-electron spin-orbit operators

Journal of the American Chemical Society

Volumn 122, Issue 38, 2000, Pages 9206-9218

  Malkina, Olga L ^a   Vaara, Juha ^b,d   Schimmelpfennig, Bernd ^b,e   Munzarová, Markéta ^b,f   Malkin, Vladimir G ^a   Kaupp, Martin ^c  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

^b MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

^c UNIVERSITY OF WÜRZBURG   (Germany)

^d UNIVERSITY OF HELSINKI   (Finland)

^e ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^f MASARYK UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

AROMATIC POLYAMIDE; METAL COMPLEX;

ANALYTIC METHOD; ARTICLE; ATOM; CALCULATION; DENSITY; ELECTRON; ELECTRON SPIN RESONANCE; VALIDATION PROCESS;

EID: 0034721434     PISSN: 00027863     EISSN: None     Source Type: Journal    
DOI: 10.1021/ja000984s     Document Type: Article

References (82)

1. See, for example: (a) Möbius, K. In Biological Magnetic Resonance; Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York, 1993; Vol. 13, pp 253-274. (b) Prisner, T. F. In Advances in Magnetic and Optical Resonance; Warren, W., Ed.; Academic Press: New York, 1997; Vol. 20, pp 245-299.
2. See, for example: (a) Möbius, K. In Biological Magnetic Resonance; Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York, 1993; Vol. 13, pp 253-274. (b) Prisner, T. F. In Advances in Magnetic and Optical Resonance; Warren, W., Ed.; Academic Press: New York, 1997; Vol. 20, pp 245-299.
3. Engels, B.; Eriksson, L. A.; Lunell, S. Adv. Quantum Chem. 1996, 27, 297.
4. See, for example: Angstl, R. Chem. Phys. 1989, 132, 435. Plakhutin, B. N.; Zhidomirov, G. M.; Zamaraev, K. I. J. Struct. Chem. 1983, 24, 3.
5. See, for example: Angstl, R. Chem. Phys. 1989, 132, 435. Plakhutin, B. N.; Zhidomirov, G. M.; Zamaraev, K. I. J. Struct. Chem. 1983, 24, 3.
6. See, for example: Un, S.; Atta, M.; Fontcave, M.; Rutherford, A. W. J. Am. Chem. Soc. 1995, 117, 10713.
7. For DFT calculations of g-tensors with semiempirical SO operators cf., for example: Geurts, P. J. M.; Bouten, P. C. P.; van der Avoird, A. J. Chem. Phys. 1980, 73, 1306. Belanzoni, P.; Baerends, E. J.; van Asselt, S.; Langewen, P. B. J. Phys. Chem. 1995, 99, 13094. Swann, J.; Westmoreland, T. D. Inorg. Chem. 1997, 36, 5348.
8. For DFT calculations of g-tensors with semiempirical SO operators cf., for example: Geurts, P. J. M.; Bouten, P. C. P.; van der Avoird, A. J. Chem. Phys. 1980, 73, 1306. Belanzoni, P.; Baerends, E. J.; van Asselt, S.; Langewen, P. B. J. Phys. Chem. 1995, 99, 13094. Swann, J.; Westmoreland, T. D. Inorg. Chem. 1997, 36, 5348.
9. For DFT calculations of g-tensors with semiempirical SO operators cf., for example: Geurts, P. J. M.; Bouten, P. C. P.; van der Avoird, A. J. Chem. Phys. 1980, 73, 1306. Belanzoni, P.; Baerends, E. J.; van Asselt, S.; Langewen, P. B. J. Phys. Chem. 1995, 99, 13094. Swann, J.; Westmoreland, T. D. Inorg. Chem. 1997, 36, 5348.
10. Lushington, G. H.; Grein, F. Theor. Chim. Acta 1996, 93, 259. Bruna, P.; Lushington, G. H.; Grein, F. Chem. Phys. 1997, 225, 1.
11. Lushington, G. H.; Grein, F. Theor. Chim. Acta 1996, 93, 259. Bruna, P.; Lushington, G. H.; Grein, F. Chem. Phys. 1997, 225, 1.
12. Lushington, G. H. Ph.D. Thesis, The University of New Brunswick, Canada, 1996.
13. Engström, M.; Minaev, B.; Vahtras, O.; Ågren, H. Chem. Phys. 1998, 237, 149. Vahtras, O.; Minaev, B.; Ågren, H. Chem. Phys. Lett. 1997, 281, 186.
14. Engström, M.; Minaev, B.; Vahtras, O.; Ågren, H. Chem. Phys. 1998, 237, 149. Vahtras, O.; Minaev, B.; Ågren, H. Chem. Phys. Lett. 1997, 281, 186.
15. Kaupp, M.; Malkina, O. L.; Malkin, V. G. In Encyclopedia of Computational Chemistry; Schleyer, P. v. R., Ed.; Wiley-Interscience: New York, 1998.
16. Bühl, M.; Kaupp, M.; Malkin, V. G.; Malkina, O. L. J. Comput. Chem. 1999, 20, 91.
17. Schreckenbach, G.; Ziegler, T. Theor. Chem. Acc. 1998, 2, 71.
18. Schreckenbach, G.; Ziegler, T. J. Phys. Chem. A 1997, 101, 3388.
19. van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597.
20. van Lenthe, E.; Wormer, P. E. S.; van der Avoird, A. J. Chem. Phys. 1997, 107, 2488.
21. Jayatilaka, D. J. Chem. Phys. 1998, 108, 7587.
22. (a) Salahub, D. R.; Fournier, R.; Mlynarski, P.; Papai, I.; St-Amant, A.; Ushio, J. In Density Functional Methods in Chemistry; Labanowski, J., Andzelm, J., Eds.; Springer: New York, 1991.
23. (b) St-Amant, A.; Salahub, D. R. Chem. Phys. Lett. 1990, 169, 387.
24. Malkin, V. G.; Malkina, O. L.; Eriksson, L. A.; Salahub, D. R. In Modern Density Functional Theory: A Tool for Chemistry, Seminario, J. M., Politzer, P., Eds.; Elsevier: Amsterdam, 1995; Vol. 2.
25. Malkina, O. L.; Schimmelpfennig, B.; Kaupp, M.; Hess, B A.; Chandra, P.; Wahlgren, U.; Malkin, V. G. Chem. Phys. Lett. 1998, 296, 93.
26. Vaara, J.; Malkina, O. L.; Stoll, H.; Malkin, V. G.; Kaupp, M. Submitted.
27. Schreckenbach, G. Ph.D. Thesis, The University of Calgary, Canada, 1996.
28. Harriman, J. E. Theoretical Foundations of Electron Spin Resonance; Academic Press: New York, 1978.
29. Malkin, V. G.; Malkina, O. L.; Casida, M. E.; Salahub, D. R. J. Am. Chem. Sec. 1994, 116, 5898.
30. A consistent and complete incorporation of spin-orbit coupling into a Kohn-Sham framework is far from trivial. Thus, for example, spin-other-orbit terms arise strictly only from relativistic contributions to the electron-electron interaction. Rather than resorting to relativistic exchange-correlation potentials, we have in this work preferred to incorporate spin-orbit coupling explicitly via suitably chosen and well-established perturbation operators (see text).
31. EAGLE is a code for the calculation of integrals of the Breit-Pauli SO Hamiltonian over molecular Cartesian Gaussian functions, written by P. Chandra and B. A. Hess.
32. Hess, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. Chem. Phys. Lett. 1996, 251, 365.
33. Schimmelpfennig, B. Atomic Spin-Orbit Mean-Field Integral Program; Stockholms Universitet, Sweden, 1996.
34. Pitzer, R. M.; Winter, N. W. J. Phys. Chem. 1988, 92, 3061.
35. Patchkovskii, S.; Ziegler T. J. Chem. Phys. 1999, 111, 5730.
36. Cornman, C. R.; Geiser-Bush, K. M., Rowley, S. P., Boyle, P. D. Inorg. Chem. 1997, 36, 6401.
37. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A. Jr.,; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998.
38. Becke, A. D. Phys. Rev. A 1988, 38, 3098.
39. Perdew, J. P. Phys. Rev. B 1986, 33, 8822.
40. Andrae, D.; Häuβermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1990, 77, 123.
41. Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866.
42. Nicklaβ, A.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1995, 102, 8942. Bergner, A.; Dolg, M.; Küchle, W.; Stoll, H.; Preuss H. Mol. Phys. 1993, 80, 1431. Dolg, M. Ph.D. Dissertation, Universität Stuttgart, Germany, 1989.
43. Nicklaβ, A.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1995, 102, 8942. Bergner, A.; Dolg, M.; Küchle, W.; Stoll, H.; Preuss H. Mol. Phys. 1993, 80, 1431. Dolg, M. Ph.D. Dissertation, Universität Stuttgart, Germany, 1989.
44. Nicklaβ, A.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1995, 102, 8942. Bergner, A.; Dolg, M.; Küchle, W.; Stoll, H.; Preuss H. Mol. Phys. 1993, 80, 1431. Dolg, M. Ph.D. Dissertation, Universität Stuttgart, Germany, 1989.
45. Kaupp, M.; Schleyer, P. v. R.; Stoll, H.; Preuss, H. J. Am. Chem. Soc. 1991, 113, 6012.
46. d-Type polarization functions have been taken from: Gaussian Basis Sets for Molecular Calculations, Huzinaga, S., Ed.; Elsevier: New York, 1984.
47. Godbout, N.; Salahub, D. R.; Andzelm J.; Wimmer, E. Can. J. Chem. 1992, 70, 560.
48. Munzarová, M.; Kaupp, M. J. Phys. Chem. A 1999, 103, 9966.
49. Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Chem. 1980, 58, 1200.
50. Perdew, J. P.; Wang, Y. Phys. Rev. B 1986, 33, 8800.
51. Perdew, J. P. Physica B 1992, 172, 1. Perdew, J. P. In Electronic Structure of Solids '91, Ziesche, P., Eschring, H., Eds.; Akademie Verlag: Berlin, 1991. Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244.
52. Perdew, J. P. Physica B 1992, 172, 1. Perdew, J. P. In Electronic Structure of Solids '91, Ziesche, P., Eschring, H., Eds.; Akademie Verlag: Berlin, 1991. Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244.
53. Perdew, J. P. Physica B 1992, 172, 1. Perdew, J. P. In Electronic Structure of Solids '91, Ziesche, P., Eschring, H., Eds.; Akademie Verlag: Berlin, 1991. Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244.
54. Kutzelnigg, W.; Fleischer, U.; Schindler, M. In NMR-Basic Principles and Progress; Diehl, P., Fluck, E., Günther, H.; Kosfeld, R., Eds.; Springer-Verlag: Heidelberg, 1990; Vol. 23, pp 165ff.
55. Edmiston, C.; Ruedenberg, K. Rev. Mod. Phys. 1963, 35, 457. Edmiston, C.; Ruedenberg, K. J. Chem. Phys. 1965, 43, 597. See also: Boys, S. F. In Quantum Theory of Atoms, Molecules and the Solid State; Löwdin, P.-O., Ed.; Academic Press: New York, 1966; p 253. This prodecure is often incorrectly attributed to Foster, S.; Boys, S. F. Rev. Mod. Phys. 1963, 35, 457.
56. Edmiston, C.; Ruedenberg, K. Rev. Mod. Phys. 1963, 35, 457. Edmiston, C.; Ruedenberg, K. J. Chem. Phys. 1965, 43, 597. See also: Boys, S. F. In Quantum Theory of Atoms, Molecules and the Solid State; Löwdin, P.-O., Ed.; Academic Press: New York, 1966; p 253. This prodecure is often incorrectly attributed to Foster, S.; Boys, S. F. Rev. Mod. Phys. 1963, 35, 457.
57. Edmiston, C.; Ruedenberg, K. Rev. Mod. Phys. 1963, 35, 457. Edmiston, C.; Ruedenberg, K. J. Chem. Phys. 1965, 43, 597. See also: Boys, S. F. In Quantum Theory of Atoms, Molecules and the Solid State; Löwdin, P.-O., Ed.; Academic Press: New York, 1966; p 253. This prodecure is often incorrectly attributed to Foster, S.; Boys, S. F. Rev. Mod. Phys. 1963, 35, 457.
58. Edmiston, C.; Ruedenberg, K. Rev. Mod. Phys. 1963, 35, 457. Edmiston, C.; Ruedenberg, K. J. Chem. Phys. 1965, 43, 597. See also: Boys, S. F. In Quantum Theory of Atoms, Molecules and the Solid State; Löwdin, P.-O., Ed.; Academic Press: New York, 1966; p 253. This prodecure is often incorrectly attributed to Foster, S.; Boys, S. F. Rev. Mod. Phys. 1963, 35, 457.
59. Pipek, J.; Mezey, P. G. J. Chem. Phys. 1989, 90, 4916.
60. Huzinaga, S.; Miguel, B. Chem. Phys. Lett. 1990, 175, 289. Huzinaga, S., Klobukowski, M. Chem. Phys. Lett. 1993, 212, 260.
61. Huzinaga, S.; Miguel, B. Chem. Phys. Lett. 1990, 175, 289. Huzinaga, S., Klobukowski, M. Chem. Phys. Lett. 1993, 212, 260.
62. Huzinaga, S. Approximate Atomic Functions; University of Alberta, Canada, 1971.
63. Metz, B.; Schweizer, M.; Stoll, H.; Dolg, M.; Liu, W. Theor. Chem. Acc. 2000, 104, 22.
64. For a justification, see: Kaupp, M.; Malkin, V. G.; Malkina, O. L.; Salahub, D. R. Chem. Phys. Lett. 1995, 235, 382.
65. See, for example: Ruud, K.; Schimmelpfennig, B.; Ågren, H. Chem. Phys. Lett. 1999, 310, 215. Maron, L.; Leininger, T.; Schimmelpfennig, B.; Vallet, V.; Heully, J.-L.; Teichteil, Ch.; Gropen, O.; Wahlgren, U. Chem. Phys. Lett. 1999, 244, 195. Fagerli, H.; Schimmelpfennig, B.; Gropen, O.; Wahlgren, U. THEOCHEM 1998, 451, 227.
66. See, for example: Ruud, K.; Schimmelpfennig, B.; Ågren, H. Chem. Phys. Lett. 1999, 310, 215. Maron, L.; Leininger, T.; Schimmelpfennig, B.; Vallet, V.; Heully, J.-L.; Teichteil, Ch.; Gropen, O.; Wahlgren, U. Chem. Phys. Lett. 1999, 244, 195. Fagerli, H.; Schimmelpfennig, B.; Gropen, O.; Wahlgren, U. THEOCHEM 1998, 451, 227.
67. See, for example: Ruud, K.; Schimmelpfennig, B.; Ågren, H. Chem. Phys. Lett. 1999, 310, 215. Maron, L.; Leininger, T.; Schimmelpfennig, B.; Vallet, V.; Heully, J.-L.; Teichteil, Ch.; Gropen, O.; Wahlgren, U. Chem. Phys. Lett. 1999, 244, 195. Fagerli, H.; Schimmelpfennig, B.; Gropen, O.; Wahlgren, U. THEOCHEM 1998, 451, 227.
68. Vaara, J.; Ruud, K.; Vahtras, O.; Ågren, H.; Jokisaari, J. J. Chem. Phys. 1998, 109, 1212.
69. SO/OZ(2c) contributions for 3d systems (similar arguments apply to the 2p shell).
70. See, for example: (a) Ivancich, A.; Mattioli, T. A.; Un, S. J. Am. Chem. Soc. 1999, 121, 5743.
71. (b) Allard, P.; Barra, A. L.; Andersson, K. K.; Schmidt, P. P.; Atta, M.; Gräslund, A. J. Am. Chem. Soc. 1996, 118, 895.
72. (c) van Dam, P. J.; Willems, J.-P.; Schmidt, P. P.; Pötsch, S.; Barra, A.-L.; Hagen, W. R.; Hoffman, B. M.; Andersson, K. K.; Gräslund, A. J. Am. Chem. Soc. 1998, 120, 5080.
73. Engström, M.; Vahtras, O.; Ågren, H. Chem. Phys. 1999, 243, 263.
74. Qin, Y.; Wheeler, R. A. J. Am. Chem. Soc. 1995, 117, 6083.
75. Olsson, L.; Cremer, D. J. Chem. Phys. 1996, 105, 8995.
76. Bühl, M.; Malkina, O. L.; Malkin, V. G. Helv. Chim. Acta 1996, 79, 742.
77. Bühl, M. Chem. Phys. Lett. 1997, 267, 251.
78. See, for example: Chan, C. C. J.; Au-Yeung, S. C. F.; Wilson, P. J.; Webb, G. A. J. Mol. Struct. 1996, 365, 125. Godbout, N.; Oldfield, E. J. Am. Chem. Soc. 1997. 119, 8065.
79. See, for example: Chan, C. C. J.; Au-Yeung, S. C. F.; Wilson, P. J.; Webb, G. A. J. Mol. Struct. 1996, 365, 125. Godbout, N.; Oldfield, E. J. Am. Chem. Soc. 1997. 119, 8065.
80. Schreckenbach, G. J. Chem. Phys. 1999, 110, 11936.
81. Alternative functionals may also be envisioned, in which exact exchange is simulated rather than treated explicitly (see, e.g.: Becke, A. D. J. Chem. Phys. 2000, 112, 4020).
82. DeVore, C.; Weltner, W., Jr. J. Am. Chem. Soc. 1977, 99, 4700.