Electronic structure of cycloheptatrienyl sandwich compounds of actinides: An(η7-C7H7)2 (An = Th, Pa, U, Np, Pu, Am)

Journal of the American Chemical Society

Volumn 119, Issue 38, 1997, Pages 9021-9032

  Li, Jun ^a   Bursten, Bruce E ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTINIDE; ORGANOMETALLIC COMPOUND;

ARTICLE; CHEMICAL BOND; CHEMICAL STRUCTURE; CONFORMATION; ELECTRON; ENERGY; IONIZATION; MOLECULAR STABILITY;

EID: 0030879550     PISSN: 00027863     EISSN: None     Source Type: Journal    
DOI: 10.1021/ja971149m     Document Type: Article

References (149)

1. (a) Marks, T. J. Acc. Chem. Res. 1976, 9, 223.
2. (b) Marks, T. J. Science 1982, 277, 989.
3. (c) Marks T. J.; Fischer, R. D., Eds. Organometallics of f-Elements; Reidel: Dordrecht, 1979.
4. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
5. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
6. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
7. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
8. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
9. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
10. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
11. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
12. Some recent reviews: (a) Richter J.; Edelmann, F. T. Coord. Chem. Rev. 1996, 147, 373. (b) Cotton, S. A. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1995, 19, 295-316; 1994, 90, 251-75; 1992, 89, 243-65. (c) Jones, C. J. Annu. Rep. Prog. Chem., Sect. A: Inorg. Chem. 1993, 88, 211-46; 1992, 87, 75-104. (d) Rogers R. D.; Rogers, L. M. J. Organomet. Chem. 1992, 442, 83-224; 1992, 442, 225-69; 1991, 416, 201-90.
13. (a) Marks, T. J.; Streitwieser, A., Jr. In The Chemistry of the Actinides Elements; Katz, J. J., Seaborg, G. T., Morss, L. R., Eds.; Chapman and Hall: New York, 1986; Vol. 2, Chapter 22.
14. (b) Marks, T. J. In The Chemistry of the Actinides Elements; Katz, J. J., Seaborg, G. T., Morss, L. R., Eds.; Chapman and Hall: New York, 1986; Vol. 2, Chapter 23.
15. Müller-Westerhoff, U.; Streitwieser, A. D. J. Am. Chem. Soc. 1968, 90, 7364.
16. Gilbert, T. M.; Ryan, R. R.; Sattelberger, A. P. Organometallics 1989, 8, 857.
17. Bursten, B. E.; Strittmatter, R. J. Angew. Chem. 1991, 103, 1085; Angew. Chem., Int. Ed. Engl. 1991, 30, 1069.
18. Bursten, B. E.; Strittmatter, R. J. Angew. Chem. 1991, 103, 1085; Angew. Chem., Int. Ed. Engl. 1991, 30, 1069.
19. Some reviews of relativistic effects in actinide chemistry: (a) Pyykkö, P. Inorg. Chim. Acta 1987 139, 243. (b) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (c) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Comp. 1994, 213/214, 191. (d) Balasubramanian, K. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr., Ering, L., Eds.; North-Holland: Amsterdam, 1994; Vol. 18, p 29. (e) Dolg, M. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr.; Ering, L., Eds.; Elsevier Science Publishers B.V.: New York, 1995; Vol. 22. (f) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1997, 1.
20. Some reviews of relativistic effects in actinide chemistry: (a) Pyykkö, P. Inorg. Chim. Acta 1987 139, 243. (b) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (c) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Comp. 1994, 213/214, 191. (d) Balasubramanian, K. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr., Ering, L., Eds.; North-Holland: Amsterdam, 1994; Vol. 18, p 29. (e) Dolg, M. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr.; Ering, L., Eds.; Elsevier Science Publishers B.V.: New York, 1995; Vol. 22. (f) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1997, 1.
21. Some reviews of relativistic effects in actinide chemistry: (a) Pyykkö, P. Inorg. Chim. Acta 1987 139, 243. (b) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (c) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Comp. 1994, 213/214, 191. (d) Balasubramanian, K. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr., Ering, L., Eds.; North-Holland: Amsterdam, 1994; Vol. 18, p 29. (e) Dolg, M. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr.; Ering, L., Eds.; Elsevier Science Publishers B.V.: New York, 1995; Vol. 22. (f) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1997, 1.
22. Some reviews of relativistic effects in actinide chemistry: (a) Pyykkö, P. Inorg. Chim. Acta 1987 139, 243. (b) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (c) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Comp. 1994, 213/214, 191. (d) Balasubramanian, K. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr., Ering, L., Eds.; North-Holland: Amsterdam, 1994; Vol. 18, p 29. (e) Dolg, M. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr.; Ering, L., Eds.; Elsevier Science Publishers B.V.: New York, 1995; Vol. 22. (f) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1997, 1.
23. Some reviews of relativistic effects in actinide chemistry: (a) Pyykkö, P. Inorg. Chim. Acta 1987 139, 243. (b) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (c) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Comp. 1994, 213/214, 191. (d) Balasubramanian, K. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr., Ering, L., Eds.; North-Holland: Amsterdam, 1994; Vol. 18, p 29. (e) Dolg, M. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr.; Ering, L., Eds.; Elsevier Science Publishers B.V.: New York, 1995; Vol. 22. (f) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1997, 1.
24. Some reviews of relativistic effects in actinide chemistry: (a) Pyykkö, P. Inorg. Chim. Acta 1987 139, 243. (b) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (c) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Comp. 1994, 213/214, 191. (d) Balasubramanian, K. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr., Ering, L., Eds.; North-Holland: Amsterdam, 1994; Vol. 18, p 29. (e) Dolg, M. In Handbook on the Physics and Chemistry of Rare Earths; Gschneider, K. A., Jr.; Ering, L., Eds.; Elsevier Science Publishers B.V.: New York, 1995; Vol. 22. (f) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1997, 1.
25. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
26. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
27. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
28. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
29. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
30. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
31. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
32. Recent theoretical studies: (a) Rösch, N.; Streitwieser, A., Jr. J. Am. Chem. Soc. 1983, 105, 7237. (b) Rösch, N. Inorg. Chim. Acta 1984, 94, 297. (c) Boerrigter, P. M.; Baerends, E. J.; Snijders, J. G. Chem. Phys. 1988, 122, 357. (d) Chang A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 2500. (e) Dolg, M.; Fulde, P.; Küchle, W.; Neumann, C.-S.; Stoll, H. J. Chem. Phys. 1991, 94, 3011. (f) King, R. B. Inorg. Chem. 1992, 31, 1978. (g) Cory, M. G.; Köstlmeier, S.; Kotzian, M.; Rösch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (h) Dolg, M.; Fulde, P.; Stoll, H.; Preuss, H.; Chang, A. H. H.; Pitzer, R. M. Chem. Phys. 1995, 195, 71.
33. Fischer, R. D. Theor. Chim. Acta (Berlin) 1963, 1, 418.
34. Arliguie, T.; Lance, M.; Nierlich, M.; Vigner, J.; Ephritikhine, M. J. Chem. Soc., Chem. Commun. 1995, 183.
35. For cycloheptatrienyl compounds of transition metals, see: (a) Deganello, G. Transition Metal Complexes of Cyclic Polyolefins; Academic Press: London, 1979; Chapter 1. (b) Green, M. L. H.; Ng, D. K. P. Chem. Rev. 1995, 95, 439.
36. For cycloheptatrienyl compounds of transition metals, see: (a) Deganello, G. Transition Metal Complexes of Cyclic Polyolefins; Academic Press: London, 1979; Chapter 1. (b) Green, M. L. H.; Ng, D. K. P. Chem. Rev. 1995, 95, 439.
37. (a) Green, J. C.; Green, M. L. H.; Kaltsoyannis, N.; Mountford, P.; Scott P.; Simpson, S. J. Organometallics 1992, 11, 3353.
38. (b) Green, J. C.; Kaltsoyannis, N.; Sze, K. H.; MacDonald, M. J. Am. Chem. Soc. 1994, 116, 1994.
39. (c) Kaltsoyannis, N. J. Chem. Soc., Dalton Trans. 1995, 3727.
40. 2+ is found in mass spectra, it is not clear whether it is a sandwich compound. See: Müller J.; Mertschenk, B. Chem. Ber. 1972, 105, 3346. For actinide and lanthanide elements, cycloheptatrienyl trianion compounds have been prepared as well: Miller, J. T.; DeKock, C. W. J. Organomet. Chem. 1981, 216, 39.
41. 2+ is found in mass spectra, it is not clear whether it is a sandwich compound. See: Müller J.; Mertschenk, B. Chem. Ber. 1972, 105, 3346. For actinide and lanthanide elements, cycloheptatrienyl trianion compounds have been prepared as well: Miller, J. T.; DeKock, C. W. J. Organomet. Chem. 1981, 216, 39.
42. (a) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; John Wiley & Sons, Inc.: New York, 1988; Chapter 21.
43. (b) Katz, J. J.; Morss, L. R.; Seaborg, G. T. In The Chemistry of the Actinides Elements, 2nd ed.; Katz, J. J., Seaborg, G. T., Morss, L. R., Eds.; Chapman and Hall: New York, 1996; Vol. 2, Chapter 14.
44. (a) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, B136, 864.
45. (b) Kohn, W.; Sham, L. J. Phys. Rev. 1965, A140, 1133.
46. (a) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University: New York, 1989.
47. (b) Dreizler, R. M.; Gross, E. K. U. Density Functional Theory; Springer: Berlin, 1990.
48. (c) Kryachko, E. S.; Ludeňa, E. V. Energy Density Functional Theory of Many-Electron Systems; Kluwer: Dordrecht, 1990.
49. (d) Labanowski, J. K., Andzelm, J. W., Eds.; Density Functional Methods in Chemistry; Springer: New York, 1991.
50. (e) Gross, E. K. U.; Dreizler, R. M. Density Functional Theory; Plenum: New York, 1995.
51. (f) Seminario, J. M., Politzer, P., Eds. Modern Density Functional Theory: A Tool for Chemistry; Elsevier: Amsterdam, 1995.
52. (g) Ellis, D. E., Ed. Density Functional Theory of Molecules, Clusters, and Solids, Kluwer Academic Publishers: Dordrecht, 1995.
53. See, for example: Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1992, 97, 7846.
54. For lighter molecules, see: Becke, A. D. J. Chem Phys. 1992, 96, 2155. Good accuracy can also be reached for heavier systems such as transition metals and lanthanides. See, for example: (a) Eriksson, L. A.; Pettersson, L. G. M.; Siegbahn, P. E. M.; Wahlgren, U. J. Chem. Phys. 1995, 102, 872. (b) Wang, S. G.; Schwarz, W. H. E. J. Phys. Chem. 1995, 99, 11687.
55. For lighter molecules, see: Becke, A. D. J. Chem Phys. 1992, 96, 2155. Good accuracy can also be reached for heavier systems such as transition metals and lanthanides. See, for example: (a) Eriksson, L. A.; Pettersson, L. G. M.; Siegbahn, P. E. M.; Wahlgren, U. J. Chem. Phys. 1995, 102, 872. (b) Wang, S. G.; Schwarz, W. H. E. J. Phys. Chem. 1995, 99, 11687.
56. For lighter molecules, see: Becke, A. D. J. Chem Phys. 1992, 96, 2155. Good accuracy can also be reached for heavier systems such as transition metals and lanthanides. See, for example: (a) Eriksson, L. A.; Pettersson, L. G. M.; Siegbahn, P. E. M.; Wahlgren, U. J. Chem. Phys. 1995, 102, 872. (b) Wang, S. G.; Schwarz, W. H. E. J. Phys. Chem. 1995, 99, 11687.
57. The 20e and 21e electron counts are derived in the "usual" way that organometallic complexes of cyclohydrocarbyl ligands are derived. The electrons included in the count are the π electrons of the Ch ligands and the valence electrons of the An atom.
58. (a) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 42.
59. (b) Baerends, E. J.; Ros, P. Chem. Phys. 1973, 2, 51.
60. (c) Baerends, E. J.; Ros, P. Int. J. Quantum Chem. 1978, S12, 169.
61. (a) Snijders, J. G.; Baerends, E. J. J. Mol. Phys. 1978, 36, 1789.
62. (b) Snijders, J. G.; Baerends, E. J.; Ros, P. Mol. Phys. 1979, 38, 1909.
63. Ravenek, W. In Algorithms and Applications on Vector and Parallel Computes; te Riele, H. J. J., DeDekker, Th. J., van de Vorst, H. A., Eds.; Elsevier: Amsterdam, 1987.
64. (a) Boerrigter, P. M.; te Velde, G.; Baerends, E. J. Int J. Quantum Chem. 1988, 33, 87.
65. (b) te Velde, G.; Baerends, E. J. J. Comput. Phys. 1992, 99, 94.
66. For the LDA exchange part, see, for example: Ziegler, T. Chem. Rev. 1991, 91, 651. For the LDA correlation part, see: Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.
67. For the LDA exchange part, see, for example: Ziegler, T. Chem. Rev. 1991, 91, 651. For the LDA correlation part, see: Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.
68. (a) Ziegler, T.; Snijders, J. G.; Baerends, E. J. Chem. Phys. 1981, 74, 1271.
69. (b) Boerrigter, P. M. Ph.D. Thesis, Vrije Universiteit, Amsterdam, 1987.
70. Becke, A. D. Phys. Rev. 1988, A38, 3098.
71. Perdew, J. P. Phys. Rev. 1986, B33, 8822; 1986, B34, 7406 (erratum).
72. Perdew, J. P. Phys. Rev. 1986, B33, 8822; 1986, B34, 7406 (erratum).
73. (a) Snijders, J. G.; Baerends, E. J.; Vernooijs, P. At. Nucl. Data Tables 1982, 26, 483.
74. (b) Vernooijs, P.; Snijders, J. G.; Baerends, E. J. Slater Type Basis Functions for the Whole Periodic System; Internal Report, Free University of Amsterdam, The Netherlands, 1984.
75. Krijn, J.; Baerends, E. J. Fit Functions in the HFS Method; Internal Report, Free University of Amsterdam, The Netherlands, 1984.
76. Ziegler, T.; Baerends, E. J.; Snijders, J. G.; Ravenek, W. J. Phys. Chem. 1989, 93, 3050.
77. For the symmetry aspects of the π MOs for cyclopolyenes and cyclopolyenyls, see, for example: Cotton, F. A. Chemical Applications of Group Theory, 3rd ed.; Wiley: New York, 1990.
78. 0 single-group orbital. We expect that the inclusion of these effects would not cause any significant change in the geometries calculated in this paper.
79. Experimental results: (a) Brewer, L. J. Opt. Soc. Am. 1971, 61, 1666. (b) Brooks, M. S. S.; Johansson, B.; Skriver, H. L. In Handbook on the Physics and Chemistry of the Actinides; Freeman, A. J., Lander, G. H., Eds.; North-Holland: Amsterdam, 1984; Vol. 1, Chapter 3.
80. Experimental results: (a) Brewer, L. J. Opt. Soc. Am. 1971, 61, 1666. (b) Brooks, M. S. S.; Johansson, B.; Skriver, H. L. In Handbook on the Physics and Chemistry of the Actinides; Freeman, A. J., Lander, G. H., Eds.; North-Holland: Amsterdam, 1984; Vol. 1, Chapter 3.
81. (c) Fred, M. S. In The Chemistry of the Actinides Elements, 2nd ed.; Katz, J. J., Seaborg, G. T., Morss, L. R., Eds.; Chapman and Hall: New York, 1986; Vol. 2, Chapter 15.
82. (d) Carnall, W. T., Crosswhite, H. M. In The Chemistry of the Actinides Elements, 2nd ed.; Katz, J. J., Seaborg, G. T. Morss, L. R., Eds.; Chapman and Hall: New York, 1986; Vol. 2, Chapter 16, 1986.
83. For theoretical results see, for example: (a) Pyykkö, P.; Laakkonen, L. J.; Tatsumi, K. Inorg. Chem. 1989, 28, 1801. (b) Bagnall, K. W. The Actinide Elements; Elsevier Publishing Company: Amsterdam, 1972; Chapter 1.
84. For theoretical results see, for example: (a) Pyykkö, P.; Laakkonen, L. J.; Tatsumi, K. Inorg. Chem. 1989, 28, 1801. (b) Bagnall, K. W. The Actinide Elements; Elsevier Publishing Company: Amsterdam, 1972; Chapter 1.
85. Because the calculations on the two-open-shell configurations have been carried out in the restricted Kohn-Sham (RKS) formalism, the spin quantum numbers for the resultant states are ambiguous. The state energies are multiplet averages of the pure singlet and triplet states. In principle, the pure triplet state energy could be obtained from unrestricted Kohn-Sham (UKS) calculations. However, upon the inclusions of spin-orbit coupling, the notion of singlet and triplet state becomes less relevant so we report only the RKS results for these configurations.
86. n configurations for Pa and U. See ref 7c and: Zhao, K.; Pitzer, R. M. J. Phys. Chem. 1996, 100, 4798.
87. For an approach to the near-degenerate problem in density functional methods, see: (a) Dunlap, B. I. In Ab initio Methods in Quantum Chemistry II; Lawley, K. P., Ed.; Wiley: New York, 1987. (b) Wang, S. G.; Schwarz, W. H. E. J. Chem. Phys. 1996, 105, 4641 and references cited therein.
88. For an approach to the near-degenerate problem in density functional methods, see: (a) Dunlap, B. I. In Ab initio Methods in Quantum Chemistry II; Lawley, K. P., Ed.; Wiley: New York, 1987. (b) Wang, S. G.; Schwarz, W. H. E. J. Chem. Phys. 1996, 105, 4641 and references cited therein.
89. (a) Bohn, R. K.; Haaland, A. J. Organomet. Chem. 1966, 5, 470.
90. (b) Haaland, A. Acc. Chem. Res. 1979, 12, 415.
91. Weast, R. C.; Lide, D. R.; Astle, M. J.; Beyer, W. H., Eds.; CRC Handbook of Chemistry and Physics, 70th ed.; CRC Press, Inc.: Boca Raton, FL, 1989; F-188.
92. 2 is 0.9 ± 0.3 kcal/mol. See: (a) Haaland, A.; Nilsson, J. E. Acta Chem. Scand. 1968, 22, 2653. (b) Laane, J. J. Coord. Chem. 1971, 1, 75. (c) Carter, S.; Murrell, J. N. J. Organomet. Chem. 1980, 192, 399. (d) Bencivenni, L.; Ferro, D.; Pelino, M.; Teghil, R. J. Indian Chem. Soc. 1980, 57, 1062. (e) Marverick, E.; Dunitz, J. D. Mol. Phys. 1987, 62, 451.
93. 2 is 0.9 ± 0.3 kcal/mol. See: (a) Haaland, A.; Nilsson, J. E. Acta Chem. Scand. 1968, 22, 2653. (b) Laane, J. J. Coord. Chem. 1971, 1, 75. (c) Carter, S.; Murrell, J. N. J. Organomet. Chem. 1980, 192, 399. (d) Bencivenni, L.; Ferro, D.; Pelino, M.; Teghil, R. J. Indian Chem. Soc. 1980, 57, 1062. (e) Marverick, E.; Dunitz, J. D. Mol. Phys. 1987, 62, 451.
94. 2 is 0.9 ± 0.3 kcal/mol. See: (a) Haaland, A.; Nilsson, J. E. Acta Chem. Scand. 1968, 22, 2653. (b) Laane, J. J. Coord. Chem. 1971, 1, 75. (c) Carter, S.; Murrell, J. N. J. Organomet. Chem. 1980, 192, 399. (d) Bencivenni, L.; Ferro, D.; Pelino, M.; Teghil, R. J. Indian Chem. Soc. 1980, 57, 1062. (e) Marverick, E.; Dunitz, J. D. Mol. Phys. 1987, 62, 451.
95. 2 is 0.9 ± 0.3 kcal/mol. See: (a) Haaland, A.; Nilsson, J. E. Acta Chem. Scand. 1968, 22, 2653. (b) Laane, J. J. Coord. Chem. 1971, 1, 75. (c) Carter, S.; Murrell, J. N. J. Organomet. Chem. 1980, 192, 399. (d) Bencivenni, L.; Ferro, D.; Pelino, M.; Teghil, R. J. Indian Chem. Soc. 1980, 57, 1062. (e) Marverick, E.; Dunitz, J. D. Mol. Phys. 1987, 62, 451.
96. 2 is 0.9 ± 0.3 kcal/mol. See: (a) Haaland, A.; Nilsson, J. E. Acta Chem. Scand. 1968, 22, 2653. (b) Laane, J. J. Coord. Chem. 1971, 1, 75. (c) Carter, S.; Murrell, J. N. J. Organomet. Chem. 1980, 192, 399. (d) Bencivenni, L.; Ferro, D.; Pelino, M.; Teghil, R. J. Indian Chem. Soc. 1980, 57, 1062. (e) Marverick, E.; Dunitz, J. D. Mol. Phys. 1987, 62, 451.
97. Li, J.; Bursten, B. E. Unpublished results.
98. 5h conformer has been found to be more stable in the gas phase by electron diffraction and in the solid state by X-ray or neutron diffraction. See: (a) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9, 373 and references cited therein. (b) Bohn, R. K.; Haaland, A. J. Organomet. Chem. 1966, 5, 470. (c) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1979, B35, 1068. (d) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1982, B38, 1741. (e) Takusagawa, F.; Koetzle, T. F. Acta Crystallogr. 1979, B35, 1074.
99. 5h conformer has been found to be more stable in the gas phase by electron diffraction and in the solid state by X-ray or neutron diffraction. See: (a) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9, 373 and references cited therein. (b) Bohn, R. K.; Haaland, A. J. Organomet. Chem. 1966, 5, 470. (c) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1979, B35, 1068. (d) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1982, B38, 1741. (e) Takusagawa, F.; Koetzle, T. F. Acta Crystallogr. 1979, B35, 1074.
100. 5h conformer has been found to be more stable in the gas phase by electron diffraction and in the solid state by X-ray or neutron diffraction. See: (a) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9, 373 and references cited therein. (b) Bohn, R. K.; Haaland, A. J. Organomet. Chem. 1966, 5, 470. (c) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1979, B35, 1068. (d) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1982, B38, 1741. (e) Takusagawa, F.; Koetzle, T. F. Acta Crystallogr. 1979, B35, 1074.
101. 5h conformer has been found to be more stable in the gas phase by electron diffraction and in the solid state by X-ray or neutron diffraction. See: (a) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9, 373 and references cited therein. (b) Bohn, R. K.; Haaland, A. J. Organomet. Chem. 1966, 5, 470. (c) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1979, B35, 1068. (d) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1982, B38, 1741. (e) Takusagawa, F.; Koetzle, T. F. Acta Crystallogr. 1979, B35, 1074.
102. 5h conformer has been found to be more stable in the gas phase by electron diffraction and in the solid state by X-ray or neutron diffraction. See: (a) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9, 373 and references cited therein. (b) Bohn, R. K.; Haaland, A. J. Organomet. Chem. 1966, 5, 470. (c) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1979, B35, 1068. (d) Seiler, P.; Dunitz, J. D. Acta Crystallogr. 1982, B38, 1741. (e) Takusagawa, F.; Koetzle, T. F. Acta Crystallogr. 1979, B35, 1074.
103. 2 is more stable in both the crystalline and gas phases. See: (a) Cotton, F. A.; Dollase, W. A.; Wood, J. S. J. Am. Chem. Soc. 1963, 85, 1543. (b) Haaland, A. Acta Chem Scand. 1965, 19, 41. (c) Keullen, E.; Jellinck, F. J. Organomet. Chem. 1966, 5, 490. (d) Schaefer, L.; Southern, J. F.; Cyvin, S. J.; Brunvoll, J. J. Organomet. Chem. 1970, 24, 913.
104. 2 is more stable in both the crystalline and gas phases. See: (a) Cotton, F. A.; Dollase, W. A.; Wood, J. S. J. Am. Chem. Soc. 1963, 85, 1543. (b) Haaland, A. Acta Chem Scand. 1965, 19, 41. (c) Keullen, E.; Jellinck, F. J. Organomet. Chem. 1966, 5, 490. (d) Schaefer, L.; Southern, J. F.; Cyvin, S. J.; Brunvoll, J. J. Organomet. Chem. 1970, 24, 913.
105. 2 is more stable in both the crystalline and gas phases. See: (a) Cotton, F. A.; Dollase, W. A.; Wood, J. S. J. Am. Chem. Soc. 1963, 85, 1543. (b) Haaland, A. Acta Chem Scand. 1965, 19, 41. (c) Keullen, E.; Jellinck, F. J. Organomet. Chem. 1966, 5, 490. (d) Schaefer, L.; Southern, J. F.; Cyvin, S. J.; Brunvoll, J. J. Organomet. Chem. 1970, 24, 913.
106. 2 is more stable in both the crystalline and gas phases. See: (a) Cotton, F. A.; Dollase, W. A.; Wood, J. S. J. Am. Chem. Soc. 1963, 85, 1543. (b) Haaland, A. Acta Chem Scand. 1965, 19, 41. (c) Keullen, E.; Jellinck, F. J. Organomet. Chem. 1966, 5, 490. (d) Schaefer, L.; Southern, J. F.; Cyvin, S. J.; Brunvoll, J. J. Organomet. Chem. 1970, 24, 913.
107. 2 is found to be more stable: (a) Zalkin, A.; Raymond, K. N. J. Am. Chem. Soc. 1969, 91, 5667. (b) Avdeef, A.; Raymond, K. N.; Hodgson, K. O.; Zalkin, A. Inorg. Chem. 1972, 11, 1083.
108. 2 is found to be more stable: (a) Zalkin, A.; Raymond, K. N. J. Am. Chem. Soc. 1969, 91, 5667. (b) Avdeef, A.; Raymond, K. N.; Hodgson, K. O.; Zalkin, A. Inorg. Chem. 1972, 11, 1083.
109. (a) Park, C.; Almlöf, J. J. Chem. Phys. 1991, 95, 1829.
110. (b) Pierloot, K.; Persson, B. J.; Roos, B. O. J. Phys. Chem. 1995, 99, 3465.
111. (c) Koch, H.; Jørgensen, P.; Helgaker, T. J. Chem. Phys. 1996, 104, 9528.
112. Ziegler, T.; Snijders, J. G.; Baerends, E. J. In The Challenge of d and f Electrons: Theory and Computation; Salahub, D. R., Zerner, M. C., Eds.; American Chemical Society: Washington, DC, 1989. The relativistic contraction of bond distances has also been rationalized in terms of the attractive Hellmann-Feynman force arising from the relativistic change in electron density: Schwarz, W. H. E.; Chu, S. Y.; Mark, F. Mol. Phys. 1983, 50, 603.
113. Ziegler, T.; Snijders, J. G.; Baerends, E. J. In The Challenge of d and f Electrons: Theory and Computation; Salahub, D. R., Zerner, M. C., Eds.; American Chemical Society: Washington, DC, 1989. The relativistic contraction of bond distances has also been rationalized in terms of the attractive Hellmann-Feynman force arising from the relativistic change in electron density: Schwarz, W. H. E.; Chu, S. Y.; Mark, F. Mol. Phys. 1983, 50, 603.
114. Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem Phys. 1993, 98, 5612.
115. Handy, N. C. In Lecture Notes in Quantum Chemistry II; Roos, B. O., Ed.; Springer-Verlag: Berlin, 1994.
116. Wang, S. G.; Pan, D. K.; Schwarz, W. H. E. J. Chem. Phys. 1995, 102, 9296.
117. The Madelung potentials of the crystal field could have a considerable influence on the bond lengths of charged molecules. See, for example: Li, J.; Irle, S.; Schwarz, W. H. E. Inorg. Chem. 1996, 36, 100.
118. (a) See, for example: Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed.; Harper Collins: New York, 1993; Chapter 14.
119. (b) For a recent theoretical analysis of actinide contraction and its comparison with the lanthanide contraction, see: Seth, M.; Dolg, M.; Fulde, P.; Schwerdtfeger, P. J. Am. Chem. Soc. 1995, 117, 6597 and references therein.
120. An electron diffraction experiment produces a bigger bent angle, 3.7(9)°: Haaland, A.; Lusztyk, J.; Novak, D. P.; Brunvoll, J.; Starowieyski, K. B. J. Chem. Soc., Chem. Commun. 1974, 54.
121. Elian, M.; Chen, M. M. L.; Mingos, M. P.; Hoffmann, R. Inorg. Chem. 1976, 15, 1148.
122. The mass-velocity effect for s-type orbitals is partially cancelled by the Darwin effects. See, for example: Schwarz, W. H. E. In Theoretical Models of Chemical Bonding; Maksić, Z., Ed.; Springer: Berlin, 1990; p 595.
123. For qualitative and quantitative discussions of direct and indirect relativistic effects, see, for example: (a) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (b) Pyykkö, P.; Desclaux, J.-P. Acc. Chem. Res. 1979, 12, 276. (c) Pyykkö, P. Chem. Rev. 1988, 88, 563. (d) Schwarz, W. H. E.; van Wezenbeek, E. M.; Baerends, E. J.; Snijders, J. G. J. Phys. 1989, B22, 1515.
124. For qualitative and quantitative discussions of direct and indirect relativistic effects, see, for example: (a) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (b) Pyykkö, P.; Desclaux, J.-P. Acc. Chem. Res. 1979, 12, 276. (c) Pyykkö, P. Chem. Rev. 1988, 88, 563. (d) Schwarz, W. H. E.; van Wezenbeek, E. M.; Baerends, E. J.; Snijders, J. G. J. Phys. 1989, B22, 1515.
125. For qualitative and quantitative discussions of direct and indirect relativistic effects, see, for example: (a) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (b) Pyykkö, P.; Desclaux, J.-P. Acc. Chem. Res. 1979, 12, 276. (c) Pyykkö, P. Chem. Rev. 1988, 88, 563. (d) Schwarz, W. H. E.; van Wezenbeek, E. M.; Baerends, E. J.; Snijders, J. G. J. Phys. 1989, B22, 1515.
126. For qualitative and quantitative discussions of direct and indirect relativistic effects, see, for example: (a) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (b) Pyykkö, P.; Desclaux, J.-P. Acc. Chem. Res. 1979, 12, 276. (c) Pyykkö, P. Chem. Rev. 1988, 88, 563. (d) Schwarz, W. H. E.; van Wezenbeek, E. M.; Baerends, E. J.; Snijders, J. G. J. Phys. 1989, B22, 1515.
127. (56) For a discussion of the effects of mass-velocity, Darwin, and spin-orbit coupling on p-type orbitals, see, for example: Wang, S. G.; Schwarz, W. H. E. J. Mol. Struct. (Theochem) 1995, 338, 347.
128. (a) Tatsumi, K.; Hoffmann, R. Inorg. Chem. 1980, 19, 2656.
129. (b) Pyykkö, P.; Lohr, L. L., Jr. Inorg. Chem. 1981, 20, 1950.
130. (c) Pyykkö, P.; Jové, J. New J. Chem. 1991, 15, 111.
131. Wadt, W. R. J. Am. Chem. Soc. 1981, 103, 6053.
132. A numerical relativistic Dirac-Fock calculation for the uranium atom indicates that the spin-orbit averaged radii of the maximum radial density are 0.86, 0.56, and 1.30 Å for the 6p, 5f, and 6d orbitals, respectively: Desclaux, J. P. At. Data Nucl. Data Tables 1973, 12, 311.
133. Brennan, J. G.; Green, J. C.; Redfern, C. M. J. Am. Chem. Soc. 1989, 111, 2373.
134. See, for example: Bursten, B. E.; Rhodes, L. F.; Strittmatter, R. J. J. Am. Chem. Soc. 1989, 111, 2758.
135. Janak, J. F. Phys. Rev. 1978, B18, 7165.
136. Unlike the Hartree-Fock method, in which virtual orbitals are artificially destabilized, in DFT methods, the Kohn-Sham virtual orbitals are generally "too low" in energy, and the addition of an electron to a molecular orbital tends to increase its energy. See: (a) Cook, D. B. Int. J. Quantum Chem. 1996, 60, 793. (b) Slater, J. C.; Mann, J. B.; Wilson, T. M.; Wood, J. H. Phys. Rev. 1969, 184, 672. (c) Slater, J. C. Quantum Theory for Molecules and Solids. The Self-Consistent Field for Molecules and Solids; McGraw-Hill: New York, 1974; Vol. 4.
137. Unlike the Hartree-Fock method, in which virtual orbitals are artificially destabilized, in DFT methods, the Kohn-Sham virtual orbitals are generally "too low" in energy, and the addition of an electron to a molecular orbital tends to increase its energy. See: (a) Cook, D. B. Int. J. Quantum Chem. 1996, 60, 793. (b) Slater, J. C.; Mann, J. B.; Wilson, T. M.; Wood, J. H. Phys. Rev. 1969, 184, 672. (c) Slater, J. C. Quantum Theory for Molecules and Solids. The Self-Consistent Field for Molecules and Solids; McGraw-Hill: New York, 1974; Vol. 4.
138. Unlike the Hartree-Fock method, in which virtual orbitals are artificially destabilized, in DFT methods, the Kohn-Sham virtual orbitals are generally "too low" in energy, and the addition of an electron to a molecular orbital tends to increase its energy. See: (a) Cook, D. B. Int. J. Quantum Chem. 1996, 60, 793. (b) Slater, J. C.; Mann, J. B.; Wilson, T. M.; Wood, J. H. Phys. Rev. 1969, 184, 672. (c) Slater, J. C. Quantum Theory for Molecules and Solids. The Self-Consistent Field for Molecules and Solids; McGraw-Hill: New York, 1974; Vol. 4.
139. Bursten, B. E.; Rhodes, L. F.; Strittmatter, R. J. J. Am. Chem. Soc. 1989, 111, 2756.
140. 2′ are all ca. 0.30.
141. Strittmatter, R. J.; Bursten, B. E. J. Am. Chem. Soc. 1991, 113, 552 and references therein.
142. e(homo) + 3082, in kcal/mol.
143. 2 molecule are lowered by nearly the same amount. Thus, the effect of spin-orbit coupling on the calculated bond energy is small. We expect that the trend in the bond energies presented in Figure 9 would be qualitatively the same if spin-orbit effects were included.
144. Slater, J. C. Adv. Quantum Chem. 1972, 6, 1.
145. Cotton, S. Lanthanides and Actinides; Oxford University Press: New York, 1991.
146. Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833; 1962, 36, 3428.
147. Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833; 1962, 36, 3428.
148. Li, J.;. Bursten, B. E Unpublished results.
149. Bursten, B. E.; Fenske, R. F. Inorg. Chem. 1979, 18, 1760.