Locating electronic degeneracies of polyatomic molecules: A general method for nonsymmetric molecules

Journal of Physical Chemistry A

Volumn 107, Issue 8, 2003, Pages 1222-1227

  Zilberg, S ^a   Haas, Y ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONIC DEGENERACIES;

ATOMS; CHEMICAL BONDS; ELECTRONIC STRUCTURE; ELECTRONS; MOLECULES; PERTURBATION TECHNIQUES; REACTION KINETICS;

MOLECULAR DYNAMICS;

EID: 0037468164     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp022287n     Document Type: Article

References (43)

1. Herzberg, G.; Longuet-Higgins, H. C. Discuss. Faraday Soc. 1963, 35, 77.
2. Longuet-Higgins, H. C. Proc. R. Soc. London, Ser. A 1975, 344, 147.
3. Klessinger, M.; Michl, J. Excited States and Photochemistry of Organic Molecules; VCH: New York, 1995.
4. Köppel, H.; Domcke, W.; Cederbaum, L. S. Adv. Chem. Phys. 1984, 57, 59.
5. Yarkony, D. R. Rev. Mod. Phys. 1996, 68, 985.
6. Fuss, W.; Lochbrunner, S.; Müller, A. M.; Schikarski, T.; Schmid, W. E.; Trushin, S. A. Chem. Phys. 1998, 232, 161.
7. Bernardi, F.; Olivucci, M.; Robb, M. A. J. Photochem. Photobiol., A 1997, 105, 365 and references therein.
8. Ben-Nun, M.; Quenneville, J.; Martinez, T. J. J. Phys. Chem. A 2000, 104, 5161.
9. Diau, E. W.-G.; De Feyter, S.; Zewail, A. H. J. Chem. Phys. 1999, 110, 9785.
10. A special issue of Chem. Phys. was recently devoted to the topic (Vol. 259, Nos. 2-3, September 2000). See also Zilberg, S.; Haas, Y. Chem. Phys. 2000, 259, 249.
11. A special issue of Chem. Phys. was recently devoted to the topic (Vol. 259, Nos. 2-3, September 2000). See also Zilberg, S.; Haas, Y. Chem. Phys. 2000, 259, 249.
12. von Neumann, I.; Wigner, E. Phys. Z. 1929, 30, 467.
13. Teller, E. J. Phys. Chem. 1937, 4, 109.
14. Michl, J. Mol. Photochem. 1972, 4, 243.
15. Salem, L. Electrons in Chemical Reactions: First Principles; Wiley: New York, 1982.
16. Shaik, S. S.; J. Am. Chem. Soc. 1981, 103, 3692. Shaik, S.; Hiberty, P. C. Adv. Quantum Chem. 1995, 26, 99.
17. Shaik, S. S.; J. Am. Chem. Soc. 1981, 103, 3692. Shaik, S.; Hiberty, P. C. Adv. Quantum Chem. 1995, 26, 99.
18. Silver, D. M. J. Am. Chem. Soc. 1974, 96, 5959.
19. Heitler, W.; London, F. Phys. Z. 1927, 44, 455.
20. Pauling, L. J. Chem. Phys. 1933, 1, 280.
21. Lewis, G. N. J. Am. Chem. Soc. 1916, 38, 762.
22. Zilberg, S.; Haas, Y. Chem.-Eur. J. 1999, 5, 1755.
23. Zilberg, S.; Haas, Y. Adv. Chem. Phys. 2002, 124, 433.
24. For a discussion of anchors, see refs 20 and 21. Anchors are most easily visualized as valence bond species in which all possible structures of a given spin-pairing arrangement are included. In particular, it includes both covalent and ionic structures. An anchor may have a minimum, but quite often a minimum is obtained only if a combination of several anchors is constructed (e.g., benzene). See also Coulson, C. A. Valence, 2nd ed. Oxford University Press: London, 1961; Chapter 5.
25. Landau, L. D.; Lifshitz, E. M. Quantum Mechanics: Non-Relativistic Theory, 3rd ed. Pergamon Press: Oxford, U.K., 1977; p 139.
26. Cohen-Tanoudji, C.; Diu, B.; Laloë F. Quantum Mechanics; Wiley: New York, 1977; Chapter 4.
27. Zilberg, S.; Haas, Y. Int. J. Quantum Chem. 1999, 71, 133.
28. Shaik, S.; Reddy, A. C. J. Chem. Soc., Faraday Trans. 1994, 90, 1631.
29. Zilberg, S.; Haas, Y.; Danovich, D.; Shaik, S. Angew. Chem., Int. Ed. 1998, 37, 1394.
30. S〉.
31. Zilberg, S.; Haas, Y. J. Photochem. Photobiol. 2001, 144, 221.
32. RS that consists of combinations of the internal coordinates. Only two of them are independent; the third can be constructed from a linear combination of the other two. The diagonal matrix elements 〈n|H|n〉 (n = P, R, or S) can be made equal to each other by varying the values of the internal coordinates of the anchors. This can be done for an arbitrary number of anchors. The interaction energy between any two anchors depends on the location along the reaction coordinate connecting them. In the space spanned by the three anchors, the interaction between any two anchors can be varied only along the two independent coordinates. Therefore, there can be only one point at which the three interactions are equal. For the fourth anchor, T, to interact equally with any other two, say P and R, a different plane must be used. That plane is defined by the reaction coordinates that connect P, R, and T. It follows that in a 2D world, the same pairwise interactions can be realized only for three anchors. The extension to three dimensions is clear.
33. Zilberg, S.; Haas, Y. J. Am. Chem. Soc. 2003, in press.
34. Zuilhof, H.; Dinnocenzo, J. P.; Reddy, A. C.; Shaik, S. J. Phys. Chem. 1996, 100, 15774.
35. Toriyama, K. Chem. Phys. Lett. 1991, 177, 39.
36. Lunell, S.; Feller, D.; Davidson, E. R. Theor. Chim. Acta 1990, 77, 111.
37. Domcke, W.; Stock, G. Adv. Chem. Phys. 1997, 1001.
38. Müller, H.; Köppel, H.; Cederbaum, L. S. New J. Chem. 1993, 17, 7.
39. Salem, L.; Rowland, C. Angew. Chem., Int. Ed. Engl. 1972, 11, 92.
40. Gerhartz, W.; Poshusta, R. D.; Michl, J. J. Am. Chem. Soc. 1976, 98, 6427.
41. For a review of the method, see Robb, M. A.; Garavelli, M.; Olivucci, M.; Bernardi, F. In Reviews in Computational Chemistry; Lipkovwitz, K. B., Boyd, D. B., Eds.; Wiley-VCH: New York, 2000; Vol. 15, pp 87-212.
42. Mead, C. A. J. Chem. Phys. 1983, 78, 807.
43. Orlandi, G.; Negri, F. Photochem. Photobiol. Sci. 2002, 1, 289.