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An Internal Coordinate Invariant Reaction Pathway

Bibliographic reference Sana, M. ; Reckinger, G. ; Leroy, Georges. An Internal Coordinate Invariant Reaction Pathway. In: Theoretica Chimica Acta, Vol. 58, no. 2, p. 145-153 (1981)
Permanent URL http://hdl.handle.net/2078.1/58371
  1. Pechukas, P.: J. Chem. Phys.64, 1516 (1976)
  2. A lot of organic quantum chemical calculations admit intuitively such a consideration without giving a precise definition to the concept of reaction pathway
  3. Murrel, J. N., Laidler, K. J.: Trans. Faraday Soc.64, 371 (1968)
  4. Mclver Jr., J. W., Komornicki, A.: J. Am. Chem. Soc.94, 2625 (1972)
  5. Stanton, R. E., Mclver Jr., J. W.: J. Am. Chem. Soc.97, 3632 (1975)
  6. McCullough Jr., E. A., Silver, D. M.: J. Chem. Phys.62, 4050 (1975)
  7. Silver, D. M.: J. Chem. Phys.57, 586 (1966)
  8. Marcus, R. A.: J. Chem. Phys.45, 4493 (1966)
  9. Fukui, K., Kato, S., Fujimoto, H.: J. Am. Chem. Soc.97, 1 (1975), see also, Ishida, Z., Morokuma, K., Komornicki, A.: J. Chem. Phys.66, 2153 (1977)
  10. 3N-6 is even true for linear structures (ifN is greater than 2) in order to provide a continuous description between linear and nonlinear nuclear configurations
  11. E.g. for three-atomic systems the internal set of coordinates (R 1 R 2 R 3) produces for linear structure a discontinuity due to the constraintR 3=R 1+R 2; such a set is not convenient in order to avoid the problem of kinks
  12. For practical computational details ofg s andH s , see Sana, M.: Intern. J. Quantum Chem. (accepted) and inclosed references
  13. In general the chain rule may be written as: (?y f) = (?yx?)(?x f)
  14. Reckinger, G.: Ph.D. Thesis, U.C.L. (in preparation)
  15. Kuntz, P. J. in: Molecular Collisions, ed. Miller, H., part B, Chap. 2, p. 74. New York: Plenum Press, 1976
  16. Wilson, E. B., Decius, G. C., Cross, P. C.: Molecular vibration. London: McGraw-Hill, 1975
  17. The expression ofG. Matrix is:G =B?B', whereB connects the cartesian displacements, ?, to the internal displacements,s:s=B? and where ? stands for the matrix of the inverse of the atomic masses
  18. Swanson, B. I.: J. A.m. Chem. Soc.98, 3067 (1976)
  19. Let us note thatH is not a positive defined matrix at the transition point; then the matrix H1/2 cannot be built
  20. Acton, F. S.: Numerical methods, that work, Chap. 13, p. 318. New York: Harper 1970
  21. Used in HVIBR program: Sana, M: Program for polyatomic harmonic vibrator analysis (1980)
  22. Sorenson, G. O.: Molecular Structures and Vibrations, Chap. 2, p. 32. Cyvin ed. Amsterdam: Elsevier 1972
  23. Tachibana, Fukui, K.: Theoret. Chim. Acta (Berl.)49, 321 (1978), Theoret. Chim. Acta (Berl.)51, 189, 275 (1979)