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Extra resources for Advances in Chemical Physics, Vol. 138
21), the nuclear Laplacian operator is modified according to Àr2 ! ðÀir À AÞ Á ðÀir À AÞ ð22Þ where the vector potential A is given by l A ¼ À rf 2 ð23Þ Hence, the method of Mead and Truhlar  yields a single-valued nuclear wave function by adding a vector potential A to the kinetic energy operator. Different values of odd (or even) l yield physically equivalent results, since they yield ÉðfÞ that are identical to within an integer number of factors of expðifÞ. By analogy with electromagnetic vector potentials, one can say that different odd (or even) l are related by a gauge transformation [6, 7].
The ÉN (symmetric under R irreps have the same symmetry under s and sÃ ; the ÉG irreps have opposite symmetries. Of the latter, let us take the irrep that is symmetric under s and antisymmetric under sÃ, which describes a reaction in which the reagents are prepared in a state that is symmetric with respect to s. In the single space, this function is antisymmetric under s when the cut line is placed at f ¼ 0, symmetric when it is placed at f ¼ Àp, and unsymmetric when it is placed at, say, f ¼ p=4.
Phys. 124, 1 (2002). 9. M. V. Berry, Proc. R. Soc. A 392, 45 (1984). 10. B. K. Kendrick, Phys. Rev. Lett. 79, 2431 (1997). 11. B. E. Applegate, T. A. Barckholtz, and T. A. Miller, Chem. Soc. Rev. 32, 38 (2003). 12. C. A. Mead, Chem. Phys. 49, 23 (1980). 13. D. Babikov, B. K. Kendrick, P. Zhang, and K. Morokuma, J. Chem. Phys. 122, 044315 (2005). 14. C. A. Mead, J. Chem. Phys. 72, 3839 (1980). 15. B. Lepetit and A. Kuppermann, Chem. Phys. Lett. 166, 581 (1990). 16. Y. M. Wu, A. Kuppermann, and B.