By Stuart A. Rice

ISBN-10: 0471682349

ISBN-13: 9780471682349

This sequence offers the chemical physics box with a discussion board for severe, authoritative reviews of advances in each zone of the self-discipline. This stand-alone targeted subject matters quantity stories contemporary advances in electron-transfer study with major, up to date chapters via across the world well-known researchers.

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**Example text**

26], are shown in Fig. 8. These results [26] reproduce those obtained earlier by Kendrick [21], and show that there are noticeable GP effects in some of the state-to-state reaction probabilities, which indicate that a small proportion of the wave function encircles the CI. 3 E(eV) Figure 8. State-to-state reaction probabilities, for H þ H2(100) ! H2(250) þ H, computed using GP (solid lines) and non-GP (dashed lines) boundary conditions. the influence of the geometric phase on reaction dynamics 23 results is the apparent alternation in sign of the difference between the GP and non-GP probabilities, ÁPn0 n ðJ; EÞ ½G ¼ Pn0 n ðJ; EÞ ½N À Pn0 n ðJ; EÞ ð35Þ as a function of J.

The influence of the geometric phase on reaction dynamics 35 Clearly, the above procedure can be continued (in principle) as many times as required. Thus, if the wave function includes n ¼ À4 Á Á Á 3 paths, we have simply to define the function É04 ðfÞ ¼ ÀÉ04 ðf þ 8pÞ, and then map onto the f ¼ 0 ! 16p cover space, which will unwind the function completely. In general, if there are h homotopy classes of Feynman paths that contribute to the Kernel, then one can unwind ÉG by computing the unsymmetrised wave function Éh in the 0 !

The symmetry group in the ^ 2p g, which is isomorphic with C2v , with a double space is then fE; sg fE; R ^ 2p s. Clearly, there are two ÉN irreps second plane of symmetry sÃ ¼ R ^ 2p ) and two ÉG irreps (antisymmetric under R ^ 2p ). 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.

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