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By Stuart A. Rice

Advances in Chemical Physics is the single sequence of references on hand that explores the leading edge of analysis in chemical physics. This sequence offers the chemical physics box with a discussion board for severe, authoritative reviews of advances in each quarter of the self-discipline.

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122 (2005). 71. O. Vendrell and H. D. Meyer, J. Chem. Phys. 122 (2005). 72. C. Iung, F. Gatti, and H. D. Meyer, J. Chem. Phys. 120, 6992 (2004). 73. S. Y. Lin and H. Guo, J. Chem. Phys. 122 (2005). 74. S. Y. Lin and H. Guo, J. Chem. Phys. 120, 9907 (2004). This Page Intentionally Left Blank QUANTUM MONODROMY AND MOLECULAR SPECTROSCOPY MARK S. CHILD Physical and Theoretical Chemistry Laboratory, Oxford University, Oxford, OX1 3QZ, United Kingdom CONTENTS I. Introduction II. Quasilinear Molecules A.

33). In a three-atom system, the analogous term is ð^ J À ^jÞ2 =ð2mR R2 Þ. Physically, these terms arise from the coupling of the total angular momentum with internal angular momentum of the system. They contain terms that are diagonal and off-diagonal in K. Thus, for each jKj J , the Coriolis terms couple the vectors vð:; kÞ to vð:; k Æ 1Þ, where k is the index that refers to quantum number K. The Coriolis terms are diagonal in all other variables and thus are extremely sparse. Since most of the Hamiltonian matrix is diagonal in K, we can decompose the Hamiltonian matrix into a block tridiagonal form with the dense matrices HK representing the portion of the Hamiltonian corresponding to a particular value of K and the sparse off-diagonal elements corresponding to the Coriolis terms; for example, 2 H0 6 c0;1 6 6 0 6 4 0 0 c0;1 H1 c1;2 0 0 0 c1;2 H2 c2;3 0 0 0 c2;3 H3 c3;4 3 0 0 7 7 0 7 7 c3;4 5 H4 ð52Þ This decomposition suggests the strategy for parallel computing.

103, 2903 (1995). 5. Y. H. Huang, S. S. Iyengar, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 105, 927 (1996). 6. R. Q. Chen and H. Guo, J. Chem. Phys. 105, 3569 (1996). 7. G. J. Kroes and D. Neuhauser, J. Chem. Phys. 105, 8690 (1996). 8. S. K. Gray, J. Chem. Phys. 96, 6543 (1992). 9. T. J. Park and J. C. Light, J. Chem. Phys. 85, 5870 (1986). 10. R. H. Bisseling, R. Kosloff, and J. Manz, J. Chem. Phys. 83, 993 (1985). 11. D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 101, 3671 (1994). 12. K.

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