Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case

Chaoyuan Zhu*, Hiroki Nakamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


A two-by-two diabatic propagation method is developed to deal with general one-dimensional multi-channel curve crossing problems. Each crossing is treated within the newly completed two-state semiclassical theory in the diabatic representation and is represented by a nonadiabatic transition matrix (I-matrix). A product of all the I-matrices yields the reduced scattering matrix for the entire system. This theory can handle the multi-channel curve crossing problems as simply as a two-state problem. An analysis of the complex crossing points in the momentum space can provide a comprehensive illustrative criterion of this method. A detailed severe numerical test is made by taking a seven-state system with 6 and 12 nonzero diabatic couplings. It is demonstrated that dominant processes among the state-to-state transitions are well reproduced by the present semiclassical theory.

Original languageEnglish
Pages (from-to)2599-2611
Number of pages13
JournalJournal of Chemical Physics
Issue number7
StatePublished - 15 Feb 1997

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