Nuclear dynamics in the vicinity of the crossing seam: Theory and application to vibrational spectrum of H3

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Abstract
Based on the equivalence of the gauge transformations for the nuclear and electronic wave functions, the physical meaning of the geometric phase effect has been disclosed for a two coupled-state system. It is found that the geometric phase A(R) is defined by the argument of the complex electronic vector state in the complex plane spanned by the two real-valued electronic components. Such an angle is identical (up to a constant) to the mixing angle γ(R). Novel generalized Born–Oppenheimer equations for the two coupled-state problem in the vicinity of the crossing seam have been derived, and numerical calculations of vibrational spectra done for H3. The results demonstrate significant differences in relation to those obtained from the assumption that A(R)=φ/2.

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