Theoretical background A representation of the total wavefunctions

1 Summary of the standard nuclear wavepacket dynamics for nonadiabatic transitions 

For the convenience, we here briefly summarize the standard formalism of quantum d3mamics of molecular dynamics of Chap. 2. 

Chemical Theory Beyond the Born-Oppenheimer Paradigm 1) The quantum-mechanical molecular Hamiltonian is written generally 

r and R denote the electronic and nuclear coordinates, respectively, and pj and Pk are the operators of their conjugate momenta. K (r R) is the Coulombic interaction potential among electrons and nuclei. 

2) The corresponding wavefunctions are usually represented in the Born-Huang expansion as 

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