The Born-Oppenheimer Approximation and its Breakdown Nonadiabatic Processes

The Born-Oppenheimer Approximation and its Breakdown Nonadiabatic Processes 

The time-independent Schrodinger equation for a molecule with N nuclei 

the nuclear and electronic parts are separated, and solving the electronic Schrodinger equation provides the electronic eigenfunctions 

Inserting the electronic solution back into the Schrodinger equation for the whole system, Eq. [1], and neglecting the effect of the nuclear kinetic energy operator on the electronic wavefunction, v[/j, gives 

Solving Eqs. [4] and [5] is the task of theoretical chemistry. Electronic structure methods capable of solving the electronic problem have progressed enormously during the past 40 years and standardized computational models have emerged. John Pople received the Nobel Prize for Chemistry in 1998 for being one of the pioneers of this evolution. Solution of the electronic part of the Hamiltonian provides structures, reaction paths and transition 

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