Instant nuclear configuration

In the chemical approach it is assumed that the wave functions for the solute, and surrounding medium, xPm(rm Rm,Rs), are known at a given instant t and with a given nuclear configuration X(t), and that an approximation to the total wave function can be written down as an antisymmetrized product ... 

Equation [73] has the same form as the equations of motion for molecules with constrained internal coordinates, and we already know that such equations can be solved effectively using the SHAKE algorithm4 ° Equations [72] and [73] play a key role in the Car-Parrinello method and enable one to run the dynamics for both ionic and electronic degrees of freedom in parallel. With carefully chosen effective mass p and a small time step, the electronic state adjusts itself instanteously to the nuclear configuration (Born-Oppenheimer principle), and, therefore, the atomic dynamics is computed along the system s Born-Oppenheimer surface. Note that there is no need to carry out the costly matrix-diagonalization procedure for performing electronic structure calculations. 

A second important example where quantum effects need to be taken into account occurs in cases where nuclear motion, for example, in a chemical reaction, leads a molecular system into regions of configurational space where the potential energy surface of the electronic ground state approaches those of one or more excited electronic states. In such cases, it is no longer automatically true that the motion of electrons adapts essentially instantly (or adiabatically) to nuclear motion, and one may have nonadiabatic behavior. Another way of expressing this is that in such regions, nuclear motion can couple to electronic motion, in such a way that the system can be partly transferred into excited electronic states as the atoms move. 

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