Correction of the Crude Adiabatic Approximation

The electronic wavefunction in the crude adiabatic approximation is defined according to Equation 1.18 at a specific nuclear configuration q and therefore it does not 

The same procedure gives for the eigenvalues (in second order) 

Expansion of A1/ in the vicinity of qg in terms of nuclear coordinates q gives 

In writing Equation 1.29, we have taken into account the linear terms from Equation 1.28 in second order and quadratic terms in q in first order. Correspondingly, the coefficients C, a(q) in (1.25) are expressed as (in second order) 

---