Solving the Electronic Eigenvalue Problem

Once we have invoked the Born-Oppenheimer approximation, we attempt to solve the electronic Schrödinger equation (171), i.e.

$$\left[ - \frac{1}{2} \sum_i \nabla_i^2 - \sum_{iA} \frac{Z_A... ...ight] \psi_e({\bf r}; {\bf R}) = E_e \psi_e({\bf r}; {\bf R})$$ (183)

But, as mentioned previously, this equation is quite difficult to solve!