Solution to the Kohn-Sham equations

We can solve the Kohn-Sham equations self-consistently, in the same spirit as we solved the Hartree-Fock equations in the previous section. The first step is to pick a suitable exchange functional.

1. Choose and appropriate atomic basis $\chi_p$
2. We write the variational ansatz as:
   

   $$\psi_k = \sum_p C_{kp} \chi_p$$ (167)

   
   

3. We compute the density as:
   

   $$n({\bf r}) = \sum_k \vert\psi_k({\bf r})\vert^2$$ (168)

   
   

4. We replace the density in the Kohn-Sham equations to find the new eigenfunctions and eigenvalues. Thsi means funding the coefficients $C_{kp}$.
5. Go to 3 to compute the new density and iterate until convergence is achieved.