Yousef Saad Department Of Computer Science And Engineering

Kohn-Sham equations → nonlinear eigenvalue Pb
− 1
2 ∇2
+ (Vion + VH + Vxc)
Ψi = EiΨi, i = 1, ..., no
ρ(r) =
➤ Both Vxc and VH, depend on ρ.
no
i
|Ψi(r)| 2
∇ 2 VH = −4πρ(r)
➤ Potentials & charge densities must be self-consistent.
➤ Broyden-type quasi-Newton technique used
➤ Typically, a small number of iterations are required
➤ Most time-consuming part: diagonalization
CSE Colloquium 11/09/09 p. 11