Siesta I - Psi-k

Functional of LWFs
Where H and S are the overlap and Hamiltonian matrices in
the basis of the (unknown) localised wave functions ϕ i .
E. B. Stechel, A. R. Williams & P. J. Feibelman, Phys. Rev. B 49, 10088 (1994)
!
E BS
J.-L. Fattebert & J. Bernholc, Phys. Rev. B 62 1713 (2000)
The inverse of the overlap matrix can been avoided:
E BS
[{" }] i
= 2 Tr{ S #1 H}
[ ] = 2 Tr 2 # S
{" } i
{ }
( )H
P. Ordejon et al. Phys. Rev. B 48, 14646 (1993)
F. Mauri & G. Galli, Phys. Rev. B 50, 4316 (1994)
!
The functionals are different but equal at the minimum