# [Pw_forum] complex band

Manoj Srivastava manoj at phys.ufl.edu
Sat Dec 27 04:26:19 CET 2008

Dear Alexander and PWSCF users,
I have two questions about complex band code based on the Choi and Ihm
paper(PRB 59,2167,(1999))
1. At the expressions where we have to use non local potential
W((k+G)_{\perp},tau-z-d), i can see the code only uses
W((k+G)_{\perp},tau-z). I guess this is because of periodicity of nonlocal
potential in the z direction. Am i right?

2. This question is about determining the coefficients of the
wavefunctions. As we can see from equations (17) for the local part of the
potential it has N*2*N_2d number of unknown cofficients. Now using the
boundary conditions, that the wavefunction and its derivative should be
continuous between the slabs, we can determine (N-1)*2*N_2d unknownns,
which leaves 2*N_2d no. of coefficients to be determined later. The same
thing applies for the solutions of nonlocal part of the potential in
equation (24). Thus the number of linearly independent solution for the
nonlocal part is 2*N_2d. we use Bloch's condition to determine these
unknown coeffiecints. This is where my question is. When we are trying to
construct the general solution as in  equation (39), the local part has
number of unknown coeffieints 2*N_2d, which is fine. But the nonlocal part
has C_{\alpha,l,m} number of unknown coefficients, which is not equal to
2*N_2d. My question is why? Are we somehow combining the coefficients of
local part with nonlocal part?
Any help will be appreciated.
Happy Holidays!

Manoj Srivastava