[Pw_forum] Projection?

[Paolo Giannozzi]

On Friday 07 November 2003 21:57, Hong, SamPyo wrote:

> As far as I know, before doing projection of each |phi_i> to |evc>, we
> should have a set of the orthogonized wavefunctions i.e, <phi_i|S|phi_j>
> = 0 if i&j are different.  For example, in the following routine,
> if we replace
>
>                temp = ZDOTC(npw,swfcatom(1,i),1,evc(1,ibnd),1)
> by
>                temp = ZDOTC(npw,swfcatom(1,i),1,wfcatom(1,i),1)
>
> Then, temp must be zero. However, it seems not to be true. Why is that?
>
> ---------------PWSCF 1.03
> projwave.F----------------------------------------
> c
> c make the projection
> c
>          do ibnd = 1, nbnd
>             psum = 0.d0
>             do i=1,natomwfc
>                temp = ZDOTC(npw,swfcatom(1,i),1,evc(1,ibnd),1)
>                work(i,1) = temp
>             enddo
> #ifdef PARA
>             call reduce(2*natomwfc,work)
> #endif

swfcatom does not contain S|phi_i> (S is the ultrasoft overlap
matrix: S=1 for norm-conserving pseudopotentials), but 
O^(-1/2) S|phi_i>, where O_(ij) = <phi_i|S|phi_j>. This is done
in the lines just above those you show:

c
c trasform atomic orbitals O^-1 psi
c
         do i=1,npw
            call setv(2*natomwfc,0.d0,work,1)
            call ZGEMV('n',natomwfc,natomwfc,(1.d0,0.d0),overlap,
     *            natomwfc,swfcatom(i,1),npwx, (0.d0,0.d0),work,1)
            call ZCOPY(natomwfc,work,1,swfcatom(i,1),npwx)
         end do 

The orthonormal atomic wavefunctions are O^(-1/2) |phi_i>
(orthonormal wrt the S operator for ultrasoft potentials).
The comment to these lines ("trasform atomic orbitals O^-1 psi")
was - as most comments in computer codes are - obscure and 
misleading. It is correct in more recent versions of the code.

Paolo
-- 
Paolo Giannozzi             e-mail:  giannozz at nest.sns.it
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