[molpro-user] Computing higher roots in MRCI

[Terry Frankcombe]

On Tue, 2009-04-14 at 16:13 +0200, Bernd Hartke wrote:
> Gerald Knizia wrote:
> > On Friday 10 April 2009 21:12, Jaffe, Richard L. (ARC-TSN) wrote:
> >> I am interested in computing the 6th root of B2 symmetry in non-linear C3.
> >> I can determine the first 6 roots, but I am trying to reduce computational
> >> cost by obtaining accurate solution only for the 6th root.
> > 
> > I don't know much about Molpros diagonalization routines, but from a purely 
> > numerical standpoint I would guess that this is impossible. I'm not aware of 
> > any matrix diagonalization algorithm that can calculate a specific 
> > eigenvector without also calculating all lower (or all higher) ones.
> >
> you may want to check out things like "inverse iteration" or "filter
> diagonalization" etc.

And variations on subspace projection methods (Davidson, Olsen) or the
Nesbet update can do it to, with some reasonable starting information.

Ciao
Terry