[molpro-user] Computing higher roots in MRCI

Alexander Mitrushchenkov Alexander.Mitrushchenkov at univ-mlv.fr
Tue Apr 14 20:24:29 BST 2009

As Bernd wrote, filter diagonalization or inverse iteration methods
find excited vectors without knowing lower states easily. Moreover, for
tri-diagonal matrix it is easy to get the root number. In any case,
it has nothing to do with the question. Molpro uses Davidson
algorithm which can not be easily reprogrammed. In principle,
there is no problem to find excited root as molpro always selects
the current approximation which has the maximum overlap
with corresponding reference state, assuming (VERY IMPORTANT) that 
correlation correction is small. So in principle simple 'state,1,6' should
work. However, as it is often for excited states, the reference state might be not
a good approximation to true correlated state, so this approach
would fail due to the root flipping problem or insufficient overlap problem. 
In this case the 'state,6;refstate,1,6;'
as documented in manual, might work, as extra vectors are generated
for lower roots without converging them. Unfortunately in this part of
the code there seems to be a bug which means that this actually does not
work as expected. So you should wait until eventually bug is fixed.
Still, if you are sure that your state is well isolated from lower states,
energetically, configurationally or by extra symmetry,
simple 'state,1,6' might work, you can always try.

Best regards,


On Tuesday 14 April 2009 20:41:52 Garnet Chan wrote:
> Gerald is correct in that one can't target the "n" th eigenvector
> directly, but, one CAN use the concept of Harmonic Ritz vectors to
> obtain excited state eigenvalues near
> a given input energy E without getting the other roots. You won't know
> then if it's say the 6th or the 7th root, but you can
> say it's the root closest to E. This is not implemented in Molpro
> currently, but it would be simple to do so.
> On Tue, Apr 14, 2009 at 9:49 AM, Gerald Knizia
> <knizia at theochem.uni-stuttgart.de> 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.
> > --
> > Gerald Knizia
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> > Molpro-user at molpro.net
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> >
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Dr. Alexander Mitrushchenkov, IGR
Laboratoire de Modélisation et Simulation Multi Echelle (MSME), FRE 3160 CNRS
Université Paris-Est Marne-la-Vallée
5 Bd Descartes
77454 Marne la Vallée, Cedex 2, France

Phone:    +33(0)160957316
Fax:      +33(0)160957320
e-mail:   Alexander.Mitrushchenkov at univ-mlv.fr

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