[molpro-user] How to read the CSFs in a MRCI calculation?
Gerald Knizia
knizia at theochem.uni-stuttgart.de
Sun Aug 23 02:32:02 BST 2015
Dear José,
this may be a bit complicated; I am actually not entirely sure how this
works internally in this program. But there are some things to consider:
- The internally contracted configurations are by themselves not
necessarily orthogonal in the internal space, and thus they need to be
orthogonalized. However, if I am not mistaken, the coefficients which
are printed are actually the coefficients for the "raw",
non-orthogonalized spaces (i.e., singlet/triplet coupled E^ab_ij
operators applied on the reference function directly, not the
orthogonalized counterparts). That means that if you just take those
coefficients, expand the internally contracted configurations (ICCs) in
determinants, and then compute the overlap (using the determinant
overlaps! not just square-summing the coefficients), you should get the
correct result. I think this is what you are doing.
- One thing to take care of are the reference coefficients used. If I am
not very mistaken (someone else: please correct me if I am wrong), then
the CI coefficients of the reference function |Phi> which are used to
define the ICCs are *NOT* updated during the MRCI iterations (as this
would require re-orthogonalization and lots of other things to be done,
and lead to inconsistencies about the external space between iterations,
which would make things hard to converge). That is: The determinants
used to define the ICCs are not equal to the determinants which you get
from the pure internal part of the wave function; rather, they stay
fixed on the original reference function. This may be easily missed.
Not sure if this helps, but at this moment I have no further ideas on
this. Btw: great work reproducing the norms in the internal and
singly-external space. That must have taken a while :).
Best wishes,
Gerald
On Thu, 2015-08-20 at 03:29 -0500, José Cortés wrote:
> Dear Professor Knizia
>
> Thank you very much for your reply. I have a question concerning the
> coefficients of
> the doubly external configurations.
>
> My aim is obtain the CI vector in terms of determinants. I know this
> can not be done
> directly in the mrci module of Molpro, so I wrote a perl script.
>
> I have no problems in the case of the reference function and simple
> external configurations.
> I can go from CSF to determinants by the genealogical coupling scheme.
> However, this
> is more difficult in the doubly external configurations case.
>
> First, i transform each contracted configuration in terms of
> uncontracted CSF´s
>
> \Psi_{ijp}^{ab}=\frac{1}{2}(\hat{E}_{ai,bj}+p
> \hat{E}_{bi,aj})\Psi_{0}
> =\sum_{P\nu}<\Psi_{ijp}^{ab}|\Psi_{P
> \nu}^{ab}>\Psi_{P\nu}^{ab}
>
> where \Psi_{0} is the reference function (p=1 singlet coupling, p=-1
> triplet coupling).
> Then, I multiply each uncontracted CSF by the associated coefficient
> with \Psi_{ijp}^{ab}
> (listed in the output). Later I express each uncontracted CSF in
> terms of determinants.
> As I understand it, the labels i, j, a, b, p in \Psi_{ijp}^{ab} refer
> to
> "I J -> K L NP" in the output of Molpro.
>
> However, performing this procedure does not achieve a square norm that
> matches the output
>
> CLASS SQ.NORM ECORR1 ECORR2
> +++++++++++++++++++++++++++++++++++++++++++++++++++
> Internals 0.00001717 0.00000000 -0.00000069
> Singles 0.00065315 -0.00263386 -0.00263924
> Pairs 0.00787253 -0.03783725 -0.03783119
>
> I do not understand that I'm doing wrong.
> Perhaps, the coefficients associated with \Psi_{ijp}^{ab} are refer to
> a non-orthonormal basis?
> I would appreciate any help that you could provide me.
>
>
> regards
>
> Jose Jara
> Universidad Nacional
> Autónoma de México
>
>
> 2015-08-12 17:01 GMT-05:00 José Cortés <zolidus at gmail.com>:
> Thank you very much for your reply.
> I had never used the MRCI module in Molpro and I thought that
> the CI expansion would be made on terms of uncontracted CSF
> like in some other programs.
>
> I also found the answer in the literature recommended for the
> MRCI module in MOLPRO (J. Chem. Phys. 89, 5803 (1988))
>
> Regards
> José Jara
>
>
> 2015-08-12 12:15 GMT-05:00 Gerald Knizia
> <knizia at theochem.uni-stuttgart.de>:
> Dear José,
> you are right about \ and / indicating spin couplings
> in the
> geneological coupling scheme. Regarding the doubly
> external
> configurations: These are not individual CSFs, but
> they indicate
> internally contracted configurations, in which
> spin-free excitation
> operators are applied to the entire reference
> function:
>
> |Phi^ij_ab> = E^{ab}_{ij} |Phi>
>
> with |Phi> being the full MCSCF-type reference
> function (not individual
> CSFs), i and j being occupied orbital labels, and a
> and b being external
> orbitals.
>
> The operator E^{ab}_{ij} denotes explicitly
>
> E^{ab}_{ij} = \sum_{\sigma \in A,B} \sum_{\tau \in
> A,B} c^{a \sigma}
> c^{b \tau} c_{j \tau} c_{i \sigma}
>
> where \sigma and \tau sum over spin labels.
>
> Best wishes,
> Gerald
>
>
> On Sun, 2015-08-09 at 21:51 -0500, José Cortés wrote:
> > Dear molpro users
> >
> > I have a question about the output of the CSFs in a
> mrci calculation.
> > As an example suppose the He2 molecule with the
> 6-311G basis,
> > where an active space of 4e,4o was chosen in the
> part of the casscf
> > calculation.
> > Such election leaves only two external orbitals. As
> I understand the
> > symbols
> > "/" and "\" concerning to relative spin couplings,
> which are related
> > to the t vectors
> > in the genealogical coupling scheme.
> >
> > For example for the following configurations (which
> are in the output
> > of the MRCI calculation)
> >
> > Reference coefficients greater than
> 0.0000000
> > ================================
> > 2200 0.9959538
> > /\/\ 0.0600897
> >
> > Coefficients of singly external
> configurations greater than
> > 0.0000000
> >
> ================================================
> > /\\0 5.1 -0.0062116
> > 20\0 6.1 -0.0055316
> >
> > the t vectors specified in the complete basis set
> would be like:
> > 220000
> > /\/\00
> > /\\0/0
> > 20\00/
> >
> > However, my question arises in the doubly external
> configurations
> >
> > Coefficients of doubly external
> configurations greater than
> > 0.0000
> > ===========================================
> > PAIR I J -> K L NP SYM
> REF
> > COEFFICIENTS
> > 4 2.1 2.1 5.1 5.1 1 1
> 1 -0.02645858
> > 1 1.1 1.1 5.1 5.1 1 1
> 1 -0.02035037
> > 4 2.1 2.1 6.1 6.1 1 1
> 1 -0.01367284
> > 9 3.1 3.1 5.1 5.1 1 1
> 1 -0.01342122
> >
> > In this case, how the t-vectors should be specified
> for each one of
> > the configurations in the complete basis set?
> > How do I get in this case each one of the
> configurations?
> > I would appreciate any information you could give me
> about it.
> >
> > Regards
> > José Jara
> > Universidad Nacional
> > Autónoma de México
> >
>
> > _______________________________________________
> > Molpro-user mailing list
> > Molpro-user at molpro.net
> > http://www.molpro.net/mailman/listinfo/molpro-user
>
>
>
>
>
>
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