<div dir="ltr">Again thank you very much for your reply<br><br><br>I have been able to obtain the expansion in terms of determinants. I was missing multiply each of the internally contracted configurations (ICC) by the normalizing factor.<br><br>In short I summarize the procedure<br>The part of the double excitations in the wave function is expressed as<br> \sum_{i>j}\sum_{ab}\sum_{p}N_{ab}^{ijp}C_{ab}^{ijp}\Psi_{ijp}^{ab}<br>Molpro prints C_{ab}^{ijp} in the output file, and where N_{ab}^{ijp} is the remaining normalization factor.<br><br>1) The first step is to convert \Psi_{0} from CSF to determinants.<br><br>2) After, the ICC are obtained in terms of determinants<br> \Psi_{ijp}^{ab}=\frac{1}{2}(\hat{E}_{ai,bj}+p\hat{E}_{bi,aj})\Psi_{0}<br>resulting in 8 cases (3 are zero) depending if i=j a=b p=1, i=j a=b p=-1, etc. In developing the algebra, everything is put in terms of creation and annihilation, where care must be taken with the phase factors (1 or -1) when applying operators, depending whether if there are an even or odd electrons number to the left in the occupation-number vector.<br><br>3) the normalization factors are then calculated<br> N_{ab}^{ijp}=\sqrt{<\Psi_{ijp}^{ab}|\Psi_{klq}^{cd}>}<br> <\Psi_{ijp}^{ab}|\Psi_{klq}^{cd}>=\frac{1}{2}\delta_{pq}(\delta_{ac}\delta_{bd}+p\delta_{ad}\delta_{bc})S_{ij,kl}^{p}<br> S_{ij,kl}^{p}=<0|\hat{E}_{ik,jl}+p\hat{E}_{il,jk}|0><br>similarly, there are eight different cases. When a!=b, an additional multiplication is performed of N_{ab}^{ijp} by \sqrt{2}.<br><br>4) Finally, the coefficients for each of the determinants are summed.<br><br>By this way, I got the CI vector norm that is indicated in the output of Molpro, and with a little more work, I could calculate the total energy of the system.<br><br><br>Regards<br>José<br></div><div class="gmail_extra"><br><div class="gmail_quote">2015-08-22 20:32 GMT-05:00 Gerald Knizia <span dir="ltr"><<a href="mailto:knizia@theochem.uni-stuttgart.de" target="_blank">knizia@theochem.uni-stuttgart.de</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear José,<br>
this may be a bit complicated; I am actually not entirely sure how this<br>
works internally in this program. But there are some things to consider:<br>
<br>
- The internally contracted configurations are by themselves not<br>
necessarily orthogonal in the internal space, and thus they need to be<br>
orthogonalized. However, if I am not mistaken, the coefficients which<br>
are printed are actually the coefficients for the "raw",<br>
non-orthogonalized spaces (i.e., singlet/triplet coupled E^ab_ij<br>
operators applied on the reference function directly, not the<br>
orthogonalized counterparts). That means that if you just take those<br>
coefficients, expand the internally contracted configurations (ICCs) in<br>
determinants, and then compute the overlap (using the determinant<br>
overlaps! not just square-summing the coefficients), you should get the<br>
correct result. I think this is what you are doing.<br>
<br>
- One thing to take care of are the reference coefficients used. If I am<br>
not very mistaken (someone else: please correct me if I am wrong), then<br>
the CI coefficients of the reference function |Phi> which are used to<br>
define the ICCs are *NOT* updated during the MRCI iterations (as this<br>
would require re-orthogonalization and lots of other things to be done,<br>
and lead to inconsistencies about the external space between iterations,<br>
which would make things hard to converge). That is: The determinants<br>
used to define the ICCs are not equal to the determinants which you get<br>
from the pure internal part of the wave function; rather, they stay<br>
fixed on the original reference function. This may be easily missed.<br>
<br>
Not sure if this helps, but at this moment I have no further ideas on<br>
this. Btw: great work reproducing the norms in the internal and<br>
singly-external space. That must have taken a while :).<br>
<br>
Best wishes,<br>
Gerald<br>
<br>
<br>
On Thu, 2015-08-20 at 03:29 -0500, José Cortés wrote:<br>
> Dear Professor Knizia<br>
><br>
> Thank you very much for your reply. I have a question concerning the<br>
> coefficients of<br>
> the doubly external configurations.<br>
><br>
> My aim is obtain the CI vector in terms of determinants. I know this<br>
> can not be done<br>
> directly in the mrci module of Molpro, so I wrote a perl script.<br>
><br>
> I have no problems in the case of the reference function and simple<br>
> external configurations.<br>
> I can go from CSF to determinants by the genealogical coupling scheme.<br>
> However, this<br>
> is more difficult in the doubly external configurations case.<br>
><br>
> First, i transform each contracted configuration in terms of<br>
> uncontracted CSF´s<br>
><br>
> \Psi_{ijp}^{ab}=\frac{1}{2}(\hat{E}_{ai,bj}+p<br>
> \hat{E}_{bi,aj})\Psi_{0}<br>
> =\sum_{P\nu}<\Psi_{ijp}^{ab}|\Psi_{P<br>
> \nu}^{ab}>\Psi_{P\nu}^{ab}<br>
><br>
> where \Psi_{0} is the reference function (p=1 singlet coupling, p=-1<br>
> triplet coupling).<br>
> Then, I multiply each uncontracted CSF by the associated coefficient<br>
> with \Psi_{ijp}^{ab}<br>
> (listed in the output). Later I express each uncontracted CSF in<br>
> terms of determinants.<br>
> As I understand it, the labels i, j, a, b, p in \Psi_{ijp}^{ab} refer<br>
> to<br>
> "I J -> K L NP" in the output of Molpro.<br>
><br>
> However, performing this procedure does not achieve a square norm that<br>
> matches the output<br>
><br>
> CLASS SQ.NORM ECORR1 ECORR2<br>
> +++++++++++++++++++++++++++++++++++++++++++++++++++<br>
> Internals 0.00001717 0.00000000 -0.00000069<br>
> Singles 0.00065315 -0.00263386 -0.00263924<br>
> Pairs 0.00787253 -0.03783725 -0.03783119<br>
><br>
> I do not understand that I'm doing wrong.<br>
> Perhaps, the coefficients associated with \Psi_{ijp}^{ab} are refer to<br>
> a non-orthonormal basis?<br>
> I would appreciate any help that you could provide me.<br>
><br>
><br>
> regards<br>
><br>
> Jose Jara<br>
> Universidad Nacional<br>
> Autónoma de México<br>
><br>
><br>
> 2015-08-12 17:01 GMT-05:00 José Cortés <<a href="mailto:zolidus@gmail.com">zolidus@gmail.com</a>>:<br>
> Thank you very much for your reply.<br>
> I had never used the MRCI module in Molpro and I thought that<br>
> the CI expansion would be made on terms of uncontracted CSF<br>
> like in some other programs.<br>
><br>
> I also found the answer in the literature recommended for the<br>
> MRCI module in MOLPRO (J. Chem. Phys. 89, 5803 (1988))<br>
><br>
> Regards<br>
> José Jara<br>
><br>
><br>
> 2015-08-12 12:15 GMT-05:00 Gerald Knizia<br>
> <<a href="mailto:knizia@theochem.uni-stuttgart.de">knizia@theochem.uni-stuttgart.de</a>>:<br>
> Dear José,<br>
> you are right about \ and / indicating spin couplings<br>
> in the<br>
> geneological coupling scheme. Regarding the doubly<br>
> external<br>
> configurations: These are not individual CSFs, but<br>
> they indicate<br>
> internally contracted configurations, in which<br>
> spin-free excitation<br>
> operators are applied to the entire reference<br>
> function:<br>
><br>
> |Phi^ij_ab> = E^{ab}_{ij} |Phi><br>
><br>
> with |Phi> being the full MCSCF-type reference<br>
> function (not individual<br>
> CSFs), i and j being occupied orbital labels, and a<br>
> and b being external<br>
> orbitals.<br>
><br>
> The operator E^{ab}_{ij} denotes explicitly<br>
><br>
> E^{ab}_{ij} = \sum_{\sigma \in A,B} \sum_{\tau \in<br>
> A,B} c^{a \sigma}<br>
> c^{b \tau} c_{j \tau} c_{i \sigma}<br>
><br>
> where \sigma and \tau sum over spin labels.<br>
><br>
> Best wishes,<br>
> Gerald<br>
><br>
><br>
> On Sun, 2015-08-09 at 21:51 -0500, José Cortés wrote:<br>
> > Dear molpro users<br>
> ><br>
> > I have a question about the output of the CSFs in a<br>
> mrci calculation.<br>
> > As an example suppose the He2 molecule with the<br>
> 6-311G basis,<br>
> > where an active space of 4e,4o was chosen in the<br>
> part of the casscf<br>
> > calculation.<br>
> > Such election leaves only two external orbitals. As<br>
> I understand the<br>
> > symbols<br>
> > "/" and "\" concerning to relative spin couplings,<br>
> which are related<br>
> > to the t vectors<br>
> > in the genealogical coupling scheme.<br>
> ><br>
> > For example for the following configurations (which<br>
> are in the output<br>
> > of the MRCI calculation)<br>
> ><br>
> > Reference coefficients greater than<br>
> 0.0000000<br>
> > ================================<br>
> > 2200 0.9959538<br>
> > /\/\ 0.0600897<br>
> ><br>
> > Coefficients of singly external<br>
> configurations greater than<br>
> > 0.0000000<br>
> ><br>
> ================================================<br>
> > /\\0 5.1 -0.0062116<br>
> > 20\0 6.1 -0.0055316<br>
> ><br>
> > the t vectors specified in the complete basis set<br>
> would be like:<br>
> > 220000<br>
> > /\/\00<br>
> > /\\0/0<br>
> > 20\00/<br>
> ><br>
> > However, my question arises in the doubly external<br>
> configurations<br>
> ><br>
> > Coefficients of doubly external<br>
> configurations greater than<br>
> > 0.0000<br>
> > ===========================================<br>
> > PAIR I J -> K L NP SYM<br>
> REF<br>
> > COEFFICIENTS<br>
> > 4 2.1 2.1 5.1 5.1 1 1<br>
> 1 -0.02645858<br>
> > 1 1.1 1.1 5.1 5.1 1 1<br>
> 1 -0.02035037<br>
> > 4 2.1 2.1 6.1 6.1 1 1<br>
> 1 -0.01367284<br>
> > 9 3.1 3.1 5.1 5.1 1 1<br>
> 1 -0.01342122<br>
> ><br>
> > In this case, how the t-vectors should be specified<br>
> for each one of<br>
> > the configurations in the complete basis set?<br>
> > How do I get in this case each one of the<br>
> configurations?<br>
> > I would appreciate any information you could give me<br>
> about it.<br>
> ><br>
> > Regards<br>
> > José Jara<br>
> > Universidad Nacional<br>
> > Autónoma de México<br>
> ><br>
><br>
> > _______________________________________________<br>
> > Molpro-user mailing list<br>
> > <a href="mailto:Molpro-user@molpro.net">Molpro-user@molpro.net</a><br>
> > <a href="http://www.molpro.net/mailman/listinfo/molpro-user" rel="noreferrer" target="_blank">http://www.molpro.net/mailman/listinfo/molpro-user</a><br>
><br>
><br>
><br>
><br>
><br>
><br>
<br>
<br>
</blockquote></div><br></div>