Use of supersymmetry

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Max
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First name(s): Latevi
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Last name(s): Lawson Daku
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Use of supersymmetry

Post by Max » 08 Oct 2015, 14:52

Dear DALTON users and developers,

I would like to use the "super symmetry" feature of DALTON to perform a CASSCF calculation on a molecule of Oh symmetry. At the beginning of the calculations, the true molecular symmetry is detected and D2h is used for the calculations. But when it comes to assign the orbitals to the irreps of the true point group, the analysis fail: the atomic coordinates are given with 6 digits and I've played with the .THRSSY threshold with no success. I've attached to the message one of the outputs. I'm not sure I will be able to use this feature. Could one of you use it? If so, could please tell me how many digits and which THRSSY value you used?

I'm interested in using the SUPSYM feature because, if I get it correctly, this may help ensure that the integrals that should be zero by symmetry effectively are zero. I don't think this is really the case in D2h [MOs from a given irrep of the supsym (for instance Eg) can have unexpected (small~tiny) contributions from AOs that should only be involved in building MOs of an other irrep of the supsym group (A1g)]. There is perhaps a simpler way to ask for more accurate integrals?!

I thank you in advances for your suggestions and comments.

Best regards,
Max
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fe2_nch.d2h.b1t_cas0.ls.out
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taylor
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Re: Use of supersymmetry

Post by taylor » 08 Oct 2015, 18:23

There are thresholds one can set for consideration/neglect of integrals, although one has to be aware that there is a fundamental limit imposed here by computer arithmetic (if the program performs a thousand operations in 64-bit arithmetic on a quantity originally accurate to machine precision, about 14 decimal digits, then the final result cannot be guaranteed to better than 11 digits, although integral evaluation is not quite as bad as this). However, I fear your problems are deeper than this.

In the exploitation of higher symmetry, one uses the fact that there are (nearly exact) degeneracies among the eigenvalues of a totally symmetric operator to further block the structure of operator matrices beyond what D2h and its subgroups provide. A key element of this is the comparison of these eigenvalues between different D2h or subgroup symmetries. Consider for example a molecule with C3v symmetry, treated by Dalton in Cs. Basis functions for symmetry species of E symmetry in C3v (that is, basis functions for specific rows of the E irreducible representation [irrep]) will appear in the A' irrep of Cs and in the A'' irrep. Comparing eigenvalues between these irreps will identify the symmetry species of E in C3v. Unfortunately, this scheme is predicated on the symmetry species of the degenerate higher-point-group irreps appearing in different D2h symmetries. If the symmetry species of a degenerate irrep in the higher symmetry appear in the same D2h symmetry, they can (and probably will) mix arbitrarily. They are determined only to within a unitary transformation, and if they are in the same lower-group symmetry then there is no simple way to eliminate this arbitrary mixing, whereas if they are in different lower-group symmetries there is no arbitrariness because they cannot mix (at least assuming there are no numerical issues, such as might arise at very large internuclear distances).

As I recall, the two rows of the E representations in Oh appear in the same A representations of D2h. If this is the case, no numerical procedure based on diagonalizing matrices of totally symmetric operators can possibly guarantee a clean separation into symmetry species of Oh. A more elaborate procedure based on examining the matrices of non-totally symmetric operators like the dipole moment (say) might be able to, but I know of no electronic structure program that does this. In some cases (D4h is an example, Paul Bagus tells me, although I have not investigated this myself) it may be possible to make progress by reorienting the molecule, say by putting some atoms "between" the axes rather than on the axes. You could try this but my guess is that this will still not work for Oh.

In summary, while it may be that your problems can be solved by tightening thresholds, I think this is unlikely. I do not see how the "supersymmetry" procedure in Dalton (or in other codes like Molcas or Molpro) can deal successfully with certain point groups in the way you want. To ensure the desired degeneracies are observed, yes, at least in principle. But to obtain true symmetry species, and thus implicitly the full selection rules on integrals, I fear no.

Best regards
Pete

Max
Posts: 8
Joined: 16 Jan 2014, 17:27
First name(s): Latevi
Middle name(s): Max
Last name(s): Lawson Daku
Affiliation: University of Geneva
Country: Switzerland

Re: Use of supersymmetry

Post by Max » 09 Oct 2015, 15:18

Dear Pete,

I do thank you for your clear and detailed explanation.

I will continue without SUPSYM, using tightened thresholds, and more especially paying attention to whatever I can (AOs contributions to MOs, occupation numbers) to make sure that the CASSCF solutions do not exhibit (too much) symmetry contamination :)

Best regards,
Max

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