[CP2K:10298] Re: MO coefficients not normalized?

[Krack Matthias (PSI)]

Dear Daniel

Did you try to restart with DIAGONALISATION and ADDED_MOS using a wavefunction restart file from a well-converged OT run?

Best regards

Matthias

From: cp... at googlegroups.com [mailto:cp... at googlegroups.com] On Behalf Of Dan_M
Sent: 10 May 2018 13:46
To: cp2k
Subject: [CP2K:10298] Re: MO coefficients not normalized?


Thanks a lot Matt for your very fast answer. I was so concerned with technical issues that I forgot about the basics.

Actually maybe you or some other expert can help me out with the actual issue I am having. The situation is this:

I want to get the MOs (eigenvalues and eigenvectors) for both the occupied and unoccupied states in a somewhat involved system (~100-200 waters plus one proton, i.e. total charge +1, geometry let's say far from any local minima). For this I tried two routes:

1) converge the wfn with OT and request NLUMO to be computed after convergence. With this I find two problems:
  - The calculation of the LUMOs does not converge (I get "WARNING : did not converge in ot_eigensolver" even if I increase MAX_ITER_LUMO to 1000 which I think should be enough). I note that I could get it converged for EPS_LUMO 1.0E-4 but I tried with a much tighter convergence (2.0E-07 as with the occupied states) since what I get otherwise is the energy of the LUMO below that of the HOMO. I am aware of this happening often when the system is metallic and OT is not well suited but I think it should not happen in a protonated water system (I would expect finding the LUMO as a lone state somewhere in the middle of the band gap, but not this).
  - Even when it converges (which I managed to do in toy systems but not on my system of interest), this only works for getting the eigenvalues which can be done either requesting the NLUMO in the &PDOS or in the &MO_CUBES sections, but not the eigenvectors even if I try to do the trick of asking for MO_INDEX_RANGE 1 [nhomo+nlumo] in the &MO section.

2) converge the wfn with diagonalization in any flavor (standard, davidson, lanczos or filter_matrix) requesting ADDED_MOS. Here the problem is that the diagonalization is a complete pain and I am struggling a lot to get it converged, which I did not manage yet. I am trying to do the usual tricks (playing with the ALPHA in &MIXING, etc), but still I have not managed to converge it. I tried doing the trick of computing the wfn with OT and then use that wfn as guess in a run with diagonalization with ADDED_MOS, but in that case the coefficients seem to be rescaled or ignored (since there are less MOS in the restart wfn than expected) and I don't get any improvement.

Maybe somebody could give me some tips for improving the diagonalization in charged systems (some combination of mixing methods, parameters, etc.) or some workaround to make it work with OT?

Thanks again!
D.


El miércoles, 9 de mayo de 2018, 22:21:37 (UTC+2), Matt W escribió:
Dear Daniel,

the Gaussian basis set is not orthonormal, so the overlap matrix is required to provide a metric that converts to an orthonormal basis. Due to symmetry the pz orbital is orthogonal to the others in your example, so in that case every thing is easy.

In general, the relation is C^T S C = I, where C is the matrix of MO coefficients, S is the overlap matrix and I is the identity matrix. You can print of the S matrix and check this. It is somewhere in the AO_MATRICES section of DFT % PRINT.

See, for instance, Szabo and Ostlund, Modern Quantum Chemistry, Introduction to Advanced Electronic Structure Theory - exercise 3.10 in my version.

Matt

On Wednesday, May 9, 2018 at 8:20:13 PM UTC+1, Dan_M wrote:
Dear all,

After requesting the printing out of the MO coefficients, I have observed that the coefficients do not seem to be normalized. For instance, here are the MOs for 1 water molecule with a SZV basis (after a single point calculation on the "real" geometry, with diagonalization algorithm standard):

 MO EIGENVALUES, MO OCCUPATION NUMBERS, AND SPHERICAL MO EIGENVECTORS

                              1              2                3                4
                           -0.952554    -0.496599    -0.304175    -0.250528

                            2.000000     2.000000     2.000000     2.000000

     1     1  O  2s        0.807460    -0.000000     0.542312     0.000000
     2     1  O  3py      -0.246487    -0.000000     0.810927     0.000000
     3     1  O  3pz      -0.000000     0.000000    -0.000000     1.000000
     4     1  O  3px       0.000000    -0.661844    -0.000000    -0.000000

     5     2  H  1s        0.125677    -0.390214    -0.194623    -0.000000

     6     3  H  1s        0.125677     0.390214    -0.194623    -0.000000

So only the MO 4 is trivially normalized, but the others are not. Am I missing something (some correction factor, etc) or is this just the way it is?

Thanks and best
Daniel
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