[CP2K:10300] Re: MO coefficients not normalized?

Dan_M danielm... at gmail.com
Fri May 11 09:48:25 UTC 2018


Hi Matthias,

I did what you suggested and even though it seemed to make the convergence 
a bit smoother for OT, still it does not improve the diagonalization.
Specifically, I set EPS_DEFAULT 1.0E-14 and dropped the *_CUTOFF and XC 
smoothing, and converged with OT and EPS_SCF 1.0E-8.
With this optimized wfn I started the diagonalization (algorithm standard, 
direct_p_mixing, alpha 0.1) and doesn't work:

  Step     Update method      Time    Convergence         Total energy    
Change
  
------------------------------------------------------------------------------
     1 P_Mix/Diag. 0.10E+00    5.9     1.04345518     -2483.7051317469 
-2.48E+03
     2 P_Mix/Diag. 0.10E+00    6.2     0.21526298     -2483.6950681260  
1.01E-02
     3 P_Mix/Diag. 0.10E+00    6.3     0.18583657     -2483.6983718168 
-3.30E-03
     4 P_Mix/Diag. 0.10E+00    6.2     0.15912799     -2483.7005021331 
-2.13E-03
     5 P_Mix/Diag. 0.10E+00    6.6     0.13537782     -2483.7018913141 
-1.39E-03
     6 P_Mix/Diag. 0.10E+00    7.2     0.11457317     -2483.7028012278 
-9.10E-04
     7 P_Mix/Diag. 0.10E+00    6.2     0.09655329     -2483.7033951772 
-5.94E-04
     8 P_Mix/Diag. 0.10E+00    6.2     0.08107945     -2483.7037777217 
-3.83E-04
     9 P_Mix/Diag. 0.10E+00    6.4     0.06788010     -2483.7040173663 
-2.40E-04
    10 P_Mix/Diag. 0.10E+00    6.2     1.05830128     -2483.7041598673 
-1.43E-04
    11 P_Mix/Diag. 0.10E+00    6.4     0.27282434     -2483.6885022250  
1.57E-02
    12 P_Mix/Diag. 0.10E+00    6.2     0.19477670     -2483.6934564774 
-4.95E-03
    13 P_Mix/Diag. 0.10E+00    6.3     0.15900657     -2483.6966522751 
-3.20E-03
    14 P_Mix/Diag. 0.10E+00    6.3     0.13501187     -2483.6987689554 
-2.12E-03
    15 P_Mix/Diag. 0.10E+00    6.2     0.11406673     -2483.7002037460 
-1.43E-03
    16 P_Mix/Diag. 0.10E+00    6.3     0.09597285     -2483.7011950370 
-9.91E-04
    17 P_Mix/Diag. 0.10E+00    6.3     0.08046688     -2483.7018901542 
-6.95E-04
    18 P_Mix/Diag. 0.10E+00    6.3     0.06782297     -2483.7023829252 
-4.93E-04
    19 P_Mix/Diag. 0.10E+00    6.3     1.04290747     -2483.7027348383 
-3.52E-04
    20 P_Mix/Diag. 0.10E+00    6.2     0.21550410     -2483.6899786616  
1.28E-02
    21 P_Mix/Diag. 0.10E+00    6.2     0.18544263     -2483.6942956542 
-4.32E-03
....

BTW, that was after I set EPS_DIIS in &SCF below EPS_SCF, since otherwise 
things get much worse after DIIS starts:

  Step     Update method      Time    Convergence         Total energy    
Change
  
------------------------------------------------------------------------------
     1 P_Mix/Diag. 0.10E+00    5.9     1.04345518     -2483.7051317469 
-2.48E+03
     2 P_Mix/Diag. 0.10E+00    6.5     0.21526298     -2483.6950681260  
1.01E-02
     3 P_Mix/Diag. 0.10E+00    6.5     0.18583657     -2483.6983718168 
-3.30E-03
     4 P_Mix/Diag. 0.10E+00    6.6     0.15912799     -2483.7005021331 
-2.13E-03
     5 P_Mix/Diag. 0.10E+00    6.5     0.13537782     -2483.7018913141 
-1.39E-03
     6 P_Mix/Diag. 0.10E+00    6.5     0.11457317     -2483.7028012278 
-9.10E-04
     7 P_Mix/Diag. 0.10E+00    6.5     0.09655329     -2483.7033951772 
-5.94E-04
     8 DIIS/Diag.  0.26E-02    6.6     1.09993086     -2483.7037777217 
-3.83E-04
     9 P_Mix/Diag. 0.10E+00    6.5    98.45213358     -2482.2918306873  
1.41E+00
    10 P_Mix/Diag. 0.10E+00    6.5    88.61338472     -2479.1562224901  
3.14E+00
    11 P_Mix/Diag. 0.10E+00    6.4   738.84827806     -2413.5998990757  
6.56E+01
    12 P_Mix/Diag. 0.10E+00    6.5   726.38204744     -2239.0573891721  
1.75E+02
...

So probably you are right, there may be something else wrong. The possible 
issue that comes to my mind is that the system is not that simple. It is a 
water slab periodic in 2 dimensions and with a ~12 angstroms spacing in the 
3rd dimension, treated as fully periodic (e.g. &Poisson periodic XYZ) but I 
made sure that the net dipole is very small and slab-slab interactions are 
negligible for the neutral water slab. Then there is a proton placed close 
to a water in the slab surface, geometry very far from optimal (some could 
say "unphysical" but it should be treatable --and actually it works with 
OT--, H+ is 1.14 angstrom away from the closest O and 1.47 to the closest 
H). I am aware that of course I can not expect to converge the wfn for any 
kind of crazy geometry, but what I don't understand is why if OT converges 
(despite all the issues like charged cell, exotic geometry, etc) then 
diagonalization does not. Is it possible that simply the difficult geometry 
screws up that much the diagonalization of the OT converged wfn?

Thanks a lot for your comments,
Daniel


El jueves, 10 de mayo de 2018, 18:43:47 (UTC+2), Matthias Krack escribió:
>
> Hi Daniel
>
>  
>
> If your preceding OT run converged properly (tightly), the restart with 
> diagonalisation should converge immediately or after a few steps, otherwise 
> something is wrong.
>
>  
>
> There are some issues in your input which I would change without claiming 
> that this will solve your problem. I would
>
> 1)      use a smaller EPS_DEFAULT, e.g. at least 1.0E-12 (smaller is also 
> fine), 1.0E-10 is not tight enough
>
> 2)      drop the *_CUTOFF values in the &XC section unless you have a 
> good reason to set some of these values explicitly
>
> 3)      drop the smoothing unless you have any good reason to use it 
> (e.g. with BLYP), since you are using with 700Ry a rather high cutoff anyway
>
> 4)      use diagonalisation  with direct_p_mixing and a mixing alpha of 
> about 0.1 for restart, if that does not converge immediately or at least 
> within a few SCF steps starting from a converged OT run, then most likely 
> something else is wrong and it is unlikely that any other mixing method 
> will work better and solve the problem
>
> I understood that you are dealing with a condensed phase system. If yes, 
> did you check that the QZV3P basis sets you are using are suited for that 
> setup?
>
>  
>
> Best regards
>
>  
>
> Matthias
>
>  
>
> *From:* cp... at googlegroups.com <javascript:> [mailto:
> cp... at googlegroups.com <javascript:>] *On Behalf Of *Dan_M
> *Sent:* 10 May 2018 18:04
> *To:* cp2k
> *Subject:* Re: [CP2K:10300] Re: MO coefficients not normalized?
>
>  
>
> Hi Matthias,
>
> yest I did but it does not converge, for instance this is what I get when 
> using Davidson diagonalization (defaults parameters for &MIXING):
>
>   Step     Update method      Time    Convergence         Total energy    
> Change
>   
> ------------------------------------------------------------------------------
>      1 P_Mix/Dav.  0.40E+00    8.1     0.00309369     -2483.1531852407 
> -2.48E+03
>      2 P_Mix/Dav.  0.40E+00    2.5     0.15334223     -2483.1531847710  
> 4.70E-07
>      3 P_Mix/Dav.  0.40E+00    2.4     0.14839060     -2483.1496260655  
> 3.56E-03
>      4 P_Mix/Dav.  0.40E+00    2.4     0.06204907     -2483.1516643558 
> -2.04E-03
>      5 P_Mix/Dav.  0.40E+00    2.4     0.72149356     -2483.1519086893 
> -2.44E-04
>      6 P_Mix/Dav.  0.40E+00    2.4     0.44697821     -2483.0750573108  
> 7.69E-02
>      7 P_Mix/Dav.  0.40E+00    2.4     0.21458187     -2483.1176203039 
> -4.26E-02
>      8 P_Mix/Dav.  0.40E+00    2.4     0.09370387     -2483.1338242392 
> -1.62E-02
>      9 P_Mix/Dav.  0.40E+00    2.4     1.08948074     -2483.1415463487 
> -7.72E-03
>     10 P_Mix/Dav.  0.40E+00    2.4     0.67563179     -2482.9378947719  
> 2.04E-01
>     11 P_Mix/Dav.  0.40E+00    2.4     0.32819448     -2483.0539735944 
> -1.16E-01
>     12 P_Mix/Dav.  0.40E+00    2.4     0.15275080     -2483.0996929120 
> -4.57E-02
>     13 P_Mix/Dav.  0.40E+00    2.4     1.06118539     -2483.1220162257 
> -2.23E-02
>     14 P_Mix/Dav.  0.40E+00    2.4     0.77108692     -2482.9213332983  
> 2.01E-01
>     15 P_Mix/Dav.  0.40E+00    2.4     0.32374229     -2483.0459012328 
> -1.25E-01
>     16 P_Mix/Dav.  0.40E+00    2.4     0.16259590     -2483.0951505330 
> -4.92E-02
>     17 P_Mix/Dav.  0.40E+00    2.3     0.10138969     -2483.1193594430 
> -2.42E-02
>     18 P_Mix/Dav.  0.40E+00    2.4     0.06424836     -2483.1326526033 
> -1.33E-02
>     19 P_Mix/Dav.  0.40E+00    2.4     0.03960077     -2483.1403233567 
> -7.67E-03
> ...
>
> Similar behavior happens with the other diagonalization flavors, I am 
> playing around with the mixing parameters but no success so far.
>
> In passing there is a curious thing I observed with OT: the wfn is 
> converged and the eigenvalues are printed in the PDOS but they are not 
> printed correctly together with the MO coefficients (I request eigenvalues, 
> eigenvectors and occupations), instead I get:
>
>  MO EIGENVALUES, MO OCCUPATION NUMBERS, AND SPHERICAL MO EIGENVECTORS
>
>                               1            2            3            4
>                            0.000000     0.000000     0.000000     0.000000
>
>                            2.000000     2.000000     2.000000     2.000000
>
>      1     1  H  1s        0.041699    -0.021600     0.017105     0.034420
>      2     1  H  2s       -0.001594     0.001644    -0.000409    -0.000568
>      3     1  H  3s       -0.011532     0.007340    -0.005061    -0.008943
>      4     1  H  4s       -0.005753     0.006757    -0.005764    -0.009668
> ...
>
> For what it is worth, I am using version 5.1 (svn 18091) and the relevant 
> parts of the electronic structure are these (for the diagonalization I just 
> turn &OT F and uncomment the relevant parts; also I tried with and without 
> ADDED_MOS/NLUMO etc etc...)
>
> &FORCE_EVAL
>   METHOD QS
>   &DFT
>     CHARGE 1
>     BASIS_SET_FILE_NAME ./GTH_BASIS_SETS
>     POTENTIAL_FILE_NAME ./GTH_POTENTIALS
>     &PRINT
>       &MULLIKEN ON
>         &EACH
>             JUST_ENERGY 1
>         &END EACH
>       &END
>       &HIRSHFELD
>         &EACH
>             JUST_ENERGY 1
>         &END EACH
>       &END
>       &MO_CUBES
>           WRITE_CUBE F
> !          NLUMO 576
>       &END
>       &MO ON
>         &EACH
>           JUST_ENERGY 1
>           QS_SCF 0
>         &END
> !        MO_INDEX_RANGE 1 1152
>         EIGENVALUES
>         EIGENVECTORS
>         OCCUPATION_NUMBERS
>       &END
>       &PDOS
>         &EACH
>           JUST_ENERGY 1
>         &END
>         APPEND
> !        NLUMO 576
>       &END
> !      &AO_MATRICES ON
> !        OVERLAP T
> !      &END
>     &END
>
>     &MGRID
>       REL_CUTOFF 70.0
>       NGRIDS     5
>       CUTOFF  700.0
>     &END MGRID
>     &QS
>       METHOD GPW
>       EPS_DEFAULT 1.0E-10
>       MAP_CONSISTENT
>     &END QS
>     &SCF
>       &PRINT
>         &RESTART
>            BACKUP_COPIES 1
>         &END RESTART
>       &END PRINT
>       SCF_GUESS  RESTART
> !     ADDED_MOS 576 
>       MAX_SCF 20
>       EPS_SCF 2.0E-7
>  !     EPS_LUMO 2.0E-7
>  !     MAX_ITER_LUMO 10000
>       &OUTER_SCF
>         EPS_SCF 2.0E-7
>         MAX_SCF 300
>       &END OUTER_SCF
> !      &MIXING
> !        ALPHA 0.01
> !      &END
> !      &DIAGONALIZATION
> !        ALGORITHM  DAVIDSON
> !      &END
>       &OT T
>         MINIMIZER DIIS
>         PRECONDITIONER FULL_KINETIC  !  FULL_ALL
>         SAFE_DIIS  T
>       &END OT
>     &END SCF
>     &XC
>       &XC_FUNCTIONAL PBE
>       &END XC_FUNCTIONAL
>       DENSITY_CUTOFF     1.0000000000000000E-10
>       GRADIENT_CUTOFF     1.0000000000000000E-10
>       TAU_CUTOFF     1.0000000000000000E-10
>       &XC_GRID
>         XC_SMOOTH_RHO NN50
>         XC_DERIV NN50_SMOOTH
>       &END XC_GRID
>     &END XC
>     &POISSON
>       PERIODIC XYZ
>     &END POISSON
>   &END DFT
>   &SUBSYS
>     &CELL
>       ABC 1.5200509080292399E+01  3.3000000000000E+01  
> 1.3178605533387005E+01
>       PERIODIC XYZ
>     &END CELL
>     &TOPOLOGY
>       COORD_FILE_NAME ./mystruc.xyz
>       COORDINATE XYZ
>     &END TOPOLOGY
>     &KIND O
>       BASIS_SET QZV3P-GTH-q6
>       POTENTIAL GTH-PBE-q6
>     &END KIND
>     &KIND H
>       BASIS_SET QZV3P-GTH-q1
>       POTENTIAL GTH-PBE-q1
>     &END KIND
>     &END
>   &END SUBSYS
>   &PRINT
>     &TOTAL_NUMBERS  ON
>     &END TOTAL_NUMBERS
>   &END
> &END FORCE_EVAL
>
>
> Thanks again and best
>
> Daniel
>
>
>
>
> El jueves, 10 de mayo de 2018, 14:23:28 (UTC+2), Matthias Krack escribió:
>
> 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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