SCF Convergence issues when performing a TD-DFT calculation (DIIS_GDM algorithm) on silicon nanoclusters

Hello,

I am currently running TD-DFT calculations on multiple silicon quantum dots, using the DIIS_GDM algorithm. For the first time, I stumbled accross what seems like an SCF convergence issue, with the Si71H84 molecule (spheroidal shape, Td symmetry)

Here is the geometry, it was obtained through a Gaussian 16 geometry optimization with B3LYP/def2-TZVP:

$molecule
   0 1
 Si        2.564423983323      5.801276835919      2.564423983323
 Si        5.801276835919      2.564423983323      2.564423983323
 Si        2.564423983323      2.564423983323      5.801276835919
 Si        4.127882545076      1.384809362379      1.384809362379
 Si        1.384809362379      1.384809362379      4.127882545076
 Si        1.384809362379      4.127882545076      1.384809362379
 Si        2.771610583248     -0.001653148516      2.771610583248
 Si        5.494442808983     -2.925524373593      2.925524373593
 Si        2.925524373593     -2.925524373593      5.494442808983
 Si        4.134899191666     -1.410360991400      4.134899191666
 Si        4.134899191666     -4.134899191666      1.410360991400
 Si        1.410360991400     -4.134899191666      4.134899191666
 Si        1.382988496147     -1.382988496147      1.382988496147
 Si        2.925524373593     -5.494442808983      2.925524373593
 Si        2.925524373593      5.494442808983     -2.925524373593
 Si        5.494442808983      2.925524373593     -2.925524373593
 Si        2.771610583248      2.771610583248     -0.001653148516
 Si        4.134899191666      4.134899191666     -1.410360991400
 Si        4.134899191666      1.410360991400     -4.134899191666
 Si        1.382988496147      1.382988496147     -1.382988496147
 Si        1.410360991400      4.134899191666     -4.134899191666
 Si        5.421908562296      0.000000000000      0.000000000000
 Si        2.771610583248      0.001653148516     -2.771610583248
 Si        5.801276835919     -2.564423983323     -2.564423983323
 Si        2.771610583248     -2.771610583248      0.001653148516
 Si        4.127882545076     -1.384809362379     -1.384809362379
 Si        1.384809362379     -4.127882545076     -1.384809362379
 Si        1.384809362379     -1.384809362379     -4.127882545076
 Si        2.564423983323     -5.801276835919     -2.564423983323
 Si        2.925524373593      2.925524373593     -5.494442808983
 Si        2.564423983323     -2.564423983323     -5.801276835919
 Si       -2.925524373593      5.494442808983      2.925524373593
 Si       -0.001653148516      2.771610583248      2.771610583248
 Si       -2.925524373593      2.925524373593      5.494442808983
 Si       -1.410360991400      4.134899191666      4.134899191666
 Si       -1.382988496147      1.382988496147      1.382988496147
 Si       -4.134899191666      1.410360991400      4.134899191666
 Si       -4.134899191666      4.134899191666      1.410360991400
 Si        0.000000000000      0.000000000000      5.421908562296
 Si       -2.771610583248      0.001653148516      2.771610583248
 Si        0.001653148516     -2.771610583248      2.771610583248
 Si       -2.564423983323     -2.564423983323      5.801276835919
 Si       -1.384809362379     -1.384809362379      4.127882545076
 Si       -1.384809362379     -4.127882545076      1.384809362379
 Si       -4.127882545076     -1.384809362379      1.384809362379
 Si       -2.564423983323     -5.801276835919      2.564423983323
 Si        0.000000000000      5.421908562296      0.000000000000
 Si       -2.564423983323      5.801276835919     -2.564423983323
 Si        0.001653148516      2.771610583248     -2.771610583248
 Si       -2.771610583248      2.771610583248      0.001653148516
 Si       -1.384809362379      4.127882545076     -1.384809362379
 Si       -1.384809362379      1.384809362379     -4.127882545076
 Si       -4.127882545076      1.384809362379     -1.384809362379
 Si        0.000000000000      0.000000000000      0.000000000000
 Si       -2.771610583248     -0.001653148516     -2.771610583248
 Si       -0.001653148516     -2.771610583248     -2.771610583248
 Si       -2.771610583248     -2.771610583248     -0.001653148516
 Si       -1.382988496147     -1.382988496147     -1.382988496147
 Si       -1.410360991400     -4.134899191666     -4.134899191666
 Si       -4.134899191666     -4.134899191666     -1.410360991400
 Si       -4.134899191666     -1.410360991400     -4.134899191666
 Si        0.000000000000     -5.421908562296      0.000000000000
 Si       -2.925524373593     -5.494442808983     -2.925524373593
 Si       -2.564423983323      2.564423983323     -5.801276835919
 Si        0.000000000000      0.000000000000     -5.421908562296
 Si       -2.925524373593     -2.925524373593     -5.494442808983
 Si       -5.494442808983      2.925524373593      2.925524373593
 Si       -5.801276835919     -2.564423983323      2.564423983323
 Si       -5.801276835919      2.564423983323     -2.564423983323
 Si       -5.421908562296      0.000000000000      0.000000000000
 Si       -5.494442808983     -2.925524373593     -2.925524373593
 H         3.281169077705      6.648496194615      1.579323701234
 H         3.544673966205      5.286275514187      3.544673966205
 H         1.579323701234      6.648496194615      3.281169077705
 H         5.286275514187      3.544673966205      3.544673966205
 H         6.648496194615      3.281169077705      1.579323701234
 H         6.648496194615      1.579323701234      3.281169077705
 H         3.544673966205      3.544673966205      5.286275514187
 H         3.281169077705      1.579323701234      6.648496194615
 H         1.579323701234      3.281169077705      6.648496194615
 H         6.000626673498     -3.914663193815      3.914663193815
 H         6.678028071202     -2.298208202704      2.298208202704
 H         2.298208202704     -2.298208202704      6.678028071202
 H         3.914663193815     -3.914663193815      6.000626673498
 H         4.996354434129     -0.553098808549      4.996354434129
 H         4.996354434129     -4.996354434129      0.553098808549
 H         0.553098808549     -4.996354434129      4.996354434129
 H         2.298208202704     -6.678028071202      2.298208202704
 H         3.914663193815     -6.000626673498      3.914663193815
 H         2.298208202704      6.678028071202     -2.298208202704
 H         3.914663193815      6.000626673498     -3.914663193815
 H         6.678028071202      2.298208202704     -2.298208202704
 H         6.000626673498      3.914663193815     -3.914663193815
 H         4.996354434129      4.996354434129     -0.553098808549
 H         4.996354434129      0.553098808549     -4.996354434129
 H         0.553098808549      4.996354434129     -4.996354434129
 H         6.314679342165     -0.834893029320      0.834893029320
 H         6.314679342165      0.834893029320     -0.834893029320
 H         6.648496194615     -1.579323701234     -3.281169077705
 H         5.286275514187     -3.544673966205     -3.544673966205
 H         6.648496194615     -3.281169077705     -1.579323701234
 H         3.544673966205     -5.286275514187     -3.544673966205
 H         1.579323701234     -6.648496194615     -3.281169077705
 H         3.281169077705     -6.648496194615     -1.579323701234
 H         3.914663193815      3.914663193815     -6.000626673498
 H         2.298208202704      2.298208202704     -6.678028071202
 H         3.281169077705     -1.579323701234     -6.648496194615
 H         1.579323701234     -3.281169077705     -6.648496194615
 H         3.544673966205     -3.544673966205     -5.286275514187
 H        -2.298208202704      6.678028071202      2.298208202704
 H        -3.914663193815      6.000626673498      3.914663193815
 H        -3.914663193815      3.914663193815      6.000626673498
 H        -2.298208202704      2.298208202704      6.678028071202
 H        -0.553098808549      4.996354434129      4.996354434129
 H        -4.996354434129      0.553098808549      4.996354434129
 H        -4.996354434129      4.996354434129      0.553098808549
 H        -0.834893029320      0.834893029320      6.314679342165
 H         0.834893029320     -0.834893029320      6.314679342165
 H        -3.281169077705     -1.579323701234      6.648496194615
 H        -1.579323701234     -3.281169077705      6.648496194615
 H        -3.544673966205     -3.544673966205      5.286275514187
 H        -3.544673966205     -5.286275514187      3.544673966205
 H        -1.579323701234     -6.648496194615      3.281169077705
 H        -3.281169077705     -6.648496194615      1.579323701234
 H        -0.834893029320      6.314679342165      0.834893029320
 H         0.834893029320      6.314679342165     -0.834893029320
 H        -3.281169077705      6.648496194615     -1.579323701234
 H        -3.544673966205      5.286275514187     -3.544673966205
 H        -1.579323701234      6.648496194615     -3.281169077705
 H        -0.553098808549     -4.996354434129     -4.996354434129
 H        -4.996354434129     -4.996354434129     -0.553098808549
 H        -4.996354434129     -0.553098808549     -4.996354434129
 H         0.834893029320     -6.314679342165      0.834893029320
 H        -0.834893029320     -6.314679342165     -0.834893029320
 H        -2.298208202704     -6.678028071202     -2.298208202704
 H        -3.914663193815     -6.000626673498     -3.914663193815
 H        -3.544673966205      3.544673966205     -5.286275514187
 H        -3.281169077705      1.579323701234     -6.648496194615
 H        -1.579323701234      3.281169077705     -6.648496194615
 H         0.834893029320      0.834893029320     -6.314679342165
 H        -0.834893029320     -0.834893029320     -6.314679342165
 H        -2.298208202704     -2.298208202704     -6.678028071202
 H        -3.914663193815     -3.914663193815     -6.000626673498
 H        -6.678028071202      2.298208202704      2.298208202704
 H        -6.000626673498      3.914663193815      3.914663193815
 H        -6.648496194615     -1.579323701234      3.281169077705
 H        -5.286275514187     -3.544673966205      3.544673966205
 H        -6.648496194615     -3.281169077705      1.579323701234
 H        -5.286275514187      3.544673966205     -3.544673966205
 H        -6.648496194615      3.281169077705     -1.579323701234
 H        -6.648496194615      1.579323701234     -3.281169077705
 H        -6.314679342165     -0.834893029320     -0.834893029320
 H        -6.314679342165      0.834893029320      0.834893029320
 H        -6.000626673498     -3.914663193815     -3.914663193815
 H        -6.678028071202     -2.298208202704     -2.298208202704
$end

And here are my input file parameters:

 $rem
   MEM_TOTAL            48000
   MEM_STATIC           960
   JOBTYPE              sp
   EXCHANGE             b3lyp
   BASIS                def2-tzvp
   CIS_N_ROOTS          4
   SCF_ALGORITHM        diis_gdm
   CIS_SINGLETS         true
   CIS_TRIPLETS         true
   CALC_SOC             true
   STS_MOM              true
   IQMOL_FCHK           true
$end

This is the content of the SCF section of the output file:

 A restricted SCF calculation will be
 performed using DIIS, GDM
 SCF converges when RMS gradient is below 1.0e-08
 ---------------------------------------
  Cycle       Energy         DIIS error
 ---------------------------------------
    1  -19978.6268538015      4.40e-01  
    2 -868701.3259110240      1.84e+02  
    3 -869541.8446004504      1.84e+02  
    4 -874907.6143515166      1.85e+02  
    5 -872315.8721118229      1.84e+02  
    6 -874380.5545428591      1.85e+02  
    7 -873057.0238735870      1.84e+02  
    8 -873750.4279140406      1.85e+02  
    9 -875646.7400514059      1.85e+02  
   10 -875297.7247332566      1.85e+02  
   11 -874758.4417308006      1.85e+02  
   12 -875971.4873713489      1.85e+02  
   13 -875946.2102140816      1.85e+02  
   14 -875544.2167887952      1.85e+02  
   15 -875609.3253957893      1.85e+02  
   16 -874929.9464730512      1.85e+02  
   17-5918614.1796252886      7.46e+02  
   18-8411371.7196255270      6.05e+02  
   19-9239859.8480598200      5.43e+02  
   20-8462890.3776093889      5.53e+02  
   21-9425088.8142104074      5.36e+02  
   22-9389125.3470191248      5.33e+02  
   23-9322178.7411765363      5.39e+02  
   24-9303958.0940554701      5.41e+02  
   25-9388023.0849448685      5.34e+02  
   26-9418683.0211817622      5.30e+02  
   27-11398627.0720297545      3.41e+02  
   28-12083747.1433884297      2.58e+02  
   29-12421928.1767782159      1.70e+02  
   30-12664239.2634986900      6.52e+01  
   31-12665369.5182279497      1.76e+01  
   32-12775983.9653341155      1.16e+00  
   33-12692651.1173310149      2.79e+00  
   34-12787790.3589690179      3.32e+00  
   35-12668022.7303298395      3.15e+00  
   36-12666112.7696821690      3.08e+00  
   37-12753351.3547777440      1.58e+00  
   38-12751844.9793572165      1.48e+00  
   39-12719318.4688073117      5.24e-01  
   40-12739439.7589352801      7.91e-01  
   41-12743181.2375025228      1.83e-01  
   42-12744384.3223299738      1.31e-01  
   43-12743250.7788753062      8.09e-02  
   44-12741312.3330480475      1.03e-01  
   45-12733907.0411213841      3.56e-01  
   46-12734053.0460137893      3.61e-01  
   47-12737983.5762829240      2.72e-01  
   48-12738421.4643373061      2.61e-01  
   49-12740007.8599114008      2.54e-01  
   50-12742818.8809344303      2.07e-01  
 ---------------------------------------
  Cycle       Energy        RMS Gradient
 ---------------------------------------
    1-12744205.5375410728      1.01e-01   Descent step
    2-12742608.1800612491      1.08e-01  Line search: overstep
    3-12744044.9431627262      1.02e-01  Line search: overstep
    4-12744189.4697686527      1.01e-01  Line search: overstep
    5-12744203.9306781590      1.01e-01  Line search: overstep
    6-12744205.3768520672      1.01e-01  Line search: overstep
    7-12744205.5214719158      1.01e-01  Line search: overstep
    8-12744205.5359343290      1.01e-01  Line search: overstep
    9-12744205.5373863392      1.01e-01  Line search: understep
   10-12744205.5360760503      1.01e-01  Line search: overstep
   11-12744205.5372521952      1.01e-01  Line search: understep
   12-12744205.5361998565      1.01e-01  Line search: overstep
   13-12744205.5371464584      1.01e-01  Line search: understep
   14-12744205.5362927373      1.01e-01  Line search: overstep
   15-12744205.5370594729      1.01e-01  Line search: understep
   16-12744205.5363764372      1.01e-01  Line search: overstep
   17-12744205.5369913429      1.01e-01  Line search: understep
  GDM::   16 failed line searches.  Resetting
   18-12744205.5364361964      1.01e-01  Line search: overstep
  GDM::   17 failed line searches.  Resetting
   19-12744205.5369385742      1.01e-01  Line search: understep
  GDM::   18 failed line searches.  Resetting
   20-12744205.5364850853      1.01e-01  Line search: overstep
  GDM::   19 failed line searches.  Resetting
   21-12744205.5368925780      1.01e-01  Line search: understep
  GDM::   20 failed line searches.  Resetting
   22-12744205.5365233868      1.01e-01  Line search: overstep
  GDM::   21 failed line searches.  Resetting
   23-12744205.5368542839      1.01e-01  Line search: understep
  GDM::   22 failed line searches.  Resetting
   24-12744205.5365555398      1.01e-01  Line search: overstep
  GDM::   23 failed line searches.  Resetting
   25-12744205.5368215945      1.01e-01  Line search: understep
  GDM::   24 failed line searches.  Resetting
   26-12744205.5365804769      1.01e-01  Line search: understep
  GDM::   25 failed line searches.  Resetting
   27-12744205.5365576241      1.01e-01  Line search: overstep
  GDM::   26 failed line searches.  Resetting
   28-12744205.5365797319      1.01e-01  Line search: understep
  GDM::   27 failed line searches.  Resetting
   29-12744205.5365645606      1.01e-01  Line search: overstep
  GDM::   28 failed line searches.  Resetting
   30-12744205.5365754142      1.01e-01  Line search: overstep
  GDM::   29 failed line searches.  Resetting
   31-12744205.5365804341      1.01e-01  Line search: understep
  GDM::   30 failed line searches.  Resetting
   32-12744205.5365759619      1.01e-01  Line search: overstep
  GDM::   31 failed line searches.  Resetting
   33-12744205.5365765132      1.01e-01  Line search: overstep
  GDM::   32 failed line searches.  Resetting
   34-12744205.5365834795      1.01e-01  Line search: understep
  GDM::   33 failed line searches.  Resetting
   35-12744205.5365766622      1.01e-01  Line search: understep
  GDM::   34 failed line searches.  Resetting
   36-12744205.5365773048      1.01e-01  Line search: understep
  GDM::   35 failed line searches.  Resetting
   37-12744205.5365784094      1.01e-01  Line search: understep
  GDM::   36 failed line searches.  Resetting
   38-12744205.5365777556      1.01e-01  Line search: understep
  GDM::   37 failed line searches.  Resetting
   39-12744205.5365779288      1.01e-01  Line search: understep
  GDM::   38 failed line searches.  Resetting
   40-12744205.5365773607      1.01e-01  Line search: understep
  GDM::   39 failed line searches.  Resetting
   41-12744205.5365755595      1.01e-01  Line search: overstep
  GDM::   40 failed line searches.  Resetting
   42-12744205.5365782138      1.01e-01  Line search: understep
  GDM::   41 failed line searches.  Resetting
   43-12744205.5365786180      1.01e-01  Line search: understep
  GDM::   42 failed line searches.  Resetting
   44-12744205.5365768299      1.01e-01  Line search: understep
  GDM::   43 failed line searches.  Resetting
   45-12744205.5365782399      1.01e-01  Line search: understep
  GDM::   44 failed line searches.  Resetting
   46-12744205.5365781412      1.01e-01  Line search: understep
  GDM::   45 failed line searches.  Resetting
   47-12744205.5365748014      1.01e-01  Line search: overstep
  GDM::   46 failed line searches.  Resetting
   48-12744205.5365792867      1.01e-01  Line search: understep
  GDM::   47 failed line searches.  Resetting
   49-12744205.5365831405      1.01e-01  Line search: understep
  GDM::   48 failed line searches.  Resetting
   50-12744205.5365778171      1.01e-01  Line search: understep
gen_scfman_exception: SCF failed to converge

 Q-Chem fatal error occurred in module libgscf/gen_scfman/gen_scfman_main.C, line 218:

 Error in gen_scfman

I did not encounter any problem with the previous, smaller quantum dots.

Did I do something wrong? How can I resolve this problem?

Thank you for your help !

Best regards!

Iacobellis Nicolas, Ph.D. Student

It was known that Q-Chem’s old integral code might have some issues with highly symmetric systems (the system here turns out to have Td point group symmetry). I believe the SCF energies will be back to normal once you add “SYMMETRY = false” to the $rem section.

2 Likes

I would say (a) do you know that normal DIIS fails to converge? Otherwise you’re setting yourself up for a lot of cycles unnecessarily. (b) The magnitude of the error suggests a problematic guess, might try BASIS2 (basis set projection) as an alternative, with something small like STO-3G or maybe 6-31G*.

But Yeuzhi’s suggestion is also valid: at the first sign of trouble for a highly symmetric molecule, turn symmetry off (SYM_IGNORE=TRUE).

1 Like

Thank you for your help! I turned the scf algorithm back to DIIS and it seems to work just fine. I don’t know why but I somehow convinced myself that DIIS_GDM was the superior option and I just ended up using it by default.

I’ll keep in mind the BASIS2 option and your warnings about symmetry, although I want to use symmetry as much as possible in order to have a better understanding of the spin-orbit coupling results.