Jobex increases the energy from reference geometrical minimum

[glebreto]

Dear all,

I am trying to handle TM for my use in optimizing molecular geometries. To do so, I compared the results obtained for a "small" system between Gaussian and TM: I found almost the same geometry with a very large speed-up using TM.

Now, I try to do the same with a Zr complex, 97 atoms / M062X/def2TZVP/gas phase. I did not get the same results between Gaussian and TM, and TM spends hundreds of cycles to converge. Worst, starting from the geometry that Gaussian found to be the minimum, the energy of the electronic part increases during the jobex iteration! It thus seems that the gradient/hessian/structure update has an issue.

I tried the RI and the non-RI versions, which led to the same geometry and error. I also tried to use RELAX instead of STATPT with internal coordinates: I also observed an increase in the electronic energy, but slower (RELAX pushes the system out of equilibrium slower compared to STATPT). The M4 and 2 grid lead to similar results.

I am using TM V7-8, here are my initial coordinates:
$coord
    0.00000000000000      3.83042950118945     -0.00000566917837      zr
   -0.25332345618446      6.69581555478113     -3.51138892929500      cl
    0.25334613289795      6.69591382053961      3.51130011216714      cl
    3.67206289304131      2.96298095929798     -0.57568994605824       o
   -3.67205911358906      2.96298851820248      0.57572396112849       o
    2.31875253642568     -1.13182689590499     -4.84648610552148       n
   -1.18171944504735      0.09075976631353     -2.51131562852505       n
    1.18169676833386      0.09073519987391      2.51131940797730       n
   -2.31874119806894     -1.13197618426883      4.84653712812685       n
    4.93904111165340      0.92012654734153      0.19589278953096       c
    7.49573851306134      0.49315993701746     -0.31920686779341       c
    8.48992531695308     -1.85224907612219      0.40270819606225       c
   10.44057999128904     -2.24309735102629     -0.03633376419818       h
    7.10891724452882     -3.67884323037646      1.68996695544383       c
    4.64182687649839     -3.07549903221045      2.40538514088303       c
    3.60193137710420     -4.34233741108932      3.63280761225446       h
    3.55883239337986     -0.80162182206625      1.68293150508185       c
   -0.46492364926330     -1.59246275659151      3.24142643458321       c
   -0.36477005438426     -3.54252405692434      2.56518038198138       h
   -4.93903922192728      0.92013221651991     -0.19584932583009       c
   -7.49573473360909      0.49316938564809      0.31925600067265       c
   -8.48993854503595     -1.85222073023032     -0.40270252688388       c
  -10.44058943991966     -2.24307089486055      0.03634321282880       h
   -7.10894936987294     -3.67879787694947     -1.69000474996632       c
   -4.64185711211638     -3.07545745823571     -2.40541537650102       c
   -3.60196917162669     -4.34226938094883     -3.63287375266882       h
   -3.55884373173660     -0.80160481453113     -1.68291260782060       c
    0.46493687734618     -1.59240795453390     -3.24140942704809       c
    0.36484564342925     -3.54246736514060     -2.56514825663726       h
   -2.39584958285817      1.20818316969661      6.28705834539395       c
   -0.47219531539086      1.86087567588111      6.60435658980149       h
   -3.41869786288211      2.67625848358689      5.27870237501976       h
   -3.33045332204046      0.82455175886246      8.08187675486264       h
   -4.40167481140257     -2.88879787054967      5.13838076163568       c
   -4.56469770472179     -3.46486387210671      7.11184254056974       h
   -6.16063377793036     -2.00187381121781      4.53203945783600       h
   -4.08668203286707     -4.53886892805040      3.94985452308742       h
    2.39578155271768      1.20835513477395     -6.28696763853997       c
    0.47210838798913      1.86100228753146     -6.60423942678176       h
    3.41859959712363      2.67643422811648     -5.27858521200004       h
    3.33038151244772      0.82478230544967     -8.08180116581765       h
    4.40177307716105     -2.88854842670122     -5.13834674656543       c
    4.56451062183545     -3.46501882964893     -7.11171592891939       h
    6.16075283067621     -2.00133145982004     -4.53250055101041       h
    4.08715446439823     -4.53837948898412     -3.94938587100851       h
   -9.17313312059803      2.58647948513204      1.41166131989182       c
  -11.89054794945315      1.68341149551750      1.81768976475504       c
  -11.98808994282795      0.13342411302920      3.17872910122038       h
  -13.01170734138462      3.24559139096189      2.56050897900131       h
  -12.76864887750913      1.06648961514605      0.05713775910418       h
   -8.19604077922966      3.59689714670819      3.94746024008752       c
   -7.97858243516447      2.07743828976322      5.32949443379746       h
   -6.39948571145244      4.56746237404211      3.71878070229431       h
   -9.55706121843375      4.94649986066730      4.71266703973223       h
   -9.22234347860941      4.77224632498943     -0.50280320943143       c
   -7.32822374074389      5.50980832115700     -0.83160232703344       h
  -10.00254525505303      4.13701677792261     -2.30337772467573       h
  -10.40410827708376      6.30619749158416      0.21316110685779       h
   -8.21887811944576     -6.23527607012695     -2.45355048034749       c
  -10.93134186585435     -6.57518677734177     -1.51980278709965       c
  -12.19986399071026     -5.17499798475255     -2.34638222209384       h
  -11.61548886338324     -8.44288058508053     -2.06401556510000       h
  -11.04952722741457     -6.43035627742432      0.53474713984210       h
   -6.60160703829016     -8.35931311639732     -1.31744902394860       c
   -4.64728440554630     -8.24868665933561     -1.96519611686495       h
   -6.60196419652771     -8.24704070788106      0.74352030263851       h
   -7.34994047336809    -10.20394092705890     -1.86318870065765       h
   -8.22098705380084     -6.48126360949562     -5.34424752565241       c
   -9.03191577703087     -8.29489613226108     -5.90446817365447       h
   -9.34011121069609     -4.97467000800710     -6.19818830520505       h
   -6.31465212626573     -6.37543516706432     -6.11998198953741       h
    8.21881764820977     -6.23535543862419      2.45344087623226       c
    8.22081886817575     -6.48148470745220      5.34412469345431       c
    6.31445559474877     -6.37569405954340      6.11979679637720       h
    9.03172302496616     -8.29514557610953      5.90428675994650       h
    9.33991278945301     -4.97493645939067      6.19818074630055       h
    6.60158625130279     -8.35933579311082      1.31717312393441       c
    4.64723338294094     -8.24872634358422      1.96483517917515       h
    6.60204167529882     -8.24697645719282     -0.74379053347433       h
    7.34988378158435    -10.20399383939039      1.86286366776421       h
   10.93131729941473     -6.57522835131651      1.51978200011228       c
   12.19980729892653     -5.17507546352366      2.34647103922169       h
   11.61544162023012     -8.44294483576876      2.06393430687665       h
   11.04958013974606     -6.43030525481896     -0.53475658847273       h
    9.17317280484665      2.58647003650142     -1.41155738495496       c
    8.19610691964402      3.59698596383605     -3.94732606953267       c
    7.97862211941309      2.07757246031807     -5.32940750639572       h
    6.39957074912804      4.56758520624021     -3.71862574475209       h
    9.55716137391836      4.94658111889066     -4.71248751575039       h
    9.22245686217689      4.77217829484895      0.50297328478264       c
    7.32836924965549      5.50981588006149      0.83178185101528       h
   10.00261895437189      4.13686182038039      2.30353457194407       h
   10.40429535997010      6.30609922582568     -0.21293433972283       h
   11.89055739808377      1.68333212702027     -1.81761984488842       c
   12.76863564942625      1.06631387061646     -0.05708862622494       h
   11.98805025857934      0.13339387741121     -3.17871776286363       h
   13.01176781262060      3.24550635328628     -2.56037858789871       h
$end

my initial control file:
$coord file=coord
$atoms
    basis =def2-TZVP
    jbas  =def2-TZVP
$dft
   functional m06-2x
   grid 2
$eht charge=0 unpaired=0
$symmetry c1
$rij
$marij
$scfinstab rpas
$end
and my submission file using statpt:
module purge
export TURBODIR=/work/shared/icmub/TurboMole/TmoleX2024/TURBOMOLE                                                                                                         
export PARA_ARCH=MPI
export PATH=$TURBODIR/scripts:$PATH
export PATH=$TURBODIR/bin/`sysname`:$PATH

tmpdir='/tmp3/'${JOB_ID}'/TMP'
mkdir -p $tmpdir
export TURBOTMPDIR=$tmpdir

export PARNODES=32
# export OMP_NUM_THREADS=32
echo $NSLOTS

date
jobex -ri
date
The job.start:
jobex WAS CALLED AS: jobex -ri
AN OPTIMIZATION WITH MAX. 100 CYCLES WILL BE PERFORMED
CONVERGENCY CRITERION FOR TOTAL SCF-ENERGY IS 10**(-6)
CONVERGENCY CRITERION FOR MAXIMUM NORM OF SCF-ENERGY GRADIENT IS 10**(-3)
CONVERGENCY CRITERION FOR MAXIMUM NORM OF BASIS SET GRADIENT IS 10**(-3)
PROCEDURE WILL START WITH A dscf like STEP
LOAD MODULES WILL BE TAKEN FROM DIRECTORY /work/shared/icmub/TurboMole/TmoleX2024/TURBOMOLE/bin/x86_64-unknown-linux-gnu_mpi
DSCF  = /work/shared/icmub/TurboMole/TmoleX2024/TURBOMOLE/bin/x86_64-unknown-linux-gnu_mpi/ridft
GRAD  = /work/shared/icmub/TurboMole/TmoleX2024/TURBOMOLE/bin/x86_64-unknown-linux-gnu_mpi/rdgrad
STATPT = /work/shared/icmub/TurboMole/TmoleX2024/TURBOMOLE/bin/x86_64-unknown-linux-gnu_mpi/statpt

and the beginning of the control file once TM started to emphasize the energy increase from the initial "converged" geometry at step 1:

$coord file=coord
$atoms
    basis =def2-TZVP
    jbas  =def2-TZVP
$dft
   functional m06-2x
   grid 2
$eht charge=0 unpaired=0
$symmetry c1
$rij
$marij
$scfinstab rpas
$actual step      rdgrad
$basis file=basis
$ecp file=basis
$jbas file=auxbasis
$xctype hybrid-MGGA X= 0.54000 (not to be modified here)
$closed shells
 a       1-174                                  ( 2 )
$scfmo    file=mos
$energy      SCF               SCFKIN            SCFPOT
     1 -2665.211463114      2624.387872133     -5289.599335247
     2 -2665.209268313      2624.517485925     -5289.726754238
     3 -2665.209496432      2624.547455834     -5289.756952266
     4 -2665.209615105      2624.539209705     -5289.748824811
     5 -2665.209563968      2624.540673977     -5289.750237945
 ....

Do you have an idea that can explain this issue? I am not a TM expert, so if I miss something obvious, please do not hesitate to tell me!

Thx a lot for your help!
Guillaume
 

[yannickf]

Dear Guillaume,

The Minnesota functionals are said to be grid sensitive, so it is best to use at least a medium-sized grid such as "gridsize 3" or even a large grid such as "gridsize 4". Additionally, you can turn on the XC weight derivatives, which is often helpful to avoid the behavior you observed. Then, the DFT group reads as follows.

$dft
  functional m06-2x
  gridsize 3
  weight derivatives on


Usually, it should read "gridsize" instead of "grid" in the data group $dft.This avoids M-grids (c.f. output "iterations will be done with small grid"). There is no reason to use the M-grids with hybrid functionals (your computation time is dominated by exact exchange and using smaller grids in the SCF iterations will only come with a loss of accuracy). Additionally, the M-grids can lead to issues for some functionals and response properties. With gridsize 3, it starts to get better. The norm of the gradient is already small in the first cycle and a run jobex for five cycles.

  cycle =      1    SCF energy =    -2665.2124386120   |dE/dxyz| =  0.004486
  cycle =      2    SCF energy =    -2665.2123311550   |dE/dxyz| =  0.004276
  cycle =      3    SCF energy =    -2665.2123607860   |dE/dxyz| =  0.003078
  cycle =      4    SCF energy =    -2665.2124498240   |dE/dxyz| =  0.002643
  cycle =      5    SCF energy =    -2665.2125095600   |dE/dxyz| =  0.001462

I assume that the geometry convergence behavior will get even better with gridsize 4. These are the results from the first few cycles. After a "wrong" initial move, which is properly detected (gradient and energy both get worse), the geometry starts to move back in terms of relaxation.

  cycle =      1    SCF energy =    -2665.2131558740   |dE/dxyz| =  0.001065
  cycle =      2    SCF energy =    -2665.2128582950   |dE/dxyz| =  0.006480
  cycle =      3    SCF energy =    -2665.2129874270   |dE/dxyz| =  0.004899
  cycle =      4    SCF energy =    -2665.2130925560   |dE/dxyz| =  0.003729
  cycle =      5    SCF energy =    -2665.2131519440   |dE/dxyz| =  0.002038


If neither larger gridsize nor weight derivatives help, you can turn off pruning with "fullshell on" or you can increase the number of radial points using radsize (see manual). Alternatively, you can use the a-grids (gridsize 4a etc.), these set the number of radial points based on the atom number instead of the row of the periodic table as done with the usual grids.

Hope this helps.

Best wishes,

Yannick