Lowdin analysis

[Matthias Krack]

Hi Teo,

I checked that already before my first reply. There is no numerical
problem in this case, i.e. there is no warning about quenched
eigenvalues.

Matthias

On Dec 7, 9:35 am, Teodoro Laino <teodor... at gmail.com> wrote:
> Hi Matthias,
>
> maybe yes - maybe no -
> I did not look into the condition number of that matrix -
> A definitive answer (and not just assumptions like mines or yours) would  be confirmed or discarded by a more serious check.
>
> Best,
> Teo
>
> On Dec 7, 2010, at 9:30 AM, Matthias Krack wrote:
>
> > Hi Teo,
>
> > I doubt that the applied computational scheme or the numerics are part
> > of the problem, especially not in the case of a single water molecule,
> > and thus any clever approach to evaluate S**(1/2) won't change
> > anything. Maybe, my previous reply unintentionally implied that I
> > would blame the MOLOPT basis set to be the only problem in this case.
> > So let it put me more clearly: just the way how the Lowdin approach is
> > partitioning the charge does not work properly, i.e. giving physically
> > meaningful results, for all kinds of basis sets and the MOLOPT basis
> > sets (but not its SR variants) belong to this group.
>
> > Best,
>
> > Matthias
>
> > On Dec 6, 8:03 pm, Teodoro Laino <teodor... at gmail.com> wrote:
> >> Hi Matthias, Mahn,
>
> >> The real problem is not in the basis set itself but in how the population analysis is computed in CP2K.
> >> Diagonalizing S to evaluate S**(1/2) is probably not the smartest thing to do.
>
> >> There are ways to evaluate S**(1/2), definitely numerically more stable, that would allow to have meaningful population analysis even with these "problematic" basis sets (although I still think that it's not the basis set itself to be problematic, rather the computational scheme used).
>
> >> Best,
> >> Teo
>
> >> On Dec 5, 2010, at 3:06 PM, Matthias Krack wrote:
>
> >>> Hi Manh,
>
> >>> population analyses are known to be very sensible to the basis set
> >>> choice. I guess also in this case the TZV2P MOLOPT basis set is the
> >>> reason for the unexpected result. The MOLOPT basis sets include
> >>> relatively small exponents which might cause linear dependencies in
> >>> the overlap matrix. The Lowdin population analysis requires the
> >>> calculation of S**(1/2) which involves (in CP2K) a diagonalisation of
> >>> the overlap matrix. However, an ill-conditioned overlap matrix will
> >>> most likely result in a weird charge partition. Therefore, I would
> >>> suggest to employ different basis sets, e.g. the MOLOPT-SR or the DZVP/
> >>> TZVP basis sets.
>
> >>> Best,
>
> >>> Matthias
>
> >>> On 3 Dez., 17:46, Manh <manht... at gmail.com> wrote:
> >>>> Hello everyone,
>
> >>>> I calculate the Mulliken and Lowdin charges for a water molecule. The
> >>>> results are:
>
> >>>> ----------------------------------------------------------------
>
> >>>>  MULLIKEN POPULATION ANALYSIS
>
> >>>>  # Atom  Element  Kind  Atomic population                Net charge
> >>>>       1     H        1           0.780838                  0.219162
> >>>>       2     H        1           0.780981                  0.219019
> >>>>       3     O        2           6.438182                 -0.438182
> >>>>  # Total charge                  8.000000                  0.000000
>
> >>>>  LOWDIN POPULATION ANALYSIS
>
> >>>>  # Atom  Element  Kind  Atomic population                Net charge
> >>>>       1     H        1           1.210449                 -0.210449
> >>>>       2     H        1           1.210473                 -0.210473
> >>>>       3     O        2           5.579079                  0.420921
> >>>>  # Total charge                  8.000000                  0.000000
>
> >>>> --------------------------------------------------------
>
> >>>> I think that the Lowdin analysis has some problem.
>
> >>>> Here is my input:
>
> >>>> ---------------------------------------------
>
> >>>> &FORCE_EVAL
> >>>>   METHOD Quickstep
> >>>>   &DFT
> >>>>     BASIS_SET_FILE_NAME ../../../BASIS_MOLOPT
> >>>>     POTENTIAL_FILE_NAME ../../../GTH_POTENTIALS
> >>>>     RESTART_FILE_NAME H2O-RESTART.wfn.wfn
> >>>>     &QS
> >>>>       METHOD GPW
> >>>>       EXTRAPOLATION ASPC
> >>>>       EXTRAPOLATION_ORDER 3
> >>>>     &END QS
> >>>>     &MGRID
> >>>>       CUTOFF 400
> >>>>       NGRIDS 5
> >>>>     &END
> >>>>     &SCF
> >>>>       MAX_SCF 20
> >>>>       SCF_GUESS RESTART
> >>>>       EPS_SCF 1.0E-6
> >>>>       &OT
> >>>>         PRECONDITIONER  FULL_SINGLE_INVERSE
> >>>>         MINIMIZER  CG
> >>>>       &END
> >>>>       &OUTER_SCF
> >>>>         MAX_SCF 10
> >>>>         EPS_SCF 1.0E-6
> >>>>       &END
> >>>>       &PRINT
> >>>>         &RESTART
> >>>>           &EACH
> >>>>             QS_SCF 0
> >>>>             GEO_OPT 2
> >>>>           &END
> >>>>           ADD_LAST NUMERIC
> >>>>           FILENAME RESTART.wfn
> >>>>         &END
> >>>>         &RESTART_HISTORY OFF
> >>>>         &END
> >>>>       &END
> >>>>     &END SCF
>
> >>>>     &XC
> >>>>       &XC_FUNCTIONAL PBE
> >>>>       &END XC_FUNCTIONAL
> >>>>     &END XC
>
> >>>>     &PRINT
> >>>>      &MULLIKEN
> >>>>      &END MULLIKEN
>
> >>>>      &LOWDIN
> >>>>      &END LOWDIN
> >>>>     &END
>
> >>>>   &END DFT
> >>>>   &SUBSYS
> >>>>     &CELL
> >>>>    ABC [angstrom]   30 30 30
> >>>>     &END CELL
> >>>>     &TOPOLOGY
> >>>>       COORD_FILE_NAME water.xyz
> >>>>       COORDINATE xyz
> >>>>     &END
>
> >>>>     &KIND O
> >>>>       BASIS_SET TZV2P-MOLOPT-GTH
> >>>>       POTENTIAL GTH-PBE-q6
> >>>>     &END KIND
> >>>>     &KIND H
> >>>>       BASIS_SET TZV2P-MOLOPT-GTH
> >>>>       POTENTIAL GTH-PBE-q1
> >>>>     &END KIND
>
> >>>>   &END SUBSYS
>
> >>>> &END FORCE_EVAL
>
> >>>> &GLOBAL
> >>>>   PRINT_LEVEL LOW
> >>>>   PROJECT H2O
> >>>>   RUN_TYPE ENERGY
> >>>>   WALLTIME 285000
> >>>> &END GLOBAL
>
> >>>> &MOTION
> >>>>     &GEO_OPT
> >>>>      MAX_ITER 5000
> >>>>      MAX_FORCE 0.00010
> >>>>      OPTIMIZER BFGS
> >>>>     &BFGS
> >>>>     &END
> >>>>   &END
> >>>> &END
>
> >>>> ------------------------------------------------
> >>>>  the water.xyz file is
> >>>> ----------------------------------------
> >>>>        3
> >>>>  water
> >>>>   H         8.4351137971        5.1620318678       12.1510352783
> >>>>   H         8.5534822942        3.6347695084       12.1803075532
> >>>>   O         7.9011326518        4.3528437024       12.1874564118
> >>>> ------------------------------------------------
>
> >>>> Regards,
> >>>> Manh
>
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