Lowdin analysis

[Matthias Krack]

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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