Lowdin analysis

Matthias Krack matthia... at psi.ch
Tue Dec 7 10:36:35 CET 2010


Hi Teo,

On Dec 7, 10:10 am, Laino Teodoro <teodor... at gmail.com> wrote:
> Hi Matthias,
>
> Ok - in this case, if you checked already before your first post, why mention linear dependencies and problems with
> diagonalization?

Since such problems exist with MOLOPT basis sets certainly for larger
and especially condensed systems. Like each basis set, MOLOPT basis
sets have to be used with care.

> These are pure numerical issues that can be solved skipping the diagonalization of S to evaluate S**(1/2).

As I explained, finally this doesn't help, the problem of unphysical
charges will persist, even if you are able to calculate S**(1/2) in
any case.

cheers,

Matthias

>
> Best
> Teo
>
> ---------------------------------------------
> Teodoro Laino
> Zurich Switzerland
>
> Contact info:
> Tel.:    http://www.jajah.com/Teo
> E-mail: teo... at laino.eu
>              teodor... at gmail.com
> ---------------------------------------------
>
> On 7 Dec 2010, at 09:54, Matthias Krack <matthia... at psi.ch> wrote:
>
> > 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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