Lowdin analysis

Matthias Krack matthia... at psi.ch
Tue Dec 7 11:16:51 CET 2010


Hi Teo,

you are now referring to purely technical issues concerning the
calculation of functions of S like S**(1/2), which is not (just to
recall it) the original topic of this thread. However, I would
certainly appreciate if you could come up with a more robust scheme to
calculate S**(1/2) within CP2K, accurately. However, this won't change
the pathological results of the Lowdin analysis using MOLOPT basis
sets.

cheers,

Matthias

On Dec 7, 10:51 am, Laino Teodoro <teodor... at gmail.com> wrote:
> Hi Matthias,
>
> I do not agree : there several cases where diagonalization of S (done to compute functions of S) leads to huge numerical noise on the eigenvalues (due to almost linear dependencies of the C vectors) - with only 1-2 significant digits if you work in double precision - whether this is that case or not, I cannot say. I trust what you said: if you checked than for sure this is not that case.
>
> Nonetheless, for peculiar cases (numerically speaking) skipping the diagonalization of S is the way to go to compute functions of S.
>
> 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 10:36, Matthias Krack <matthia... at psi.ch> wrote:
>
> > 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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