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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