[CP2K:2975] Re: Lowdin analysis

[Teodoro Laino]

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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