[CP2K:2975] Re: Lowdin analysis
Teodoro Laino
teodor... at gmail.com
Tue Dec 7 09:35:28 CET 2010
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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