[CP2K:2979] Re: Lowdin analysis

Laino Teodoro teodor... at gmail.com
Tue Dec 7 10:51:35 CET 2010


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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>> 
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