# Lowdin analysis

Matthias Krack matthia... at psi.ch
Sun Dec 5 14:06:15 UTC 2010

```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
>           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
```