Lowdin analysis
Manh
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
&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
&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
Matthias Krack
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
Manh-Thuong Nguyen
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Teodoro Laino
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
Matthias Krack
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
Teodoro Laino
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
Matthias Krack
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
Laino Teodoro
Ok - in this case, if you checked already before your first post, why mention linear dependencies and problems with diagonalization? These are pure numerical issues that can be solved skipping the diagonalization of S to evaluate S**(1/2).
Best
Teo
---------------------------------------------
Teodoro Laino
Zurich Switzerland
Contact info:
Tel.: http://www.jajah.com/Teo
E-mail: teo...@laino.eu
teodor...@gmail.com
---------------------------------------------
Matthias Krack
On Dec 7, 10:10 am, Laino Teodoro <teodoro.la...@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?
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).
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
> teodoro.la...@gmail.com
> ---------------------------------------------
Laino Teodoro
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...@laino.eu
teodor...@gmail.com
---------------------------------------------
Matthias Krack
you are now referring to purely technical issues concerning the
calculation of functions of S like S**(1/2), which is not (just to
recall it) the original topic of this thread. However, I would
certainly appreciate if you could come up with a more robust scheme to
calculate S**(1/2) within CP2K, accurately. However, this won't change
the pathological results of the Lowdin analysis using MOLOPT basis
sets.
cheers,
Matthias
>
> 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
> teodoro.la...@gmail.com
> ---------------------------------------------
>
> read more »
Teodoro Laino
I focused on this "purely technical issues" because of your original reply. "Just to recall it":
>>>>>>>> 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.
the fact that an ill-conditioned overlap matrix will most likely result in a weird charge partition IS a purely technical issue.
A more robust scheme? It's easy: just do an SVD of the C matrix. The condition number of S is the square of the condition number of C.
This means that a condition number of 10^-14 in S, is only 10^-7 in C. This is by far numerically more stable if you work in double precision.
Hope this helps you.
Best,
Teo
Matthias Krack
thanks for the proposal, but finally it does not help, since the weird
Lowdin charges using MOLOPT basis sets won't change even if all
numerical problems are accurately tackled as shown by the simple case
of the single water molecule.
cheers,
Matthias
>
> read more »