Hi Stefan,

In regards to your questions=
about MP2, one has to be extremely careful with such an approach, because =
the denominator is of the form (energy_1 - energy_2) which causes the denom=
inator to become zero when energy_1 =3D energy_2. This can cause perturbati=
on methods to blow up. For this reason, I generally prefer non-perturbative=
methods such as CCSD, when a higher-level calculation result is needed. I =
would recommend CCSD as opposed to MP2, simply because CCSD has a more well=
-defined mathematical limit on the results of the calculation. Personally, =
I don't use MP2 calculations for this reason, but this doesn't nece=
ssarily mean others can't. However, I wouldn't go so far as to say =
that MP2 calculations don't have a well-defined basis set limit. I beli=
eve that for most systems the complete basis set limit would be well-define=
d for MP2 calculations. In this sense, the MP2 calculations are much more w=
ell-defined than Mulliken or Lowdin populations, which definitely do not ha=
ve a basis set limit.

> If the set is small (minimal) the derived atomic char=
ges are chemically reasonable and correlate well with those from other meth=
ods for well understood reasons.

The populations of the density matrix projected onto a smal=
ler basis set is usually referred to by a different name. At least in Gauss=
ian programs, it is called Pop=3DMBS. In Gaussian programs, this is a diffe=
rent algorithm than Pop=3DRegular which performs Mulliken analysis in the c=
urrent basis set. In my experience, the Pop=3DMBS method is not very useful=
and tends to crash a large percentage of the time. It seems to crash espec=
ially often for heavier atoms and for those with pseudopotentials. Also, pe=
ople have tested the idea to project plane-wave basis sets onto minimal loc=
alized atomic orbital basis sets, but this results in charge leakage where =
the density matrix in the smaller basis set does not accurately represent t=
he true density matrix. In general, the small basis sets do not represent t=
he density matrix with high accuracy. Therefore, in general, I cannot recom=
mend the approach you mentioned. There are certainly much better approaches=
if the goal is to compute net atomic charges.

Best,

Tom

=
On Thu, Sep 10, 2015 at 2:04 PM, Stefan Grimme grimme,,thch.uni-bonn.de <owner-chemistry/a\ccl.net>=
; wrote:

Sent to CCL by: "Stefan=C2=A0 Grimme" [grimme|*|thch.uni-bonn.de]

Dear Tom,

I followed this discussion quietly for some time but now can't resist t= o

comment on this too extreme viewpoint:

1. Methods can be useful and reasonable without a definite mathematical lim= it. A Mulliken or Loewdin population analysis gives a definite result for a= given well-defined AO basis set. If the set is small (minimal) the derived= atomic charges are chemically reasonable and correlate well with those fro= m other methods for well understood reasons. I don't want to defend orb= ital based partitionings (I prefer observables) but making the mathematical= limit

to the encompassing requirement seems nonsense to me.

There are other useful and widely used QC methods like Moeller-Plesset

perturbation theory which are often divergent (or at least convergence isunlcear) in large one-particle basis sets and hence also do not have aCHEMISTR= Y/a\ccl.net or use:

definite mathematical limit. Is this a good reason to abandon all MP2

calculations?

2. The word "observe" in our context can only mean "observab= le" in a QM

sense. Hence, because there is no operator for "atomic charge" an=

observable atomic charge does not exist in a strict sense. You probably mea= n

correlations of spectroscopic signatures with atomic charges when writing"They can be observed and measured through spectroscopy experiments&qu= ot;.

If you have another opinion on that I would like to know more details on

how to measure atomic charges.

Best wishes

Stefan

>Hi Peeter,

>There is a fundamental distinction between the current conversation foc= used on exchange-correlation theories and basis sets and the earlier discus= sion focused on atomic properties. If one increases the basis set size, exc= hange-correlation functionals such as B3LYP, M06, or whatever one you care = to use will approach a well-defined mathematical limit. We can then discuss= what the relative accuracy of that mathematical limit is in comparison to = experimental properties and also discuss how close we are to that mathemati= cal limit with a particular basis set. Thus, it is meaningful to discuss ho= w adequate an exchange-correlation theory or basis set are for a particular= research problem. Of course, the goal is to choose an adequate level that = is not too computationally expensive for the particular research question b= eing studied.

>In contrast, Mulliken and Lowdin population analysis schemes do not hav= e any defined mathematical limits. As the basis set is increased and the en= ergy and electron density approach the complete basis set limit, the Mullik= en and Lowdin populations behave erratically and blow up. This is how we kn= ow for sure that Mulliken and Lowdin population analysis schemes are utter = nonsense and should never be used for publication results. As pointed out b= y one person, their only purpose is for debugging calculations to see if th= e symmetry or other basic features of the input geometry are malformed.

>It is not the earlier discussion on atomic charges that is "= ;nonsense" but rather the Mulliken and Lowdin populations that are non= sense, because they have no defined mathematical limits. This has nothing t= o do with atomic charges, per se. The Mulliken and Lowdin populations do no= t measure anything physical. They do not measure atomic charges. Probably t= he confusion has been propagated by calling Mulliken and Lowdin populations= as types of "atomic charges", but really the Mulliken and Lowdin= populations cannot be atomic charges, because they have no defined mathema= tical limits. In the future, I shall try to avoid referring to Mulliken and= Lowdin populations as types of atomic charges, because I think this error = is responsible for the confusion surrounding the definition of atomic charg= es. While we may not be able to measure atomic charges as precisely as ener= gies in experiments, it is not true to say atomic charges are not experimen= tally observable. They can be observed and m!

=C2=A0easured through spectroscopy experiments, albeit wit= h much less precision than we are able to measure energies. I could go into= more extensive details and examples if you are interested.

-=3D This is automatically added to each message by= the mailing script =3D-

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