CCL:G: Case Studies of QM Computational Chemistry in Reactivity



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 denominator to become zero when energy_1 =
 energy_2. This can cause perturbation 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 necessarily 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 believe that for most systems the
 complete basis set limit would be well-defined for MP2 calculations. In
 this sense, the MP2 calculations are much more well-defined than Mulliken
 or Lowdin populations, which definitely do not have a basis set limit.
 > If the set is small (minimal) the derived atomic charges are chemically
 reasonable and correlate well with those from other methods for well
 understood reasons.
 The populations of the density matrix projected onto a smaller basis set is
 usually referred to by a different name. At least in Gaussian programs, it
 is called Pop=MBS. In Gaussian programs, this is a different algorithm than
 Pop=Regular which performs Mulliken analysis in the current basis set. In
 my experience, the Pop=MBS method is not very useful and tends to crash a
 large percentage of the time. It seems to crash especially often for
 heavier atoms and for those with pseudopotentials. Also, people have tested
 the idea to project plane-wave basis sets onto minimal localized atomic
 orbital basis sets, but this results in charge leakage where the density
 matrix in the smaller basis set does not accurately represent the true
 density matrix. In general, the small basis sets do not represent the
 density matrix with high accuracy. Therefore, in general, I cannot
 recommend 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  Grimme" [grimme|*|thch.uni-bonn.de]
 > Dear Tom,
 > I followed this discussion quietly for some time but now can't resist to
 > comment on this too extreme viewpoint:
 >
 > 1. Methods can be useful and reasonable without a definite mathematical
 > limit. 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 from other methods for well understood reasons. I don't want to
 > defend orbital 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 is
 > unlcear) in large one-particle basis sets and hence also do not have a
 > definite mathematical limit. Is this a good reason to abandon all MP2
 > calculations?
 >
 > 2. The word "observe" in our context can only mean
 "observable" 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
 > mean
 > correlations of spectroscopic signatures with atomic charges when writing
 > "They can be observed and measured through spectroscopy
 experiments".
 > 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
 > focused on exchange-correlation theories and basis sets and the earlier
 > discussion focused on atomic properties. If one increases the basis set
 > size, exchange-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 mathematical limit with a particular basis set. Thus, it is meaningful
 > to discuss how 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 being studied.
 >
 > >In contrast, Mulliken and Lowdin population analysis schemes do not
 have
 > any defined mathematical limits. As the basis set is increased and the
 > energy and electron density approach the complete basis set limit, the
 > Mulliken and Lowdin populations behave erratically and blow up. This is how
 > we know for sure that Mulliken and Lowdin population analysis schemes are
 > utter nonsense and should never be used for publication results. As pointed
 > out by one person, their only purpose is for debugging calculations to see
 > if the 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 nonsense, because they
 > have no defined mathematical limits. This has nothing to do with atomic
 > charges, per se. The Mulliken and Lowdin populations do not measure
 > anything physical. They do not measure atomic charges. Probably the
 > 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 mathematical 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 charges.
 > While we may not be able to measure atomic charges as precisely as energies
 > in experiments, it is not true to say atomic charges are not experimentally
 > observable. They can be observed and m!
 >  easured through spectroscopy experiments, albeit with much less precision
 > than we are able to measure energies. I could go into more extensive
 > details and examples if you are interested.>
 >
 >