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



 Sent to CCL by: "N. Sukumar" [nagams]![rpi.edu]
 
Since this list includes a large number of non-specialists, one should be careful to avoid making sweeping statements like "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 measured through spectroscopy experiments, albeit with much less precision than we are able to measure energies."
 
"Atomic charges" are about as measurable as the divinity of an orbital! Both are entirely theoretical properties of theoretical objects. I joint Stefan in asking how to "measure atomic charges" - and before that please also clarify what you mean by "atomic."
 --
 N. SUKUMAR
 Professor & Head, Department of Chemistry
 Director, Center for Informatics
 Shiv Nadar University, India
 On 2015-09-11 05:32, Thomas Manz thomasamanz-*-gmail.com wrote:
 
 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 [1] <owner-chemistry]~[ccl.net> wrote:
 
 Sent to CCL by: "Stefan  Grimme" [grimme|*|thch.uni-bonn.de [1]]
 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.
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 --
 N. SUKUMAR
 Professor & Head, Department of Chemistry
 Director, Center for Informatics
 Shiv Nadar University, India