From owner-chemistry: at :ccl.net Thu Sep 10 20:09:01 2015 From: "Thomas Manz thomasamanz-*-gmail.com" To: CCL Subject: CCL:G: Case Studies of QM Computational Chemistry in Reactivity Message-Id: <-51702-150910200217-25569-XEGze+UI5r58Ul8PhtoYgA++server.ccl.net> X-Original-From: Thomas Manz Content-Type: multipart/alternative; boundary=001a11400d6a68dd4f051f6d6d57 Date: Thu, 10 Sep 2015 18:02:10 -0600 MIME-Version: 1.0 Sent to CCL by: Thomas Manz [thomasamanz|gmail.com] --001a11400d6a68dd4f051f6d6d57 Content-Type: text/plain; charset=UTF-8 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.> > > --001a11400d6a68dd4f051f6d6d57 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
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 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 "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.



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