SUMMARY: Mulliken Population Analysis and Basis Sets

 	Dear CCLNet,
 Last Monday I asked a question on how much charges from
 Mulliken population analysis can depend upon basis set,
 especially using diffusive functions.
 Thanks to all you who replied. I think that every suggestion
 is worth reading. Thank a lot
 Yours sincerely
 		Grzegorz Bakalarski
 		Warsaw University
 This is summary of replies I've got until Friday morning:
 Original query:
         Dear Netters,
 Maybe this is a very naive question, but ....
 I'd like to ask you Dear Quantum Chemists, how much charges from
 Mulliken population analysis can depend upon basis set ?
 Particular problem is that I and coworkers have calculated Mulliken
 charges using different programs using different basis sets e.g..
 gaussian 6-31G** basis set ( in GAUSSIAN)  and double numerical
 with polarization basis set (DNP in DMol). And of course we've got
 different Mulliken charges. (As we've expected and as it is well
 know that Mulliken charges depend on basis sets). But we've noticed
 that for some atoms differences are quite large. For example when
 a methyl group is bound to nitrogen atom changes are about 0.7-0.8 e
 (6-31G** : -0.188 [MP2] ;-0.193 [B3-LYP] and DNP: -0.962 [LDF]; -0.786 [NLDF]).
 I'd like to ask especially about comparison between DNP and gaussian + diffusive
 basis sets, because as I know numerical basis sets  are "more
 than gaussian ones  (they have "good tails").
 I'd like to add that we've also calculated ESP charges and they are O.K.
 less than 0.1 e), that means that electron density is calculated correctly.
 Any comments, references and hints  would be nice. Thanks in advance for
 anyone who replies. If I get any useful information I'll summarize to the NET.
 Best wishes and have a nice week.
                                 Grzegorz Bakalarski
                                 Dept. of Biophys. UW
                                 & Interdisciplinary Centre
                                 for Modelling (ICM)
                                 Warsaw University
                         e-mail: grzesb -8 at 8-
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 From: Ferenc.Molnar -8 at 8- (Ferenc Molnar)
 There is a very nice review related to this topic:
 Reviews in Computational Chemistry, Vol. 5, Libkowitz, Boyd (Eds.).
 I can't remember by whom it was, right now, but if you look
 in the book you will surely find it. The author favors Loevdin populations
 over Mulliken populations and discusses the "atoms in molecules"
 by Baader. The shortcomings of each method are discussed!
 Hope this helps,
 Ferenc Molnar
 Institut fuer Physikalische und Theoretische Chemie
 - Lehrstuhl Prof. Dick -                   Tel.:  (+49) 941 943-4466 /-4486
 Universitaet Regensburg                    Fax.:  (+49) 941 943-4488
 Universitaetsstrasse 31
 D-93053 Regensburg
 Deutschland / Germany
 From: "Erin Duffy" <eduffy -8 at 8->
 Hi -  You might want to take a look at the following:
 (1)  Carlson, HA; Nguyen, TB; Orozco, M.; Jorgensen, WL.
      "Accuracy of Free Energies of Hydration for Organic
      Molecules from 6-31G(d)-Derived Partial Charges."  J.
      Comput. Chem.  (1993) v.14, 1240-1249.
 (2)  Wiberg, KB; Rablen, PR.  "Comparison of Atomic Charges
      Derived via Different Procedures."  J. Comput. Chem.
      (1993) v.14, 1504-1518.
 Ciao -  Erin
         erin -8 at 8- (Erin Duffy)
 From: "FOUNTAIN, KEN" <SC18%NEMOMUS.bitnet -8 at 8->
 The answer is "Lots!"  In Gaussian computations fluctuations
 abound, depending on the level of theory.
 In fact the entire area of populations seems to be murky.
 From: "Robert K. Szilagyi" <szilagyi -8 at 8->
 Dear Dr. Grzegorz Bakalarski,
         we found some systematical changes in Mulliken Population analysis
 while varying basis sets. Our system contains transition metal and we are
 utilizing effective core potentials. The magnitude of the charges was changed,
 the inductive effects, electrophility, etc. remain the same.
 I will send you a note if this article will accepted by the publisher.
         Sincerely Yours,
 Robert K. Szilagyi                     University of Veszprem   METMOD FF
 research fellow                        Dept. Org. Chem.            L1
 Email: szilagyi -8 at 8-          Veszprem, H-8201         L2 |
        szilagyi -8 at 8-      Egyetem u. 10
 Phone: +36-(88)-422022/156             P.O.Box 158              L3 |   R2
 FAX:   +36-(88)-426016                 HUNGARY                     L4
 From: young -8 at 8- (Dave Young)
         There was a question about basis set dependence of the
 mulliken population analysis.  Generally, the answer is that there
 is a basis set dependence and it is often very large.
         The arbitrary 50-50 split of overlap populations makes some
 sense for minimal basis sets and covalent compounds.  For ionic
 compounds, 50-50 split should be suspect immediately.  With diffuse
 basis sets, the diffuse functions may be so far from the nucleus they
 are centered on that they are describing the other nuclei more than
 the one they are centered on.
         Somewhat better results are obtained with the Reid & Weinhold
 natural orbital analysis.
         Probably the least basis set dependent results come from the
 electrostatic analysis in which atomic charges are determined by
 a least squares fit to the electrostatic potential.
         Hope this helps.
                                 Dave Young
                                 young -8 at 8-
                                 youngdc -8 at 8- msucem
 From: evaldera -8 at 8- (Elmer Valderrama)
  Just in case you haven't check this source,
  I. Levine in "Quantum Chemistry" (1991) wrote:
  `One should not put too much reliance on numbers calculated by
   population analysis. Mulliken's assignment of half the overlap
   population to each basis function is arbitrary and sometimes leads
   to unphysical results (see Mulliken & Ermler, Diatomic Molecules, (1977)
   p. 36-38, 88-89). Moreover, a small change in basis set can produce
   a large change in the calculated net charges. For example, net
   charges on each H atom in CH4, NH3, and H2O calculated by the STO-3G
   and 3-21G basis set are (Hehre et al. Ab Initio Molecular Orbital
   Theory (1986), Sec. 6.6.2)
                      CH4    NH3    H2O
      STO-3G         0.06    0.16   0.18
      3-21G          0.20    0.28   0.36
   Comparison of values calculated with the same basis set correctly shows
   increasing charge on each H atom as the electronegativity increases
   from C to N to O, but comparison of the values calculated with different
   basis sets could erroneously lead one to say that the C-H bond in CH4
   is more polar than the O-H bond in H2O."
      "Many other methods have been proposed to assign charges to atoms
   in molecules. See P. Polizer et al. Theor.Chim. Acta 38 101 (1975);
   J. Cioslowsky, J.Am.Chem.Soc 111 8333 (1989); Hehre, Sec. 6.6.2)"
   -What follows is that you could carry out a detailed analysis of the
    results from both DNP and n-nnG type calcns but since no unitary
    transformation connect these wave functions, all would be reduced to
    just a basis-set-dependent effect.
 From: inoue -8 at 8- (Yoshihisa Inoue)
 Dear Dr. Grzegorz Bakalarski,
 I think Mulliken population analysis is historically important, but
 actually sometimes perplexes researchers. As you know, the charges
 are used for molecular dynamics or monte carlo calculations. Then,
 I think they should have physicochemical meaning.
 Following two reports might be useful for you.
 TI Comparison of Atomic Derived via Different Procedures
 AU Kenneth B. Wiberg and Paul R. Rablen
 SO J.Comp.Chem.,14(12), 1504-1518 (1993)
 TI Electron Density Distribution Analysis for Nitromethane,
    Nitromethide, and Nitramide
 AU James P. Ritchie
 SO J.Am.Chem.Soc.,107,1829-1837 (1985)
 The former examined the charges with physicochemical properties.
 You seems to use DMol, so I suggest to use Hirshfeld charges.
 We also reported that Hirshfeld charges are very good at WATOC'93
 at Toyohashi, Japan.
 Dr.Ritchie made Rhosys and it can handle gaussian basis functions.
 According to the JACS report, he provided the program. And
 Drs.Wiberg and Rablen wrote that the Hirshfeld charges were
 obtained using programs written at Yale.
 Hope this help.
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