Subject: Summary: Opinions on the quantum charges

From: "Eugene Radchenko" <[email-masked]>
Date: Fri, 7 Jul 1995 14:31:47 +0400 (MSD)

Hi CCLers!
Recently I asked a question on the QC-derived atomic charges:
>I would like to know what is the current opinion concerning the atomic
>charges calculated by the quantum-chemical methods, especially for the
>charged species. I mean their strong tendency to produce over-pronounced
>charge separation. I might even try to reconcile myself with slight negative
>charge on nitrogen in ammonium, but rather high POSITIVE charge on carbon
>in (fluorinated) carbANIONS absolutely kills me.
>I wonder whether it might actually be computational artifact induced by,
>for instance, improper basis set selection or atom partitioning?

I have received quite a few responses. Following is the summary (in no
particular order). I have also taken the liberty to comment on some points.

**********************************************************************
>Date: Thu, 22 Jun 1995 08:37:08 -0500
>From: Lipkowitz <[email-masked]>
>
>An introductory chapter entitled "Population Analysis and Electron Densities
>from Quantum Mechanics" explains all that to you. It was written by Steve
>Bachrach and published in Volume 5 of Reviews in Computational Chemistry, VCH
>Publishers, 1994.

************************************************************************
>Date: Thu, 22 Jun 95 15:50:55 +0200
>From: [email-masked] (van duijnen)
>
>First, 'atomic charges' are not 'observables': they are usually obtained by
>some arbitrary allocation of parts of the electronic charge distribution to
>atoms. Most methods are systemitical: the Mulliken prodecure assigns
>electrons to atoms via the centers of the basis functions (e.g. even if the
>maximum of an a.o. lies closer to another atom onwhich it's centered!).
>Two-center distributions are split equally between the two associated
>atoms, regardless of where that distribution resides in space. Only the
>total number of electrons is preserved.
>Mulliken charges are, as a consequence strongly basis dependent, and their
>use as 'chemical indicators' for extended basis sets is very doubtful.
>
>Second, for what are 'charges' used. If one's only interest is generating
>electrostatic potentials (ESPs) outside a molecule, fitting the charges to
>the expectation values of the ESP is an option.  It may be combersome,
>because one needs a relatively large number of 'measuring points' for which
>the ESP has to be computed.  The results are generally good, within the
>standard multipole expansion philosophy, i.e. any set of point charges
>inside the molecular volume which reproduces the ESP is acceptable.  Fit
>procedures are dumb but obedient: any set of charges is OK, but they don't
>have to make (chemical) sense. Often the charges in two molecules (e.g.
>differing only in conformation) may look very different, but both sets are
>still 'good'.
>
>We have been satisfied with a compromise: constructing Dipole Preserving
>Charges.  (Theor.Chim. Acta (1983) 63  209-221). They are obtained from the
>standard Mulliken analysis-by contracting the density and overlap matrices-
>extented with a similar procedure for the dipole matrices. Hence, both the
>total charge and the overall dipole moment is reproduced by the resulting
>charges.  The procedure makes sure that 'local' charge distributions are
>kept as local as possible. The charges of course vary in the same way as
>Mulliken charges, so their value as analytical tools are the same.
>
>Our experience is that the DP charges give very good ESPs. Recently we
>tried to 'improve' the method (more expansion centers, higher moments,...)
>but at no avail.
>
>There are other methods, of course. My memory tells me about Ahlrichs and
>coworkers (I think it is also in Theor.Chim. Acta 1983) using a projecting
>procedure which makes charges virtually basis independent.
>
>I hope  this helps a bit.
>
>Best regards, Piet.
>
>Dr.P.Th. van Duijnen, Chemistry Department (OMAC), University of Groningen,
>Nijenborgh 4, 9747 AG Groningen, The Netherlands.
>tel. (int)-3150-634373  fax. (int)-3150-634296 e-mail: [email-masked]

*********************************************************************
>Date: Thu, 22 Jun 1995 09:50:15 -0400
>From: [email-masked] (Michael K. Gilson)
>
>I am not expert in this field, but I do know a couple of papers that might be
>relevant.  They deal with the problem of fitting charges to external
>electrostatic potentials computed by electronic structure calculations.
>
>The papers address the problem that atoms that are not near the "surface" of
>the molecule need not be assigned reasonable charges.  The reason is that
>their charges do not influence the potential much anyway!  So standard fitting
>does not work too well for them.
>
>The references are:
>
>@Article{resp1,
>  author =       "Wendy D. Cornell and Piotr Cieplak and Christopher
>                  I. Bayly and Peter A. Kollman",
>  title =        "Application of {RESP} charges to calculation
>                  conformational energies, hydrogen bond energies, and
>                  free energies of solvation.",
>  OPTcrossref =  "",
>  OPTkey =       "",
>  journal =      "J. Am. Chem. Soc.",
>  year =         "1993",
>  volume =       "115",
>  OPTnumber =    "",
>  pages =        "9620-9631",
>  OPTmonth =     "",
>  OPTnote =      "",
>  OPTannote =    ""
>}
>
>@Article{resp2,
>  author =       "Christopher I. Bayly and Piotr Cieplak and Wendy D.
>                  Cornell and Peter A. Kollman",
>  title =        "A well-behaved electrostatic potential based method
>                  using charge-restraints for deriving charges: {T}he
>                  {RESP} model.",
>  OPTcrossref =  "",
>  OPTkey =       "",
>  journal =      "J. Phys. Chem.",
>  year =         "1993",
>  volume =       "97",
>  OPTnumber =    "",
>  pages =        "10269-10280",
>  OPTmonth =     "",
>  OPTnote =      "",
>  OPTannote =    ""
>}
>
>Good luck
>
>Mike Gilson
>CARB Fellow

***********************************************************************
>From: [email-masked]
>Date: Thu, 22 Jun 1995 09:50:33 -0500 (CDT)
>
>   Your question has been addressed ad nauseam in the literature and has been
>a topic of some debate since the mid 1930's. Our own contribution has been
>the development of Class IV charge models which employ semiempirical mapping
>parameters to improve charges derived from other methods by fitting against
>experimental dipole moments. I note that the paper is fairly recent (J.
>Comput.-Aid. Mol. Des. 9 (1995) 87-110) and provides a comprehensive
>listing of references to other work in the field--thus, you might find it
>useful as a starting point if you decide to immerse yourself in this topic.
>Moreover, it as available on the WWW at
>http://wucmd.wustl.edu/jcamd/278/paper.html (kudos to ESCOM).
>
>Chris
>
>--
>Christopher J. Cramer
>University of Minnesota
>Department of Chemistry
>207 Pleasant St. SE
>Minneapolis, MN 55455-0431
>(612) 624-0859
>[email-masked]
>http://dionysus.chem.umn.edu/

************************************************************************
>From: tj ODonnell <[email-masked]>
>Date: Thu, 22 Jun 1995 10:12:21 -0500 (CDT)
>
>Yes, schemes for assigning charges to atom sometimes give unexpected results.
>I think it is due simply to the too-simple assumption that charge CAN be
>partitioned among atoms. What I mean is: it is always an arbitrary choice one
>makes when partitioning a molecular charge among its component atoms. While
>nuclei may retain their identity within molecules, electrons don't - certainly
>not the valence electrons. In addition, many charge schemes "look at" the
>molecule from a distance (esp fitting procedures, e.g.), evaluating properties
>(esp) at points which are influenced by nuclei and electrons contributed by
>several atoms.  Is it any wonder that this "average" effect cannot clearly be
>attributed then to individual atoms?
>
>Just my opinion,
>TJ O'Donnell
>[email-masked]
>http://www.eecs.uic.edu

************************************************************************
>From: [email-masked]
>Date: Thu, 22 Jun 1995 08:49:42 -0700
>
>There is a discussion of charge fitting for molecular mechanics on
>http://www.amber.ucsf.edu/amber/ under "Charge fitting philosophy."
>
>Bill Ross

**********************************************************************
>Date: Thu, 22 Jun 95 18:52:51 +0100
>From: [email-masked] (Johannes Richardi)
>
>It might be interesting for you that I am currently calculating multipole
>moments of standard organic molecules by ab initio methods
>(chloroform,acetone,pyridine). I compare the multipoles obtained directly and
>by  the partial charge models. I sometimes observe a strong derivation of some
>percents. As the partial charge models are quite important for computer
>simulations of liquids these results are generally interesting to my mind.
>
>Now concerning your remark, I believe you should compare the multipole moments
>obtained directly by ab initio or experiments and by the partial charge model.
>If you find a good correspondence, the results are correct, even when they
>don't correspond to our chemical common sense. If not, you should try to fit
>your partial charge model to the exact multipoles. I have written programms to
>cope with multipoles and partial charge models and I would agree to any
>cooperation.
>
>Please send me a copy of the answers obtained !!!
>
>Johannes
>
>
>Johannes Richardi
>
>---------------------------------------------------------------------------
>Institut fuer Physikalische und Theoretische Chemie
>- Lehrstuhl Prof. Barthel -            Tel.:  (+49) 941 943-4743
>Universitaet Regensburg                Fax.:  (+49) 941 943-4488
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>D-93053 Regensburg
>Deutschland / Germany
>---------------------------------------------------------------------------
>EMail (SMTP):  [email-masked]
>---------------------------------------------------------------------------
> E PUR SI MUOVE    -- GALILEO GALILEI

***********************************************************************
>From: [email-masked]
>Date: Thu, 22 Jun 1995 12:58:38 EDT
>
>You have entered into a very controversial subject area with your posting!
>There are many different ways of approaching the "charge" problem, and
>you get different results using different methods.  Perhaps the use of
>a common term ("charge") is not even appropriate for comparing these results.
>In my opinion, a distribution of electron density can be queried for a number
>of things, one of them being electrostatic potential.  If one wants to
>define atomic point charges which duplicate this potential (to the best fit
>approximation, anyway), then this is a good model of "atomic charges".  If
>one wants to partition electron density and perform sub-structure quantum
>mechanics, it is necessary to use a partitioning method which ultilizes
>interatomic zero-flux surfaces which amount to discrete atomic boundaries.
>When the electron population within these atomic volumes are subtracted from
>the nuclear charge, you will get a number which is NOT to be confused with
>the former electrostatic "charge" definition given above.  IF, however, these
>"charged" regions are considered in addition to their internal dipole moments,
>the molecular dipole moments can be reproduced EXACTLY.  Hence, there are
>more ways to think of "charge" than most people consider.
>
>        Curt Breneman
>        Assoc. Prof. of Chem.
>        RPI, NY

*************************************************************************

>Date: Thu, 22 Jun 1995 16:47:06 +0200
>From: Shcherbukhin Vladimir <[email-masked]>
>
>The QC charges you have written about don't look strange at all.
>Especially if you consider that they are non-existing values -- there is
>no *unique* way to project the electron density calculated from the
>wavefunction into atomic positions.
>
>    Yours,
>    Volodya
>
> -----------------------------------------------------------------
>Vladimir Shcherbukhin ! phone:  (+46-31)-776-2560
>ASTRA Haessle AB      ! FAX:    (+46-31)-776-3710
>Molndal S-43183       ! e-mail:
>SWEDEN                ! [email-masked]

************************************************************************
>From: [email-masked]
>Date: Mon, 26 Jun 1995 16:09:45 +0200 (DFT)
>
>The problem of charges is not a trivial one. The most often used
>Mulliken's population analysis has a priviledged importance as far as the
>MATHEMATICAL structure of the finite basis theory is concerned [cf. I.
>Mayer, Chem. Phys. Letters 97, 270 (1983); THEOCHEM 255, 1 (1992)] but it
>is strongly basis dependent. It usually gives chemically "reasonable"
>results (especially when one interested in TRENDS in series of related
>molecules) if the "well balanced" STO-3G or 6-31G** basis sets are used,
>but may lead to completely mad results for other basis sets, in particular
>for anions, especially if DIFFUSE functions are present in the basis -
>these are formally attributed to one of the atoms but, in fact, spread
>over the whole molecule. In such a case the best is to turn to
>Lowdin-orthogonalized basis and calculate the charges in the latter.
>
>We think the over-sensibility of Muilliken's charges is partly due to some
>INTRA-molecular BSSE-like effects and could be reduced by the exclusion of
>the latters. However, it is to be emphasised that there exists no perfect
>solution of the charge problem if an OVERLAPPING basis is used. There are
>no definitions which could simultaneously fulfil the requirements:
>
>1. The population on each atomic orbital is always between 0 and 2;
>
>2. The population is related to strictly atomic quantities;
>
>3. The population on different AO-s (or atoms) sums up to the total
>   number of electrons.
>
>Mulliken's populations do not strictly fulfil requirement 1; the charges
>calculated in Lowdin-orthogonalized basis do not fulfil requirement 2, as
>are is related to some delocalized orthogonal orbitals, reflecting some
>global effects, too: as a consequence, one may change them by adding some
>EMPTY orbitals to the basis, i.e. without changing the wave function [c.f.
>I.Mayer, Chem. Phys. Lett. 110, 440 (1984)]; the so called Robby's charge
>violates requirement 3 (e.g. in the HF molecule it gives negative
>resulting charge on both H and F).
>
>I have discussed above "partitioning the electronic charge in the Hilbert
>space" of AO-s (G.G. Hall). A completely different - very useful - charge
>concept emerges in Bader's "topological theory of atoms in molecules", in
>which the 3-dimensional PHYSICAL space is partitioned into "atomic
>domains", and the charge distribution in each of them integrates to the
>atomic charges. Unfortunately, the calculation of these charges is more
>complicated computationaly.
>
>Yours sincerely,
>
>Prof. Istvan Mayer
>
>            e-mails: [email-masked]
>                     [email-masked]
>                     [email-masked]
>
>Central Research Institute for Chemistry
>of the Hungarian Academy of Sciences
>H-1525 Budapest, P.O.Box 17
>Hungary

*********************************************************************
>From: [email-masked]
>Date: Mon, 26 Jun 1995 12:04:00 -0400
>
>From what I can glean from the literature, most researchers seem to agree
>that HF/6-31G* MEP charges are "best" or "good" or at least adequate in
>determining atom-centered charges and there is little benefit (significant
>change in atom-centered charges) in going to MP2/6-31G* MEP charges.
>Alternatively, to save time, scaled MNDO MEP charges may be used since they
>have been shown to have a high correlation correlation to HF/6-31G* MEP
>charges, at least for CHNO compounds.  MEPs are generally preferred since
>it is argued that they reflect what is "seen", i.e., the Coulombic
>interaction experienced, by other molecules.  Atom-centered charges derived
>by partitioning methods, including emprical electronegativity balancing
>schemes such as Del Re's (avialble QCPE) and Gasteiger methods and
>semiemprical or ab initio natural atomic or Mulliken charges, are
>considered to be inferior if not unreliable.  However, recently, Cramer has
>introduced a modified Mulliken method, for, I believe AM1, which is claimed
>to reproduce MEP HF/6-31G* charges at a substantially lower computational
>cost and leading to an improved semiempirical solvation model.
>
>As for "their strong tendency to produce over-pronounced charge separation"
>and apparently odd charges, certainly MEP HF/6-31G* charges appear to
>display more highly polarized molecules (larger atom-centered charges) than
>the partitioning methods and one may see signifcant differences in
>predicted relative charges and even charge sign changes.  But which method
>is correct?  How can one tell?  I am not aware of any correlations of
>predicted/derived atom-centered charges with direct measurements, though
>chemically modified STM may provide an opportunity to do so if the
>resolution is fine enough.  Alternatively, one might look at NMR shift
>data, but this too, includes solvation effects.  Might it be possible to
>combine NMR with MS to measure gas phase atomic environments and therefore
>the charge?  I beleive some work has been done trying to correlate electron
>denisty maps from X-ray studies with charge, but this too has a
>partitioning problems and involves crystal lattice effects.  To complicate
>matters further, derived atom-centered charges may also be conformationaly
>dependent! [There have been a few references on modifying empirical
>partitioning methods either to include through space interactions
>(Gasteiger published a variation of his method) or, I believe, to include
>conformationally dependent paramters, e.g., similar to molecular mechanics
>1-4 interactions.  Efforts have also been made to solve such equations
>directly rather than by itterative schemes so that charges may be updated
>more frequently in molecular dynamics studies].
>
>Many would say that atom-centered charges aren't very meaningfull anyway so
>ignore them or don't worry too much.  They are an artificial, albeit
>methodical and reproducible construct, a convenience for counting or
>partitioning electrons.  But choice of charge models can have a signficant
>impact on studies particularly in molecular mechanics and molecular
>dynamics calculations in which accurate representation of intermolecular
>potentials is crucial.
>
>So what is a reasearcher to do?  First be consistent;  don't mix charge
>models.  Next, from a completely pragmatic standpoint, use the charge model
>which best fits your set of data.  Don't be overly concerned with absolute
>values unless there is corroborative direct or indirect evidence that they
>are "wrong" or inconsitent with other observations.
>
>What's wrong with a negative charge on N in amonnium compounds?  That is,
>why is it important and what significance does it have?  Does it lead to
>incorrect conformations?  Presumably one might be more interested in the
>charge on the -N+H protons which might be expected to reflect H-bonding
>potential and acidity, i.e., compared with water, methanol, etc., and that,
>no doubt, has to be more positive to compensate for the negative N.
>
>Positive C-charge on flourinated carbanions?  Why is this a problem?  Does
>it disagree with chemical reactivity, i.e., nuclephilicity of the
>carbanion?  Is it more positive than the neutral compound?
>
>In my own work, I have also observed "bothersome" charges but more often
>than not such observations are distractions and not relevant to the study.
>
>In the end, there is no easy answer.  This controversy is likely to go on
>for some time until methods permit us to reliably measure charges of
>individual atoms.
>
>My appologies for not referencing the many researchers who have made
>valuable contributions to this area of research.
>
>Karl
> _______________________________________________________________________
>/                                                                       \
>| Comments are those of the author and not Unilever Research U. S.      |
>|                                                                       |
>| Karl F. Moschner, Ph. D.                                              |
>|                                                                       |
>| Unilever Research U. S.      e-mail: [email-masked] |
>| 45 River Road                Phone:  (201) 943-7100 x2629             |
>| Edgewater, NJ 07020          FAX:    (201) 943-5653                   |
>\_______________________________________________________________________/

**************************************************************************
>Date: Thu, 22 Jun 1995 15:41:12 -0400
>From: "E. Lewars" <[email-masked]>
>
>There was a question about QM charges and fluorocarbanions reccently.
>Some of these species were said to show a positive C, and the question of the
>reliability of quantum mechnically calc charges arose.
>  There seems to be no one, right way to calc charges on atoms in molecules,
>and these charges evidently can't be measured ("are not QM observables") --
>but see Pearlman and Kim, J Mol Biol 211 p 171 (1990).
>General refs to calculating charges:
>Wiberg et al, J Comp Chem 14 p1504 (1993)
>Basis set dependence:
>Rodrigues et al, J Comp Chem 14 p922 (1993)
>Other refs:
>
>JACS 107 p1829 (1985)
>JACS 113 p 5203 (1991)
>JACS 115 p614 (1993)
>JACS 115 p1084 (1993)
>JACS 116 p6812 (1994)
>J Comp Chem 14 p530 (1993)
>J Comp Chem 14  799 (1993)
>J Comp Chem 15  200 (1994)
>Rev in Comp Chem II, 219 (1991)
>
>I did a few calcs on some fluorocarbanions: the electrostatic potential charges
>look very reasonable, and hardly change with the basis:
>
>H-F level              CH3-              F-CH2-               F-CH-F-
>charge on
>C  3-21G/6-31G*     -1.53/-1.43       -1.07/-1.03           -0.70/-0.71
>F    " / "            -----           -0.26/-0.27           -0.24/-0.22
>H    " / "          0.18/0.14          0.17/0.15             0.17/0.15

*******************************
(But I really seen the positive values for CHF2 and CF3 anions. they must
have been Mulliken ones ;-)

Evidently, any QM charges can be used to characterize the qualitative
tendencies within a series of compounds and do nicely correlate with ESCA
and NMR shifts. (Although qualitative tendencies usually can be formulated
without any (let alone non-empirical) calculations at all. It is the
comparison within diverse sets that usually requires computations :-).
The MEP charges seem more chemically reasonable and more suited in the
context of the molecular recognition.

Concerning the question of what exactly bothers me in the charges (see the
posting by K.F.Moschner above).
As to ammonium cation, I evidently overlooked the fact that the actual
charge in NH3 is anything but the formal zero. Sorry.
As to carbanions, I think that although nucleophilicity is not solely
controlled by charge (it is orbital interaction, not electrostatic),
positive charge on C might be expected to shift major nucleophilic center
>from C to F atoms. Moreover, as the electronegativity of carbon is greater
than that of hydrogen, carbon in (neutral) hydrocarbons should have slight
negative charge.
Also, it raises interesting ambiguity. One might expect positively charged
Lewis base to have very compact lone pair and consequently to be very hard
base. On the other hand, inductive delocalization caused by F atoms might
be expected to increase the base softness. I would like to know whether
someone have studied this problem.

         Thank you for your time                 Eugene

--
--------------------------------------------------------------------
Eugene V. Radchenko           Graduate Student in Computer Chemistry
E-mail: [email-masked]                Fax: +7-(095)939-0290 
Ordinary mail:  Chair of Organic Chemistry, Department of Chemistry,
                      Moscow State University, 119899 Moscow, Russia
*****************  Disappearances are deceptive  *******************