CCL: atomic population analysis



Hi Peeter,
 Thanks for your insightful comment and encouraging words.
 To understand which atomic population analysis methods perform best, you
 have to compare a variety of properties across an extremely diverse set of
 material classes.
 If only only considers net atomic charges across a few small molecules, it
 may be hard to distinguish the best methodologies.
 But there are a vast array of materials: small molecules, large
 biomolecules and polymers, porous solids, non-porous solids, 1-D and 2-D
 nanostructured materials, organometallic complexes, solid surfaces, liquid
 solutions, and so forth.
 Not only does one have to consider a broad range of materials, but a broad
 range of atomistic properties should also be considered. For example, one
 should consider not only net atomic charges, but also atomic spin moments,
 bond orders, atomic multipole moments, atomic polarizabilities, dispersion
 coefficients, etc. Of course, these are too much to consider in a single
 journal article, but one could envision a series of journal articles that
 look
 into various of these properties. An atomic population analysis method is
 thus not just a recipe for computing net atomic charges, but a systematic
 way to assign various atomic properties. And these assigned atomic
 properties can be compared to experimental results. It is possible, for
 example, to use atomic population analysis methods to predict the overall
 polarizability of a molecule without computing it via perturbation theory
 or via application of electric field. Similarly, the overall dispersion
 coefficients can be predicted using variants of Tkatchenko-Scheffler type
 methods without requiring a time-dependent DFT calculation. These can be
 compared to experiments, and we are currently doing this in a project I'm
 involved with collaborators. When this is done, one finds that some atomic
 population analysis methods perform better than others for the prediction
 of observable experimental properties.
 There are also the tests that the assigned net atomic charges should have
 reasonable conformational transferability, should retain core electrons on
 the host atom, should assign atomic charges that follow electronegativity
 trends on *average* (but not in every material individually) over a large
 ensemble of materials, should assign net atomic charges that are consistent
 with the assigned atomic spin moments and bond orders, etc. The assigned
 bond orders should be consistent with established chemical principles. For
 example, the sum of computed bond orders for C atom in methane (and many
 other organic molecules) should be approximately 4.
 Special materials can be used to judge the consistency between assigned
 atomic charges and atomic spins. As one example, consider an endohedral Eu
 atom in C60 cage, where the system carries a net +1 charge. Eu atom has a
 half-filled 4f shell, and experiments and computations show these remain
 attached to the Eu atom in this complex. Normally Eu atom carries two 6s
 valence electrons, but owing to the +1 charge of the system one of these
 has been removed. The empty C60 cage, via computation and spectroscopy, has
 a rather large ionization energy and electron affinity (on the order of
 several eV). When Eu+1 ion is placed inside the C60 cage, the remaining 6s
 electron will be shared between the Eu atom and the C60 cage. Owing to
 their deep pairing, the other electrons on the C60 cage remain attached
 there. Also, the other electrons on the Eu cation (i.e., the core electrons
 and the half-filled f-shell) remain attached there. Thus, only one electron
 is labile in the system. The system has 8 unpaired electrons of the same
 spin (the seven 4f electrons and the one labile electron). Thus, the spin
 magnetization (divided by bohr magnetons) transferred from the Eu cation to
 the C60 shell should approximately equal the negative electric charge
 (divided by the elementary charge e) transferred from the Eu cation to the
 C60 shell. Other materials with weak bonding and a single labile electron
 can provide similar tests. It is thus possible to quantitatively assess the
 consistency between assigned net atomic charges and assigned atomic spin
 moments and we have done so. Not surprisingly, the atomic population
 analysis methods that perform the best across a variety of other metrics
 are also the ones that perform the best on this metric.
 We see the consistent theme emerge that atomic population analysis methods
 that give inaccurate net atomic charges are consistently the poorest
 performing when evaluating a host of other properties such as consistency
 between assigned atomic charges and spins, atomic polarizabilities, bond
 orders, etc. All of the atomic properties seem to be connected so that
 those that get it right get it consistently right and those that get it
 wrong get it consistently wrong.
 We have not found, for example, atomic population analysis methods that
 consistently get the net atomic charges correct but get the spin moments,
 bond orders, or atomic polarizabilities wrong. What we have found is that
 the atomic population analysis methods that get these other properties
 wrong are the same ones that get the net atomic charges wrong.
 One should also consider convergence properties. Does the atomic population
 method simply fail to converge for certain kinds of materials or levels of
 theory? A surprisingly large percentage of existing atomic population
 methods are non-convergent for many materials or levels of theory.
 In the end, this does not mean that only one atomic population analysis
 method can be correct. However, in my experience, when subjected to such
 testing, the vast majority of existing atomic population analysis methods
 fail.
 It does not need to be this way. One can develop accurate and robust atomic
 population analysis methods that are applicable across an extremely broad
 range of materials and properties and we are doing so.
 Regards,
 Tom
 On Sun, Sep 13, 2015 at 12:35 AM, Peeter Burk peeter.burk::ut.ee <
 owner-chemistry!^!ccl.net> wrote:
 >
 > Sent to CCL by: Peeter Burk [peeter.burk_+_ut.ee]
 > Dear Tom,
 >
 > I can understand your passion against atomic charges, and I do believe
 > that your work on them is methodologically as scientific as it can be.
 >
 > But if you compare the atomic charges with airplane, then for tha airplane
 > there is a clear "moment of truth" - will it fly? What is the
 similar thing
 > for atomic charges? Can you provide experimental charges? How are those
 > MEASURED? To my limited knowledge there are no such experiment, which will
 > measure atomic point charges... If you could convince me that comparison to
 > experiment is possible I would not argue any more, but at the moment the
 > discussion reminds me rather a theology than science as one party does not
 > believe that atomic point charges can be obtained from experiment and other
 > one does...
 >
 > Best regards
 > Peeter
 >
 > On 09/12/2015 04:24 PM, Thomas Manz thomasamanz]-[gmail.com wrote:
 >
 >> Hi Robert,
 >>
 >> The notion of atomic population analysis methods as being arbitrary
 >> reflects the practical state of affairs in decades past. It is
 certainly
 >> true that the earliest methods such as Mulliken and Lowdin populations
 >> are inherently arbitrary because they lack a basis set limit. But, the
 >> notion of arbitrariness doesn't accurately characterize the most
 >> recently developed methods which not only have a well-defined basis set
 >> limit but also have been developed with extensive and rigorous
 >> comparisons to experimental data.
 >>
 >> At the time the textbooks you mentioned were written, things had only
 >> begun to improve in the area of atomic population analysis. I'm sure
 the
 >> authors of those textbooks did the best they could with the information
 >> available at that time. Since those textbooks were written, newer
 >> methods have been developed that are at least an order of magnitude
 more
 >> accurate in comparisons to experiments than the crude, early methods.
 If
 >> one were going to write a textbook today, it would be appropriate to
 say
 >> that many of the early atomic population analysis methods were
 arbitrary
 >> but that some of the most recent ones have been developed through a
 >> legitimate scientific design process.
 >>
 >> This is an area in which I currently do research. In my research group,
 >> atomic population analysis methods are developed using scientific
 >> methods. The procedure we use is not unlike the one used to design
 >> airplanes. Yes, there is some flexibility in the design of an airplane.
 >> One could make it longer or shorter, for example. Yet, it is not quite
 >> accurate to say the design of an airplane is arbitrary. Airplanes, like
 >> my atomic population analysis methods, are designed to meet certain
 >> performance criteria. An airplane should fly, for example. Not only
 >> should it fly, but it should have stable control, take off and land
 >> smoothly, etc. There is some flexibility when choosing the shape of
 >> airplane, but it is not quite accurate to say the shape of an airplane
 >> is arbitrary. Proposed airplane shapes are tested in wind tunnels to
 see
 >> how they react to air turbulence, how much drag they produce, etc.
 There
 >> is a real engineering design element involved with scientific process
 of
 >> engineering and testing prototypes to continuously improve the design.
 >> Saying that airplane designs are arbitrary somehow doesn't do justice
 to
 >> the enormous amount of design work, prototype building, and scientific
 >> testing that goes into producing an efficient airplane.
 >>
 >> The same principle applies to the development of accurate atomic
 >> population analysis methods in my research group. We use a legitimate
 >> and rigorous process that involves engineering design, prototype
 >> building and scientific testing with comparisons to experimental data.
 I
 >> realize that many other research groups do not use such a rigorous
 >> process, but if you are going to say that atomic population analysis
 >> methods are arbitrary, please restrict this designation to those that
 >> actually are arbitrary and mention that some of the recent efforts use
 a
 >> legitimate scientific design process.
 >>
 >> The diborane molecule you mentioned does present an interesting
 example.
 >> Please find below the net atomic charges and bond orders I computed for
 >> this molecule:
 >>
 >> B atomic charge: -0.0221
 >> bridging H atomic charge: 0.131
 >> outer H atomic charge: -0.054
 >>
 >> B-H(bridging) bond order: 0.423
 >> B-B bond order: 0.627
 >> B-H(outer) bond order: 0.940
 >>
 >> sum of bond orders for B atom: 3.39
 >> sum of bond orders for bridging H atom: 0.91
 >> sum of bond orders for outer H atom: 1.01
 >>
 >> Sincerely,
 >>
 >> Tom
 >>
 >>
 >> On Fri, Sep 11, 2015 at 2:25 PM, Robert Molt
 >> r.molt.chemical.physics%x%gmail.com <http://gmail.com/>; <owner-chemistry
 >> . ccl.net <mailto:owner-chemistry . ccl.net>> wrote:
 >>
 >>     There is nothing problematic with saying "there is no such
 thing as
 >>     the quantum mechanical operator for atomic charge." Any atomic
 >>     charge model requires an /arbitrary /partitioning of density as
 >>     "belonging" to certain atoms. None of the laws of physics
 are
 >>     written in terms of atoms! We don't write the force between atoms,
 >>     we write the force between charges. Trivializing the problem of
 >>     partitioning is brushing under the rug the inherent problem: we
 >>     cannot partition it without arbitrary choices.
 >>
 >>     An atomic charge model is especially problematic when the electron
 >>     density is delocalized. There is no way to say to "whom"
 the density
 >>     "belongs" in diborane or a metal conducting a current.
 >>
 >>     Moreover, this is the accepted view of the community. See Cramer,
 >>     chapter 9; see Jensen's book (don't recall the chapter; see Szabo
 >>     and Ostlund, chapters 1-3.http://www.ccl.net/chemistry/sub_unsub.shtmlConferences:
 > http://server.ccl.net/chemistry/announcements/conferences/>;
 >
 >