From owner-chemistry@ccl.net Mon Sep 14 13:55:01 2015 From: "Thomas Manz thomasamanz!=!gmail.com" To: CCL Subject: CCL: atomic population analysis Message-Id: <-51737-150914132334-25287-aN0TkxQr6E1QwmMmFTEXFA|-|server.ccl.net> X-Original-From: Thomas Manz Content-Type: multipart/alternative; boundary=001a11c14836ca6221051fb85206 Date: Mon, 14 Sep 2015 11:23:26 -0600 MIME-Version: 1.0 Sent to CCL by: Thomas Manz [thomasamanz ~~ gmail.com] --001a11c14836ca6221051fb85206 Content-Type: text/plain; charset=UTF-8 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 > . 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/> > > --001a11c14836ca6221051fb85206 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Hi Peeter,

Thanks for your insightful c= omment and encouraging words.=C2=A0

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 methodologie= s.=C2=A0

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, so= lid surfaces, liquid solutions, and so forth.

Not = only does one have to consider a broad range of materials, but a broad rang= e of atomistic properties should also be considered. For example, one shoul= d consider not only net atomic charges, but also atomic spin moments,
=
bond orders, atomic multipole moments, atomic polarizabilities, disper= sion coefficients, etc. Of course, these are too much to consider in a sing= le journal article, but one could envision a series of journal articles tha= t look
into various of these properties. An atomic population ana= lysis method is thus not just a recipe for computing net atomic charges, bu= t 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 overa= ll polarizability of a molecule without computing it via perturbation theor= y or via application of electric field. Similarly, the overall dispersion c= oefficients can be predicted using variants of Tkatchenko-Scheffler type me= thods without requiring a time-dependent DFT calculation. These can be comp= ared to experiments, and we are currently doing this in a project I'm i= nvolved with collaborators. When this is done, one finds that some atomic p= opulation analysis methods perform better than others for the prediction of= observable experimental properties.=C2=A0

There a= re also the tests that the assigned net atomic charges should have reasonab= le 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 o= f 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, th= e sum of computed bond orders for C atom in methane (and many other organic= molecules) should be approximately 4.=C2=A0

Speci= al materials can be used to judge the consistency between assigned atomic c= harges 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-fill= ed 4f shell, and experiments and computations show these remain attached to= the Eu atom in this complex. Normally Eu atom carries two 6s valence elect= rons, but owing to the +1 charge of the system one of these has been remove= d. 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, t= he other electrons on the C60 cage remain attached there. Also, the other e= lectrons on the Eu cation (i.e., the core electrons and the half-filled f-s= hell) remain attached there. Thus, only one electron is labile in the syste= m. The system has 8 unpaired electrons of the same spin (the seven 4f elect= rons and the one labile electron). Thus, the spin magnetization (divided by= bohr magnetons) transferred from the Eu cation to the C60 shell should app= roximately equal the negative electric charge (divided by the elementary ch= arge e) transferred from the Eu cation to the C60 shell. Other materials wi= th 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. No= t surprisingly, the atomic population analysis methods that perform the bes= t across a variety of other metrics are also the ones that perform the best= on this metric.=C2=A0

We see the consistent theme= emerge that atomic population analysis methods that give inaccurate net at= omic charges are consistently the poorest performing when evaluating a host= of other properties such as consistency between assigned atomic charges an= d spins, atomic polarizabilities, bond orders, etc. All of the atomic prope= rties seem to be connected so that those that get it right get it consisten= tly right and those that get it wrong get it consistently wrong.=C2=A0
We have not found, for example, atomic population analysis methods th= at 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 wro= ng are the same ones that get the net atomic charges wrong.

<= /div>
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 popul= ation 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 d= evelop accurate and robust atomic population analysis methods that are appl= icable across an extremely broad range of materials and properties and we a= re doing so.

Regards,

Tom=



On Sun, Sep 13, 2015 at 12:35 AM, Peeter Burk peet= er.burk::ut.ee <owner-chemistry!^!ccl.n= et> 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 sim= ilar thing for atomic charges? Can you provide experimental charges? How ar= e those MEASURED? To my limited knowledge there are no such experiment, whi= ch will measure atomic point charges... If you could convince me that compa= rison to experiment is possible I would not argue any more, but at the mome= nt the discussion reminds me rather a theology than science as one party do= es not believe that atomic point charges can be obtained from experiment an= d 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 th= e
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 t= o
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-ch= emistry . ccl.net>> wrote:

=C2=A0 =C2=A0 There is nothing problematic with saying "there is no su= ch thing as
=C2=A0 =C2=A0 the quantum mechanical operator for atomic charge." Any = atomic
=C2=A0 =C2=A0 charge model requires an /arbitrary /partitioning of density = as
=C2=A0 =C2=A0 "belonging" to certain atoms. None of the laws of p= hysics are
=C2=A0 =C2=A0 written in terms of atoms! We don't write the force betwe= en atoms,
=C2=A0 =C2=A0 we write the force between charges. Trivializing the problem = of
=C2=A0 =C2=A0 partitioning is brushing under the rug the inherent problem: = we
=C2=A0 =C2=A0 cannot partition it without arbitrary choices.

=C2=A0 =C2=A0 An atomic charge model is especially problematic when the ele= ctron
=C2=A0 =C2=A0 density is delocalized. There is no way to say to "whom&= quot; the density
=C2=A0 =C2=A0 "belongs" in diborane or a metal conducting a curre= nt.

=C2=A0 =C2=A0 Moreover, this is the accepted view of the community. See Cra= mer,
=C2=A0 =C2=A0 chapter 9; see Jensen's book (don't recall the chapte= r; see Szabo
=C2=A0 =C2=A0 and Ostlund, chapters 1-3.




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