# CCL: net atomic charges

• From: Thomas Manz <thomasamanz%gmail.com>
• Subject: CCL: net atomic charges
• Date: Fri, 11 Sep 2015 17:00:09 -0600

Hi Robert,

from the Merriam-Webster dictionary: arbitrary (adjective) - (a) not planned or chosen for a particular reason, (b) not based on reason or evidence, (c) done without concern for what is fair or right
(http://www.merriam-webster.com/dictionary/arbitrary)

Saying the partitioning is "arbitrary" is not quite accurate. It is more accurate to say there is some flexibility in how to partition the electron density among atoms.
The reason it is not arbitrary is because several candidates are proposed and then comparisons to experiments are made to determine which algorithms perform the best.
This does allow for some flexibility in the partitioning, but "arbitrary" is clearly not the right word since experimental comparisons rule out the poor performing algorithms.
In this sense the development of charge assignment methods is a scientific process.

My example of an airplane mentioned early on is a good analogy. It is certainly true that there is some flexibility in the design of an airplane. One can make the airplane
lighter, heavier, longer, taller, with two or four wings, etc. There is certainly flexibility here. But, it is not quite correct to say that airplane design is "arbitrary".
The notion of arbitrariness somehow misses the point that airplane designs are subjected to scientific testing and their performance is evaluated and refined over time.
My charge assignment schemes go through a similar development and rigorous testing phase. Therefore, it would not be quite to correct to say that they are "arbitrary" since
they have been subjected to rigorous testing and refinement via the scientific method.

You can apply this same kind of reasoning to any kind of technical product. Usually when developing software or methods, there is testing and evaluation that goes on.
So it is somewhat unfair, for example, to say that design of an automobile is "arbitrary". Yes, there is some flexibility in the design of an automobile and that is why we
have different models and so forth. But, the automobiles have been designed to perform in certain ways, to meet certain safety features, to meet emission standards, to
meet minimum fuel efficiency requirements, to have certain comforts, to look good, and so forth. These designs are put through rigorous testing and go through refinements and
improvements. It isn't quite fair to dismiss the enormous amount of development, design, testing, and optimization as "arbitrary". Somehow the word "arbitrary" doesn't capture
the essence of the extensive testing and development involved. It doesn't give due and fair credit to those who put in the extensive work to develop and test a method in order
to make it accurate, broadly applicable, computationally efficient, and robustly convergent.

I have found through experience that those who characterize the properties of atoms in materials as "arbitrary" are almost universally using seriously defective methods.
It is somewhat ironic, since they are using the worst methods available and yet they extend these criticisms to reliable methods. By analogy to my discussion above,
it is if they are claiming that automobile designs are "arbitrary" and then they go out and drive a 50 year old broken car and then criticize all automobile manufactures
for the "arbitrariness" of their car designs. They would have a much different experience and impression if they tried driving a new car instead of a 50 year old broken one.

By the way, diborane is one of the easiest molecules to compute net atomic charges for. It is somewhat trickier to compute bond orders for.
Here are my calculations for the net atomic charges and bond orders of diborane:

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  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.

On 9/11/15 1:57 PM, Víctor Luaña Cabal victor- -fluor.quimica.uniovi.es wrote:
Sent to CCL by:
=?iso-8859-1?Q?V=EDctor_Lua=F1a?= Cabal [victor%fluor.quimica.uniovi.es]
On Fri, Sep 11, 2015 at 06:25:07AM -0400, Robert Molt
r.molt.chemical.physics-*-gmail.com wrote:

Atomic charges, as a computational model, are
an approximation which is
completely independent of DFT. No Nobel Prize has been given for atomic
charges (and never will be, because there is no such thing as the
quantum mechanical operator for atomic charge).


To all,
$Q = \int \rho(\bm{r}) d\bm{r} = \int \abs{\Psi}^2 d\bm{x}.$
The quantum mechanical operator involved is \hat{1}. No problem
with its definition or properties (analytic, hermitic, ...).
The question of atomic charges is completely different and it is not
related with the existence or not or an operator, but with the definition
of the boundary of an atom in a molecule or solid. The problem is here
$Q = \sum_i Q_i = \sum_i \int_{\Omega_i} rho(\bm{r}) d\bm{r}$
What is $\Omega_i$? It is a problem of partitioning.
Can we partition the bulk modulus of a crystal into ionic components?
Elastic constants, energíes, multipolar moments, ...?  Yes, we and
others did ... if you accept the QTAIM concepts. Can we partition any
property? The QTAIM concepts assumes that, and there is a large school
of people working on it.
The e-mail by Stephan Grimme on this discussion mentioned clearly and
appropriately the point. I believe in the QTAIM ideas, but they are
not the only ones and they are not the ultimate and exclusive truth.
So the sentence "there is no such thing as the quantum mechanical
operator for atomic charge" is quite problematic and I can say with
absolute property that "there is a perfectly defined operator of the
atomic charge ... if you are studying an atom". And, believe me, there
are also chemists studying atoms ... and solids ... and liquids ... and
materials ... and ...
in the discussiond and can defend his opinions by himself.
Peace (Shalom, Salam, Paz, ...),
Víctor Luaña
--
.  .    "In science a person can be convinced by a good argument.
/ ' \   That is almost impossible in politics or religion"
/. \/ .'\  "Lo mediocre es peor que lo bueno, pero también es
peor
/   ''   \ que lo malo, porque la mediocridad no es un grado, es una
|  \''/  | actitud" -- Jorge Wasenberg, 2015
|  |''|  | (Mediocre is worse than good, but it is also worse than
\/'''\/  bad, because mediocrity is not a grade, it is an
attitude)
===(((==)))==================================+=========================
! Dr.Víctor Luaña, in silico chemist & prof. !"I have two
kinds of problems,
! Departamento de Química Física y Analítica ! the urgent and the
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Dr. Robert Molt Jr.
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Indiana University-Purdue University Indianapolis
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On Fri, Sep 11, 2015 at 9:06 AM, Thomas Manz thomasamanz##gmail.com wrote:

Hi Robert,

I'm copying this discussion on net atomic charges to a new thread.

From the Nobel prize website: "The Nobel Prize in Chemistry 1998 was divided equally between Walter Kohn "for his development of the density-functional theory" and John A. Pople "for his development of computational methods in quantum chemistry"." From my email: "In 1998, Walter Kohn received the Nobel prize in chemistry for his development of density functional theory." From your email: "Your comment is a very incorrect characterization of the 1998 Nobel Prize."

My point is that the Hohenberg-Kohn theorems tell us what types of computations can give us meaningful physical properties. As stated in the Hohenberg-Kohn theorems, the Hamiltonian of a non-degenerate ground state system is determined by the ground-state electron density distribution up to an arbitrary constant potential offset. Since the Hamiltonian determines the system's wavefunction, and the wavefunction determines the system's properties, it directly follows from the Hohenberg-Kohn Theorems that all of the observable properties of a non-degenerate ground state quantum chemical system are functionals of the ground state electron distribution. This is what the Hohenberg-Kohn theorems state. The energy is included as one of the observables, but the Hohenberg-Kohn theorems are not limited to the system’s energy alone.

Therefore, it is a direct corollary of the Hohenberg-Kohn theorems that a physically valid definition of net atomic charges must be constructed to give values that are a functional of the electron density distribution. Any definition that is constructed in such a way as to lack a complete basis set limit is therefore physically invalid. This follows directly from the Hohenberg-Kohn theorems.

It is true that after ruling out such unphysical methodologies as Mulliken and Lowdin populations, that flexibility in how to define the net atomic charges as functionals of the electron distribution still remains. Yes, the possibility of overlap of three-dimensional electron distributions between the atoms is a challenge to sort out, but it is not a problem that cannot be studied. This is where application of the scientific method comes into play. By comparing different proposals to experimental data across a wide variety of systems, it is possible to draw meaningful scientific conclusions about which methods for assigning net atomic charges give closer agreement to experimental data and are therefore more scientifically accurate. This does not mean we will be able to compute net atomic charges with the same level of precision as we can measure system energies, but it still means that net atomic charges are a valid scientific concept and that they follow known theorems and obey the scientific method.

Sincerely,

Tom

-----------

> Dr. Manz:

> Your comment is a very incorrect characterization of the 1998 Nobel Prize.

> a.) You're addressing Stephen Grimme, a leader of DFT in computational chemistry in the world; trust me, he is well aware of DFT. This is like lecturing Newton on a new subject called "trigonometry."

> b.) DFT's contribution to science is NOT "The density is an observable." This has been known since the days of classical electromagnetics that you can write all the entire theory of classical EM in terms of density. It's what we spend every day of classical EM classes solving for. Wavefunction people defined and were using the electron density of chemical systems LONG before there was a DFT; just read Szabo and Ostlund. Rather, DFT is a statement about being able to calculate the energy as a function of density directly practically, with no calculation of the wavefunction necessary (there is more to it than this, but as a bird's eye-view statement).

> c.) Your statement has a huge assumption in it that is in no way associated with DFT. You wrote:

> "A direct corollary is that since net atomic charges are a property of a chemical system..."

> This is NOT a direct corollary. There is no such thing as atomic charges, that's the point of another thread. The TOTAL charge of a system is well-defined, but defining the charge of an arbitrary subsystem is not always possible. There are many reasons you cannot do this rigorously. One is that you are trying to represent a function of 3 variables (the density, a real observable) by ONE number (the "atomic charge"); this is impossible. The change in the density, spatially, at different points on a 3D grid (let alone the fact we have spin!) cannot be represent by one number.

> Atomic charges, as a computational model, are an approximation which is completely independent of DFT. No Nobel Prize has been given for atomic charges (and never will be, because there is no such thing as the quantum mechanical operator for atomic charge).

> Robert Molt r.molt.chemical.physics-*-gmail.com