CCL: atomic population analysis

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



On Fri, Sep 11, 2015 at 2:25 PM, Robert Molt <owner-chemistry^> 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.