Thursday, July 26, 2012

Pauling on the role of quantum theory in chemistry

In an article The Nature of the Chemical Bond - 1992, Linus Pauling makes the following fascinating statement:
The concept of quantum mechanical resonance and the theorem that in quantum mechanics the actual structure of a system has a lower energy than any other structure have turned out to be especially important in chemistry. The energy could be calculated for an assumed wave function for a molecule. Any change that lowered the energy indicated some addition to the picture of the chemical bond. The polarization of bond orbitals and the partial ionic character of bonds were discovered in this way. The minimum-energy theorem led to the formulation of the electronegativity scale. Modern chemistry and molecular biology are the products of quantum mechanics. Chemistry has been changed by quantum mechanics even more than physics.
In 1936 in the Preface to The Nature of the Chemical Bond he also emphasized how quantum physics led to new chemical concepts.


  1. This goes both ways. The early pioneers of theoretical chemistry contributed FUNDAMENTALLY to the development of quantum mechanics. An easy and obvious example is the Löwdin orthogonalization. This was subsequently noted to be a very general mathematical tool that is useful in other parts of applied linear algebra (c.f. Goldstein, J., & Levy, M. (1991). Linear algebra and quantum chemistry. American Mathematical Monthly, 710–718.).

    So, now, if I open a book on fundamental quantum mechanics or quantum statistics, and if I spend enough time to see through the different language, I usually find that I know a lot of it already. The reason for this is that quantum chemistry was an early hotbed of problems in finite-dimensional many-particle systems. So, it is an excellent place to be introduced to many apparently abstract ideas in quantum information, measurement theory, etc.

    Another example is Heller's work on molecular dynamics. I was pleasantly surprised when I realized that I had known all along what "coherent states" were - they're gaussian wavepackets.

    Then, of course, there is Miller, Stock, Levine...

    It is a dangerous conceit of physicists to ignore the chemical literature. Unfortunately, I think it is also a common one.

    Oh, and BTW all of the above is an excellent case for the establishment of a molecular physics course at UQ Physics!

  2. Whoops. I meant a "CHEMICAL physics" course!

  3. I want to follow this up with an explicit example of what I'm talking about.

    In 1979, Holevo (Kholevo) published an article (Theory of Prob. & App. v. 23 p. 411) on the basis for asymptotically optimal quantum hypothesis testing. He determined that the optimal basis for distinguishing a set of non-orthogonal states was given by multiplying that state set by the inverse of the square root of the Gram matrix (also called the "overlap"). Holevo is a big name in quantum statistical estimation theory. I see it all over the literature of the quantum measurement problem nowadays.

    The result in the 1979 paper was already almost 3 decades behind the chemistry literature! Löwdin's result was published originally in J. Chem. Phys. v. 18 p. 365 (1950)) is a general method for determining the orthogonal basis which is closest in a least-squares (i.e. Hilbert-Schmidt norm) sense to a given non-orthogonal basis (i.e. "Riesz basis").

    So, in conclusion, there are important results in quantum estimation and detection theory which are basically quantum chemistry dressed with some statistical jargon.