The Wilson's on quality in quantum chemistry

Ken Wilson is very well known for developing the renormalisation group and applying it to critical phenomena and the Kondo problem. There is a long and interesting (but somewhat meandering) interview with him about his career. Amongst various choice tid-bits there is the exchange below about his father, E. Bright Wilson, a pioneer in quantum chemistry.

PoS

Did your father use computers? Did you know of his models for getting infrared spectra? Did things like that play a role in your thinking?

KGW

What I remember from discussions with my father was that he used get very wrought up about computational quantum chemists. Garbage in, garbage out. That set me up to spend some time at Ohio State studying quantum chemistry. I had done a little bit towards the end of my stay at Cornell, but took it more seriously while I was at Ohio State. And so then I had to find out from my father who were the good people. And he knew them, he had a list of them.

PoS

And who did he say were the good people?

KGW

There was [Isiah] Shavit. There was Ernie Davidson, John Pople from Carnegie Mellon. What's interesting about this is that later when I became interested in the history of physics and [Thomas S.] Kuhn's book, one of the characteristics of the pre-paradigm phase he discusses, and there really are pre-paradigm phases --you know, people don't want to admit that--is that everybody is arguing with each other and somebody comes in from outside and tries to figure out what's going on, like my father interacting with the quantum chemists, they learn who the good people are. And yet, they won't admit that there are good people, unless you ask them, otherwise they are more interested in complaining about the poor quality of the research by others in the field....

PoS

And the criterion for being good? I mean what makes a person good?

KGW

These are the people who are smart, take serious problems to work on...

PoS

The generative quality comes in?

KGW

For instance, consider quantum chemistry for a moment. What I found was that the people who did the important work worked on algorithms. They improved the algorithms for solving quantum chemistry problems on computers. They couldn't do the calculations they wanted to do, so they worked on algorithms. And it was the algorithmic work that was absolutely essential. When the computers got better, and they could do serious things, it was the work on algorithms that made the difference and the people that my father knew made contributions to serious algorithm developments. At the same time, there was just a lot of stuff published where people were running programs and they were paying no attention to whether they worked or didn't work, and claiming all sorts of fancy things.

Improper hydrogen bonds

Most common hydrogen bonds involve an interaction of the form X-H...Y where the donor X and acceptor Y are highly electronegative atoms such as O, N, and F. Signatures of H bond formation include lengthening of the X-H bond, softening of the X-H stretch frequency, and increase in the X-H stretch IR intensity. For strong H bonds these effects on the X-H bond are substantial, of the order of 10-100 per cent. I presented a unified picture of this in a recent paper.

However, over the past 15 years it has been discovered that there are a class of (very weak) bonds, best described as improper H bonds which are distinctly different. Generally, the donor X is not particularly electronegative (e.g. a carbon atom) and bond formation results in

• contraction of the X-H bond (by a few milliAngstroms)
• hardening of the X-H stretch frequency (by less than one per cent)
• decrease in the X-H stretch IR intensity

There is a nice 2007 JACS paper Red-, Blue-, or No-Shift in Hydrogen Bonds:  A Unified Explanation by Jorly Joseph and Eluvathingal D. Jemmis.

The key idea is as follows

The factors which affect the X−H bond in all X−H···Y HBs can be divided into two parts:  (a) The electron affinity of X causes a net gain of electron density at the X−H bond region in the presence of Y and encourages an X−H bond contraction. (b) The well understood attractive interaction between the positive H and electron rich Y forces an X−H bond elongation. For electron rich, highly polar X−H bonds (proper HB donors) the latter almost always dominates and results in X−H bond elongation, whereas for less polar, electron poor X−H bonds (pro-improper HB donors) the effect of the former is noticeable if Y is not a very strong HB acceptor.

In different words due to interaction with the acceptor the relative amount of covalent and ionic character of the X-H bond changes.

Hence, I think this goes beyond my simple two diabatic state picture which does not allow the X-H diabatic state to vary in character with the interaction. 

I thank Pranav Shirhatti for stimulating my interest in this problem.

The Higgs boson and condensed matter physics

This week at the Quantum Science seminar Ben Powell gave a tutorial about the Higgs boson, highlighting its conceptual origin in condensed matter physics. The talk followed some of Section 12.6 of Piers Coleman's nice book Introduction to Many Body Physics (free online). It is a nice clear and helpful discussion.

One of the key ideas first emphasized by Phil Anderson in 1963 was that a massless gauge field can aquire a mass in the presence of a coupling to a spontaneously broken field. A concrete realisation of this occurs in superconductors. In the Meissner effect a superconductor thicker than the penetration depth expels magnetic fields. This is like the photon acquires a mass.

In the electro-weak theory of Weinberg-Salam there is a combined U(1) x SU(2) gauge symmetry. Due to coupling to the Higgs field (whose symmetry is spontaneously broken)
one gauge field remains massless (the photon) and the other three become massive. These massive particles are the W+, W-, and Z bosons.

In a type II superconductor, vortices are allowed in the superconducting order parameter field. Can such vortices occur in the Higgs field? They may have been important in the early universe.
On fascinating thing I learnt is that for the Higgs field the crucial ratio [between the London penetration length and the superconducting coherence length] that determines whether type II behaviour is possible is the ratio of Higgs boson mass to W mass. The LHC results suggest that type II behaviour is possible!

In summary, here is an extract from Coleman's book (page 246).

Shortly after the importance of this mechanism for relativistic Yang Mills theories was noted by Higgs and Anderson, Weinberg and Salem independently applied the idea to develop the theory of “electro-weak” interactions. According to this picture, the universe we live is a kind of cosmological Meissner phase, formed in the early universe, which excludes the weak force by making the vector bosons which carry it, become massive. It is a remarkable thought that the very same mechanism that causes superconductors to levitate lies at the heart of the weak nuclear force responsible for nuclear fusion inside stars. In trying to discover the Higg’s particle, physicists are in effect trying to probe the cosmic superconductor above its gap energy scale.

Aside: Later Coleman discusses how (in a slave boson formulation) "the Anderson-Higgs effect in the Kondo problem endows the composite f−electron with charge."

A sad tale of publishing gone mad

I found this sad story interesting and disturbing because of what it reveals about journal impact factors, university rankings, self-citations, Elsevier, scientific crack pots, lawsuits....
More of the weird history is here and here.

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.

The gravity of the situation

On monday night I heard Paul Davies give an interesting public lecture The origin and the end of the Universe in Brisbane. One small aspect that I was particularly interesting was the discussion of the second law of thermodynamics in gravitational systems. He emphasized the following puzzle (in my words).

For an isolated system the entropy can never decrease. In some sense this means that the "order" cannot increase. However, a long time ago matter in the universe was relatively uniform, and now it is not just ordered into galaxies and stars, but even biological life!

The key to resolving this is to realise that in a gravitational system the second law looks different. Uniform "disordered" states do not have low entropy. If you start with a fairly uniform system this is not an equilibrium state. The natural tendency of the system is to evolve to a non-uniform state with clumps of matter. Hence, the "clumpy" state [with a sun which transfers energy to order and sustain biological systems] can actually have the lower entropy.

Clarifying these issues, particularly in a quantitative manner, turns out not to be easy. I found a nice one page article by Mark Buchanan in Nature Physics. It summarises a 2009 paper Gravity, Entropy, and Cosmology: a search for clarity by physics philosopher David Wallace.

Blowing ourselves up

APS News has a fascinating article A Cold-War Folly? by Nina Byers. She describes a course entitled Nuclear Power: Power plants and weapons of war that she teaches UCLA undergraduates.

A couple of things I found particularly interesting. First, the graph below showing the dramatic variation in nuclear weapon stockpiles with time. Second, the diverse views that  physicists (esp. famous ones) had about the use of nuclear weapons, both against Japan, and after the war. Third, it was a good reminder that our current undergraduates were actually born after the end of the cold war!

A great strength of the US college system compared to Australia and Europe is the flexibility of the curriculum and broad general education requirements that allow and encourage such courses.