Should experimentalists have to "explain" their data?

Sometimes when I talk to experimentalists about their latest results they say something like, "We have this really interesting data. But we can't explain it and so we are not going to publish it until we can explain it." No doubt this is sometimes what referees say.
But, I disagree. The most interesting experimental results have no clear explaination!
Furthermore, many of the "explainations" I read in experimental papers seem to be either naive, wrong, or highly speculative.

The point of non-radiative decay

The rate and efficiency of many photophysical processes is determined by conical intersections (points or more correctly seams) where two potential energy surfaces touch.
Much effort has been expended in the computational chemistry community in developing methods to simulate the dynamics of vibrational wave packets moving through such conical intersections. These methods have been used to simulate a number of important photophysical processes in condensed phases (e.g., the isomerisation of retinal in the protein rhodopsin).

I have often wondered what are the key energy, length, and time scales in this problem?

While in Toronto, Valentyn Prokhorenko, brought to my attention a really nice PRL that answers my questions. Unfortunately, this paper does not seem to have drawn the attention that it deserves.

The authors define a semi-classical expansion parameter g which is essentially the ratio of the particle deBroglie wavelength to the scattering length associated with the conical intersection. They estimate that for typical photochemical processes this parameter will be small, justifying the semi-classical approximation.


The probability of a wave packet to remain on the diabatic surface it starts on is shown to be
Pd = exp (-pi alpha^2/2)
where alpha is a dimensionless parameter proportional to the ratio of the impact parameter a of the wave packet and the scattering length rs.

A few questions I have are:

How do these results change with the shape of the conical intersection? e.g., if it is tilted?

How do these results relate to earlier work of Teller and Nikitin and more recently Malhado & Hynes?

How does decoherence change these results?

Theoretical chemistry at UW

Today I am giving a talk to the theory group in Chemistry at University of Washington.

I am looking forward to meeting Oleg Prezdho. I am currently learning a lot from reading a very nice review article he wrote with W.R. Duncan on modelling the ultrafast electron transfer (femtoseconds) from organic molecules to titanium dioxide. This is a key process in Gratzel solar cells.

A new class of chemical bonds

Shason Shaik and collaborators have a nice article in the latest Nature Chemistry, "charge-shift" bonding which is the essential component of the bonding of pairs of very electronegative identical atoms (e.g., flourine).

The essential physics of covalent bonding can be described by a two-site Hubbard model (with U>>t).

Can a negative U (or V>U) two-site Hubbard model describe the essential physics of charge-shift bonding?

The power of thermodynamics

Chapter 6 of Nelson's Biological Physics ends with a nice extract from a 2001 Science paper describing optical tweezer experiments which reversibly unfold single RNA molecules.

Figure b above shows how the amount of unfolded RNA as a function of applied force can be fit simply that predicted for a two-state equilibrium distribution (which has the same mathematical form as a Fermi-Dirac distribution!) The fit also gives a good estimate of the free energy of unfolding (about 80 k_B T at room temperature).

Nelson also gives simple arguments that give the probability distribution P(t) for the different waiting times t for folding and unfolding, P(t)=kexp(-kt) where k is the rate. The right panel of c. above shows the RNA length as a function of time for different applied forces. The resulting range of distribution times (note they are the order of seconds) are shown in panel d.

What is real new and cool here is observing all this for single molecules. Decades ago people found that the two-state model could describe the folding and unfolding of many biomolecules.



Here are slides for a lecture I have given previously on how this two-state equilibria can quantitatively describe the unzipping of DNA and unfolding of proteins. The right panel figure above is just one example of a measurement the amount of unfolded molecule as function of temperature. It can be fit to the same two-state distribution.

As Nelson note, it is amazing and impressive that such incredibly simple expressions based on simple thermodynamic considerations can describe such complex systems and processes.

Informative section headings

As I posted before, I really like the way that Phil Nelson uses informative section headings in his book, Biological Physics: Energy, Information, and Life. More of us need to do this in papers we write. Specifically, we need to go beyond Introduction, Methods, Results, Discussion, and Conclusion!

Here are some headings from the chapter I am currently reading:

6.2.2 Entropy is a constant times the maximal value of disorder

6.4.1 Entropy increases spontaneously when a constraint is removed

6.5.1 The free energy of a subsystem reflects the competition between entropy and energy

6.5.2 Entropic forces can be expressed as derivatives of the free energy

6.5.3 Free energy transduction is most efficient when it proceeds in small, controplled steps

6.6.3 The minimum free energy principle also applies to microspcopic subsystems

6.6.4 The free energy determines the populations of complex two-state systems

Here is a challenge for you. How many of these can you prove without looking at the book?

A chemist, physicist, and mathematician.....

Since I am on holidays this week, all I have to offer is a joke I heard last week in Toronto. Apparently, David Tannor told it the week before at a Gordon Conference on Quantum Control. Here is my version:

A chemist, a physicist, and a pure mathematician all check into the same hotel. Unfortunately, a fire breaks out in each of their rooms in the middle of the night. The chemist wakes up rushes into the bathroom fills the bath with water and uses a wastepaper basket to rapidly bail water onto the fire. He quickly extinguishes the fire and goes back to bed.

The physicist wakes up sees the fire, looks at the thermometer on the wall, and does an order of magnitude estimate of the fire temperature and how fast it is spreading. He sits down at the desk and does a couple of quick calculations. He estimates it will require 3 liters of water to extinguish the fire. He measures out this water and pours it on the fire. He is very pleased that his estimate was correct. He goes back to sleep content that he has solved the problem.

The pure mathematician wakes up, sees the fire, and realises there is a problem to be solved. He sits at the desk in profound thought and then writes out some careful notes, ending with QED. He says to himself, "As I thought, there is a solution, but it is not necessarily unique." He goes back to bed content he has solved the problem.