Friday, June 29, 2012

Talk on hydrogen bonding

Tomorrow I am giving a talk A unified picture of hydrogen bonding and proton transfer via a two state Hamiltonian.
It is based on this paper. The main point is

A simple model Hamiltonian
with just two parameters
is physically and chemically transparent
a unified picture of different types of H-bonds and of proton transfer
insight into the H-bond puzzle
a semi-quantitative description of empirical correlations between bond lengths, binding energies, vibrational frequencies….

Thursday, June 28, 2012

Refuting the dynamic hypothesis for enzymes

How do enzymes work? Are they any different from other catalysts?
The traditional view is no. They simply lower the energy barrier of the transition state between the reactants and products. The only difference from man-made catalysts is that due to their complexity (and evolution) enzymes can lower this barrier by more than
an eV leading to an increase in reaction rate by tens of orders of magnitude.

In the traditional view the only role of the dynamics of the nuclei in the enzyme is that statistical thermal fluctuations provide access to the transition state. Furthermore, quantum dynamics of the nuclei does not play any significant role. Tunneling below the barrier may provide small corrections to the reaction rate for light nuclei such in proton, hydrogen, or hydride (hydrogen anion) transfer reactions.

Over the past decade some people have been advocating a radical non-traditional view of how (some) enzymes work. They claim that non-trivial (and non-local) dynamics plays
a key role. I think it should be emphasized that this is a radical point of view.
Proponents of this view include Steven Schwartz and Judith Klinman.
They also emphasize the role of quantum tunneling and suggest that enzymes have evolved to enhance it.
I have a paper which is skeptical of quantum tunneling playing a significant role.
A disparaging opponent of dynamical effects is Arieh Warshel.

At the worshop yesterday Tom Miller gave a stimulating talk based on a recent PNAS paper Dynamics and dissipation in enzyme catalysis. He addresses this controversy considering the specific case of hydride transfer in dihydrofolate reductase. This has attracted interest because double mutants (very distant from the active site) lead to non-additive effects on the rate activation energy.

Boekelheide, Salomón-Ferrer, and Miller calculated the reaction rate using a path integral approach (ring polymer molecular dynamics = RPMD)  for which it is claimed
In contrast to mixed quantum-classical and transition state theory methods, RPMD yields reaction rates and mechanisms that are formally independent of the choice of dividing surface or any other reaction coordinate assumption 
They compared both statistical and dynamical correlations in the enzyme nuclei in the reactant state, transition state, and product state. The former were sizeable over different parts of the enzyme as one might expect from its rigidity. However, the dynamical correlations were only significant close to the hydride donor and acceptor.

This talk led to the most animated discussion in the workshop so far. I got the impression (perhaps wrongly) that some people were concerned
  • whether one could make a clear division between statistical and dynamical correlations
  • whether the RPMD is really as assumption free as claimed
  • one should not be surprised the claimed dynamical correlations do not exist
  • transition state theory is very robust.
A recent PNAS paper from Steve Boxer's group addressed the issue (on a different enzyme) from an experimental view. It concluded that simple electrostatics (as advocated by Warshel) rather than dynamics were determinant.

A recent Nature Chemistry Perspective argues that transition state theory is adequate to describe enzymes.

Similar issues about protein dynamics are also relevant for claims of quantum coherent effects in photosynthetic proteins (an earlier post discussed work showing that the claimed dynamical correlations did not exist.)

Wednesday, June 27, 2012

Quantum effects, hydrogen bonds, and climate change

At the workshop today Tom Markland gave a nice talk on work described in a recent PNAS paper Unraveling quantum effects in water using isotopic fractionation.

It turns out that the amount of deuterium in liquid water depends on the temperature at which the water was condensed. This can be measured very accurately and has proven to be a sensitive probe in climate change studies (see for example, figure 1 in this Nature paper).

For most temperatures there is a preference for HOD to reside in the liquid rather than the vapour phase. This is a purely quantum effect! According to the Born-Oppenheimer approximation the intermolecular and intramolecular interaction potentials for H2O and HOD are identical. However, different isotopic masses lead to different vibrational frequencies, zero point energies, and free energies.

Calculating the free energy of the liquid phase where one treats the H and D atoms fully quantum mechanically is a highly non-trivial exercise. Markland has done this using a path integral method based on mapping quantum dynamics to fictitious polymer beads.
The vertical scale is 1000 times the difference between the HOD and H2O free energy difference between liquid and vapour, divided by k_B T.

A few notes:
  • Different models for the water interactions give quite different results. It seems including the anharmonic part of the OH stretch potential is important.
  • This is an extremely small effect. The differences in free energies are less than k_B T/10 ~ 3 meV at T=300 K. Hence, it is impressive that one can calculate it successfully (provided one has the "right" potential).
  • The effect gets smaller with increasing temperature because the density of the liquid phase (along the liquid-vapour co-existence line) decreases with increasing temperature and vanishes at the critical temperature (around 650 K). For example, between 300 and 600 K the density of the liquid decreases by a factor of 1.5. This corresponds to an increase of the average oxygen atom separation from 3.0 to 3.4 Angstroms. I would estimate this corresponds to an eight-fold decrease in the hydrogen bonding energy. There will be an associated significant change in the intermolecular potential, it becoming much more like that in the vapour phase.

Tuesday, June 26, 2012

Condensed phase dynamics in the Rockies

This week I am in Colorado at the Telluride Science Research Center for the workshop on Condensed Phase Dynamics. Many of my favourite theoretical chemical physicists are here so I am really looking forward to it. I am going to give a talk based on my recent paper about hydrogen bonding.

Sunday, June 24, 2012

Nice book on spectroscopy of biomolecules

Bill Parson has published a nice book Modern Optical Spectroscopy: with examples from biochemistry and biophysics.

I like it because it includes real experimental data from a range of specific biomolecular systems.
It covers all the important topics and is not scared of a full quantum mechanical treatment.
Hence, it has a good balance of theory and experiment.

It is also available as an e-book.

Saturday, June 23, 2012

Mixing may not be irreversible

There is an interesting article Entropy: Order or information by Arieh Ben-Naim in the Journal of Chemical Education.
He points out two related and common misconceptions about entropy:
  • mixing is always irreversible (and so must involve an increase in entropy)
  • entropy is related to disorder
This is illustrated with the three processes of mixing shown below. All involve mixing, but only the first is irreversible.
What determines the entropy change is not the mixing (or amount of disorder) but the change in volume of each gas. That can be related to information (or ignorance) about the state of the gas molecules.

Thursday, June 21, 2012

Is photosynthesis highly efficient?

One should be careful about comparing apples and oranges!

There is a helpful and interesting article in Science Comparing Photosynthetic and Photovoltaic Efficiencies and Recognizing the Potential for Improvement
written by an Aussie Rules football team (18 co-authors!).

It points out that quantifying the efficiency of photosynthesis is not completely straightforward. It is sometimes claimed that it has evolved to have an optimum efficiency and that it has a quantum efficiency of 100% because every photon that is absorbed produces a desired chemical product. The authors state:
For comparison with PV electrolysis over an annual cycle, the energy efficiency of photosynthesis is a more useful parameter and is defined as the energy content (heat of combustion of glucose to CO2 and liquid H2O at STP) of the biomass that can be harvested annually divided by the annual solar irradiance over the same area. Using this definition, solar energy conversion efficiencies for crop plants in both temperate and tropical zones typically do not exceed 1%, a value that falls far below the benchmark for PV-driven electrolysis.
The authors note that the main evolutionary pressure on photosynthetic organisms is that they survive not that they have the optimum thermodynamic efficiency!

If one wants to compare photosynthesis to photovoltaics one should not consider the efficiency of the latter to produce electrical energy but rather chemical energy. The authors suggest an appropriate measure is the efficiency of photovoltaics to produce hydrogen gas from the water splitting reaction.

Tuesday, June 19, 2012

Coupled electron-proton transfer II

I had a nice visit this morning at University of Washington with Jim Mayer who has worked extensively on coupled electron-proton transfer [see this post for an earlier discussion]. Here are a few things I learnt.

CPET is involved in one of the most important processes in biology, whereby we get all of our oxygen! This is the Kok S-state mechanism of Photosystem II: the amino acid tyrosine-Z is oxidised to yield a neutral tyrosyl radical. Specifically, the electron is transferred 14 Angstroms (i.e. a long way!) to a photoexcited chlorophyll radical and the proton is transferred across a hydrogen bond to a nearby histidine residue (e.g. see this 2003 PNAS paper for evidence).

It is important to note that the proton and the electron are spatially separated and "attached" to different atoms. Nevertheless, their motion is concerted, i.e. the transfer is not sequential.

A major question concerns whether this process is adiabatic or non-adiabatic. Uncertainty about the answer is highlighted in a recent issue of Chemical Reviews. One article is by Hammes-Schiffer and Stuchebrukov which advocates a non-adiabatic approach.
A different article by Siegbahn and Blomberg considers DFT based calculations and implicitly assumes an adiabatic approach.

We agreed there is a need for some simple models to describe this fascinating phenomena.

Aside: a recent Science paper from Mayer's group shows that similar chemistry occurs in transition metal oxides which are important in energy research. Titanium dioxide has been the subject of 58,000 papers!

Monday, June 18, 2012

Solvent viscosity determines excited state lifetimes

A series of earlier posts have considered how the excited dynamics of a range of organic dyes is determined by the viscosity of the solvent.
This essentially determines the friction associated with torsional motion on the excited state potential energy surface.

Seth Olsen brought to my attention a very nice paper from 1987.
Torsional dynamics of molecules on barrierless potentials in liquids. II. Test of theoretical models by Ben-Amotz, D. and Harris, C.

They test three alternative models, comparing to experimental data for auramine O and Crystal Violet. Thus this paper is very similar to the 2000 paper by van der Meer, Zhang, and Glasbeek that I discussed in an earlier post.
They find experimentally that the excited state lifetime scales with the solvent viscosity. This scaling is required by the Smoluchowski equation (for overdamped stochastic motion in an external potential), regardless of the form of the potential energy.

The experimental data is most consistent with model (a) above.

Sunday, June 10, 2012

Living and breathing quantum entanglement

Take a deep breath. You just created an entangled quantum state!

There is a really interesting paper on the arXiv

Quantum entanglement and Hund's rule are determinants to respiration
Cedric Weber, David D. O'Regan, Nicholas D. M. Hine, Peter B. Littlewood, Gabriel Kotliar, Mike C. Payne

They use DFT-DMFT (Density Functional Theory + Dynamical Mean-Field Theory) to study the binding of oxygen and carbon monoxide to iron-porphyrin (heme).

This is the process by which respiration occurs. Oxygen binds reversibly to the heme group in myoglobin. Unfortunately, CO does not bind reversibly and you die!

[Aside: Haemoglobin consists of four myoglobin molecules and they exhibit some interesting and important collective behaviour (allostery) first elucidated by Linus Pauling (who else!) from simple thermodynamic considerations.
This is nicely described in Thermal Physics by Kittel and Kroemer].

This new work shows that as the iron atom Hund's rule coupling J varies from 0 to 1 eV significant qualitative changes occur in the ground state. Specifically, it becomes a superposition of different iron spin (and valence) states.
Such behaviour cannot be captured by purely DFT-(Kohn-Sham) based calculations which are by assumption of single determinant character and so involve only one spin and charge state for the Fe atom.

As far as I am aware this is the first concrete application of DMFT to quantum chemistry. A few recent developments (e.g. this PRL from Columbia) were concerned with benchmark studies.

Earlier DFT studies show fine different states within 15 kJ/mole [~0.15 eV] of one another. Hence, it is reasonable that small J value variations could change the character of the ground state.

The TOTAL spin of the ground state must be definite. If I recally correctly, experimentally it is found to be a singlet with oxygen bound.

The authors don't mention that back in 1979 Case, Huynh, and Karplus studied a Pariser-Parr-Pople (like an extended Hubbard) model for heme-O2 and heme-CO. They found that the ground state of the former was an equal mixture of Fe2+(S=0)O2(S=0) and Fe2+(S=1)O2(S=1).

In a Barley Peroxidase there is experimental evidence for a Quantum Mixed-Spin Heme State consisting of a superposition of S=5/2 and S=3/2.

Friday, June 8, 2012

Exam hints for students

Many physics exam questions I set are meant to be "simple" and "easy", i.e. they aim to test understanding rather than the ability to
-do complicated algebra/calculus
-regurgitate large amounts of information

Hence, always look for a simple way to solve the problem. Never think "It can't be that simple", e.g., just plugging numbers into a single equation  or just restating in different terms/words the answer to a previous part of the question.

If your answer involves pages of algebra you are almost certainly on the wrong track...

Try and be neat enough that the examiner can actually understand what you have done. Clearly explain what you are doing, including stating assumptions and results you are using. Don't just write lines of equation.

Don't try and fake derivations.

Include and keep track of physical units in all calculations.

Clearly label axes and scales of all graphs.

Don't waffle. If you don't have an explanation don't make up one by stringing together buzzwords.

Tuesday, June 5, 2012

Contrasting classes of superconductors

I think the Figure below is a really nice one which compares the variation of the superconducting order parameter on the Fermi surfaces for four different classes of superconductor:
a. elemental
b. cuprates
c. MgB2
d. iron pnictides

The figure is taken from a 2010 Perspective in Nature by Igor Mazin.

A recent post considered how to unify b. and d.

Don't be so negative!

There is a good editorial in the Journal of Chemical Education Cherry Picking: Why We Must Not Let Negativity Dominance Affect Our Interactions with Students
by Melanie M. Cooper

She emphasizes how it is easy to get discouraged by just a few students whose performance,  preparation, actions, or attitude is disappointing to us. Furthermore, what is even worse is if that small minority ends up changing how and what we teach or what attitude we have to the majority of students.

I thought the following line was particularly important:

We must teach the students we have, not the students we want (or the students we imagine we were back in the mists of time).

Monday, June 4, 2012

Effect of disorder on the Mott-Hubbard transition

I have been reading through a very interesting review paper
Mott-Anderson Transition in Molecular Conductors: Influence of Randomness on Strongly Correlated Electrons in the κ-(BEDT-TTF)2X System
by Takahiko Sasaki

It reviews some very nice experiments done by Sasaki and collaborators where they used X-ray irradiation to systematically vary the amount of disorder.

There are several things I find puzzling about the experimental results for X=Cu[N(CN)2]Br. I also think they are inconsistent with the offered interpretation in terms of Anderson localisation.
It is observed that irradiation does longer than 200 hours drive the material from a metallic phase to a Mott insulating phase.

First, I don't think invoking Anderson localization is relevant because the amount of disorder is relatively small, compared to the electronic bandwidth. Specifically, even for doses of 200 hours the sample is still a superconductor [probably d-wave] with a Tc of about 6 K, reduced from about 12 K in non-irradiated samples. This means [cf. Figure 9 in the paper] that the scattering rate due to impurities is about 6 K ~ 0.5 meV which is two orders of magnitude less than the hopping integral t.

Second, theory [at least at the level of DMFT] predicts that disorder [much less than the band width] stabilises the metallic phase not the Mott insulating phase. This can be seen in the phase diagram below taken from this PRL by Krzysztof Byczuk, Walter Hofstetter, and Dieter Vollhardt.
In the experiment Delta would be much less than 1 and U slightly less than 1.

I also note that the experiments found that the for X=Cu[N(CN)2]Cl and X=Cu2(CN)3 irradiation (disorder) drove the Mott insulating phase towards the metallic phase, consistent with the above phase diagram.

So I think the paper shows how a metallic system very close to the Mott transition can be driven into the insulating phase by a relatively small amount of disorder. Current theory seems unable to explain this.

[I thank Andrew Bardin for bringing the paper to my attention at a cake meeting.]

Saturday, June 2, 2012

Observing the dynamics of a collapsing ecosystem

I think I heard a distinguished mathematical ecologist claim that there are very few actual systems which do behave like the simple textbook models.
Hence, I was very interested to see in Science this week a really nice experimental paper

Generic Indicators for Loss of Resilience Before a Tipping Point Leading to Population Collapse 
by Lei Dai, Daan Vorselen, Kirill S. Korolev, and Jeff Gore
Theory predicts that the approach of catastrophic thresholds in natural systems (e.g., ecosystems, the climate) may result in an increasingly slow recovery from small perturbations, a phenomenon called critical slowing down. We used replicate laboratory populations of the budding yeast Saccharomyces cerevisiae for direct observation of critical slowing down before population collapse. We mapped the bifurcation diagram experimentally and found that the populations became more vulnerable to disturbance closer to the tipping point. Fluctuations of population density increased in size and duration near the tipping point, in agreement with the theory.
Our results suggest that indicators of critical slowing down can provide advance warning of catastrophic thresholds and loss of resilience in a variety of dynamical systems.
Below is the "phase diagram" of the model.
It is interesting that the work was done in a Physics department.

Friday, June 1, 2012

Good titles for the arXiv

Previously I have posted about the importance of choosing a good title for your paper.

Perhaps on a lighter note, I stumbled across this, which shows that sometimes people use really creative titles.