How can living organisms be so highly ordered?

This may seem to violate the second law of thermodynamics.

In the Intermediate Biophysics class meeting today we agreed to start reading through Philip Nelson's excellent book, Biological Physics: Energy, Information, and Life.

Each chapter begins with a biological question, and a terse slogan encapsulating a physical idea relevant to the question. Chapter 1 begins with:

Biological question: How can living organisms be so highly ordered?
Physical idea: The flow of energy can leave behind increased order.

He introduces the idea of free energy as the useful energy or quality of energy. The distinction between high and low quality energy is a matter of order or organisation.

Living beings consume order not energy.
Free energy transduction is what the biosphere does to create order.

The figure below is a nice way to illustrate transduction of free energy.
A machine uses osmotic flow to convert disorder (random molecular motion) into work in the upper part of the figure.

In the lower part of the figure doing work pulling on the weight increases the order in the system, i.e., the sugar solution becomes more concentrated (reverse osmosis).

More fundamentalism

Which is more fundamental? Elementary particles or elastic solids?

In his book A Different Universe, Bob Laughlin considers the implications of the observation that quantities such as the Josephson constant and the von Klitzing resistance are known will incredible accuracy, the latter to one part in ten billion (pp.15-16):

``Paradoxically, the existence of these highly reproducible experiments leads us to think in two mutually incompatible ways about what is fundamental. One is that exactness reveals something about the primitive building blocks out of which our complicated, uncertain world is made…. The other is that exactness is a collective effect that comes into existence because of a principle of organization…. There is no way to reconcile these two ideas; they are exact opposites. Yet we use the fundamental to describe both.”

Laughlin points out:

“The fractional quantum Hall effect reveals that ostensibly indivisible quanta—in this case the electron charge e—can be broken into pieces through self-organization of phases. The fundamental things, in other words, are not necessarily fundamental.”

He further claims that in quantum field theory the vacuum state is not fundamental but is “an emergent phenomena characteristic of a phase of matter” (p.110-115).

Laughlin claims that if Einstein were alive today then he would,

“conclude that his beloved principle of relativitiy was not fundamental at all but emergent – a collective property of the matter constituting space-time that becomes increasingly exact at long length scales but fails at short ones.’’ (p. 126)

Key concepts in molecular electronics

This morning at MM2009 Abe Nitzan gave a beautiful talk which gave a unified physical picture of many of the important processes (electron transfer, solvation, transition state theory, vibrational relaxation, ....) that are key to understanding molecular conduction. On his website I found an earlier and more detailed version of the talk, given a few years ago in Cape Town.

This makes a nice companion to reading his book.

Observing the collapse of the wave function

Here is the talk I just gave at the MM2009 meeting.

One point I tried to bring out was how the "peak shift" that one observes in photon echo spectroscopy (see figure below which is taken from this paper by Cho, Carlsson, and Jimenez) is actually the time scale involved in the collapse of the wavefunction due to the environment making a continuous "measurement" of the quantum state of the chromophore.
The first photon pulse creates a coherent superposition of the electronic ground and first excited states.This is discussed in more detail in this review I wrote with Joel Gilmore.

Can we truly predict crystal structures?

This post was stimulated by a nice talk that Richard Catlow gave at MM2009 last night.
He began with the fact that twenty-one years ago, the Editor of Nature, John Maddox made the provocative claim,

"One of the continuing scandals in the physical sciences is that it remains impossible to predict the structure of even the simplest crystalline solids from a knowledge of their composition."

Woodley and Catlow recently wrote a nice review in Nature Materials, entitled, Crystal structure from first principles, which highlights recent progress and future challenges. I acknowledge the impressive progress, particularly with the developing of ingenious new algorithms for searching configuration space that has been made, but most of this seems to be using semi-empirical force fields and/or empirically based cost functions based on bond valence sums.

I think I would rewrite Maddox claim as,

One of the greatest scientific and philosophical challenges in the physical sciences is that it remains impossible to consistently predict from Schrodinger's equation the structure of crystalline solids solely from a knowledge of their composition and without knowledge of the structure of related materials.

I include "philosophical" challenge because this strikes at the heart of issues relating to emergence and reductionism.

Teaching biological physics

Preparing to teach PHYS3170 Intermediate Biophysics I have been looking at some material on Phillip Nelson's website. He is author of one of the nicest texts, Biological Physics: Energy, Information, and Life.

Several things particularly worth looking at are:

Teaching biological physics, an article in Physics Today.

A course on physical models for biological systems, a talk to the Biophysical Society.
(the syllabus of the actual course is here).

Modelling complex molecular materials

Tomorrow I head down to the Gold Coast to attend MM2009, a conference on Molecular Modelling, mostly attended by computational chemists. There are several great international speakers. Some I look forward to hearing and talking to are:

Richard Catlow (UCL)
He has worked on many things, including cerium oxides. I want to talk to him about some recent results that Elvis Shoko recently obtained concerning charge distribution near oxygen vacancies in cerium oxides.

Weitau Yang (Duke)
Besides being the Y in B2LYP, he has recently written some really nice papers elucidating the limitations of density functional theory (DFT). This short paper in Science gives a nice introduction to the issues.

Abraham Nitzan (Tel Aviv)
Most of his research interests in and approach to chemical physics are similar to my own. He is also author of the only modern text I am aware of on the important topic , Chemical dynamics in condensed phases. I wish I had this when I started working in the area.

Entanglement in quantum chemistry

Quantifying the amount of quantum entanglement in a many-body state is a difficult problem that has stimulated a lot of papers but a limited amount of progress. This is largely because there are few good measures of multi-party entanglement. Even before finding a good measure one needs to decide how to partition your Hilbert space. (i.e., who are the parties: Alice, Bob, Charles, David, Erwin, Felix, Gerard,...?)

Why should we care?
Two ambitious outcomes one might aim for are:

-use the entanglement in chemical bonds as a resource to perform quantum information processing tasks
-use insights from quantum information theory to develop new quantum chemistry algorithms

I recently stumbled across a nice paper by Ziesche, Gunnarsson, John, and Beck, that was written in 1997, before quantum information became fashionable. Hence, the word entanglement is actually not in the paper! But, they do calculate it. They consider the one-particle density matrix for the two-site Hubbard model and the BCS ground state. They then calculate the "correlation entropy" of the ground state. This is essentially the von-Neumann entropy and corresponds to the entanglement of one electron with all the other electrons in the system. They reference earlier papers that perform similar calculations for the hydrogen molecule and several other systems.
The main goal of the paper is to test a conjecture of Collins that this entropy should be proportional to the "correlation energy" in quantum chemistry. This is usually the difference in energy between the true ground state energy and that calculated from a Hartree-Fock wave function, i.e., a single Slater determinant.

I really like the paper because it uses a simple model to illustrate not just entanglement but also issues such as correlations, natural orbitals, Heitler-London vs. Hartree-Fock.

Probing quantum coherence

Coherent two-dimensional spectroscopy is proving to be a powerful probe of quantum coherence in biomolecular systems. I found the figure below in the review by Minhaeng Cho very useful.


Figure 2 Schematic representation of a 2D spectrum (at a fixed value of the waiting time T) showing cross peaks. In general, both ground-state bleaching and stimulated emission (positive) and excited-state absorption (negative) features appear. Negative features can partially or even wholly cancel positive features. Partial cancellation leads to distortions in the line shapes, as seen in the highest frequency diagonal peak. Note that the 2D spectrum is not symmetric around the diagonal. Cross (off-diagonal) peaks appear (for T = 0) only when coupling between chromophores is present. Cross peaks can also be generated by energy transfer, coherence transfer, chemical exchange, physical transformation, and so on for larger values of the waiting time T. Note that the orientation of the cross peaks is controlled by whether the fluctuations of two different transition frequencies are positively or negatively correlated with each other. Modulation of coupling strength by bath or intramolecular degrees of freedom produces an antidiagonally elongated cross peak, whereas any modulation of site energies (monomeric transition frequency) makes the peak diagonally elongated at short time T.

Key concepts in biophysics

Thinking through what to include in the PHYS3170 Intermediate Biophysics reading course it is good to reflect on what do we really want the students to learn. Here, off the top of my head, are some of the important ideas in biophysics that I have learned from scratch the past 5 years.

* Structure determines property which determines function

* Function is often about transduction (e.g., conversion of energy) and optimisation of efficiency, speed, and selectivity.

* Water is an amazingly unique substance.

* The hydrophobic interaction has a big effect on how proteins fold and the emergence of other biomolecular structures. (A dry protein is a dead protein!)

* The hierarchy of energy, time, and length scales.

* Both excitonic and vibrational energy transfer occurs via resonant energy transfer.

* Hush-Marcus theory describes electron transfer in proteins and elucidates the role of the environment.

* The size of kBT sets the scale for many phenomena.

* Entropy and Gibbs free energy (the chemical potential) are key concepts.

* Entropy describes elasticity of DNA, the hydrophobic interaction, and concentration gradients producing electrochemical potential differences.

* Transition metals play a key role in many biomolecular functionalities.

* The interplay of Emergence and reductionism associated with the hierarchy of energy, time, and length scales.

* What details matter? Physicists say none, chemists, most, and biologists all!

* Biochemistry is the search for the chemistry that works.

* Enzymes work by lowering the energy of the transition state over which the reaction proceeds.

* Biomimetics: understanding the underlying physical principles behind specific biomolecular functionalities (e.g., conversion of light energy to chemical energy) may allow us to design synthetic analogues which have optimum efficiency.

* Skepticism I. Heed Kauzmann's maxim: people will tend to believe what they want to believe rather than what the evidence before them suggests they should believe.

* Skepticism II: just because someone can do a simulation on a computer that looks what you expect to see does not mean:
1. the simulation is reliable, reproducible, and correct
2. you actually understand the phenomenon that is being simulated.

* More skepticism: von Neumann on wagging the elephants trunk.

* Biological physics vs. Biophysics vs. Biologists using tools that physicists invented

Is quantum consciousness only sleeping?

Does this figure show an array of qbits in your brain? I doubt it.

Following up on a previous post, my collaborators and I just had a paper with the modest title, The Penrose-Hameroff Orchestrated Objective-Reduction Proposal for Human Consciousness is Not Biologically Feasible,
accepted for publication in Physical Review E.

Converting energies

Some numbers I find useful and worth remembering are 1 eV equals about 12,000 K and 8000 cm-1. But I still struggle to remember anything about kcal/mol, the chemists favourite unit. I found this very useful Table today when I was struggling with some conversions.

Electron vs. hole transport in organic materials

A general observation is that the mobility for electron transport in organic materials used in electronic and photonic devices can be orders of magnitude smaller than the mobility for hole transport. A rough explanation for this is given in a useful review by Bredas et al. The figure below is the basis for the discussion of how for a pair of adjacent molecules the splitting of HOMO's is larger than that of LUMO's.


This splitting is proportional to the matrix element (t in a Huckel model) between orbitals on different molecules. This is larger for the HOMO's because the wavefunction has fewer nodes than the LUMO does and so the intermolecular overlap is less.
The mobility is proportional to t^2 (see the review by Horowitz) and so is much smaller for electron than hole transport.

However, this is not the end of the story since one also needs to consider effects such as whether impurities in an actual material are more effective at trapping charge carriers for electrons or for holes. Such issues are discussed in this Nature paper concerning n-type organic FET's.

What is an explanation? What is the ultimate cause?

George Ellis points out that the question, ``Why does an aircraft fly?’’ has several different answers, ranging from ``because it is on the airlines schedule’’ to ``because the air molecules produce a differential force between the top and bottom of the wings.’’ Which answer is ``correct’’ depends on the context of the original question. Furthermore, different individuals and different social groups will have different standards and values that will determine what constitutes a ``satisfactory’’ explanation.

In his book, A Different Universe, Bob Laughlin states,

``microscopic laws are true and could plausibly cause phases; therefore we are sure they do cause them, even though we cannot prove this deductively. The argument does have the strange effect of giving the word ``cause’’ a meaning it does not customarily have. One could say that the laws of chemistry ``caused’’ the destruction of Tokyo, but what really did it was Godzilla.’’

``Symmetries are caused by things, not the cause of things.’’ (p.124)

He further claims that ``protection’’ obscures ultimate causes,

``The elastic rigidity of the solid state, hides the existence of atoms, because the elastic properties are universal consequences of ordering and would be the same if the solids were made of something else. (p. 144)

A radical (emergent) approach to teaching a course

Below is an email I sent out to the 5 students enrolled in a third year undergraduate class. I was wondering if anyone has any experience with this approach to teaching a course. Subconsciously, I was inspired by the two pages on "Synergy in the classroom" in The 7 Habits of Highly Effective People, by Stephen R. Covey. I just re-read it. He says:

As a teacher, I have come to believe that many truly great classes teeter on the very edge of chaos. Synergy tests whether teachers and students are really open to the principle of the whole being greater than the sum of the parts.

----------------------------------

Dear students,

Currently only 5 students are enrolled in PHYS3170 Intermediate Biophysics.Normally, this would mean that the course would be cancelled.

However, Dr. Seth Olsen and I are willing to offer to run the course in an alternative mode of delivery, where you all take greater ownership for learning and administrative activities.

There would be no formal lectures. Most learning would take place via readings and a class blog. Emphasis will be on co-operation rather than competition.

We would meet face to face on thursdays at 12 noon and possibly 2pm. This would be an informal discussion and question section. Students would each give at least one presentation during this time.

I would propose we try and negotiate an assessment arrangement which will be based on your extent of involvement and contribution to the learning activities of the class. You would collectively write the course profile.

The main role of Seth and I would be to select the readings/topics and help you understand them.

I believe you would actually learn more and have more fun.

But, I can understand why you might prefer the safety and predictability of a conventional course.

Please let me know if you are still interested.

cheers,

Ross McKenzie

Emergence in molecular biology

A key framework for molecular biophysics is that structure determines property which in turn determines function. But `function’ is not a reducible concept (something Michael Polanyi emphasized).
John Hopfield is a Professor of Molecular Biology at Princeton University and also was recently President of the American Physical Society. In a helpful piece in Nature about physicists working in molecular biology Hopfield states, ``The word `function’ does not exist in physics, but physicists need to learn about it, otherwise they will be in a sandbox playing by themselves.’’

In molecular biology, a dramatic, puzzling, and fascinating manifestation of emergence is how differences in a string of letters (the nucleotides A,G,T, and C) encoded at the molecular level in DNA lead to different cell types, different acquired characteristics, and even different species.

Over the top or tunnel through? Quantum reaction rate theory

Chemistry is all about change. It is about chemical reactions.
A major theoretical challenge is to calculate the rate of a chemical reaction.
Most reactions proceed by a rearrangement of the geometrical arrangement of the atoms in the reactant molecules leading to the product molecules. This can be described by a potential energy surface (PES) in which the reactants and pproduct configurations are local minima (R and P, respectively) separated by some saddle point known as the transition state (TS). The concept of the TS was introduced by Eyring in 1935. In the Figure below R is at q=0.
The difference in energy between the TS and the R configurations is the activation energy for the reaction. Pauling had the brilliant idea that how catalysts (and particularly enzymes) work is that they lower the activation energy. Calculating (in a rigorous manner) the rate at which a reaction proceeds from a knowledge of the PES turns to be highly non-trivial theoretical problem since one must include the "friction" along the reaction co-ordinate. For purely classical dynamics this problem was solved by Kramers in 1940. A complete quantum theory is still an open problem.
The classic review of the field is by Hanggi, Talkner, and Borkovec. The figures in this post are from a paper by Riseborough, Hanggi, and Freidkin.
In the full quantum problem one must include the effects of quantum tunneling
below the potential barrier and the effects of the friction/environment.

Significant progress was made beginning in 1975 when Bill Miller (a chemist) showed that in the semi-classical limit tunneling through a potential barrier V(q) could be described by a periodic solution to the classical equations of motion for the inverted potential -V(q).
This corresponds to motion in imaginary time, tau.

Two trivial (but physically important) solutions are the constant solutions corresponding the top of the barrier and the reactant position.

At finite temperature T the periodic solution must have period (in imaginary time) equal to theta = hbar/(k_B T).

The value of the action for this periodic solution determines the transmission probability and agrees with the WKB approximation. This periodic solution is known as the "bounce" and after it was re-discovered by physicists in 1977 as the "instanton." Examples of bounce solutions for different temperatures are shown below.

The bottom right figure corresponds to the lowest temperature and most of the imaginary time trajectory is spent near q=0, i.e., at the bottom of the potential and corresponds to tunneling from the bottom of the well.

The bounce solution only exists if the temperature is sufficiently low and the curvature of the potential barrier large enough.
If not, no tunneling below the barrier occurs. i.e., the reaction can only proceed via activation over the barrier.

In the early 1980's Caldeira and Leggett showed with path integral methods how the effects of dissipation due to the environment could be included. Again, tunneling is described by a periodic solution to motion in an inverted potential with a non-local "frictional" force.
Again tunneling only occurs if the temperature is sufficiently low.

Scientific fame (or notoriety) without responsibility

The latest issue of Nature Physics has a review by Mike Norman of the book, Plastic Fantastic: How the Biggest Fraud in Physics Shook the Scientific World By Eugenie Samuel Reich. The book chronicles the antics of Hendrik Schon earlier this decade. Norman points out,

"many readers will take exception to how leniently Schon's senior coauthors were dealt with in the book, perhaps because they were willing to be interviewed (those who refused were treated more harshly). In fact, a serious discourse of the responsibilities of senior authors, management, journal editors and referees in the scientific process would have been a welcome addition."

Putting quantum conciousness to sleep

A video and book that has received a lot of attention in popular culture over the past few years is What the bleep do we know?

The protagonist, Amanda, played by Marlee Matlin, finds herself in a fantastic Alice in Wonderland experience when her daily, uninspired life literally begins to unravel, revealing the uncertain world of the quantum field hidden behind what we consider to be our normal, waking reality.

The video contains a strange mix of quantum physics, pop psychology, and new Age mysticism. A main thesis of the video is that there is a connection between quantum physics and how we think. Indeed, by thinking quantum thoughts we can create our own quantum reality and control our destiny. Since I am interested in science and theology several people had recommended it to me. A teacher at my daughter's school was enthralled with it, and encouraged students to watch it. When I finally watched the video I was alarmed. It completely mis-understands and mis-represents quantum physics. None of the scientists interviewed in the movie is actually a bona fide quantum physicist (i.e., someone who regularly publishes research papers in international refereed journals).

So what do we know? There are many things we don't understand. Quantum physics and consciousness are both strange and poorly understood. However, that does not mean they are related. There is a reality which is independent of what I think about it. How I think can have a significant effect on my perception of that reality, but it won't change that reality. This is psychology, but has nothing to do with quantum physics.


Stuart Hameroff, a Professor of Anesthesiology at the University of Arizona is featured in the video. He is a vocal proponent of "quantum consciousness" and has co-authored papers on the subject with Sir Roger Penrose FRS, a distinguished mathematical physicist.

Recently, Jeff Reimers, Laura McKemmish, Noel Hush, Alan Mark, and I published a detailed scientific critique of key ideas of Hameroff and Penrose in the Proceedings of the National Academy of Sciences (USA). You can read Hameroff's response here. The paper also stimulated some debate on the Nature network. I will leave you to draw your own conclusions about whether Hameroff's reponse is convincing.

My experience with this enterprise confirms Kauzmann's warnings.

Fundamentalism in science

What is fundamental?

Reductionists always claim that what is fundamental is what occurs at the shortest length scales and involving the constituent particles of a system, i.e., the microscopic is more fundamental than the macroscopic. However, claims as to what is fundamental is sometimes a matter of personal choice and preference. As pointed out by Alister Rae , work by Ilya Prigogine on the relationship between microscopic dynamics and thermodynamics, can be argued to support the view that the macroscopic can be more fundamental than the microscopic:

“[In a chaotic system] It is … the positions and velocities of the component molecules, that change chaotically whereas the thermodynamic quantities (which are traditionally thought to be derived from the microscopic substructure) are well behaved. These facts led Ilya Prigogine to suggest …. we should consider the thermodynamic quantities to be the primary reality and the allegedly more fundamental description in term of microscopic structure to be secondary.”

A. Rae, Quantum Physics: Illusion or Reality? (2nd ed.; Cambridge: Cambridge University Press, 2004), pp. 120-123.

Such a view is completely the opposite of what a reductionist would claim. In a later post I will give Bob Laughlin's answer to the question, "What is fundamental?"

The effect of the environment

I attach some rough notes on Hush-Marcus electron transfer theory, which I have referred to in a few previous posts. I think contains very important concepts and equations that are very relevant to many biomolecular processes and issues in organic electronics and photonics.

A few points I stress:

This theoretical formalism does not just apply to electron transfer but also many other processes involving transitions between two weakly coupled quantum states which are strongly coupled to an environment which can be treated classically. (The result can be derived from a spin-boson model)

A key physical quantity is the reorganisation energy.

The Marcus inverted parabola shows that the process occurs at the greatest rate, not when the two states are at the same energy, but rather when their energy separation equals the reorganisation energy. (i.e, how much the energy of the environment changes as a result of the process).

The matrix element coupling the two states (e.g, donor and acceptor molecules) falls off exponentially with increasing spatial separation. As a result, I think charge transfer won't be fast enough for many desired processes (e.g, charge separation in organic bulk heterojunction solar cells) unless there is pi-stacking of molecules. Sulfur atoms (as in thiophenes) are also desirable for this reason.

Quantum tunneling of protons in small molecules

A really nice article, Houdini molecule escapes energy trap, in Chemistry World last year sat in my "enzyme paper" folder. I just read it today. It is a fascinating story of beautiful science including serendipity, and a healthy interaction of theory and experiment. The News and Views piece and the Nature paper are also worth a read.

Multiple hypotheses in action (speed up the rate of doing science)

I am excited. This post ties together a previous post about doing science as opposed to just publishing papers and the controversy about the role of dynamics and quantum tunneling of protons in enzymes. I just reread a beautiful paper, entitled, "A Compelling Experimental Test of the Hypothesis That Enzymes Have Evolved To Enhance Quantum Mechanical Tunneling in Hydrogen Transfer Reactions", by Doll and Finke. It contains the figure below which clearly illustrates its goal, to test Kliman's hypothesis:

“The optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of tunneling and thereby accelerate the reaction rate

Furthermore, the authors formulate three alternative hypotheses.


Read the abstract. It is brilliant.

Through some very clever synthetic chemistry they make several molecules that undergo the same hydrogen abstraction reaction as in the enzyme. They then compare reaction rates and kinetic isotope effects.

I will leave you to read the conclusion in the abstract...

Later I will present an alternative hypothesis which is also consistent with the data: the only role of quantum effects is the interplay of quantum and thermal fluctuations at the transition state.

Scientific papers have their day in court?

Ben Powell brought to my attention this really nice piece in the Careers section of Nature about a creative and effective way to run group meetings that look at the recent literature. I think it is worth a try, particularly because it gets more people, especially junior group members, more engaged.

p.s. I just scored a century, not in cricket but in the blogosphere. I just noticed this is my 101st post on this blog.!

A design principle for organic photovoltaics and explosive sensors

The underlying physics behind bulk heterojunction organic solar cells is the following. A donor molecule D is excited by light to D* and then there is rapid electron transfer to an acceptor molecule A:

D*A -> D+A- (1)

One wants this to proceed much faster than than radiative or non-radiative decay of D, i.e.:

D*A -> DA + photon or heat (2)

or charge recombination

D+A- -> DA

In terms of a qualitative understanding in terms of molecular orbitals the picture below may be helpful.

However, to be quantitative one should think in terms of the full quantum many-body states which I have denoted above DA, D*A, and D+A-.

The rate of charge separation in (1) can be described by Hush-Marcus electron transfer theory.



















This rate will be largest when the optical excitation energy equals the sum of the donor ionistation energy and the acceptor electron afinity plus the reorganisation energy (of the environment) associated with the charge separation.
[see the figures above to see how the electron tranfer rate drops significantly with detuning]

I believe this is may be an important design principle which I have never seen clearly stated in the literature; most people try to line up the (non-existent) LUMO energies of D and A.

A good solar cell has (1) much faster than (2).

Exactly the same physics is relevant for organic molecules used to detect trace amounts of explosives (i.e., nitroaromatics) by flourescent quenching. D the sensor should be a flourescent molecule which will bind to the nitroaromatic A strongly enough so that (1) proceeds much faster than (2), i.e, the flourescence is quenched.

A key challenge is to find donor molecules D which are only sensitive to specific nitroaromatics A. This has recently been done in a paper, that we will discuss at tomorrow's thursday COPE meeting.

Quantum biology? Tunneling in enzymes

Over the past two decades the possibility of quantum tunneling of protons in enzymes
has attracted considerable attention. (See for example a piece in Nature by Philip Ball (my favourite science writer) or the proceedings of a meeting at the Royal Society

The observed large kinetic isotope effects and their temperature dependence are inconsistent with semi-classical transition state theory, whereby the chemical reaction occurs via thermal activation over an energy barrier. These discrepancies have been interpreted as evidence for the presence of tunneling. However, it should be stressed that this evidence is indirect, being based on the values of fitting parameters for Arrhenius plots where the absolute temperature only varies by about ten per cent.
In contrast, for chemical reactions involving simpler organic molecules, such as benzoic acid much more definitive signatures of proton tunneling have been observed. These include a temperature independent rate at low temperatures and tunnel splitting of the ground
state energy.
Key questions that need to be answered include:

• Can all the known experimental results be explained without tunneling?
• To what extent is it necessary to go beyond the traditional semi-classical transition state theory to explain the observed kinetic isotope effects of enzymes?
• If tunneling does occur, is it actually important for the function of the enzyme?
• Have enzymes evolved in a manner that enhances the contribution of tunneling?

There are currently a wide range of views on the answers to these questions.
For example, a review in Science, How Enzymes Work: Analysis by Modern Rate Theory and Computer Simulations by Mireia Garcia-Viloca, Jiali Gao, Martin Karplus, and Donald G. Truhlar states that,

``the entire and sole source of the catalytic power of enzymes is due to the lowering of the free energy of activation and any increase in the generalized transmission co-efficient, as compared to that of the uncatalyzed reaction."

Villa and Warshel state that,

``the most important contribution to catalysis comes from the reduction of the activation free energy by electrostatic effects ... the popular proposal that enzymes catalyze reactions by special dynamical effects is not supported by a consistent simulation study ... the interpretation of recent experiments as evidence for dynamical contributions to catalysis is unjustified.''

In contrast, Klinman and collaborators stated in a 1999 Nature paper that,

``Our present findings on hydrogen transfer under physiological conditions cannot be explained without invoking both quantum mechanics and enzyme dynamics.''

In a paper that focused on simulations Schwartz and collaborators express a similar view,

``The action of the enzyme in speeding the chemical reaction, however, is postulated to be intimately connected to the directed vibrational motion identified in this paper. Thus, it appears that evolution has designed the protein matrix of an enzyme not just to hold substrates or stabilize transition state formation, but rather to channel energy in a specific chemically relevant direction.''

I align myself with the skeptics in a paper I am working on..... more to come..

The dirt on spin liquids

The organic charge transfer salt -(ET)₂Cu₂(CN)₃ has attracted a lot of attention the past few years because there is significant experimental evidence that the ground state of the Mott insulating phase is a spin liquid.

One important and puzzling observation is that the NMR lines are much more broadened than those of comparable materials undergo antiferromagnetic ordering. Furthermore, this broadening increases significantly with decreasing temperature.

A nice paper by Gregor and Motrunich performs several model calculations to see if they can explain this large broadening by taking into account the role of disorder. They find they can only explain the experimental data above about 5 K, if there is much larger disorder than expected and that it is strongly temperature dependent.

It is interesting that the authors have done comparable calculations for a kagome antiferromagnetic and they can explain the experimental data for that.

Gregor and Motrunich mention that it is hard to estimate the strength of the disorder and the role of temperature dependent screening.

A recent paper by two of my UQ colleagues may help a:

Toward the parametrization of the Hubbard model for salts of bis(ethylenedithio)tetrathiafulvalene: A density functional study of isolated molecules

J. Chem. Phys. 130, 104508 (2009)

http://link.aip.org/link/?JCPSA6/130/104508/1

They find that the difference in the site energies for BEDT-TTF molecules in the staggered and eclipsed conformations is 0.12 eV.

I note that this is comparable to the single dimer Hubbard U ~ 0.2 eV estimated from the optical conductivity. This could have a big effect on the exchange interaction between the localised spins in the Mott insulating phase (see equation B2 in Gregor & Motrunich).

Hopefully, the findings in these two papers can be combined to pin down just how large the disorder is in this material, which is such a promising candidate for a spin liquid.

The two really hard questions that remain are:

Is the large line broadening a definitive signature of a gapless spin liquid?

Is disorder essential to understand this line broadening?

Increasing our scientific productivity (but writing less papers)

There is a article in Science that I have now read three times and am wrestling with. I reproduce a few quotations below:

Strong inference consists of applying the following steps to every problem in science, formally and explicitly and regularly:

1) Devising alternative hypotheses;
2) Devising a crucial experiment (or several of them), with alternative possible outcomes, each of which will, as nearly as possible, exclude one or more of the hypotheses;
3) Carrying out the experiment so as to get a clean result;
1') recycling the procedure, making subhypotheses or sequential hypotheses to refine the possibilities that remain; and so on.
......
"But what is so novel about this?" someone will say. This is the the method of science and always has been; why give it a special name? The reason is that many of us have almost forgotten it. Science is now an everyday business. Equipment, calculations, lectures, become ends in themselves. ... we do busywork. We become "method-oriented" rather than "problem" oriented. .. We fail to teach our students how to sharpen up their inductive inferences.
.....
Whether it is hand-waving or number-waving or equation-waving, a theory is not a theory unless it can be disproved.

[but a single hypothesis is difficult to disprove. Furthermore,]
"our trouble is that when we make a single hypothesis, we become attached to it"

[this is why] some great scientists are so disputatious

To avoid this grave danger [of people being attached to theories], the method of multiple working hypotheses is urged. It differs from the simple working hypothesis in that it distributes the effort and divides the affections.

[Examples are given from Faraday, Roentgen, Fermi, Watson & Crick, and Pasteur]
these men believed in the effectiveness of daily steps in applying formal inductive methods to one problem after another

[we should all] devote a half hour or an hour to analytical thinking every day, writing out the logical tree and the alternatives and crucial experiments explicitly in a permanent notebook.

The article is by John R. Platt, a distinguished molecular spectroscopist from the University of Chicago. It was published in 1965, but seems just as relevant and important today!

I welcome comments, and especially examples of multiple hypotheses.

A further twist on optically active molecules

Understanding the quantum dynamics of the excited states of complex molecular materials is a scientific challenge that is of great technological importance.
From a physics point of view we would like to know which details really do matter in determining functionalities such as the light induced charge separation required in solar cells.

Methine dyes are an important class of materials for organic photonics.
Previously I discussed how Seth Olsen and I published a paper

A diabatic three-state representation of photoisomerization in the green fluorescent protein chromophore

J. Chem. Phys. 130, 184302 (2009)

http://link.aip.org/link/?JCPSA6/130/184302/1

We have also done a very detailed study of the topology and geometry of the potential energy surfaces for the low-lying singlet states for an effective Hamiltonian describing the three valence bond states relevant to methine dyes.

Important degrees of freedom are the different twists shown below.
Even this simple model exhibits much of the rich geometry and several key properties found previously in very sophisticated quantum chemistry calculations: the existence of conical intersections between different states and charge localisation connected with excited state twisting. Just one case is shown below.

Philosophers wrestle with emergence

The concept of emergence has received significant attention in philosophical circles, from early in the twentieth century. Here, it is important to make the distinction between "weak" emergence and "strong" emergence. Philosophers such as Broad and Alexander were advocates of what would be now called "strong" emergence. A position of strong emergence holds that emergent properties cannot, even in principle, be deduced from the properties of the constituents of the system. Vitalism, the notion that living matter, is not purely physical, is an example of such a view.

A reductionist would claim we can always understand all the properties of a complex system in terms of the properties of its constituent particles and their interactions. Given sufficient computational resources we can predict properties of the whole system. In contrast, someone advocating "weak" emergence acknowledges it may be possible "in principle" to deduce emergent properties from properties of the constituents of the system. However, they would emphasize that in practice (at least, at this point in time) we cannot make such deductions. Furthermore, such deductions do not necessarily provide significant insight or allow one to deduce the organizing principles of the system under study.

Sometimes a "strong" emergence position is associated with "top-down causation" or "downward causation", in contrast to the notion of "bottom-up causation" which a reductionist advocates.

Silberstein and McGeever discuss how the distinction between "weak" and "strong" emergence can also be viewed as a distinction between epistemological emergence and ontological emergence:

A property of an object or system is epistemologically emergent if the property is reducible to or determined by the intrinsic properties of the ultimate constitutents of the object or system, while at the same time it is very difficult for us to explain, predict or derive the property on the basis of the ultimate constituents.

Ontologically emergent features are neither reducible to nor determined by more basic features. Ontologically emergent features are features of systems or wholes that possess causal capacities not reducible to any of the intrinsic causal capacities of the parts nor to any of the (reducible) relations between the parts.

They claim that the existence of entangled states in quantum mechanics provides the most conclusive evidence for the existence of ontological emergence and that this completely explodes the ontological picture of reality as divided into a `discrete hierarchy of levels’ and they quote Humphreys statement ,

even if the ordering on the complexity of structures ranging from those of elementary physics to those of astrophysics and neurophysiology is discrete, the interactions between such structures will be so entangled that any separation into levels will be quite arbitrary

However, this argument overlooks the fact that entangled quantum states are very fragile and their interaction with the environment can quickly "decohere" them and destroy the entanglement. This is how classical mechanics emerges from quantum mechanics. It is possible to show that in biomolecules this decoherence occurs in less than a picosecond, which is why large scale quantum entanglement does not play a role in biochemical phenomena.

In considering the relationship between chemistry and physics, Lombardi and Labarca reject the separation of ontological and epistemological emergence. They work within the framework of Hilary Putnam’s internal realism, which aims to find middle ground between metaphysical realism and radical relativism. Conceptual schemes and descriptions are required to define objects, even though reality exists independent of our subjective description.

Getting the elephant's trunk to wiggle

The Nature essay, A meeting with Enrico Fermi, by Freeman Dyson is worth digesting. I quote below a few bits that stood out to me:

I am eternally grateful to him for destroying our illusions and telling us the bitter truth.

we could calculate the atomic processes precisely. By 1951, we had triumphantly finished the atomic calculations and were looking for fresh fields to conquer. We decided to use the same techniques of calculation to explore the strong nuclear forces.

[Fermi said:]
"There are two ways of doing calculations in theoretical physics", he said. "One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither...
....To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics....
....my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

Orbitals that do exist

Previously I discussed why I don't like the way some people talk about LUMO's and HOMO's. They don't really exist, i.e., they have no measurable properties.
They are very useful for qualitative discussions though.

Is there something better, that respects the fact that the ground state of molecules is really
a highly correlated quantum many-body state?

Yes. Natural orbitals. These are the eigenfunctions of the full one-particle density matrix.
The corresponding eigenvalues are the occupation of these orbitals.
Note these can have non-integer values.
There is a connection to Fermi liquid theory, which I hope to come back to....

A nice introduction can be found in
Sections 1.5 & 1.6 of the wonderful book, Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective, by Frank Weinhold and Clark Landis.
The book shows how to ground chemical intuition (orbitals, lewis pairs, bonding) in a rigorous theoretical framework.

The excitement of when theory meets experiment

I was delighted to see that Jukka Pekola is going to be at UQ on friday to give the physics colloquium. He is a very gifted experimentalist. i.e., he can do many experiments that other people can't get to work.

I first met Jukka (hard to believe!) 20 years ago. I had just completed a Ph.D with the onerous title, "Nonlinear interaction of zero sound with order parameter collective models in superfluid 3He-B."
This explored various acoustic analogues of non-linear optical effects.

I gave a talk on this work at a conference in Florida and later we went to lunch and Jukka said, "we tried to do the experiment you proposed and it did not work." I was delighted that someone had tried! The proposed experiment was to observe two-phonon absorption by the real squashing mode (one of the 18 order parameter collective modes in 3He-B). This required keeping the superfluid at a constant and uniform millikelvin temperature while dumping large amounts of energy into it to produce large amplitude density oscillations. A very difficult experiment....

Jukka's group had tried the experiment at high pressures. I suggested to Jukka that the effect may be more observable at lower pressures because the non-linear coupling would be larger due to the pressure dependence of a relevant Landau Fermi liquid parameter.

Jukka went back to Helsinki and successfully did the experiment! This was exciting for me. We wrote a paper together describing the results. Later we realised this non-linear effect could be used to map out the dispersion relation for the squashing mode (described in this PRL). I was also invited to a conference in Helsinki and I got to see the lab where it all happened! ( see the photos). I gave an overview/summary of all the work in my conference paper.

This was the first of many fruitful collaborations I have now had with experimentalists. Thanks are due to Jukka for getting me started. I look forward to catching up with him on friday.