Role of quantum nuclear motion in biomolecular systems

 Total I am giving a talk, "Effect of quantum nuclear motion on hydrogen bonds in complex molecular materials" at Light-matter Interactions from scratch: Theory and Experiments at the Border with Biology 

Here are the slides

The talk provides a concrete example of the tutorial on constructing simple model Hamiltonians for complex materials that I give before the talk. It relates to the bio theme of the meeting through work on isotopic fractionation in proteins and the recent paper below. It makes use of the simple model that I talk about.

Unusual Spectroscopic and Electric Field Sensitivity of Chromophores with Short Hydrogen Bonds: GFP and PYP as Model Systems

Chi-Yun Lin and Steven G. Boxer

Tutorial on modelling quantum dynamics in biomolecules

This week I am giving two (virtual) talks at a meeting

Light-matter Interactions from scratch: Theory and Experiments at the Border with Biology 

supported by the ICTP (International Center for Theoretical Physics) in Trieste.

In the ICTP tradition, one talk is a tutorial and the second talk is about my research.

Here are the slides for the tutorial on Effective Model Hamiltonians for Quantum Dynamics in Complex Molecular Materials. Feedback is welcome.

The research talk is about hydrogen bonding. I will post slides for that later.

Nanoscale machines in nature

Part two of the Biology brief in The Economist is Cells and how to run them: All life is made of cells, and cells depend on membranes

A few of the main ideas are the following. Cells are either prokaryotic (bacterium) or eukaryotic (animals). Cell membranes are made of lipids that spontaneously form structures due to an interplay between hydrophobic and hydrophilic interactions. The boundary of prokaryotic cells is the membrane. Eukaryotic cells are more complex, containing many organelles (mitochondria), whose boundary are membranes.

Cells are little factories that can multiply themselves and perform distinct biological functions. It requires energy to maintain the cell shape and for it to manufacture new things. Inside and out is maintained by a difference in the concentration of protons (hydrogen ions) across the membrane. There are two aspects to this. First, the electron transport chain produces the protons. Second, a specific protein in the membrane, ATP synthase, pumps protons across the membrane.

The electron transfer chains are driven either by respiration or photosynthesis. 

Energy for processes in the cell is provided by breaking ATP down to ADP. The reverse process is driven by the kinetic energy of rotation (at about 6000 rpm) of the part of the ATP synthase protein.  ATP is Adenosine triphosphate.

To me the amazing/awesome/cool/miraculous thing is what the hardware can do. These are nanoscale chemical machines and factories. The video below shows a simulation of the ATP synthase protein that is located within cell membranes. It acts as a proton pump to maintain the concentration imbalance between the outside and inside of the cell and to convert ADP to ATP.

I learnt from this how the ATP synthase spins in only one direction and the rotation corresponds to sequential conformational changes in the protein subunits.

There is a beautiful discussion of the underlying physics in a chapter in Biological Physics by Phil Nelson. I have written a brief summary here.

The underlying quantum chemistry is explored in

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase

Shayantani Mukherjee and Arieh Warshel

Isotope effects in spin crossover materials

A range of isotope substitution experiments have been performed on spin-crossover materials. 

Just like for other systems such as superconductors their interpretation is subtle.

The first studies are reviewed in Section 2.3.5 of this review article.

Isotopic exchange was investigated for a tris(picolylamine)iron(II) system which exhibits a two-step spin transition. Results are shown in the figure below. Significant changes in the spin-state transition curve were observed only when the isotopic substitution (H/D and 14N/15N) was made for atoms directly involved in the hydrogen-bonding network that connects the spin-crossover molecules. For example, with C2H5OD/ND2 the crossover temperature was shifted to higher temperatures by about 15 K and the middle step was no longer present. 

I would not have expected such a large effect given the chemical complexity of these systems and that the H atoms are not immediately bonded to the iron atoms which undergo the spin-state transition.

I now mention two other studies. They are particularly helpful because they also measured how the enthalpy and entropy change associated with the spin-state transtion changed with isotopic substitution.

Weber et al. studied the iron(II) spin-crossover complex [FeL1(HIm)2] and the deuterium-substituted [FeL1(DIm)2] where Him is (not a man but) imidazole. Both exhibit a single-step transition with hysteresis. H/D exchange decreased both the transition temperature and the hysteresis width by a few K. Deuteration decreased the value of the enthalpy and entropy differences between the low spin and high spin states (determined from differential scanning calorimetry) by about twenty and ten percent, respectively. (See Table 2 in the paper). They estimated an interaction parameter J = 560 K, indicating strong intermolecular interactions, which they attributed to a hydrogen bond. They reference some earlier studies showing how the magnitude of the ligand field in a transition metal complex can be modified by hydrogen bonds involving the complex. 

Very recently, Jornet-Mollá et al. studied the iron(ii) salt [Fe(bpp)2](isonicNO)2·HisonicNO·5H2O, which with decreasing temperature undergoes a transition at 162 K. There is a width of about 5 K, associated with hysteresis. With deuteration, the transition temperature decreases to 155 K, the width increases to 7 K, and the enthalpy and entropy differences both increase by about fifteen percent. “Annealing the compound at lower temperatures results in a 100% LS phase that differs from the initial HS phase in the formation of a hydrogen bond (HB) between two water molecules (O4W and O5W) of crystallisation. Neutron crystallography experiments have also evidenced a proton displacement inside a short strong hydrogen bond (SSHB) between two isonicNO anions.” 

I am particularly interested in this because of previous work I have done on strong hydrogen bonds.

Again I am surprised at the magnitude of these effects because the zero-point energy associated with the relevant H atoms is only a small fraction of the total zero-point energy and the entropy contribution from vibrations.

I now start a preliminary discussion of how these experiments might be interpreted in terms of an Ising model picture, such as in a recent preprint. The Hamiltonian is

 where the pseudospin sigma=+1/-1 corresponds to high spin and low spin states.

The crossover temperature is independent of the Ising interactions J's and given by 

Thus, it is a property of the individual molecules and not directly dependent on the intermolecular interactions.

The presence of hysteresis and the difference between the transition temperature for increasing and decreasing temperature sweeps are determined by the magnitude of the Ising interactions. 

Our results in Appendix A of the preprint imply that there should be no dynamical isotope effects on the J’s, i.e., provided other parameters such as structural details and bond lengths do not change with isotope substitution.

This does not rule out changes in the crossover temperature. Both the enthalpy and entropy differences can change with isotope substitution (as is observed). The former due to changes in zero-point energies, and the latter due to changes in the vibrational contribution to the entropy change. 

Interpretation of isotope effects can be subtle

 Isotopic substitution has provided significant insights into molecular and solid-state physics. This involves the substitution of particular atoms in a compound by the same chemical element with a different nuclear mass (i.e. a nuclear isotope). An example is hydrogen/deuterium substitution which has shown the significant role that quantum nuclear motion can play in hydrogen bonding, particularly in strong hydrogen bonds. Of particular relevance to the discussion below is that isotopic substitution does not only change vibrational frequencies but can also change bond lengths. 

 A key piece of evidence on the road to the BCS theory of superconductivity in 1957 was the observation of an isotope effect. In 1950 a shift in the transition temperature of mercury was observed, suggesting that superconductivity resulted from electron-phonon interactions, as argued by Frohlich that same year. In particular, the magnitude of the shift was consistent with theoretical work by Herbert Frohlich. (Whether he predicted or postdicted the observed effect is a matter of debate, as discussed by Jorge Hirsch.) BCS theory gives that $\Delta T_c/T_c = - {1/over 2} \Delta M /M$, which arises from the fact that phonon frequencies scale with $1/\sqrt{M}$, consistent with the mercury experiments. 

However, in the 1960s there were many observations of “anomalous” isotope effects, particularly in transition metals, that were inconsistent with the prefactor in this equation. These anomalies were resolved by going beyond the BCS theory and allowing for strong-coupling effects. Following the discovery of cuprate superconductors in 1986, isotope effects were observed in some cuprates. However, the consensus now is that these observations do not support an electron-phonon mechanism for superconductivity but rather are due to structural changes due to the isotope substitution. For example, isotopic substitution changes the zero-point energy, and that can alter the unit cell volume and the hopping parameter t in a Hubbard model. 

This illustrates that there are subtleties in interpreting isotope experiments. This is because there are both structural and dynamical isotope effects. Changes in isotope can lead to changes in structure, such as bond lengths or lattice constants, and even in changes in crystal symmetry. These structural changes arise because the equilibrium structure of the system is that which minimises the total energy of the system. The contribution to this energy from the zero-point energy of the atomic vibrations changes with isotope substitution and with bond lengths. Dynamical effects are those that involve exchange of phonons such as in superconductivity. 

I am not sure how to sharpen this structural/dynamical or static/dynamical distinction. Or is it secondary and primary effects?

In the next post, I will discuss observations of isotope effects in spin-crossover materials and how that relates to recenttheoretical work with my collaborators.

Square ice on graphene?

As I have written many times before, water is fascinating, a rich source of diverse and unusual phenomena, and an unfortunate source of spurious research reports.
Polywater is the classic example of the latter.
I find the physics particularly interesting because of the interplay of hydrogen bonding and quantum nuclear effects such as zero-point motion and tunneling.

There is a fascinating paper
Polymorphism of Water in Two Dimensions
Tanglaw Roman and Axel Groß

The paper was stimulated by a Nature paper that claimed to experimentally observe square ice inside graphene nanocapillaries. Such a square structure is in contrast to the hexagonal structure found in regular three-dimensional ice.
Subsequent, theoretical calculations claimed to support this observation of square ice.
Here the authors use DFT-based methods to calculate the relative energies of a range of two-dimensional structures for free-standing sheets of water (both single layer and bilayers) and for sheets bounded by two layers of graphene.

The figure below summarises the authors results for free-standing layers showing how the relative stability of the different water structures depends on the area density of water molecules [which varies the length and strength of the hydrogen bonds].

On the science side, there are several interesting questions arise.
How much do the results depend on the choice of DFT functional used [RPBE with dispersion corrections]?
Would inclusion of the nuclear zero-point energy modify the relative stability of some of the structures, as it does for the water hexamer?
Quantum nuclear effects are particularly important when the hydrogen bond length [distance between oxygen atoms] is about 2.4 Angstroms. [I am not quite sure what area density this corresponds to for the different structures].

On the sociology side, this paper is another example of a distressingly common progression:
1. A paper in a luxury journal reports an exotic and exciting new result.
2. More papers appear, some supporting and some raising questions about the result.
3. A very careful analysis reported in a solid professional journal shows the original claim was largely wrong. This paper attracts few citations because the community has moved on to the latest exciting new "discovery" reported in a luxury journal.

I thank Tanglaw Roman for helpful discussions about his paper.

Spin ice in a nutshell

What is spin ice? What its definitive and experimental signatures?

A good place to start is the lucid discussion by Roderich Moessner and Art Ramirez in a 2006 article on Geometrical Frustration. They emphasise two organising principles: local constraints on neigbouring spins and the emergence of new entities such as gauge fields.

First, let's discuss the "ice" bit since this involves some beautiful chemistry, physics, statistical mechanics, and history. In the solid phase of water at atmospheric pressure (ice Ih) the water molecules form a hexagonal lattice, with the oxygen atoms located a the vertices of the lattice. The molecules interact with one another via hydrogen bonds.

Now the key point is that there are many different ways of orienting the water molecules (arranging the protons). The only constraint is that one has to have two protons covalently bonded to the oxygen and two protons on next-nearest neighbour water molecules hydrogen bonded to the oxygen. This is known as the ice rule. Suppose we assign an Ising spin variable (+1,-1)=(in, out)  = (covalent, Hbond) to each "bond" on the lattice. Then the ice rule is that on each tetrahedron the sum of the four "spins" must be zero.

How much degeneracy is there?
There are 2^4= 16 possible spin states on a tetrahedron. But, only six (a fraction of 3/8) satisfy the ice rule. To see this, put +1 on site one, then one must put +1 on one of the other three sites, and -1 on the other two. This gives 6 = 2 x 3 options.
If one neglects the interaction between vertices, the thermodynamic entropy per tetrahedron (water molecule) is

S = k ln (3/2)

Historical asides.
This "residual" entropy in ice was observed experimentally by William Giauque in the chemistry department at Berkeley in the 1930s.
Linus Pauling explained this in 1935, even arguing it as evidence for a specific crystal structure of ice.
Pauling's picture led to the ice-type models that are very important  (from a mathematical and conceptual point of view) in classical statistical mechanics as they are exactly soluble in two dimensions.
In 1956 Phil Anderson (who else!) noted that Pauling's problem was equivalent to that of Ising spins on a pyrochlore lattice.
It was not until four decades later than an experimental realisation was observed in a magnetic material. The experimental data is shown below.

But there is much more to spin ice. The local constraints lead naturally to an emergent gauge field (a pseudo-magnetic field), analogues of "magnetic monopoles", and unusual spin correlations (algebraic correlations without criticality). I now discuss the latter as they can be viewed as a "smoking gun" of spin ice.

The "magnetic field" B satisfies the constraint Div B =0. As a result the spin correlations have a dipolar form, i.e. they have a distance and directional dependence similar to the magnetic field associated with a magnetic dipole. This means the spin correlations fall off algebraically. This is in contrast to conventional magnets where spin correlations decay exponentially, except at a critical point. Furthermore, if one plots or measures the static spin structure factor S(q) one finds "pinch points" occur in high symmetry planes. The figure below shows an experimental measurement for Holonium Titanate, taken from here.

A spicy scientific scandal

I am often on the lookout for interesting molecules and solids which involve short hydrogen bonds, particularly biomolecules where this bond may play a key role in functionality. Such bonds are of interest from a physics point of view because then the quantum motion of the proton matters.
Consequently, the following paper (published in October 2016) caught my attention.

Proton Probability Distribution in the O···H···O Low-Barrier Hydrogen Bond: A Combined Solid-State NMR and Quantum Chemical Computational Study of Dibenzoylmethane and Curcumin Xianqi Kong, Andreas Brinkmann Victor Terskikh, Roderick E. Wasylishen, Guy M. Bernard∥, Zhuang Duan∥, Qichao Wu∥, and Gang Wu

The authors state their motivation.

Curcumin was selected in our study, in part because it is being touted as a wonder drug and is of intense interest to the pharmaceutical and medical community.31−33

This sounds quite exciting. Could low barrier hydrogen bonds be important in curing cancer?
Curcumin is a major ingredient of tumeric, the yellow spice, which features heavily in Asian cooking.
This got me Googling and it turns out the claims of a "wonder drug" are dubious.

Experimental studies of curcumin turn out to be particularly problematic, as explained in a blog post
Curcumin will waste your time by Derek Lowe. It is worth reading because it highlights the need for replication studies and publication of null results.

But it gets worse. References 31 and 32 have the same last author, Bharat Aggarwal, who it turns out has been the major proponent of the "wonder drug". In 2015 he "retired" from the University of Texas, following allegations of scientific fraud. By August 2106, eighteen published papers by him had been withdrawn.

To illustrate the problem of metrics, in 2016 Aggarwal had an h-index of 160, and in 2015, Thomson Reuters (ISI Web of Science) listed him among the World's Most Influential Scientific Minds.

I should stress that none of this invalidates the results of the hydrogen bonding paper that got me on this trail.

The educational value of undergraduate research projects

This past semester I have been supervising two undergraduate research projects. One student is doing a one semester course (1/4 of the students load) for a third year student. The second student has a year long project for a fourth year student (1/2 of their load). I am very happy with how both have gone in terms of their educational value. The amount of research results is of secondary importance to me. Previously, I posted about possible ingredients for a good undergrad project. Both students are working on a simple model for hydrogen bonds. I recommend this because it has an "easy" learning curve and so they can start "doing science" quick. It also has a nice mix of theory and experiment, chemistry and physics.

Things that struck me as particularly valuable include the following very basic things. Some of which relate to basic but important skills.

Seeing calculations to completion. 
In an undergrad problem set or exam the student has limited time and gets partial marks for incomplete or wrong answers. In research you have to keep working on the problem until you have an answer and have checked it enough that you are confident it is the correct answer.

Personal attention.
Each week they get to meet one-to-one with a faculty member and get advice and feedback.

Units! 
Learning that they really do matter and you have to get them right. This converting between different unit systems.

Writing and debugging code.
Even a short Matlab or Mathematica code.

Reading papers not textbooks.
Gifted students can find textbooks quite manageable and understandable. Papers are in a different league.

Experiencing what research is often like.
Hard. Confusing. Boring. Tedious... But, progress and understanding can be quite satisfying.

Communication skills.
Giving a talk and writing reports, and getting feedback on them.

Job skills.
Time management. Showing up for meetings on time. Writing meeting summaries. Coming up with action plans. Listening to constructive criticism. Working with others.

A dirty secret in molecular biophysics

The past few decades has seen impressive achievements in molecular biophysics that are based on two techniques that are now common place.

Using X-ray crystallography to determine the detailed atomic structure of proteins.

Classical molecular dynamics simulations.

However, there is a fact that is not as widely known and acknowledged as it should be. These two complementary techniques have an unhealthy symbiotic relationship.
Protein crystal structures are often "refined" using molecular dynamics simulations.
The "force fields" used in the simulations are often parametrised using known crystal structures!

There are at least two problems with this.

1. Because the methods are not independent of one another one cannot claim that a because in a particular case they give the same result that one has achieved something, particularly "confirmation" of the validity of a result.

2. Classical force fields are classical and do not necessarily give a good description of the finer details of chemical bonding, something that is intrinsically quantum mechanical. The active sites of proteins are "special" by definition. They are finely tuned to perform a very specific biomolecular function (e.g. catalysis of a specific chemical reaction or conversion of light into electrical energy). This is particularly true of hydrogen bonds, where bond length differences of less than a 1/20 of an Angstrom can make a huge difference to a potential energy surface.

I don't want to diminish or put down the great achievements of these two techniques. We just need to be honest and transparent about their limitations and biases.

I welcome comments.

Should you put "theory" or "experiment" in the title of your paper?

A referee for a recent paper, entitled "Effect of hydrogen bonding on infrared absorption intensity", suggested that we should add "theory" to the title since the chosen title could equally be about an experimental paper. In the end, we declined but did make the abstract clearer that the paper was purely theoretical.

I thought this is an interesting issue, that I had not thought about explicitly before. If you look at titles of papers it is true that it is sometimes not clear whether the paper is theoretical, experimental, or joint theory and experiment. This is particularly true with theory papers with titles such as "Property X of material ABC" or experimental papers with titles such as "Strong electron correlations in materials class Y". To experts who working are on the same topic or who know the authors it may be obvious. But to others, it may not be so obvious.

Does it matter?
Surely if the abstract makes it clear then it is o.k.?
[Again it is amazing how for some abstracts in luxury journals you have to read to practically the last sentence to figure it out. This is because experimental papers can be clothed in theoretical hype].

The suggestion prompted me to do two things.
First, I looked through the titles of most of my papers and found that the only ones which contained "theory" were those which referred to a particular technique, e.g. "Dynamical mean-field theory" or "linear spin wave theory".

Second, I looked at the titles of some famous papers, such as BCS and by P.W. Anderson.
BCS is "Theory of superconductivity" and the abstract begins "A theory...".
PWA does have "theory" in some papers but not others.

The only conclusion I came to from all of this is that I think we should work hard on the titles (and abstracts) of our papers, since the title may determine whether or not they are read.

Maybe it is tangential, but it also reminded me that like Anderson, I am largely against combined theory and experiment papers.

What do you think? Does it matter?

Tuning the electronic ground state of organic crystals by isotope substitution

One puzzle concerning organic charge transfer salts (such as those based on the BEDT-TTF molecule) is how the Mott metal-insulator transition can be tuned with substituting hydrogen with deuterium. I find it particularly puzzling because the relevant hydrogen bonds are weak and so one does not expect significant isotope effects.
Similar concerns are relevant to cases of isotopic polymorphism [where the actual crystal structure changes] in molecular crystals such as pyridine.

I recently came across a nice example that I do understand.

Hydrogen-Bond-Dynamics-Based Switching of Conductivity and Magnetism: A Phase Transition Caused by Deuterium and Electron Transfer in a Hydrogen-Bonded Purely Organic Conductor Crystal 
Akira Ueda, Shota Yamada, Takayuki Isono, Hiromichi Kamo, Akiko Nakao, Reiji Kumai, Hironori Nakao, Youichi Murakami, Kaoru Yamamoto, Yutaka Nishio, and Hatsumi Mori

The key to understanding how H/D substitution changes the electronic state is that there is a hydrogen bond between two of the organic molecules with an oxygen-oxygen distance of 2.45 A. As highlighted (and explained) in this paper, around this distance the geometric isotope effect is largest (the H bond length increases to almost 2.5 A), leading to a significant change in the energy barrier for proton transfer.

The figure below nicely shows, using DFT-based calculations and the measured crystal structures for both isotopes at two different temperatures, how the barrier changes, leading to a change in the charge state of the molecules.
The H and D isotopes are at the top and the bottom, respectively.

More subtleties in protein structure and function

Almost three years ago I posted about the controversy concerning whether the photoactive yellow protein has low-barrier hydrogen bonds [for these the energy barrier for proton transfer is comparable to the zero-point energy]. I highlighted just how difficult it is going to be, both experimentally and theoretically to definitively resolve the issue, just as for an enzyme I recently discussed.
A key issue concerns how to interpret large proton NMR chemical shifts.

Two recent papers weigh in on the issue

The Low Barrier Hydrogen Bond in the Photoactive Yellow Protein: A Vacuum Artifact Absent in the Crystal and Solution 
Timo Graen, Ludger Inhester, Maike Clemens, Helmut Grubmüller, and Gerrit Groenhof

A Dynamic Equilibrium of Three Hydrogen-Bond Conformers Explains the NMR Spectrum of the Active Site of Photoactive Yellow Protein 
Phillip Johannes Taenzler, Keyarash Sadeghian, and Christian Ochsenfeld

I think the caveats I have offered before need to kept in mind.
As with understanding the active sites of most proteins the problem is that we don't have very direct experimental probes, but have to use indirect probes which produce experimental results that require significant modelling and interpretation.

I thank Steve Boxer for bringing one of these papers to my attention.

The challenge of an optimal enzyme

Carbonic anhydrase is a common enzyme that performs many different physiological functions including maintaining acid-base equilibria. It is one of the fastest enzymes known and its rate is actually limited not by the chemical reaction at the active site but by diffusion of the reactants and products to the active site.

Understanding the details of its mechanism presents several challenges, both experimentally and theoretically. A key issue is the number and exact location of the water molecules near the active site. The most recent picture (from a 2010 x-ray crystallography study) is shown below.

The "water wire" is involved in the proton transfer from the zinc cation to the Histidine residue. Of particular note is the short hydrogen bond (2.4 Angstroms) between the OH- group and a neighbouring water molecule.

Such a water network near an active site is similar to what occurs in the green fluorescent protein and KSI.

Reliable knowledge of the finer details of this water network really does matter.

This ties in with theoretical challenges that are related to several issues I have blogged about before. Basic questions concerning proton transport along the wire include:

A. Is the proton transfer sequential or concerted?

B. Is quantum tunnelling involved?

C. What role (if any) does the dynamics of the surrounding protein play?

A 2003 paper by Cui and Karplus considers A., highlighting the sensitivity to the details of the water wire.
Another 2003 paper by Smedarchina, Siebrand, Fernández-Ramos, and Cui looks at the both questions through kinetic isotope effects and suggests tunnelling plays a role.

In 2003 it was not even clear how many water molecules were in the wire and so the authors considered different alternatives.

One can only answer these questions definitively if one has extremely accurate potential energy surfaces. This is challenging because:

Barrier heights and quantum nuclear effects vary significantly with small changes (even 0.05 Angstroms) in H-bond donor-acceptor distances.

The potential surface can vary significantly depending on the level of quantum chemistry theory or density functional that is used in calculations.

I thank Srabani Taraphder for introducing me to this enzyme. She has recently investigated question C.

Pseudo-spin lattice models for hydrogen-bonded ferroelectrics and ice

The challenge of understanding phase transitions and proton ordering in hydrogen-bonded ferroelectrics (such as KDP, squaric acid, croconic acid) and different crystal phases of ice has been a rich source of lattice models for statistical physics.
Models include ice-type models (six-vertex model, Slater's KDP model), transverse field Ising model, and some gauge theories. Some of the classical (quantum) models are exactly soluble in two (one) dimensions.

An important question that seems to be skimmed over is the following: under what assumptions can one actually "derive" these models starting from the actual crystal structure and electronic and vibrational properties of a specific material?

That quantum effects, particularly tunnelling of protons, are important in some of the materials is indicated by the large shifts (of the order of 100 percent) seen in the transition temperatures upon H/D isotope substitution.

In 1963 de Gennes argued that the transverse field Ising model should describe the collective excitations of protons tunnelling between different molecular units in an H-bonded ferroelectric. Some of this is discussed in detail in an extensive review by Blinc and Zeks.
An important issue is whether the phase transition is an "order-disorder" transition or a "displacive" transition. I think what this means is the following. In the former case, the transition is driven by the pseudo-spin variables and there is no soft lattice mode associated with the transition.
Perhaps, in different language, is it appropriate to "integrate out" the vibrational degrees of freedom?
[Aside: this reminds me of some issues that I looked at in a Holstein model about 20 years ago].

There are a lot of papers that make quantitative comparisons between experimental properties and the predictions of a transverse field Ising model (usually treated in the mean-field approximation).
One example (which also highlights the role of isotope effects) is

Quantum phase transition in K3D1−xHx(SO4)2 
Y. Moritomo, Y. Tokura, N. Nagaosa, T. Suzuki, and K. Kumagai

One problem I am puzzling over is that the model parameters that they (and others) extract are different from what I would expect from knowing the actual bond lengths, vibrational frequencies, in the system and the energetics of different H-bond states. I can only "derive" pseudo-spin models with quite restrictive assumptions.

A recent paper that looks some of rich physics associated with collective quantum effects is
Classical and quantum theories of proton disorder in hexagonal water ice 
Owen Benton, Olga Sikora, and Nic Shannon

Hydrogen bonding at Berkeley

On Friday I am giving a talk in the Chemistry Department at Berkeley.
Here is the current version of the slides.

There is some interesting local background history I will briefly mention in the talk. One of the first people to document correlations between different properties (e.g. bond lengths and vibrational frequencies) of diverse classes of H-bond complexes was George Pimentel. 
Many correlations were summarised in a classic book, "The Hydrogen Bond" published in 1960.
He also promoted the idea of a 4-electron, 3 orbital bond which has similarities to the diabatic state picture I am promoting.
There is even a lecture theatre on campus named after him!

The "twin" excited electronic state in strong hydrogen bonds

One of the key predictions of the diabatic state picture of hydrogen bonding is that there should be an excited electronic state (a twin state) which is the "anti-bonding" combination of the two diabatic states associated with the ground state H-bond.
Recently, I posted about a possible identification of this state in malonaldehyde.

The following recent paper is relevant.

Symmetry breaking in the axial symmetrical configurations of enolic propanedial, propanedithial, and propanediselenal: pseudo Jahn–Teller effect versus the resonance-assisted hydrogen bond theory
Elahe Jalali, Davood Nori-Shargh

The key figure is below. The lowest B2 state is the twin state.
In the diabatic state picture, Delta is half of the off-diagonal matrix element that couples the two diabatic states.
Similar diagrams occur when O is replaced with S or Se.

The paper does not discuss twin states, but interprets everything in terms of the framework of the
 (A₁ + B₂) ⊗ b₂ pseudo-Jahn-Teller effect. 

Two minor issues might be raised about this work.
It uses TD-DFT (Time-dependent Density Functional Theory). It is contentious how reliable that is for excited states in organic molecules.
The diabatic states are not explicitly constructed.
These issues could be addressed by using higher level quantum chemistry and constructing the diabatic states by a systematic procedure, as was done by Seth Olsen for a family of methine dye molecules.

The role of simple models and concepts in computational materials science

Today I am giving the first talk in a session on Computational materials science at the 4th International Conference on Advances in Materials and Materials Processing.

Here are the slides for my talk "The role of simple models and concepts in computational materials science".

I will be referring the audience to the article such as those mentioned here, here and here that give a critical assessment of computer simulations and stress the importance of concepts.

I welcome comments, particularly as I think the talk could be stronger and clearer.

Hydrogen bonding talk at IIT-Kgp

Today I am giving a seminar, "Effect of quantum nuclear motion on hydrogen bonding" in the Chemistry Department at IIT Kharagpur. My host is Srabani Taraphder.

Here are the slides. The talk is mostly based on this paper.

H-bond correlations and NMR chemical shifts

For a diverse range of chemical compounds, the strength of hydrogen bonds [parametrised by the binding energy and/or bond length] is correlated with a wide range of physical properties such as bond lengths, vibrational frequencies and intensities, and isotope effects. I have posted about many of these and a summary of the main ones is in this paper.

One correlation which is particularly important for practical reasons is the correlation of bond strength (and length) with the chemical shift associated with proton NMR.

The chemical shift is the difference between the NMR resonant frequency of the proton in a specific molecule and that of a free proton. The first important point is that although this shift is extremely small (typically one part in 100,000!) one can measure it extremely accurately.
More importantly, this shift is quite sensitive to the local chemical bonding and so one can use it to actually identify the bonding in unknown molecules (e.g. protein structure determination).
Indeed, if you go to the library and open up a book on NMR or organic chemistry you will find tables and figures giving the chemical shifts associated with different functional groups.

The figure below (taken from here) shows proton chemical shifts for some different molecules.

Why does this happen?
Very roughly the chemical shift is largely determined by the local electronic charge density near the proton and this is modified by the local chemical bonding.

What about hydrogen bonds?
The figure below shows the correlation between the chemical shift and the donor-acceptor distance R for a range of molecules, as found in a 1980 paper.

Confusing aside: the figure shows the chemical shift relative to the standard TMS and so involves negative values.

Why does this matter?
The correlation provides a means to accurately "measure" the donor-acceptor bond length when one does not have direct measurements (e.g. by X-ray diffraction). This is particularly useful in proteins. Indeed, some of the first claims in 1994 on the controversial topic of low-barrier H-bonds (i.e. strong H-bonds) in enzymes were largely based on the observation of unusually small chemical shifts. Some of the subtle issues are discussed here. Another signature is the isotopic fractionation factor.

Although one can calculate these chemical shifts with "black box" computational chemistry, using formulae originally derived by Ramsey in 1950, understanding the underlying physics of the correlations is not clear.

I thank my student Anna Symes for helpful discussions about this topic.