Why you might worry about classical models of water

A nagging question for the whole field of (classical) molecular dynamics simulations of biomolecules is whether they can have an adequate description of water. This is particularly important because almost all biomolecular processes involve subtle interactions of the biomolecule of interest with its aqueous environment.

I learnt a lot from reading the article On the origin of the redshift of the OH stretch in Ice Ih: evidence from the momentum distribution of the protons and the infrared spectral density, by C. J. Burnham, G. F. Reiter, J. Mayers, T. Abdul-Redah, H. Reichert and H. Dosch.

They highlight several problems and state:

Clearly there is something missing from water models. All of the above difficulties have been consistently tackled by experimentalists, but they remain either unrecognized or unacknowledged by much of the simulation community.

Here are the 4 main difficulties they list concerning the differences between the properties of a water monomer and the water molecule in ice Ih [most common phase of ice]:

1. the magnitude of the measured anharmonicity parameter of the OH stretch X_OH (=difference between 1/2 of the second overtone frequency and the fundamental) of the OH stretch in the condensed phase is increased from 87 cm-1 in the gas-phase to 134 cm-1 in ice Ih. This behavior cannot be reproduced by a simple anharmonic oscillator (such as a Morse oscillator), for which elongation of the OH stretch by the ice H-bond results in a decrease in |XOH|.

2. the enormous observed increase (25 fold) of the integrated IR intensity in the OH stretch mode in ice compared to that of the gas-phase monomer. Most water models (even including polarizable ones) predict almost no increase at all.

3. The gas-phase molecular dipole moment derivative with respect to the OH stretch is observed to be in a direction some 25 degrees outside of the OH stretch vector. In contrast, it is observed that this derivative becomes nearly parallel to the OH vector in ice.

4. The HOH angle increases from the gas-phase value of 104.5 to 107 degrees in ice. This is in contrast to virtually all empirical water models, which predict a lowering of the HOH angle from the gas-phase value.

The authors propose their own (classical) solution to these problems.
I am not in a position to judge the validity or reasonableness of the solution.
However, I have a prejudice that ultimately the origins of these problems is that the H-bond has a significant covalent and quantum character.

Scepticism and caution is usually the best response

All the media attention to recent anomalies in the speeds of neutrinos raises some interesting scientific and sociological questions. Should you go to the media before you have results published in a peer reviewed journal?

A few things to bear in mind.

These deviations from the speed of light are one part in 100 thousand. They require measuring the distance travelled to the same precision, i.e. an accuracy of 20 cm!

Relative measurements rather than absolute measurements are usually more reliable. As the Nature News (n.b. not paper) article said

Most troubling for OPERA is a separate analysis of a pulse of neutrinos from a nearby supernova known as 1987a. If the speeds seen by OPERA were achievable by all neutrinos, then the pulse from the supernova would have shown up years earlier than the exploding star's flash of light; instead, they arrived within hours of each other.

An earlier anomaly in neutrino physics was of the 17 keV neutrino that was "discovered" in 1985. It is worth reading the historical reviews in Reviews of Modern Physics and Nature which discuss what went wrong. These articles should sober theorists who jump on  a bandwagon once some apparent experimental anomaly is observed.

On the other hand, the solar neutrino problem is a case where experimental anomalies did lead to interesting new physics. But note, there the anomalies were by a factor of three in the observed neutrino flux.

A quantum chemist tries to solve cuprate superconductivity

Journal of Physical Chemistry Letters has a paper Origin of the Pseudogap in High-Temperature Cuprate Superconductors  by Jamil Tahir-Kheli and William A. Goddard, III

I can't say I really follow the details here. The doping dependence of the pseudogap they calculate seems to be a percolation effect. A key issue is whether they can produce the anisotropy in the pseudogap in momentum space. It is not clear they do since everything seems to be done in real space.

There is some interesting history here, going back to the early days of high-Tc.
Sparks fly over conflicting theories from Chemical and Engineering News in 1988, discusses conflict between Phil Anderson and Goddard.
A clash erupts between scientific subculture is a New York Times article from 1989 which quotes a Dr. Anderson who is presumably Phil Anderson.

I thank Seth Olsen for bringing some of these articles to my attention.

Quantum computational matter

Stephen Bartlett gave a colloquium on this topic today.
The ground states of quantum antiferromagnets contain substantial amounts of entanglement (although how much is hard to quantify). Hence, one might hope they are a resource that might be used in quantum computation. Stephen described some recent work [see this PRL and this PRL ] which considers how this might be done. The focus seems to be on gapped systems which have hidden symmetries and can be described as tensor network states. The prime example is the Haldane spin-1 antiferromagnetic Heisenberg chain which is adiabatically connected to the AKLT model.

I was reminded of some work I was involved in a few years ago (described in this PRL) which showed how one could take any spin singlet state [not just the ground state!] from a spin-1/2 chain and perform projective Bell measurements (on pairs of spins) along the chain and teleport quantum states with perfect fidelity along the chain. I was wondering what the relationship (similarities and differences) of our work was with this more recent work.

Where is theoretical chemistry going?

There is an Editorial Theoretical Chemistry - Quo Vadis? by Walter Thiel in Angewandte Chemie International Edition.
["Quo Vadis" is latin for "where are you going?"]

It is worth reading. It is particularly good that he offers some concrete precautions for experimentalists running computational codes.
I thought the following characterisation of theoretical chemistry was disappointingly narrow:

Theoreticians are primarily interested in testing the performance and limitations of newly developed computational methods, for example by systematic validation on established benchmarks or through proof-of-principle calculations. 

Overall I prefer the articles I highlighted in 5 papers every computational chemistry student should read, together with Hoffmann's 1974 article on theory in chemistry and Zewail's article on the future of chemical physics.
Those articles place a much greater emphasis on theory providing unifying concepts.

I thank Seth Olsen for bringing the article to my attention.

Writing effective personal statements

Most applications for scholarships or admission to graduate school require a personal statement. I found a very useful site at Penn State, Writing Personal Statements online.

I read the two sample statements from applicants for a Marshall Scholarship. Both were very impressive. They illustrate several key ingredients

• Distinctly personal. It is about you. Only you could write this. Avoid generics "I am really interested in subject X and want to study at University Y because it is a world class university."
• Personally engaging. A natural outcome is that the reader should want to meet you.
• Specific connection between applicant and the target institution/program. Mentioning specific courses, faculty, and research projects is key.
• Polished and well written. This means writing and rewriting and getting feedback on drafts.

For those of us reading and reviewing applications I see two important consequences of this material being freely available.

First, the bar is higher. Any student with a little "get up and go" can Google "personal statements scholarship applications" and find material such as this. They should then aim to produce something of comparable quality.

Second, we need to be wary of plagiarism and so running applications through Turnitin or Googling suspect sentences may be a necessary precaution.

As an aside, I mention the movie Spanglish has an amusing opening scene [which I could not find on YouTube] where an admissions officer at Princeton is reading personal statements from undergraduate applicants.

The case for effective Hamiltonians

When trying to understand complex molecular materials, the dominant approach in chemistry to is to do DFT-based calculations for the system of interest. However, a case needs to be made for an alternative "physics" approach. Recent Anthony Jacko, Ben Powell and I wrote an article Models of organometallic complexes which makes the case below for effective Hamiltonians.


Another approach to modeling the optoelectronic properties of organometallic complexes is to construct a model with fewer states but an accurate treatment of the electronic correlations. This contrasts with first principles calculations, which include several basis states for each atom but neglect some electronic correlations. The small number of degrees of freedom in such semi-empirical models allows one to make fewer approximations on the interactions and correlations in the model. It also allows one to identify key trends that describe broad classes of materials. This approach has proven itself incredibly powerful in wide areas of materials science. For example, the Anderson single impurity model can describe a wide range of systems including magnetic impurities in metals, quantum dots in semiconductor heterostructures, carbon nanotubes , and single molecule transistors.47,48

In principal an effective model Hamiltonian is found by starting with the exact Hamiltonian and ‘integrating out’ high energy states.49 This procedure is computationally expensive,50 so often one simply chooses a reduced basis set, motivated by the physical processes one wishes to capture.49 DFT can be used to estimate the values (or trends in values) of some of the parameters of these effective models. The model Hamiltonian can then be solved, retaining correlations that the approximate DFT functional does not include.51–55

Identifying the frontier orbitals which dominate the photophysics is one of the most significant steps of the effective model approach. In this reduced basis set one can define an effective Hamiltonian with just a few parameters. Conjugated polyenes have been investigated in this way via the Hückel, Hubbard, Heisenberg and Pariser-Parr-Pople models.49 This approach has been applied to organometallic complexes, for example mixed valence binuclear systems including magnetic atoms in proteins (Hubbard and double exchange models; Ref. 56), molecular magnets (Ref. 57), Anderson impurity models for cobalt based valence tautomers (Ref. 58), and a series of metal-coredbipyridine complexes (Ref. 22). It has also been shown recently that this approach naturally explains the sensitivity of the photophysical properties of organometallic complexes to small chemical changes.18

To correctly describe the character of the excited states the model must capture the key interactions. There are many important features of the system that might be included in such a model, for example electronic ‘hopping’ terms between the frontier molecular orbitals, direct Coloumb interactions between electrons in those orbitals, spin interactions, and relativistic effects such as spin–orbit coupling. The relative energy scales of these various interactions will define the composition of the excited states and therefore their properties. 


I welcome comments and suggestions on any review articles that persuasively make the case for effective Hamiltonians as an important tool in materials modelling.