Condensed concepts

How important are electron-electron interactions in organic molecules? There is a really nice old (1975) paper Why is azulene blue and anthracene white?  by Michl and Thulstrup, which highlights the relevant issues. They point out that these two molecules 1 and 3 have similar ionisation energies (IP) and electron afinities (EA) but their lowest lying singlet (S) and triplet (T) excited states have quite different energies (see the Table below). If a simple molecular orbital (Huckel) picture which ignores electron-electron interactions was valid than the energy difference between the LUMO and HOMO would equal IP-EA = T = S. However, the Table clearly shows this is not the case. At the Hartree-Fock level the discrepancies provide a measure of J = Coulomb integral ~ Hubbard U ~ 5 eV 2K= Exchange integral = Singlet-Triplet splitting ~ 1 eV. Michl and Thulstrup give a nice simple explanation of why the exchange integral K is smaller in azulene than in anthracene. (This is what l

I enjoyed reading the article  An economic analogy to thermodynamics by Wayne Saslow. It proposes mapping different economic variables to thermodynamic ones. It learnt a little about economics which was nice. He suggests the following analogies between thermodynamic and economic variables. Wealth, utility, surplus, price, and number of goods, correspond to free energy, internal energy, TS, chemical potential, and particle number respectively. The Maxwell relations correspond to what in economics are known as Slutsky conditions! The economic temperature T is identified with the level of economic development. Economic entropy is expected to be related to "economic variety, which in turn may be a measure of the economic value of leisure." Here is a small extract to give you the flavour. It considers the application of the analogue of the Gibbs-Duhem relation  Ndmu = -SdT + VdP I did not think the papers review of thermodynamic concepts was particularly insightful. But

I wonder if over the past decade the number of co-authors of condensed matter papers in high profile journals has increased significantly. It seems quite common now to have more than ten authors. Is this really justified? Have all of these people really made a substantial contribution to the paper? Are they all willing to stake their scientific reputations on all of the results in the paper? Many of these journals require a statement of the contributions of the different authors. But, most of the statements I read are quite generic. I realise that some of these papers involve theory and experimental collaborations. Some report measurements using complementary probes (e.g., x-rays + neutrons + optical spectroscopy). However, for many of these papers I would have thought that the numbers would be: 1-2 people make the sample 2-3 make the measurements 1 is a friendly theorist who helps in the interpretation. This adds up to 4-6 not 15! Why should we care? Here are some possibl

I am slowly learning that many students think that because of the second law of thermodynamics that the entropy of a system must increase in any process. They forget or ignore that this is only true for an isolated system.   Nice counter examples at fixed temperature and pressure are freezing of a liquid condensation of vapour slow compression of a gas many chemical reactions: e.g., combination of hydrogen gas and oxygen gas to form liquid water in a fuel cell For all of these processes the entropy of the system decreases. These are possible because there is a net decrease in the Gibbs free energy. The entropy of the system plus surroundings increases. I am trying to address this by continually testing understanding of this point with online quizzes and in class "clicker" quizzes.

Jaime Merino and I just finished a paper Effective Hamiltonian for the electronic properties of the quasi-one-dimensional material Li0.9Mo6O17 This is a really strange and interesting material. It has featured in earlier posts. We discuss how the observed properties of both the "metallic" phase and the "insulating" phase are quite unusual and don't seem to fit into any "standard" picture [Fermi liquid, Luttinger liquid, quantum critical, ...]. We then propose the simplest possible lattice model Hamiltonian that might capture its properties. This is worthy of further study. We thank Nigel Hussey for getting us interested in this fascinating material. He has a forthcoming PRL about the unconventional (possibly triplet) superconductivity. Comments welcome.

8 days ago the hard drive on my MacBook Pro died. It was 2 and half years old. Fortunately, I had Time Machine backups and had purchased the Apple Care Protection plan which lasts 3 years. I had not got around to registering it and so had to. This all went pretty smoothly. An Apple technician came and picked up the computer, repaired it, and returned. This took 8 days, but there was a 2 day delay because I had to get the registration done and approved. The Time Machine backup worked beautifully. This is a lot better experience than I ever had with PCs that died. Repair always took much much longer and restoration of backup was much messier.

It can actually be different things to different people. The same applies to the "adiabatic" approximation. There is a nice old article from 1977, What does the term "vibronic coupling" mean? . It clearly distinguishes different approximations that often get called "Born-Oppenheimer" such as crude adiabatic, Condon, Born-Huang,... Then there are "corrections" to "Born-Oppenheimer" such as Herzberg-Teller. The paper is useful because it clearly defines everything and has two nice Tables. One gives the relevant equations for the different approximations. Another compares the actual terminology used by different authors (pre-1975). Does it matter? Besides Born-Oppenheimer breaking down near conical intersections it also matters for "intensity borrowing" where "forbidden" electronic transitions gain oscillator strength by coupling to the vibrational degrees  electronic isotope effects: isotope exchange reacti

If you want someone else to do something then the reality is the more you are in their presence the more likely they are to act on it. Everyone is busy and has many people trying to get their attention. I think this is particularly true of technical staff and many faculty, particularly those with a lot of admin responsibility. Hence, depending on how urgent your request stopping by someones office every day (every couple of hours?) is a good idea. Of course, you have to be careful not to be too pushy that they get turned off and will drag their feet. But this is also why physical presence is better than email because you can sense their mood. So, don't assume that just because you emailed a request a week ago they are working on it. They are probably working on the request of the last person who walked into their office. I believe this can be a difficult issue for people from non-Western countries. It can be quite hard for international students to be so demanding. However, th

With in class exams there are several options on what access to background material that students should have: 1. Students can bring any material (texts, notes, assignment solutions). 2. Students can just bring a copy of the text without annotations. 3. Students can bring a one or two page sheet of formulas that they write themselves. 4. The lecturer provides a formula sheet. Which do you favour? 1. Provides the most realistic "real world" type of assessment, but it can be hard to write new and suitable questions. Given the choice very few students will choose this option. I have used 2. before. I found it surprising (and disappointing) that I could set questions whose answer could be found in the text but there were still a significant fraction of students who could not do them. I have been using 3. lately for my solid state physics class (4th year undergraduates). The students hand in their formula sheets with their exam answers. I suspect I started doing this

When students first learn solid state physics the concept of holes and its utility is not easy to grasp. I find it really helpful to use the Solid state simulations program ziman very helpful to illustrate the difference between electrons and holes. One can consider the motion of electrons in Bloch states for a band structure with the energy contours shown in green in the figure below. One can vary the external magnetic and electric field. If one goes to preset 6 (which has zero electric field) one can start an electron on an electron or a hole Fermi surface. One sees that the motion in a magnetic field has the opposite circulation for electrons and holes, in both real and Bloch wave vector space. Hence, the holes really do act like positively charged particles.

Before introducing the Gibbs free energy in my thermodynamics class I asked the students to say which variables they thought were generally the "easiest" to control in chemistry and physics experiments: volume and temperature, volume and energy, pressure and temperature, ...., or all? Many students thought volume and temperature. (Maybe because what they mostly learn about is gases!). I think the "correct" answer is pressure and temperature because * these are environmental not system variables * it is very hard to control the volume of a solid. Am I right? I now realise this is a rather subtle point and worth getting students to think about. Appreciating it makes students think about experiments rather than mathematics and helps motivate why the Gibbs free energy is actually the most useful thermodynamic function.

A recent issue of the Journal of Chemical Education has several excellent articles responding to a recent controversial article by Alexander Grushow  suggesting that hybrid atomic orbitals have no real physical and chemical basis and so should not be included in the undergraduate chemistry curriculum. There are good articles rejecting this argument. Two of the articles are written by pairs of my favourite quantum chemists  Landis and Weinhold , and Hiberty and Shaik. They are worth reading because they highlight some key issues in quantum chemistry and chemical bonding. At the heart of the matter is whether one favours a  delocalised picture (with canonical molecular orbitals) or a localised picture ( hybrid atomic orbitals and valence bonds). Neither picture is incorrect. They are complementary ways of looking at the same chemical reality. [See for example this post discussing the old MO-VB rivalry]. Both sets of authors emphasize this by stressing that a single Slater deter

I think that Mathematical Physics as a research area struggles with its identity at times. Is it mathematics or physics or neither? I don't think Chemical Physics has a comparable identity crisis, with its value being appreciated by both communities. Many? theoretical physicists (particularly great ones like Feynman and Anderson) will claim that most big breakthroughs in theory occur using old mathematics and with little regard to mathematical rigour. Sometimes a focus on mathematical formalism is an impediment rather than a aid to real progress. (See for example, this post about Anderson's views). Whether string theory is actually theoretical physics or just beautiful mathematics is debatable (Anderson had a nice review of Peter Woit's book a while back). However, there are times where Mathematical Physics does really produce some nice new mathematics. A recent case is the work by Stanislav Smirnov on conformal invariance and was honoured by award of a 2010 Fields M

This may seem a strange claim. You have a grant or your department has a position. You fail to attract the quality of candidates you hoped, particularly after some attrition as the better candidates accepted positions elsewhere. But, you should hire someone. Otherwise the grant will go to waste, you will lose the position, or at least everything will be delayed for a year. Voices (both internal and external) will say you should just hire someone. No! This can be a mistake. Sometimes there will be people (whether graduate students or faculty members) who will turn out to be a net drain on your resources (not just money but time, energy, and lab consumables) and relationships (harmonious research group or departmental). Be particularly wary of people who have a history of not getting along with others. You may wish you never hired them. Fortunately, I have never experienced this first hand. However, I have seen disasters happen. Sometimes for this reason I have postponed hiring someo

Previously I posted about just how hard it is to predict new phases of matter, particularly in a specific material. I more or less claimed this has never be done. I was incorrect. Ben Powell pointed out to me two significant counter examples: Bose Einstein Condensates (BECs) and Topological Insulators. Both represent monumental and profound achievements. But, how impressed (or smug) should we be? After all, both these examples involve non-interacting particles , or at least particles just interacting at the mean-field level. Hence, this just further underscores to me just how hard it is to actually predict truly emergent phenomena, involving "non-trivial" quantum many-body physics.

I just encountered this simple and helpful question in the context of how and what we teach students. If we teach science as a static body of knowledge (particularly facts, theories, and techniques) we are acting as if science is a noun. By contrast, if we focus on teaching students to think scientifically and critically, to solve problems, and to ask questions, then we act as if science is a verb.

It is just the voltage from a battery (electrochemical cell)! Soon I will give a lecture introducing the free energy in a thermodynamics course. It is an incredibly important concept. We try and get the students to learn the course mantra, "the Gibbs free energy must be minimised (at constant temperature and pressure)". Two significant points for students to learn about the Gibbs free energy -it is directly measurable -where many of the tabulated values for delta G for chemical reactions come from The voltage of an electrochemical cell V (in Volts) is related to delta G (in Joules per mole) by V = -delta G/n F where F = Faraday constant = 96485 J/mol/V and n=number of electrons transferred at the electrode. In my lecture I will show two really nice videos from Chemistry Comes Alive on the electrolysis of water.  I particularly like how the second video (below) shows how the ratio of the volume of the gas produced at the cathode (hydrogen) is twice that produced a

Seth Olsen and I have just finished a paper  An Effective Hamiltonian for Symmetric Diarylmethanes from a Series of Analogous Quantum Chemical Models . Finding simple effective Hamiltonians for classes of complex chemical systems is not easy. Justifying them from quantum chemistry is even harder. We consider a family of organic dye molecules related to Michler's hydrol blue, including auramine-O and malachite green.  These molecules are increasingly being used as sensors of the local environment in biomolecules. The three lowest singlet states can be described by a 3x3 matrix Hamiltonian whose parameters vary across the family of the dyes. This variation appears to be correlated with an empirical parameter [Brown-Okamoto] used to characterise the effect of substituents. There is also a subtle and interesting variation in the character of the diabatic states as one traverses the family of dyes.

At last weeks cake meeting (condensed matter group meeting/journal club) I gave a talk about an interesting recent paper Incommensurate correlations in the anisotropic triangular Heisenberg lattice by Andreas Weichselbaum and Steve White. The model is the spin-1/2 Heisenberg model on the anisotropic triangular lattice with antiferromagnetic interactions. By varying the relative strength (or spatial anisotropy) of the interactions the model can interpolate between the square lattice, triangular lattice, and weakly coupled chains (with a frustrated interchain interaction J'). Back in 1998 I argued that this is the minimal model for the spin excitations in the Mott insulating phase of a family of organic superconductors. I have since written 7 papers on the model. A recent review article looks at the model in light of theoretical and experimental studies, which reveal its richness including the possibility of spin liquid ground states. Weichselbaum and White perform extensive D