Condensed concepts

At the end of 2009 I posted the most viewed posts on this blog. Here is the list from 2010. The number of pageviews are from Google Analytics and are an under-estimate. 1.  Nature publishes 17 parameter fit to 20 data points    2,900 pageviews 2.  There is no perfect Ph.D project    1,000 3. A Ph.D without scholarship ?   310 4. Breakdown of the Born-Oppenheimer approximation 300 5. Beware of curve fitting  280 6.  OPV cell efficiency is an emergent property   230 7. Artificial photosynthesis 224 8. Want ad: measure for quantum frustration  180 9.  100 most influential living British scientists    176 10.  Ph.D without knowledge   154

I have just started reading a beautiful little book by  Denis Noble  entitled  The Music of Life: Biology beyond genes . It highlights the limitations of a reductionistic approach to biology and the value of an emergent perspective, as in systems biology. Some of the material is in an earlier article.  He considers the following two paragraphs which both discuss the role of genes in an organism: Now they swarm in huge colonies, safe inside gigantic lumbering robots, sealed off from the outside world, communicating with it by tortuous indirect routes, manipulating it by remote control. They are in you and me; they created us, body and mind; and their preservation is the ultimate rationale for our existence. Now they are trapped in huge colonies, locked inside highly intelligent beings, moulded by the outside world, communicating with it by complex processes, through which, blindly, as if by magic, function emerges.  They are in you and me; we are the system that

David Griffiths taught at Reed College   for 30 years (a rather unique undergraduate institution in Portland, Oregon) and is author of several widely used textbooks. He has a provocative piece  Illuminating physics for students  in Physics World. [I first encountered the article on the noticeboard outside the Mott lecture theatre at Bristol University]. The summary is: He says that the role of a physics teacher should be to illuminate the subject's intrinsic interest, beauty and power – and warns that attempts to make it more marketable using gimmicks, false advertising or dilution are bound to be counterproductive It is worth reading in full. But here are a few extracts to picque your interest: What we have on offer is nothing less than an explanation of how matter behaves on the most fundamental level. It is a story that is magnificent (by good fortune or divine benevolence), coherent (at least that is the goal), plausible (though far from obvious) and true (that is the most re

There is a nice article by Michael S. Fuhrer in Physics about tuning the Fermi surface area in graphene and using it to observe qualitatively different temperature dependence of the resistivity due to electron-phonon scattering.

In the past this has been an issue. But, last trip at Radio Shack I bought one of these Virgin Broadband2Go  devices. The rates have now decreased so that on this trip I am paying just $40 for a month of unlimited access. The coverage is pretty good although it is occasionally slow at remoter locations.

There is a good Opinion piece in the November Scientific American, Fudge Factor: a look at Harvard science fraud case  by Scott O. Lillienfeld. He discusses the problem of distinguishing intentional scientific fraud from confirmation bias , the tendency we have as scientists to selectively interpret data in order to confirm our own theories. This is a good reminder that the easiest person to fool is yourself.

The pyrochlore lattice consists of a three-dimensional network of corner sharing tetrahedra. In a number of transition metal oxides the metal ions are located on a pyrochlore lattice. The ground state of the antiferromagnetic Heisenberg model on a pyrochlore lattice is a gapped spin liquid (see this PRB by Canals and Lacroix). The ground state consists of weakly coupled RVB (resonating valence bond) states on each tetrahedra. The conditions necessary for deconfined spinons has been explored in Klein type models on the pyrochlore lattice. The material KOs2O6 has a pyrochlore structure and was discovered  to be superconducting with a transition temperature of about 10 K. Originally it was thought  (and hoped) that the superconductivity might be intimately connected to RVB physics. However, it now seems that the superconductivity is not unconventional. It can be explained in terms of strong coupling electron-phonon interaction which arises because of anharmonic phonons associated

Hydrogen bonds are ubiquitous in biomolecules and a key to understanding their functionality. This was first appreciated by Pauling and exploited by Watson and Crick to decode the structure of DNA. It is also the origin of the unique and amazing properties of water. There is a helpful review article Hydrogen bonding in the solid state by Steiner. Here are a few things I learnt. Energies vary by 2 orders of magnitude, 0.2-40 kcal/mol [10 meV to 2 eV]. This spans the energy range from van der Waals to covalent and ionic bonds. The amount of electrostatic, covalent, and dispersion character of the bond varies within this range. For O-H ... O bonds the shift in frequency of the O-H bond correlates with the distance between the oxygen atoms. The O-H distance is correlated with the O..H distance. All hydrogen bonds can be considered as incipient hydrogen transfer reactions. Hydrogen bonds exhibit some unexplained isotope effects. Simple zero-point motion arguments suggest that deuter

The book Quantum mechanics and path integrals by Feynman and Hibbs is a classic that was out of print and an old hardback edition is currently going for $799! The good news is the book has been reprinted by Dover and you can now buy a copy on Amazon for only US$12. My copy arrived today.

I quite like the new journal Physics from APS because it has nice overview articles which are particularly good for learning something about topics outside ones expertise. There is a good article Can we test inflationary expansion of the early universe? It explains the basic ideas behind inflation [including the broken symmetry associated with the inflaton field], why it is necessary in standard big bang cosmology, to solve the "horizon" and "flatness" problems, and the hope of actually finding more than circumstantial evidence for inflation.

The Linus Pauling archive at Oregon State University has lots of nice resources including original manuscripts, videos, quotes, and photos. Above is a photo of Heitler and London with Pauling's wife.

This comic in the Pearls before Swine series appeared in the newspaper today. I thank my family for bringing it to my attention. The previous days cartoon was about Australia and alternative energy.

I am trying to get a better understanding of resonant raman scattering as a probe of properties of excited states of organic molecules. The figure below [taken from a JACS paper ] shows how in the Green Flourescent Protein one sees an enhanced coupling to  vibrations [blue curve in lower panel]. There is a nice site on Resonant Raman Theory  set up by Trevor Dines (University of Dundee). It emphasizes that in the Born-Oppenheimer approximation one only sees a significant signal when the excited state involves a displacement of the vibrational co-ordinate. This raises a question about whether in a completely symmetric molecule one can have a resonant Raman signal due to effects that go beyond Born Oppenheimer.

This was the key question in Watergate scandal. But, this post is actually about what a Ph.D student should know and when they should know it. Here are a few different answers I have heard: When the student knows more about the topic than their advisor/supervisor they are ready to submit their thesis. At the end of your Ph.D you should know more about the topic than anyone else in the world. The student should know more about the project than their advisor by the time they do their comprehensive exam (a few years into a US Ph.D).

Valence bond theory provides an intuitive picture of not just chemical bonding but bond breaking and making. For a reaction ab + c -> ac + b, one can write done the energy of the total system in terms of pairwise exchange J and coulomb integrals Q. This can be used to produce semi-empirical potential energy surfaces and/or diabatic states and coupling between them. This is at the heart of the treatment of coupled electron-proton transfer by Hammes-Schiffer and collaborators, discussed in previous posts. I struggled a bit to find the background of this. It goes back to London-Eyring-Polanyi-Saito (LEPS). A nice summary is the paragraph below taken from a paper by Kim, Truhlar, and Kreevoy.  It provides a way to parametrise the Qs and Js in terms of empirical Morse potentials for the constituent molecules. At the transition state the gap to the next excited state is related to a singlet-triplet gap, a point emphasized by Shaik and collaborators. More background is in material  in the

In many biochemical processes electron transfer and proton transfer are important and have featured in many of my posts. However, another process that is important and fascinating is coupled electron proton transfer. This is the process discussed in a previous post about the enzyme soybean lipoxygenase. Sometimes this can be viewed as a hydrogen atom transfer, but in some cases the electron and proton start or end at different sites on the donor or acceptor molecule. Describing this process (even for the H-atom transfer case) theoretically has proven to be a challenge which has recently attracted significant attention. A recent review is by Sharon Hammes-Schiffer. Basic questions that arise include: What is the reaction co-ordinate? Is it the proton (or H-atom) position? Or the solvent (or heavy atoms) configuration? Or both? What is the role of proton tunneling? Are the dynamics of the electron and the proton both adiabatic or non-adiabatic?  Under what conditions is the elec

This attempts to answer questions raised in a previous post. Here is one point of view. Tunneling is always present and as one lowers the temperature (or increases the coupling to the environment) one just has a crossover from transitions dominated by activation over the barrier to tunneling under the barrier. Instantons [or the "bounce solution" which is a solution to the classical equations of motion in an inverted potential] are just a convenient calculational machinery which arises when evaluating a path integral approximately by finding saddle points. There is always a contribution from the trivial solution corresponding to the top of the barrier. Quadratic fluctuations about this saddle point give a "prefactor" which includes quantum corrections due to tunneling and reflection. Below the crossover temperature T0 this first saddle point becomes unstable and there is  a second saddle point, which is the instanton solution. I thank Eli Pollak for sharing his t

Yesterday I had a really helpful discussion with Judith Klinman about the question of quantum tunneling of hydrogen in enzymes. [An accessible summary of her point of view is a recent Perspective with Zachary Nagel in Nature Chemical Biology ]. Here are a few points I came to a better appreciation of: There are a number of enzymes (e.g. soybean lipoxygenase) which have very small activation energies (Ea~0-2 kcal/mol ~ 100 meV) for hydrogen atom transfers. (n.b. this is a coupled electron and proton transfer). They exhibit kinetic isotope effects which are very large in magnitude (~100) weakly temperature dependent (difference in Ea for H and D ~ 1 kcal/mol ~ 50 meV) change their temperature dependence significantly with mutation [In the figure above the hydrogen atom (black in the centre of the figure) is transfered to the oxygen atom (red, to the left of the H atom). Mutations correspond to substituting the amino acids Ile553 and/or Leu754.] The key physics is the following

As I have posted previously finding a realistic Heisenberg spin model Hamiltonian which has a spin liquid ground state has proven to be difficult. The model on the Kagome lattice was thought to be a prime candidate for many years, partly because the classical model has an infinite number of degenerate ground states. However, a few years ago Rajiv Singh  and David Huse performed a series expansion study which suggested that the ground state was actually a valence bond crystal with a unit cell of 36 spins. In the picture below the blue lines represent spin singlets, and H, P, and E, denote Hexagons, Pinwheels, and Empty triangles respectively. This result was confirmed by my UQ colleagues Glen Evenbly and Guifre Vidal using a completely different numerical method based on entanglement renormalisation. However, there are new numerical results using DMRG which appeared on the arXiv this week, by Yan, Huse, and White . They find a spin liquid ground state, with a gap to both singlet an

Here are the slides for a talk I will give in the physics department at Berkeley this afternoon. Some of what I will talk about concerns a paper with Michael Smith, which appeared online in PRB this week,  Fermi surface of underdoped cuprate superconductors from interlayer magnetoresistance: Closed pockets versus open arcs

An important question came up in the seminar I gave today. It concerns something I have been confused about for quite a while and I was encouraged that some of the audience got animated about it. Consider the problem of quantum tunneling out of the potential minimum on the left in the Figure below If one considers a path integral approach than one says that tunneling occurs when there is an "instanton" solution (i.e., a non-trivial solution) to the classical equations of motion in imaginary time with a period determined by the temperature. This only occurs when the temperature is less than  which is defined by curvature of the top of the potential barrier. At temperatures above this there is only one solution to the classical equations of motion, the trivial one x(tau)=x_b, corresponding to the minima of the inverted potential. One can then calculate the quantum fluctuations about this minimum, at the Gaussian level. This gives a total decay rate  which is well defined, pr

On the Condensed Matter Physics Journal Club Patrick Lee has a nice summary of recent work concerning very subtle problems concerning large N expansions of gauge theories with non-Fermi liquid ground state.

I am giving a seminar, Limited role of quantum dynamics in biomolecular function in the Chemistry department at Berkeley this afternoon.

On the plane from Brisbane to LA I watched some of The Trials of J. Robert Oppenheimer  [you can also watch it online] which gave an excellent portrayal (using exact testimony) of the trial and background that led to Oppenheimer losing his security clearance. It also had some excellent background on Oppenheimer's youth and time as a young faculty member at Berkeley. [Mental health issues feature somewhat]. Other physicists who were "tarred and feathered" in the McCarthy era were David Bohm [who was basically fired by Princeton University because he refused to testify] and Frank Oppenheimer [younger brother of J. Robert] who was forced to resign from a faculty position at University of Minnesota. He later founded the Exploratorium in San Francisco. Last year Physics Today published a fascinating article by J.D. Jackson [of electrodynamics textbook fame], Panosky agonistes: The 1950 loyalty oath at Berkeley , which chronicles more problems from that era. [Coincidentall

This follows up on a previous post about measurements of the rate at which electron transfer occurs in a photosynthetic protein. I noted several deviations of the experimental results from what is predicted by Marcus-Hush electron transfer theory. This is not necessarily surprising because one is not in quite in the right parameter regime. In principle [at least to me] this should be described by a spin boson model which has the Hamiltonian and the spectral density contains all the relevant information about the protein dynamics, So the question I have is: if one has the correct parameters and spectral density can one actually describe all the experiments? Below is the spectral density found by Parson and Warshel in molecular dynamics simulations.

Frank Fenner (1914-2010), one of Australia's most distinguished scientists died this week. He was an immunologist who is best known for leading the world-wide eradication of the smallpox virus and for introducing myxomatosis to stop the rabbit plague in Australia. The latter led to an interesting study in evolution and genetics, described in a recent Cambridge University Press book, Myxomatosis he recently co-authored (in his nineties!). He was also author of a classic text, Medical Virology , first published in 1970, now in its fourth edition. I partly know of Fenner because my father knew him, through working at the John Curtin School of Medical Research (JCSMR) at the ANU in Canberra. The prolific Fenner also wrote an exhaustive history of the JCSMR . [Three Nobel Prizes have been awarded for work done in the JCSMR]. What has immunology got to do with emergence and physics? I have always been fascinated by the existence of the Reviews of Modern Physics article, Immunolo

This morning I was at home struggling with some Bessel function identities. I really wanted to look at the copy of Abramowitz and Stegun: Handbook of Mathematical Functions   that I have in my office but, I discovered that the complete text  is  available online. I know Wolfram Mathworld can be useful but it does not have the same level of detail as A&S.

While on the subject of money .... Research income is a good measure of .... research income, and not much more. Consider the following: Obituaries and Nobel Prize citations do not mention how much research income someone received. Grants are a means to an end, not an end in themselves. Sometimes they are necessary to do good research, either to hire people to do the work, or to purchase or build equipment. But, grants are not a sufficient condition to do good research. Many significant discoveries, especially experimental ones, come from people doing "tabletop" science with small budgets. The discovery of graphene is a significant example. A distinguished elderly colleague expressed his disappointment to me that his department newsletter was always trumpeting the grants that people got. He asked, "Why aren't there any articles about what discoveries they make with the money?" I find it easier to get grants than to do really significant and original re

Phil Anderson finishes his classic More is Different article from Science in 1972 with the cheeky and amusing conclusion: Marx said that "Quantitative differences become qualitative ones." But a dialogue in Paris from the 1920’s sums it up even more clearly: FITZGERALD: The rich are different from us. HEMMINGWAY: Yes, they have more money. I often wondered what this was all about. It is worth reading Quote/Counterquote which explains that the dialogue never actually happened.

I was asked to publicise a position in Condensed Matter Theory that has been advertised at University of Melbourne. I am always keen to see more Condensed Matter Theory in Australia! All the details are here. I believe that  a pplications will still be received for a week or two after the advertised closing date (30 November), but after the closing date should also be submitted directly to Professor  Les Allen  or Professor Lloyd Hollenberg . 

Previously I posted about the anisotropic scattering scattering rate in the optimally doped to overdoped cuprates. Both Angle-Dependent Magnetoresistance (ADMR) and Angle-Resolved PhotoEmission Spectroscopy (ARPES) suggest that it  has a d-wave variation around the Fermi surface and that it has a "marginal Fermi liquid" dependence on energy and temperature. ADMR measurements found that the strength of this scattering scales with the transition temperature, and hence increases as one moves towards optimal doping. This raises three important questions: 1. What is the physical origin of this scattering [and the associated self energy]?  Superconducting, D-density wave, antiferromagnetic, or gauge fluctuations? 2. Is this scattering relevant to the superconductivity? i.e., do the same interactions produce the superconductivity and/or do these interactions make the metallic state unstable to superconductivity? 3. Is this relevant to formation of the pseudogap in the underd

If you don't think mental health problems will strike anyone you know it is worth reading this column by Kathleen Noonan which appeared in our local newspaper a few weeks back.

Are you preparing a talk? There was a provocative article What's Wrong with Those Talks by David Mermin, published by Physics Today back in 1992. It is worth digesting, even if you do not agree with it. He does practice what he preaches. I once remember him reading a referee report from PRL once in a talk on quasi-crystals. (He claimed the referee was Linus Pauling). One of his main points is we need to be very modest about what we hope we can achieve in a talk, particularly a colloquium. People will rarely complain if the talk is too basic and they understand most of it. The primary purpose is to help people understand why you thought the project was so interesting that you embarked on it.

The Big Bang Theory seems to be getting better all the time, both in terms of humour and scientific content. This weekend we watched The Einstein Approximation (Season 3, Episode 14). Sheldon is obsessed with understanding how the electrons in graphene are "massless". His brain is stuck and so he seeks out a mind numbing job that he hopes will remove this mental block [inspired by Einstein working in the Swiss patent office, hence the title]. Eventually, he realises the problem was that he was thinking of the electrons as particles rather than as waves diffracted off the hexagonal lattice formed by the carbon nuclei. The Big Blog Theory has a good discussion about graphene. I could not find a clip on YouTube of the relevant scenes where the physics is discussed. Let me know if you know of one. A synopsis is here. Finally, I wonder if this episode helped sway the Nobel Committee?

When I was in Bristol a few months ago Nigel Hussey gave me a proof copy of a nice paper that has just appeared in the New Journal of Physics, A detailed de Haas–van Alphen effect study of the overdoped cuprate Tl2Ba2CuO6+δ by P M C Rourke, A F Bangura, T M Benseman, M Matusiak, J R Cooper, A Carrington and N E Hussey It is part of  a  FOCUS ON FERMIOLOGY OF THE CUPRATES Here are a few things I found particularly interesting and significant about the paper. 1. It is beautiful data! 2. Estimating the actual doping level and "band filling" in cuprates is a notoriously difficult problem. But, measuring the dHvA oscillation frequency gives a very accurate measure of the Fermi surface area (via Onsager's relation). Luttingers theorem then gives the doping level. [see equation 15 in the paper]. 3. The intralayer Fermi surface and anisotropy of the interlayer hopping determined are consistent with independent determinations from Angle-Dependent MagnetoResistance (ADMR) per

At the physics colloquium today recent experimental data was highlighted that has been interpreted as evidence for dark matter. I thought this looked familiar and recalled I wrote an earlier blog post Trust but verify , urging caution. If one does a search on the arxiv with the words "dark matter AND positron AND FERMI" one finds more than one hundred papers, many proposing exotic theoretical scenarios. It will be interesting to see in a decade whether all this theoretical hyper-activity was justified.

Seth Olsen and I had a nice discussion this week about Monkhorst's paper, Chemical physics without the Born-Oppenheimer approximation: The molecular coupled-cluster method, who emphasizes that corrections to the Born-Oppenheimer approximation can be as large as ten per cent. This raises important questions about the dreams and dogmas of computational quantum chemists. The goal is to calculate energies (especially heats of reaction, binding energies, and activation energies) to "chemical accuracy" which is of the order of kBT, about 1 kcal/mol or 0.03 eV. This is much better than most methods can do.  The claim of computational chemists is that it just a matter of more computational power. In principle, if one uses a large enough basis set (for the atomic orbitals) and a sophisticated enough treatment of the electronic correlations, then one will converge on the correct answer. However, this is all done assuming the Born-Oppenheimer approximation and "clamped"

Since I am marking many first year exams here are a few tips. They are all basic but it is amazing and discouraging how few students do the following: Clearly state any assumptions you make. Don't just write down equations. e.g, explicitly state, "Because of the Newtons second law ..." or "we neglect transfer of heat to the environment." Keep track of units at each stage of the calculation. Don't just add them in at the end. All physical quantities DO have units. If you make a mistake it will often show up in getting the wrong units. Clearly state the answer you obtain. Maybe draw a box around it. e.g, "The change in entropy of the gas is 9.3 J/K". Try and be neat and set out your work clearly. If you make a mess just cross out the whole section and rewrite it. I see many students exam papers where I really have no idea what the student is doing. It is just a random collection of scribbles, equations, and numbers.... Think about the answe

Telluride Science Research Center runs some great programs each northern summer, mostly with a chemistry orientation. One I would recommend, especially to physics postdocs and graduate students who want to see how quantum and stat. mech.  is relevant to chemistry is the Telluride School of Theoretical Chemistry which will run July 10-16 next year.

Understanding how photosynthetic systems convert photons into separated charge is of fundamental scientific interest and relevant to the desire to develop efficient photovoltaic cells. Systematic studies could also provide a laboratory to test theories of quantum dynamics in complex environments, for reasons I will try and justify below. When I was at U. Washington earlier this year Bill Parson brought to my attention two very nice papers from the group of Neal Woodbury at Arizona State. Protein Dynamics Control the Kinetics of Initial Electron Transfer in Photosynthesis Unusual Temperature Dependence of Photosynthetic Electron Transfer due to Protein Dynamics The Figures below are taken from the latter paper. I think the basic processes involved here are  P + H_A + photon ->  P* + H_A -> P+ + H_A- where a photon is absorbed by the P, producing the excited state P* which then decays non-radiatively by transfer of an electron to a neighbouring molecule H_A. The graphs below

This beautiful picture is on the cover of A Chemist's guide to Valence Bond Theory by Shaik and Hiberty. It summarises the main idea in a paper, The Twin-Excited State as a Probe for the Transition State in Concerted Unimolecular Reactions: The Semibullvalene Rearrangement . It illustrates how the use of diabatic states (K1 and K2) based on chemical intuition can lead to adiabatic potential energy surfaces with complex structure. Furthermore, it illustrates the notion of an excited state (K1 - K2) which is a "twin state" to the ground state, K1+K2. The relevant vibrational frequency is higher in the excited state than in the ground state. An earlier post discussed the analogous picture for benzene.

It is great how interesting physics still gets a mention in The Big Bang Theory. Last night my family watched The Maternal Congruence (Season 3, Episode 11). Leonard's mother [Beverley] comes for a visit and on the ride from the airport it turns out she and Sheldon have been in correspondence, unbeknown to Leonard. Here is the scene and dialogue I was delighted about: Beverley: Yes, dear. Mommy’s proud. I’ve been meaning to thank you for your notes on my paper disproving quantum brain dynamic theory. Sheldon: My pleasure. For a non-physicist, you have a remarkable grasp of how electric dipoles in the brain’s water molecules could not possibly form a Bose condensate. Leonard: Wait, wait, wait. When did you send my mom notes on a paper? On the Big Blog Theory , David Saltzberg [the UCLA Physics Professor who is a consultant to the show] discusses the "quantum dynamic brain theory" at length and mentions Roger Penrose and says: Quantum Brain Dynamicists entertain

Previously I have written several posts about charge transport in organic materials for plastic electronic and photovoltaic devices. This week I looked over two recent articles in Accounts of Chemical Research that discuss progress at the very ambitious task of using computer simulations to calculate/predict properties of real disordered molecular materials beginning with DFT calculations of specific molecules. I was pleased to see that Marcus-Hush electron transfer theory plays a central role in both papers, Electronic Properties of Disordered Organic Semiconductors via QM/MM Simulations   (from the group of Troy Van Voorhis at MIT).  Modeling Charge Transport in Organic Photovoltaic Materials   (from Jenny Nelson's group at Imperial College London). I have several questions and concerns about the latter paper. The authors do a rather sophisticated simulation of a time of flight experiment where they put a charge accumulation on one side of the sample, apply an electric field, a

This morning I started to read a fascinating paper by Henrik Monkhorst,  Chemical physics without the Born-Oppenheimer approximation: The molecular coupled-cluster method . It begins discussing a controversy I did not know about which  Later there is a fascinating discussion of the coupled cluster (CC) method. Note the superlatives in the last sentence.

My son and I just watched a great episode of The Big Bang Theory. It is called the Gorilla Experiment and in it Penny decides that she wants to learn some physics so she can talk to Leonard about his experiment testing the Aharonov-Bohm effect with electric fields. She begs Sheldon to teach her leading to this amusing scene.

The Diabatic Picture of Electron Transfer, Reaction Barriers, and Molecular Dynamics .  This is the review article that we will be discussing at the cake meeting tomorrow.  It is clear and helpful. Adiabatic states are the eigenstates of the electronic Schrodinger equation in the Born-Oppenheimer approximation. There are several problems with them -they can vary significantly in character with changes in nuclear geometry [in particular they can be singular near conical intersections] -they are not a good starting point for describing non-adiabatic processes such as transitions between potential energy surface -they are hard to connect to chemical intuitive concepts such as valence bond and ionic states Diabatic states  overcome some of these problems. They do not vary significantly with changes in nuclear geometry. However, determining them is non-trivial. The article describes these issues.

It was nice having Peter Wolfle visit UQ the past few days and give a colloquium style talk on the Kondo effect. A nice accessible article which discusses the basics of the Kondo effect and how it occurs in quantum dots, carbon nanotubes, and "quantum corrals" is this 2001 Physics World   article   by Leo Kouwenhoven and Leonid Glazman. In his talk Peter gave a nice discussion of the problem of the Kondo lattice (a lattice of localised spins interacting with a band of itinerant electrons). There is still an open question (originally posed by Doniach) of what happens in between the two limits of weak coupling (one expects magnetic ordering of the spins due to the RKKY interaction mediated by the itinerant electrons) and strong coupling (where the individual spins are Kondo screened by the itinerant electrons). Is there a quantum critical point? Does a non-Fermi liquid occur near it? All of this is discussed in a nice review article Peter co-authored,  Fermi liquid instabil