Condensed concepts

Chemists and physicists tend to talk different languages, including when discussing the same thing. One important parallel is the common concept of the molecular orbitals in a molecule and the energy bands in a crystal. Specifically, the Huckel method to describe electronic properties of conjugated organic molecules is identical to the tight-binding method in solid state physics. Yet these important parallels seem to rarely be pointed out in textbooks. [One exception is a brief mention in Walter Harrison's Electronic Structure and the Properties of Solids ]. Recently when I have taught solid state I have pointed out the connection and sometimes worked through the nice treatment of Huckel theory in  chapter 8 of the classic book  Coulson's Valence by Roy McWeeny. Besides showing the molecule-solid connection this can illustrate a few useful things including: How Bloch's theorem works in a finite system. How energy bands emerge in the thermodynamic limit (see above).

Here are a few reasons why you should work hard at picking the title of your papers. * They are one of your only chances to get people interested in actually reading your paper. * When people are reviewing your CV many will just look at the title of your papers, as well as the journal they are published in. Interesting, diverse, informative, and understandable titles create a good impression. Boring, repetitive, and highly technical titles create a bad impression. Make sure all your papers don't have essentially the same title! * They are fun. What I generally do is to write down as many as five possible titles for the paper and then consider their relative merits and discuss them with co-authors and colleagues. This helps sharpen the title. If you want to see some good examples look over the publication list of Roald Hoffmann. Here are just a few from the past decade: A Molecular Perspective on Lithium-Ammonia Solutions A Little Bit of Lithium Does a Lot for Hydrogen A

In German ansatz means "educated guess". For quantum many-body physics two dimensions is very different to one. In the last two days I have heard talks from graduate students of my UQ colleague Guifre Vidal [who is moving to Perimeter Institute] about using tensor network states to describe quantum many-body states. A nice statement of the problem and the approach is in a Physics Viewpoint by Subir Sachdev. It is first important to appreciate that Tensor Network states are essentially a convenient way to write a variational wave function  for the ground state of a quantum many-body system. Like any such wave function they will only be useful/accurate/reliable if this choice is specific enough to capture the essential physics and/or if it is general enough to describe any state. Writing down a good variational wave function is an art worthy of a Nobel Prize (BCS, Laughlin, Anderson,...). The one-dimensional version of a Tensor Network is a matrix product state (MPS).

What is the ground state of the two-dimensional Hubbard model?  What "causes" high-Tc superconductivity: is it antiferromagnetic fluctuations, condensation of "pre-formed pairs", or proximity to the quantum critical point of a d-density wave state, or something else? I read a nice paper today d-Mott phases in One and Two Dimensions by Andreas Lauchli, Carsten Honerkamp, and Maurice Rice, which highlights to me why it is so hard to answer the above questions. But it does gives some clues about the essential physics. Another paper by Maurice Rice, Resonating Valence Bond Theory - The Approach from Weak Coupling , puts this work in a broader context. They start with a Hubbard model in the weak coupling limit. Momentum space is divided up into a few "patches" and one performs renormalisation on a reduced Hamiltonian defined on these patches. New effective interactions arise as a result of this renormalisation. There is a mutual reinforcement of antiferro

This morning I read a really interesting paper  Biradicaloid and Polyenic Character of Quinoidal Oligothiophenes Revealed by the Presence of a Low-Lying Double-Exciton State  by an Italian group. These molecules are of particular interest because of their possible applications in photonics (non-linear optics, photovoltaic cells). A biradical is a molecule which has two spatially separated unpaired (or weakly paired) spins. One of the main results of the paper is that as one increases the number of thiophene groups in the middle of the molecule the energy gap to the lowest optically active state decreases, the amount of biradical character of the ground state increases and there is a lower lying "dark" state which has "double exciton" character, analogous to the 2A_g state in polyenes. I found the paper particularly interesting because I believe it should be possible to make a connection with the valence bond description of the excited states in polyenes. Below a

Over the years I have made many visits to different institutions, hosted many visitors, and met with many visitors at my home institution. These interactions have varied greatly in their value and success. Some have been incredibly interesting and fruitful. Indeed, many of my best new research ideas have had their beginnings in such discussions. On the other hand, some of the meetings seem to be rather "slow" and a waste of time. So here are a few thoughts on making the most of these meetings, from both sides. The better prepared you are the greater the chance of a productive meeting. You want to find some common ground and common interest , i.e., something they have done you need to know about or something you have done you would like them to know about. A minimum preparation is to scan the titles of the publications of the person you are meeting with. This will hopefully help find some common interests. Perhaps pick one paper that you would most like to ask them about.

How do quantum states in organic molecules couple to their environment (e.g., a solvent and/or protein)? Is the dynamics of excited states quantum or classical or something in between? These questions are not just of fundamental scientific interest. Dye molecules are now widely used as a means to monitor biomolecules and nanoconfined water. A nice way to investigate the above questions experimentally is with ultrafast laser spectroscopy.  For example, to optically excite a molecule and monitor the emission (fluorescence) in real time. A nice combined theoretical/experimental study is in the paper Femtosecond fluorescence upconversion studies of barrierless bond twisting of auramine in solution  by van der Meer, Zhang, and M. Glasbeek. Upon photoexcitation the auramine  dye molecule (below) is believed to undergo twisting of the phenyl (benzene) rings on the left and right side of the central C=NH2 bridge. With increasing time [1-100 psec] this leads to redshift in the light emi

It is amazing but I never took an introductory Solid State Physics course, either as an undergraduate or as a graduate student! As an undergraduate at ANU, the course was an elective and so I avoided the course because my previous experience with the lecturer was he was incompetent. At Princeton I had to pass a "General exam" which covered solid state, nuclear, particle physics, and general relativity. I taught myself solid state physics by reading a library copy of Ziman's Principles of the Theory of Solids. I don't remember why I made this choice but I suspect it was partly that Solid State Physics by Ashcroft and Mermin seemed too big. I bought a second hand copy of Ashcroft and Mermin when I was a postdoc, but only started to really read it later. I think the way it progresses is brilliant. It works from the Drude model for metals to the Sommerfeld model, highlighting their successes and failures. Only then does it introduce crystal structures, motivated by th

On the arxiv Phil Anderson has a fascinating and informative article Personal History of my engagement with cuprate superconductivity, 1986-2010. Phil lecturing at Aspen in 2002

It is surprising to me how little theoretical attention has been given to this important question. The development of new high magnetic field facilities (50 to 100 Tesla) means that there will be a new generation of experimental data available. A few basic questions are the following: What is the magnetic field scale that is required to significantly modify the metallic state of a strongly correlated material? What is the relative importance of coupling of the field to orbital and spin degrees of freedom? Several interesting experiments that are relevant are: In heavy fermion metals a large magnetic field can suppress the effective mass enhancement. In an organic charge transfer salt a magnetic field can be used to drive the system from the metallic state into the Mott insulating state [see this PRL ]. In cuprates when one measures quantum oscillations is the role of the magnetic field just to suppress the superconducting state or does it also change the character of the metal

I have been working through a really nice paper  Using Valence Bond Theory to Understand Electronic Excited States: Application to the Hidden Excited State (21Ag) of C2nH2n+2 (n = 2−14) Polyenes  by Wu, Danovich, Shurki, and Shaik. [ An earlier pos t discusses some of the interesting photophysics associated with these molecules]. Here are just a few of the key ideas. First, the ground and low lying singlet (covalent) states are written in a Rumer basis set of valence bond states [these are not orthogonal]. See R1 and R2 below for C4H6 (butadiene)  There is only one parameter in the Hamiltonian, lambda, and this is extracted from DFT based calculations. The eigenstates and energies are shown on the right.  For larger molecules one needs to include a larger number of basis states (e.g., see below for the case of hexatriene). Simple energy correlation (Walsh) diagrams can then be used to understand how these states interact to produce the low lying excited states. This approach is com

I have written many posts about organometallic compounds, particularly those that are on interest in organic LEDs and photovoltaic cells. Almost all quantum chemical treatments are based on density functional theory (DFT). But given that both transition metals and the excited states of conjugated organic molecules are typically strongly correlated I wonder about how reliable this is. For a while I have been wondering about a valence bond theory description of these materials. A key effect that needs to be taken into account is that of "back-bonding" and the Dewar-Chatt-Duncanson model.  Hence, I was quite delighted when yesterday I stumbled across a 2007 Inorganic Chemistry paper, Valence Bond Approach to Metal-Ligand Bonding in the Dewar-Chatt-Duncanson Model. The VB wavefunctions they include A few key findings are: -the importance of including back-bonding -a VB wavefunction including back-bonding captures a lot of the correlation energy calculated by the CCSD(T) meth

I really like the "popular" book The Cambridge Guide to the Material World by Rodney Cotterill . It was out of print for a while but I was delighted to see that the published issued a new expanded edition in 2008. A scan of the chapter on  Crystal structures and symmetry  from the first edition  here.  I encourage my solid state physics students to read this as it has beautiful pictures and gives a nice non-mathematical introduction.

This week Jure Kokalj [currently a postdoc with me] gave a nice Quantum Sciences seminar at UQ where he discussed his Ph.D work with Peter Prelovsek about spinon deconfinement in frustrated quantum spin chains. [See this PRB ]. They used a new numerical method to calculate finite temperature dynamical correlation functions for the Heisenberg spin chain with next-nearest neighbour exchange interactions J'.  When J' is large enough a gap opens in the spin excitation spectrum and there is spontaneous breaking of the discrete lattice symmetry and long range dimer spin correlations. The low lying excitations are deconfined spinons (spin-1/2 domain walls). The new feature they found was that at non-zero temperature a large peak appears in the dynamical spin susceptibility at zero frequency and wave vector pi. I think the physics is that the finite temperature populates low lying triplet states which couple significantly to degenerate singlet excitations via spin flip operators. Th

Some people may attack me for this post. However, I actually think you can over-prepare for lectures. I notice that if I spend too much time preparing I start to go over the material too fast and also start to focus too much on little subtleties that I found interesting. In contrast, if I have to think through how to do a problem on the board in real time it slows me down to pace that is more appropriate for students who are encountering the problem for the first time. I am also told students like to see lecturers sweat it out!

Organic chemists are continually looking for new molecules which have large non-linear optical response, particularly in the near-infrared, motivated for the need for such materials in telecommunication systems. Cyanine dyes (see above) are one candidate material which have attracted a lot of attention, particularly by Seth Marder and collaborators. A key feature is that the more delocalised the electrons in the ground and excited states the larger the non-linear response. This occurs when these quantum states are superpositions of two valence bond structures with distinctly different charge distributions. [For a more detailed discussion see this forthcoming J. Chem. Phys. paper by Seth Olsen and I]. A recent development has been the synthesis and characterisation of a family of porphyrin dimer carbocations (shown above), as described in this Angewandte Chemie paper . The large optical response is perhaps surprising because it involves triple bonds near the central carbon cation [t

I have written posts previously about the dangers of perfectionism in research and teaching. Hence, there was a quote in a New York Times article about the nuclear accidents in Japan that got my attention. Nils J. Diaz, a nuclear engineer who led the United States  Nuclear Regulatory Commission  from 2003 to 2006 and had visited the Daiichi plant. Mr. Diaz suggested that the Japanese might have acted too slowly to prevent overheating, including procedures that might have required the venting of small amounts of steam and radiation, rather than risk a wholesale meltdown. Fear among Japanese regulators over public reaction to such small releases may have delayed plant operators from acting as quickly as they might have, he said — a problem arising in part from the country’s larger nuclear regulatory culture. “ They would rather wait and do things in a perfect manner instead of doing it as good as it needs to be now ,” Mr. Diaz said. “And this search for perfection has often led to p

On Friday at UQ we had a very stimulating colloquium A new view on quantum gravity and the origin of the Universe  by Bei-Lok Hu (University of Maryland). A key aspect of this new view is that general relativity and space time should be viewed as emergent phenomena (more below). There are six main points of experimental evidence in cosmology: 1. Hubble expansion of the universe. 2. Cosmic microwave background radiation (isotropy and uniformity). 3. Element abundance (+ nucleosynthesis) 4. Ratio of baryon/photon (entropy content of universe) 5. Structure: galaxy, clusters,...   hierarchy of scales 6. Cosmological constant ~ 0,  vacuum energy density The fact that the night sky is dark implies a finite universe, and expansion or a hierarichial structure  ( Olber's paradox ). Hu contrasted Two views of quantum gravity. 1. Bottom up view Quantum gravity = quantisation of general relativity This is the more traditional view and has been dominant. 2. Top down view Grav

Starting to teach/lecture is a daunting and often overwhelming task. Many a young faculty member has seen their research program grind to a halt as they embark on teaching their first course. Furthermore, it can be a very stressful rather than an enjoyable experience. Here are a few things I wish someone had told me or if they did that I had listened and taken to heart! Your first lectures don't have to be perfect! Limit how many hours you spend on preparation. You can always polish lectures the second and third time you give the course. Your goal should be to just survive. Don't under-estimate how little students will learn or how little they know! Most of the new insights and subtleties you are getting as you prepare the lectures will be lost on the students. Just because they had covered a subject in a pre-requisite course does not all mean that they actually know and understand that material. Technology should be your friend not a slave master. Blackboard, TurnItin, c

 I have been trying to learn some of the basics of infra-red spectroscopy of organic compounds and found this site  for an organic chemistry lab course at University of Missouri helpful. Why should a quantum many-body theorist care? Well, it turns out that the frequency, intensity, and lineshape associated with particular chemical bonds are quite sensitive to the type of bonding involved and the local environment of the bond, including valence states, orbital hybridisation, charge distribution, and the presence of resonating valence bond structures. Previously I posted about the vibrational frequencies of O-H stretches associated with hydrogen bonding. The Table below, taken from here illustrates and summarises some of these effects. But maybe someone could recommend a good book or review article. I struggled to find one online... Table 1. A summary of the principle infrared bands and their assignments. R is an aliphatic group.

The movie  The Inside Job  is an Academy Award winning documentary which considers the origins of the Global Financial Crisis (GFC). It particularly focuses on conflicts of interest, including of economists in universities who write academic papers and books, sympathetic to vested interests, but do not reveal in those publications that they have received large consulting fees from those interests. Last year, the director of the movie, Charles Ferguson, wrote a compelling and challenging article in the Chronicle of Higher Education,  Larry Summers and the Subversion of Economics , which documents these conflicts of interest, and how they represent a serious problem for the university and government. It is worth reading a post on the Creative Destruction blog . One economics faculty member from Gettysburg College writes: But are these economists corrupt? Have they been peddling the economic ideology of deregulated financial markets knowing that it is a load of crap? I don't kno

There are great videos on Youtube that can be used for teaching and to liven up seminars. I found the method described here works fine. I only post this because I seem to recall last time I did it was more involved..

This morning I read a paper,  Estimating the hydrogen bond energy , which is one of the most downloaded papers from the Journal of Physical Chemistry. It considers a relatively simple criteria (going back to Davidson in 1967) for estimating a bond energy in terms of the two-center shared electron number, sigma. It also connects to the natural bond orbital approach of Weinhold where a hydrogen bond D-H...A is viewed as an interaction between the unoccupied anti-bonding orbital of the DH bond and the the occupied nonbonded natural orbital (e.g. lone pair) of the acceptor atom A. The authors perform quantum chemistry [most DFT with B2LYP-D] calculations for hundreds of H bonds. They find correlations between sigma and the bond energy, the H...A length, the shift in the D-H stretch frequency. There were a couple of things I found strange about the paper. 1. Many quantities are calculated with quantum chemistry at different levels of theory and compared. But, I could never find a cas

There is an Opinion piece by Bob Herbert in the New York Times, College: The Easy Way  that is worth reading. He discusses a systematic study which found a large fraction of American college graduates did not seem any better educated than when they started college. The study is published in a book, Academically Adrift by Richard Arum and Josipa Roska, which raises important and fundamental questions about the responsibilities of both students, faculty, and administrators.

I found this recent PRB,   Temperature-pressure phase diagram and electronic properties of the organic metal  κ -(BETS) 2 Mn[N(CN) 2 ] 3 particularly interesting. This material has a qualitatively different band structure from many of the kappa-(BEDT-TTF)2X family of organic charge transfer salts. In terms of the relevant tight-binding model t' > t so that it is closer to the limit of weakly coupled chains rather than to the square lattice [for background see the PRL referenced below and/or this recent review , which will appear in Reports of Progress in Physics]. The figure below shows the band structure and the Fermi surface for the new kappa-BETS material. The observed pressure-temperature phase diagram is below. The system is always at half-filling and so the insulating state is a Mott-Hubbard insulator. What is the symmetry of the pairing in the superconducting state. Based on calculations reported in a PRL by Ben Powell and I, the superconductivity will have A_1 symmetr

Eric Bittner, who has been a good source of humour for this blog, sent me an abstract for a chemistry paper.  Do you think it is funny? I actually did not laugh but groaned because it is a bit too close to the truth... Actually, the chemistry abstract which made me laugh was this one, which was completely serious.

Today I was puzzling over quantisation conditions for electrons in magnetic fields and learnt a lot from a paper,  Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models  A few things I learnt: The phase mismatch gamma which occurs in the semi-classical quantisation condition (for the wavefunction) is related to the Maslov index (number of caustics) in the classical periodic orbit. Aside: I am still confused as to exactly what a caustic is and how to visualise it. This phase can be observed in the quantum Hall effect and deHaas van Alphen effect. In graphene it is found to have a different value (gamma=0) from conventional metals (gamma=1/2). This is usually stated as being due to Berry phase effects. But there is more to the story... The phase parameter gamma_L which occurs in the energy quantisation condition is NOT necessarily the same as gamma. This is only the topological part of the Berry phase. F

The concept of a transition state is one of the key concepts in understanding chemical reactivity. It is the maximum on a potential energy surface (PES), for which the reactants and products are local minima. But there is more to the story... This is nice paper Reaction Force and Its Link to Diabatic Analysis: A Unifying Approach to Analyzing Chemical Reactions , by Peter Politzer, Jeff Reimers, Jane Murray, and Alejandro Toro-Labb in JPC Letters. It discusses the notion of the reaction force, the derivative of the potential energy, and how its sign and magnitude can be used to classify different parts of a chemical reaction. The blue dashed lines below define different regions: activation -> transition -> relaxation.  It turns out that some reactions are dominated by activation (the weakening of bonds) rather than transition (the breaking of bonds). Hence, in seeking to speed up a specific reaction with a catalyst one should target that part of the reaction. This leads to

We teach it to undergraduates [as I am doing today!] and claim that it captures many properties of elemental metals? Then we say it works badly for cuprates and other strongly correlated electron metals. But, just how good is it? Surely, this should be in textbooks. But, it actually took me a long time to find the graph below. It shows the frequency dependence of the real and imaginary part of the dielectric constant for gold. The solid lines are the Drude predictions with two free parameters, the dc conductivity and the quasi-particle scattering time. The experimental data covers the range 50 to 20,000 cm-1. The figure is from an Applied Optics paper by Ordal et al.

Today Tony Wright is giving the weekly Quantum Science Seminar on Topological Insulators. Some people consider this new state of matter one of the most important discoveries and achievements of condensed matter theory in the past decade [see this Nature News feature ]. Basically they are metallic states which occur on the surfaces of insulators as a result of topological effects associated with the band structure of the solid. A really helpful introduction, The birth of topological insulators , by Joel Moore appeared in Nature last year. I think a more accurate and helpful name for this class of materials might be something like "topological surface metals" or "topological metals". What do others think?