What determines the colour of an organic dye?

This week I read most of chapter 4 of the book, Colour and Constitution of Organic Molecules by John Griffiths. I think it is a must-read for anyone working on dye molecules. It is at an elementary level and so accessible to both chemists and physicists, experimentalists and theorists. I fear much of the content has been forgotten or is unknown to many working on these materials, whether quantum chemists or biologists trying to find new molecules for fluorescent marker or people working on dye-sensitised solar cells.

Griffiths gives a nice discussion of resonance theory and then discusses its "failures", stating:

The apparent failure of resonance theory in these systems arises from the assumption that only low energy resonance forms need to be considered as contributing to the ground and first excited states.

Indeed, work by Seth Olsen and I (mostly Seth) shows for methine dyes (including flourescent proteins) how to do this in a systematic manner.

Beware of curve fitting

In a comment on a previous post about charge transport in organic materials Doug Natelson brought to my attention a recent preprint. It is a really nice paper and is a cautionary tale about drawing conclusions from curve fitting.

In a Nature Materials paper last year, Alan Heeger's group at UCSB considered the electric field and temperature dependence of the current in an organic field effect transistor. They fitted the observed dependence to that for a theory which describes slightly dirty long one dimensional conducting wires with strong electronic correlations (Tomonaga-Luttinger liquid theory). This theory gives a good description of charge transport in single carbon nanotubes. However, it is not clear if there is a physical reason to expect the TLL theory to be relevant to "dirty" crystals of small organic molecules.

However, Worne, Anthony, and Natelson show that for their data on similar devices the curve fitting to the TLL theory is problematic. In particular, the apparent "scaling collapse" is fortuitous. They state:

decreasing T moves subsequent temperature data sets up and to the right on the graph, even if the data themselves do not change with temperature at all. In fact, any weakly temperature dependent dataset that resembles a power-law can be made to fit onto a single line if plotted in this way with an appropriate choice of α. Data collapse with this plotting procedure is not sufficient to demonstrate TLL physics.

There is another reason why I am skeptical about any claim of "metalllic" behavior in these systems. Their mobility is much less than than the "minimum mobility"of 1 cm^2/Vsec that is necessary for the coherent transport associated with delocalised electrons and band structure.

Examples of inhomogeneous mixed valence

In contrast, to homogeneous mixed-valence the inhomogeneous mixed-valence case involves a mixture of different integer valence ions which occupy inequivalent lattice sites in a static charge-ordered array. Examples of this are provided by Fe3O4, Eu3O4 and Eu3S4.

The following material and figure is copied from the chemexplore web site

Magnetite (Fe3O4) has the AM₂X₄ spinel structure, of the "inverse" type :

Magnetite has the empirical formula Fe₃O₄, or Fe²⁺(Fe³⁺O₂)₂, “ferrous ferrite”. Its formula as a spinel would be Fe³⁺_tetFe²⁺_octFe³⁺_octO₄ , where "tet" and "oct" stand for tetrahedral and octahedral coordinations by the oxide anions. In the above model, the blue spheres represent the tetrahedral iron(III) cations , and the red spheres are the octahedrally coordinated iron(II) and (III) cations. The oxide anions are shown as the green spheres. Because of the fortuitous inverse nature of the magnetite structure, ferrous and ferric cations are both in the similar octahedral coordination by oxides. In "normal" spinels, such as the mineral spinel itself (magnesium aluminate), the A cation is tetrahedral and the M cations are both octahedral:

However, this inverse-spinel charge ordering has recently been challenged in favour of the normal spinel charge structure where the Fe3+ ions exclusively occupy all the octahedral sites while the Fe2+ ions reside in the tetrahedral sites.

What happens in higher order oxides of cerium is not so simple, as discussed here.

Sell your science not your hyper-activity

One of the most important sections in grant applications in Australia is where applicants have half a page to described their "significant contributions to the field".

Such material is also important in CV's and job applications.

Many people seem to write things like:

-I published a paper in a high impact journal and it has been cited and I got invited to speak on it at a conference.

-I worked on topic XYZ where I learnt how to use technique ABC and then I got offered a job at the prestigious University of Mediocrity.

-I have used state-of-the art software to calculate such and such a property of this exotic material which is a really hot topic right now.

-I previously got a grant. Therefore you should give me another one.

These are all activities not contributions to scientific knowledge.
Grants are inputs not outputs.

Instead you should write something like:

I developed a new technique to measure the position of atoms in crystals to a resolution that was an order of magnitude better than existing techniques. With collaborators from Austria, we were able to show that the actual structure of blah-blah materials was different from that predicted by the standard theoretical model....

This led theoretical chemists to develop a new model which shows that entropic effects are actually important in determining the most stable crystal structure at room temperature.....

Research is all about knowledge creation, not about busyness, metrics, or points scoring.

Bridging the chemistry-physics divide

My UQ colleague Ben Powell has written a nice set of notes An introduction to effective low-energy Hamiltonians in condensed matter physics and chemistry. They will be particularly useful for beginning graduate students. They have already been helpful to theoretical chemists and physicists who struggle to understand each other, when actually talking about the same thing. The notes will be published in a forthcoming book edited by Jeff Reimers.

Are flourescent proteins exotic?

"Biochemistry is the search for the chemistry that works."

Just how special, unique, and fine-tuned are biomolecules?

There are a wide range of proteins which have functionalities based on their optical properties. One outstanding example are flourescent proteins. Seth Olsen and I just completed a paper which uses high-level quantum chemistry calculations to show that the low-lying excited states of the chromophore

molecule in the green flourescent protein has a natural description in terms of the resonant colour theory of organic dyes developed in the middle of the twentieth century by Brooker, Platt, and Moffitt.

[Aside: this is the same Platt of multiple alternative hypothesis fame!].

Brooker showed how one could relate the absorption wavelength of an asymmetric methine dye molecule to the absorption wavelengths of two symmetric parent dyes.

The figure above shows that the anion of the

chromophore for GFP (which is what is responsible for the light emission) is a Brooker dye which is "on resonance", i.e. its ground state and first excited state contain equal superpositions of two valence bond states with electrons displaced to the left and the right of the methine bridge (central carbon atom).

How I use the h-index

I am a big fan of the h-index, when used appropriately.

I review numerous research grant applications and job applications and I find the h-index is a good filter to consider how seriously to take an application.

In comparing theory to experiment any discrepancy by an order of magnitude is usually a pretty good indicator that a theory is in trouble. Factors of 2 to 5 can also be useful.

What I find interesting and useful about the h-index is that there are often differences by factors of as much as 2 to 3 between individuals at the same career stage and applying for the same job or grant. I find it surprising that there are such large variations. Furthermore, there appears to be no correlation between the h-index and how much noise an individual makes about the significance of their work.

Some things I do keep in mind are:

-the younger the person the less reliable and useful the h-index

-differences of less than fifty per cent (e.g., 9 vs. 12 or 20 vs. 24) are of no significance

-different sub-fields have different traditions of citing each others works

One thing I never do is to look up an individual's h-index just out of curiousity. I only look it up if I have to actually evaluate the person.

Searching for a unified description of charge transport in molecular materials

Chemical Reviews just released a special issue on Materials for Electronics. There is a helpful article by David Weiss and Martin Abkowitz, Advances in Organic Photoconductor Technology. They note:

The story of the development of electrophotography is an object lesson in the connections between technology development, product development, and scientific understanding.

I found Section 6.1: Charge transport models particularly useful. It contains a critical and succinct discussion of the challenge of coming up with a model which can describe the dependence of the charge mobility on intermolecular separation, temperature, and electric field of a wide class of materials.

The conclusion is "questions remain and a complete description of charge transport in (molecularly doped polymers) MDPs remains elusive"

Rules for writing any paper

My postdoctoral advisor, John Wilkins, hammered into me Rules for Writing a PRL.

I recommend not just reading these rules, but reading them again and again, and moreover, putting it them into practice.

I think these rules are actually relevant to writing any paper.

The key point is to finish and polish the figures and the captions first. They should be self-explanatory and usually illustrate most of the key results of the paper.

Mixed valence: physicists vs. chemists II

In compounds which Varma characterized by homogeneous mixed-valence, each ion is assigned (at least by physicists) the same, non-integer, valence which is a result of a quantum mechanical superposition of two integral valences occuring on each ion.

Compounds exhibiting this type of mixed-valence include, CePd3, TmSe, SmB6 where the valences of the ions are 3.45, 2.72 and 3.7 for Ce, Tm, and Sm, respectively. In TmSe, the valence of 2.72 for the Tm ion is a result of valence fluctuations of this ion between the Tm2+ and Tm3+ states.

A distinctive experimental signature of homogeneous mixed valence is that the ground state is a spin singlet (and so has not net magnetic moment) even if one or both of the two oxidation states of the metal ion have a non-zero spin and magnetic moment. This is seen in the temperature dependence of the magnetic susceptibility. At high temperatures it has a Curie form characteristic of a magnetic moment. At low temperatures it saturates to a finite value. It also means there can be an absence of an Electron Spin Resonance (ESR) signal normally associated with metal ions with integer valence.

Other signatures were reviewed by Varma, including inter-ionic distances in the crystal structure that are intermediate between those normally associated with metal ions with integer valence. There can also be large Debye-Waller factors associated with large fluctuations in these distances.

Electronic correlations in cerium oxides

Today, Elvis Shoko had his Ph.D oral exam. He passed! Congratulations, Elvis!

I thought his talk before the interview with the assessors was a nice summary of his thesis.

The danger of complaining

As in any institution, there a many things that could be done better in universities. Just beware of letting middle and upper management aware of your complaints. They will likely put you on a committee.

Provocative quote

Biology is the search for the chemistry that works.

RJP Williams, Lecture at Oxford (1996)

Why can undergraduates be taught nuclear physics?

Nuclear physics represents a very sophisticated quantum many-body problem. A nuclei is a dense droplet of very strongly interacting fermions. Furthermore, the interaction between a pair of nucleons is nothing like the simple Coulomb interaction between a pair of electrons in a solid or a molecule. Yet nuclear physics can be taught to undergraduates!

Why? Basically, because (as in most many-body systems) one can describe the low lying quantum states in terms of an effective Hamiltonian which describes weakly interacting quasi-particles (which have the same quantum numbers as protons and neutrons). The dynamics of an individual quasi-particle is determined by the mean field (average potential) of all the other nucleons. This is known as the nuclear shell model, first proposed in 1949 and recognised by the Nobel Prize in 1963.

A nice Physics article by John Schiffer is worth reading (it is just a page) as it puts in context a recent PRL which shows how the tensor component of the average potential can explain experimental data on a wide range of nuclei.

Mixed valence: physicists vs. chemists I

The chemical concept of valence is of great utility. The valence of an atom, M, determines the number of neighbouring atoms with which M can form chemical bonds. For most metal ions, the valence, V, is equal to the oxidation number, O. Deviations from this equality occur when delocalization of electrons occurs. The simplest case is where V and O differ by one because one electron from each of the M atoms is completely delocalized in the conduction band. Mixed valency of transition metal and rare-earth ions in solids and compounds is a question of fundamental interest in materials physics, chemistry, and molecular biophysics.

In 1967, Robin and Day (chemists) published a classification scheme for mixed-valence that is still widely used today. Class 1 describes systems with two crystallographic sites that are clearly distinct and and the two sites have integral but unequal valence. There is a large energy associated with transfer of electrons between sites. At the other extreme is Class 3 for which there are two sites which are not distinguishable, and one assigns a non-integral valence to both sites. The classic case of this is the Creutz-Taube ion. The valence electrons are delocalised between the two sites. Class 2 is the intermediate case where the environments of the two sites are distinguishable but not very different. The energy associated with electron transfer is sufficiently small that it can be thermally activated and be associated with significant optical absorption in the visible range. On the time scale of the vibrations of the atoms the electrons may appear to be delocalised.

Classes 1 and 2 correspond to what Varma (a physicist) termed inhomogeneous mixed valence, although, perhaps, inhomogeneous integral valence may be more appropriate. Class 3 corresponds to homogeneous mixed valence.

more to come.....

A promising career cut short?

He excelled academically at a young age. After graduating from Harvard, he completed a Ph.D in Mathematics at the University of Michigan. At aged 25, he became an Assistant Professor at University of California, Berkeley. He published a number of papers from his Ph.D, but according to Web of Science, they have rarely been cited. After two years, he resigned from Berkeley to pursue issues he was more passionate about. He wrote a pamphlet that some considered so important it was published in the New York Times and the Washington Post.

Where is he now?

In a US Federal Prison, serving a life sentence without the possibility of parole.

Who is he?

Theodore Kaczynksi, otherwise known as the Unabomber.

What went wrong?

A court-appointed psychiatrist diagnosed Kaczynski as suffering from paranoid schizophrenia.

What is my point?

Guard your mental health. The more brilliant you are the more vunerable you may be.

Desperately seeking spin liquids II

Kumar Raman has written a helpful comment on an earlier post where I made a conjecture which rules out spin liquid ground states for wide classes of Heisenberg antiferromagnetic spin models.

He points out that one can construct SU(2) invariant models with ground states similar to the spin liquid quantum dimer models, but concedes these models are not very physical.

Section 1.10 of Roderich Moessner and Kumar's review is a helpful description

of the procedure to construct a model.

So I have some questions?

Is the claim that the Hamiltonian (1.36) may have a spin liquid ground state?

In light of these points, how does my conjecture need to be sharpened to rule out such models?

How about no terms in Hamiltonian beyond first- and second-neigbour interaction and single plaquette, and first-neighbour must have the largest interaction?

Conjecture: Consider a spin-1/2 Heisenberg model on a two-dimensional lattice with short range antiferromagnetic exchange (both pairwise and ring exchange are allowed) interactions where the nearest neigbour interaction is the strongest. The Hamiltonian is invariant under SU(2) x L, where L is a space group and there is a total of spin-1/2 in the unit cell. Then the ground state spontaneously breaks at least one of the two symmetries SU(2) and L.

A signature of resonating valence bonds

In most molecules when you different vibrational modes have the highest frequency in the electronic ground state. Another way of looking at this is that it is chemical bonding which stabilises the ground state. These bonds will be strongest and stiffest in the ground state. Excited states are associated with less bonding and so most are associated with a reduction in vibrational frequencies.

An important except is benzene. In the lowest excited state the b2u vibrational mode increases in frequency by about 20 per cent. This has a natural explanation in terms of valence bond theory (see figure below) and is discussed in a Accounts of Chemical Research paper by Shaik, Zilberg, and Haas.

The ground state (which has A1g symmetry) can be described as a linear superposition of two valence bond structures, Kr + Kl.

The lowest excited state (which has B2u symmetry) can be described as the antisymmetric superposition, Kr - Kl.

The b2u distortion couples linearly to the energy of Kr and Kl near the degeneracy point. This leads to the curves shown above.

It is clear that the b2u vibrational mode will have a higher frequency in the excited state than the ground state.

High-level quantum chemistry calculations support this simple picture, which underscores the importance of using the appropriate Hilbert space to describe strongly correlated systems.

You are too polite!

The blogosphere is not known for restrained, thoughtful, and respectful responses to posts. However, the readers of this blog certainly are! Overall the blog has been much more successful and useful (both to me and others) than I anticipated, with one big exception. It generates very few comments and virtually no online discussion. Furthermore, occasionally I get an email from a reader who carefully, thoughtfully, and respectfully points out an error or disagreement. I really appreciate these emails and usually suggest that the sender post the contents of their email as a comment on the blog, since it will be helpful to other readers. Usually I am wrong or the person has a different point of view which I think should be heard.

So, do not be shy!

Please post more comments, especially pointing out errors, ignorance, and different points of view.

A basic question about novel energy materials

A fundamental scientific question of technological importance concerning oxides of transition metals and rare earths is:

When an oxygen atom is removed from a bulk crystal of the oxide where do the two excess electrons go?

Elvis Shoko, Michael Smith, and I recently finished a review article which answers this question for the case of cerium oxide.

The approach we took was to consider high resolution crystal structures of

Ce11O20 and Ce7O12 and see how they could be viewed as ordered arrays of oxygen vacancies in an underlying CeO2 crystal. The charge distribution in the local environments of the O vacancies can then be deduced from the bond valence model.

An important finding we make is that the results are incompatible with the widely accepted standard picture of charge localization on two cerium ions next to the vacancy. Instead, we found that the charge distributes itself predominantly in the second coordination shell of cerium ions. Furthermore, one excess electron can be delocalised over more than one cerium ion.

Our conclusions concerning the charge distribution near oxygen vacancies are significant for several reasons.

First, they contradict many (but not all) atomistic simulations based on density functional theory.

Second, the actual charge distribution around the defect has important implications for the other questions we posed at the beginning of the review. For example,

1. the charge distribution has a significant effect on the relative stability of surface and subsurface vacancies.

2. the charge around oxygen surface and subsurface vacancies is not simply localised on Ce ions next to the vacancy this could change our understanding of the catalytic activity of these surfaces since it has been claimed or assumed that it is associated with Ce3+ ions at the surface.

3. the charge distribution around the vacancies has implications for the relative importance of electronic and ionic conduction, a subject we have discussed in this preprint.

Correlation does not imply causality

I think this mantra is one that is not chanted enough!

I feel I read too many papers concerning material properties that say something like "we measured both properties A and B on material 1 and material 2. Properties A and B were correlated (e.g. they both increased). Therefore A causes B."

We should do better. We should teach our students to do better.

What is more likely is that there is some other property C which causes both A and B to change. For a concrete example of this, consider the oxygen isotope effect in cuprate superconductors. The fact that Tc and other superconducting properties such as the penetration depth varies with the oxygen isotope does not imply that superconductivity is caused by electron-phonon coupling.

Perhaps, a point of even greater concern should be that this mantra is overlooked in many public discussions of social issues.

Should a major goal of high school science education be to help students learn why they should believe this mantra?

A really good book which I recommend is not a "science" book but Freakonomics. I thank my colleague, Ben Powell for giving my 15-year old son a copy. After he read it, I did. In the book, the authors several times emphasise this point in their analysis of "economic" data and show how the data can be analysed in a way to tease out true causality.

PC vs. Mac

So at the end of last year I did take the plunge, gave up on my 3 year old Dell PC laptop and bought a MacBook Pro 13 inch. I have no regrets. What helped tip me over the edge to do it was I must have talked to almost ten people who told me that had made the change in the past few years and had no regrets. A common comment was that they don't seem to slow down with use the way that PC's do.

My only recommendation is that if you do it, do NOT do it when you have important deadlines, e.g, about to go on a trip, write a grant, teaching a new class. I deliberately did it at the end of the year when I had no pressing deadlines. For the first month it was amazing how many little bugs and problems I had getting things to work (e.g. internet was o.k. at work but not home, one printer would work but not another, ...).

A good result of the change is that it forced me to update various software.

In fairness, I think some of the things that impress me, I may have also found if I had replaced my 3 year old PC with the latest.

I love the battery which can easily last 6 hours.

A mark of academic freedom?

Are you free?

"The first duty of free people is to say NO."

Jacques Ellul (1912-1994)

Professor of Law

University of Bordeaux

Besides the freedom I have found that this is one of the keys to good time management and stress reduction.

Are quasi-particles real?

Everyone would agree that electrons and protons are "real". But what about holes? magnons? rotons? quasi-particles in a Fermi liquid? I would say yes. It is interesting to find that this question has received some attention in the philosophical literature. One paper I found by Axel Gelfert, "Manipulative Success and the Unreal", who argues that quasi-particles counter a reality criterion due to Hacking, "If you can spray them, they exist." i.e., Gelfert claims that quasi-particles do not exist even though it is possible to manipulate them.

However, I agree with Falkenberg's counter-argument and I like her stock market analogy in the following:

quasi-particles are as real as a share value at the stock exchange. The share value is also due to a collective effect ...,namely to the the collective behavior of all investors. It is also possible to `spray' the share value in Hacking's sense, that is, to manipulate its quotation by purchase or sale for purposes of speculation. Its free fall can make an economy crash, its dramatic rise may make some markets flourish. And the crash as well as the flourishing may be local, i.e., they may only affect some local markets. But would we conclude that the share value does not exist, on the sole grounds that it is a collective effect? Obviously, share values as well as quasi-particles have another ontological status than, say, Pegasus. Pegasus does not exist in the real world but only in the tales of antique mythology. But quasi-particles exist in real crystals, as share values exist in real economies and markets. Indeed, both concepts have a well-defined operational meaning, even though their cause cannot be singled out by experiments or econometric studies.

Brigitte Falkenburg, Particle Metaphysics: a critical account of sub-atomic reality (Springer 2007), p. 245.

Evidence for climate change

I increasingly get asked by non-scientist friends "Do scientists really believe in climate change?". Consequently, I am trying to be better informed. I found this Summary for Policymakers from the Intergovernmental Panel on Climate Change (IPCC) helpful. The Figure above is taken from that report.

I also liked this presentation by Sir John Houghton because it gave a succinct summary of some of the history.