Hard questions about glasses

A recent book Dynamical heterogeneities in glasses, colloids, and granular media contains a fascinating chapter where four experts [Jorge Kurchan, James Langer, Thomas Witten, and Peter Wolynes] give their answers to the questions below.

I think we need more of these kind of frank discussions about scientific topics. I am slowly working through the answers. The most fascinating bit so far is Peter Wolynes inspiring response to Q9, including "I believe a young physicist who wants to work on any challenging problem in physics will eventually have to learn about glasses."

Q1) In your view, what are the most important aspects of the experimental data on the glass transition that any consistent theory explain? Is dynamical heterogeneity one of these core aspects?  

Q2) Why should we expect anything universal in the behavior of glass-forming liquids? Is the glass-transition problem well defined?  

Q3) In spin-glasses, the existence of a true spin-glass phase transition has been well established by simulations and experiments. Do you believe that a similar result will ever be demonstrated for molecular glasses? 

Q4) Why are there so many different theories of glasses? What kind of decisive experiments do you suggest to perform to rule out at least some of them? 

Q5) Can you briefly explain, and justify, why you believe your pet theory fares better than others? What, deep inside, are you worried about, that could jeopardize your theoretical construction?  

Q6) In the hypothesis that Random First-Order Theory [RFOT] forms a correct skeleton of the theory of glasses, what is missing in the theoretical construction that would convince the community?  

 Q7) Exactly solvable mean-field glass models exhibit an extraordinary complexity requiring impressive mathematical tools to solve them. 

 Q8) In your view, do the recent ideas and experimental developments concerning jamming in granular media and colloids contribute to our understanding of molecular glasses, or are they essentially complementary?  

Q9) If a young physicist asked you whether he or she should work on the glass problem in the next few years, would you encourage him or her and if so, which aspect of the glass problem would you recommend him or her to tackle?  

 Q10) In twenty years from now, what concepts, ideas or results obtained on the glass transition in the last twenty years will be remembered?  

Q11) If you met an omniscient God and were allowed one single question on glasses, what would it be?

I thank Peter Wolynes for bringing this to my attention.

Why are quasi-particles interesting?

Last week I had a phone call from a journalist Andrew Grant at Science News, asking about quasi-particles. Why are they interesting?

1. Quasi-particles exist. It is not at all obvious why they should exist in strongly interacting quantum systems. Yet they are rather robust and found in diverse systems, ranging from atomic nuclei, to magnets, to metals, to neutron stars… Thus, they are an important organising principle in quantum many-body physics.

2. Occasionally quasi-particles have different quantum numbers to the constituent particles of a system. The most striking example is the fractional charge and statistics of quasi-particles in the fractional quantum Hall effect.

3. Many electronic materials of current interest [e.g. high-temperature superconductors] are “bad metals” that do not seem to have quasi-particles [except at low temperatures].

I find all of these are profound and surprising. They illustrate emergence.

A challenging ingredient in teaching

Francis Su is a mathematics Professor at Harvey Mudd College. He is teaches a course in Real Analysis, the lectures of which you can watch on Youtube. Last year he received the Haimo award from the Mathematical Association of America for excellence in teaching.

In receiving the award he gave a deeply personal talk
The Lesson of Grace in Teaching: From weakness to wholeness, the struggle and the hope

I actually wanted to post about his talk when I first read it months ago, but was hesitant to because I feel I struggle so much with the issues he talks about. Finally posting it was prompted by two events. I got my latest student teaching evaluations and they were pretty good [more on that later]. (Sadly, this also illustrates how I am struggling with what Su is talking about: performance based identity). A friend is taking a course on teaching and he told me they had a whole session discussing clarification of personal values and how they shape your own teaching philosophy and interactions with students. I thought Su was an excellent example of this.

How good should parameterisation of simple models be?

Over the past few years I have advocated a simple diabatic state model to describe hydrogen bonding in a diverse range of molecular complexes. In my first paper I suggested the following parameterisation of the matrix element coupling the two diabatic states

with two free parameters Delta1 and b, which describe the energy scale and length scale for the interaction.
R1 is just a reference distance ~ 2.4 A, introduced so that the prefactor Delta1 corresponds to a physically relevant scale.
The two parameter values I chose give a quantitative description of a wide range of properties [bond lengths, vibrational frequencies, and the associated isotope effects, when the quantum nuclear motion is taken into account.

Last week I found this nice paper
Solvent-Induced Red-Shifts for the Proton Stretch Vibrational Frequency in a Hydrogen-Bonded Complex. 1. A Valence Bond-Based Theoretical Approach 
Philip M. Kiefer, Ehud Pines, Dina Pines, and James T. Hynes

It uses a similar two-diabatic state model and references earlier work of Hynes going back to 1991. A parameterisation like that above is used.

Below is a plot of Delta (kcal/mol) vs. R (Angstroms), comparing my parametrisation to Hynes.

The curve with the smaller slope is the parameterisation of Hynes.

I found this agreement very satisfying and encouraging. I have mostly been concerned with symmetrical complexes [where the proton affinity of the donor and acceptor is equal] and bonds of strong to moderate strength [R ~ 2.3-2.6 Angstroms] and have compared the theory to experimental data for solid state materials. In contrast, Hynes has been mostly concerned with asymmetric complexes in polar solvents with weaker bonds [R ~ 2.7-2.8 Angstroms].

I also felt bad that I had not referenced Hynes work. Then I went back and checked my first paper. To my relief, I found I had explicitly stated that the parameterisation in his 1991 paper was comparable to mine. It is amazing how quickly I forget stuff!

But the main point of this post is to raise two general questions.

1. Should I really be so happy? Aren't I missing the point of simple models: to give insight into the essential physics and chemistry and describe trends in diverse set of systems. All that matters is that the parameters are "reasonable", i.e. not crazy.

2. What is a reasonable expectation for consistent parametrisation of simple models? At what point does one abandon a model because it requires some parameters that are "unreasonable"? For example, if Hynes parameters differed by a factor of ten or more I would say there is a serious problem with the model. But I would not be that concerned by a 50 per cent discrepancy.

Here is a concrete example for 2. At a recent Telluride meeting, Dominika Zgid lampooned the fact that for cerium oxides, people doing DFT+U calculations have used values of U ranging from 1 to 10 eV in order to describe different experimental properties. To me this clearly shows that there is physics beyond DFT+U in these materials.

I welcome answers. I realise that the answers may be subjective.

Seeing enzyme catalysis with the naked eye

For my latest celebrity scientist speaking gig [at a small church youth group] my glamorous assistant [my wife] found a new demonstration to add to my repertoire, Elephants toothpaste. It is described in this Journal of Chemical Education paper.

Hydrogen peroxide is thermodynamically unstable. However, you can buy bottles of it and they will remain useful for months. It will slowly decompose into water and oxygen.
2 H
2O
2 → 2 H
2O + O
2

However, if you add some iron chloride it acts as a catalyst and increases the decomposition rate by a factor of a thousand. You will see some amount of "bubbling" due to the oxygen gas produced. If blood [which contains haemoglobin] is added the rate increases by a factor of a million. Even better, if you add the enzyme catalase, the rate increases by a factor of a billion. In the demonstration the catalase is present in the yeast that is added. Catalase is one of the fastest catalysts known. It performs an incredibly important biochemical function, that is essential to life existing. Hydrogen peroxide is a strong oxidant  that could destroy many biomolecules. It is also an unwanted byproduct of many biochemical reactions. Biological systems use catalase to rapidly destroy the hydrogen peroxide before it can do harm.

The demonstration I did (and described in the JCE article) makes use of a dilute aqueous solution [a few per cent] of hydrogen peroxide. The spectacular video below makes use of a highly concentrated solution that is quite dangerous because it can cause chemical burns of the skin.


The above discussion follows the beautiful introduction to enzymes in chapter 11 of my favourite biochemistry text by Matthews, van Holde, Appling, and Anthony-Cahill 
It contains the figure below, illustrating the key idea of how catalysts work: by lowering the energy barrier [the transition state] for a chemical reaction.

Should I join this professional scientific society?

Why are they important?
Why should you join? not join?
Why are the membership numbers of some societies declining (some dramatically)?

It seems every month the American Chemical Society (ACS) sends me a letter asking me to join. I am not sure who recommended me for membership. I find it ironic because I once tried to join the Royal Australian Chemical Institute but was rejected because they did not seem to think I was a real chemist. [ouch!] Over the years I have belonged to several societies. But, some of these memberships have lapsed. Recently, I was personally asked by one, "What do we have to do to get you to rejoin?"
I did not have an answer, stimulating this post.

First, let me say why these societies can be incredibly important. They can

• Publish good journals that are owned and run by scientists. These can avoid the problems of commercial outfits such as Nature [sensationalism over substance] and Elsevier [quantity over quality, dubious business practises].
• Organise useful conferences.
• Give prizes and awards to recognise excellence.
• Provide career services, particularly for younger members.
• Represent science and scientists to government, industry, and the community. This is not just lobbying for more funding but making important public statements on issues such as climate change.

If we don't join, we end up with the Tragedy of the Commons, whereby our long-term collective interests suffer because we prioritise our individual self-interest.

So, why not join?

• Membership is expensive, particularly if you belong to several.
• Your mail box (both hard and soft) will be clogged with magazines, newsletters, fund-raising appeals, announcements, elections, ...
• You may be asked to serve on committees.
• There are many societies to choose from, particularly if you live outside the USA and you work  at the interface of two or more disciplines [physics, chemistry, biophysics, materials science, ...]. APS, ACS, RACI, AIP, IoP, MRS, ...
• Smaller national societies are struggling for viability in an era of internationalisation. It is not clear why some still publish journals.
• Society conferences compete with a multitude of other conferences. Some national society conferences may not have a critical mass of people or seem a magnet for mediocrity.
• If you don't go to the society conferences and can read their magazine online via a library subscription there is less personal incentive to join.

So, how do you decide who to join? or not join? or let your membership lapse?

What would a society have to do to convince you to join?

Belated recognition for early work on superconducting organic charge transfer salts

In the mid-1990s, through the influence of Jim Brooks, I became interested in organic charge transfer salts. I read a very helpful paper by Kino and Fukuyama that considered a Hubbard model for the family kappa-(BEDT-TTF)2X. This led to me writing a review article and a short piece in Science, comparing the organics to the cuprates.

Aside: Being young and naive, and living before impact factor obsessions, I made the mistake of publishing the review in Comments on Condensed Matter,  which is not even listed on ISI Web of Science. I chose that journal because I knew it had published an influential review on heavy fermions by the stellar cast of Lee, Rice, Serene, Sham, and Wilkins.
Fortunately, I put the paper on the arXiv and a lot of people read it, and the Science paper often gets cited, by association.

The review stimulated a lot of work, particularly on the Hubbard model on the anisotropic triangular lattice at half filling, and the associated Heisenberg model for the Mott insulating phase. A recent review is here, with Ben Powell.

Only recently I became aware of some related work from around the same time that is never cited, literally.

κ-(BEDT-TTF)2X organics, as seen for Hubbardists 
V.A. Ivanov

Electronic structure and superconductivity of κ-(BEDT-TTF)2X salts
V. A. Ivanov, E. A. Ugolkova, M. E. Zhuravlev

The relevant Hubbard model, the importance of correlations, and the possibility of d-wave superconductivity are all discussed. These papers may not be as clear, or crisp, and comprehensive as my review but some of the key physics is there.
Ivanov should get credit for that.

What is the sociology here? Why was I influential but Ivanov was not?
Here may be some contributing factors.
I published the Perspective in Science, but back then not many physicists actually read it.
More importantly, I put my papers on the arXiv. Back then [pre-web] most people subscribed to and read the daily email listing recently posted papers. I timed my posting so my review would be the first of the daily list.
I followed up with more papers. I gave a lot of talks, both at conferences and universities around the world. I talked to experimentalists. I encouraged theorists to use their favourite technique to study the relevant Heisenberg and Hubbard models. I had postdocs work on the subject. They then went around talking about it.

Future directions for physical chemistry

At the American Chemical Society meeting last week J.T. Hynes gave a talk
Some modest proposals for 21st century physical chemists 
Here are his three main points.

(1) The most familiar problems/phenomena may in fact not be at all already understood, and can provide fertile areas for discovery;

(2) Just an experiment or a theory because it is 'old' (e.g. of a certain vintage) does not mean it is inferior/wrong despite the lack of novelty and modernity;

(3) Simple, well-constructed analytic models have a significant role to play in comprehending and advancing both theory and experiment.

Unfortunately, I was not at the meeting, but my colleague Seth Olsen was and told me I would have enjoyed the talk. These points certainly resonate with my own views.

Gratuitous graphs

Movies sometimes feature gratuitous graphic violence and sex.
Scientific papers sometimes feature gratuitous graphs.

Before desktop computers it was a lot of work to produce a single graph.
Now one can produce ten graphs in an afternoon!
Why not put them all in the paper?
The paper will be longer and give the impression of being more comprehensive.
I feel that some students want to show all their graphs to show just how productive they have been.
No! Not every graph you make should be in the paper.
Analysis, synthesis, and discipline is needed.

Figures should carry the weight of the paper.
Many people, myself included, will scan the figures looking for something potentially interesting and
important, in order to make a decision as to whether or not to actually read the paper.
Figures and their captions need to be clear, comprehensible, and have significant content.

Graphs should be like text: polished and repolished. Good authors work hard at writing, editing, polishing, re-writing, and re-writing text. Some graphs should be deleted or relegated to supplementary material. Some should be combined. Some should be split in two.

Some chemistry journals now put an author produced "summary graphic" or "graphical abstract" on the journal website for each paper. I find some of these very helpful. I also feel it is unfortunate that these are usually not in the paper. I think many papers would benefit from at least one simple schematic figure that illustrates the main point, key definitions, or approaches of the paper. I reproduce an example below from a recent paper by Seth Olsen and I.

Facing the black dog of depression

Unfortunately, this past two months has seen the tragic death by suicide of Robin Williams,  Seth Teller [an MIT Computer Science Professor], and Yoshiki Sasai [co-author of two retracted Nature papers].

I thought the following video on depression was helpful.

Scale of the Nernst effect in a bad metal

A science fiction fantasy is that we should be able to make "materials by design" that have any physical property (density, thermal conductivity, hardness, thermoelectric figure of merit, heat capacity...)  that we desire. However, it seems that there are certain physical constraints that determine the overall scale of many physical properties.

I find it helpful to have a feel for typical orders of magnitude. What is particularly interesting is that sometimes these magnitudes are related to fundamental constants [electronic charge (e), Boltzmann's constant (k_B), Planck's constant (hbar)] and basic length scales such as the lattice constant a of a crystal.

Here are three scales I have emphasised before

Resistivity ~ hbar a / e^2 ~ 100 microohm-cm  which is associated with the Mott-Ioffe-Regel limit.

Thermoelectric power,  S ~ k_B/e ~ 86 microvolt/K

Mobility, mu ~ e a^2/ hbar ~ 1 cm^2 V/sec

One can find these scales by dimensional analysis or by doing things like looking a formulas from transport theory and (assuming a bad metal) setting the mean-free path comparable to the lattice constant. One can debate whether one uses hbar or h, but for little purpose.

How about the Nernst signal, nu?

nu ~ k_B a^2 / hbar ~ 0.01 microV/KT

A few minor notes.

1. One can get this scale from the above expressions for S and mu if one uses the observation that in some strongly correlated materials
nu ~ S * Hall mobility.

2. One Volt/Tesla = m^2/sec  [One can see this easily from F = q(E + vxB)].

3. Given that the Nernst effect involves charge transport I find it surprising that the electronic charge does not appear.

The figure below, taken from a nice review by Behnia, shows that this is the right scale for bad metals such as cuprates, and heavy fermions above the coherence temperature.

One also sees this scale in recent DMFT calculations for a doped Hubbard model (see Figure 2d in this PRL ) and recent measurements (see Figure 4) on organic charge transfer salts.

Documenting harassment of women in science

There is a very disturbing article in the New York Times about sexual harassment and discrimination of female scientists and science writers.

Proton transport in phosphoric acid

There is a very interesting paper
The mechanism of proton conduction in phosphoric acid
Linas Vilčiauskas, Mark E. Tuckerman, Gabriel Bester, Stephen J. Paddison, Klaus-Dieter Kreuer

There are several reasons why neat liquid phosphoric acid (H3PO4) is such an interesting system

• the highest intrinsic proton conductivity of any known substance and is σ ≈ 0.15 S cm⁻¹ above Tmelt = 42 °C.  This is like the conductivity of a bad metal but orders of magnitude larger than that of neat water.
• hydrogen bonded phosphates are ubiquitous in bimolecular systems and often involved in proton transport
• hydrogen bonded phosphates are electrolytes in high-temperature polymer electrolyte membrane fuel cells
• hydrogen bonded phosphates feature in many ferroelectric materials
• short intermolecular hydrogen bonds (the oxygen atom separation, R_OO ≈ 2.60 Å, compared to R_OO ≈ 2.85 Å in liquid water)
• it has a high dielectric constant (61), comparable to that of liquid water, but in the gas-phase the dipole moment of a phosphoric acid molecule is only 0.45 Debye compared to 1.85 Debye for a water molecule.

The main result of this paper is to use ab initio molecular dynamics simulations to show

• Hydrogen bonded chains are central to the proton conductivity. there is an ten per cent chance of a quasi-coherent hop along four H-bonds.
• proton transport occurs via a structural diffusion mechanism similar to the Grotthuss mechanism involved in water
• however, due to the presence of the short H-bonds a co-operative compression of the bond lengths in the molecular chain, such as occurs in liquid water, is not required.

The simulation treats the nuclei in a purely classical fashion.
One thing I found a bit strange was that the presence of short H-bonds was hinted to be an argument for neglecting quantum nuclear effects. I would have thought the opposite.
It has been shown before, including by Tuckerman, that for R_OO ≈ 2.60 Å that quantum nuclear effects can be significant, because then the proton transfer potential is not barrier less but has an energy barrier comparable in magnitude to the vibrational zero-point of the O-H stretch, as  discussed here.

Hopefully, someone will do a full path integral simulation with quantum nuclei soon.
Experimentally, a first estimate of quantum nuclear effects can be found by deuterium substitution. Surprisingly, in a quick search I could not find any measurements of deuterium conductivity/mobility/diffusivity in the deuterated acid. If they have not been done, hopefully, someone will do the measurements soon.

If you do a science Ph.D what chance do you have of becoming a faculty member?

Here is a helpful graphic that summarises the statistics of the employment trajectories of people who start doing a Ph.D in biology in the USA. I guess that the percentages are similar for physics and chemistry. Does anyone know the actual numbers?

I welcome comment and critique on the numbers.

Large thermal conductivity of correlated semiconductors

Previously I posted about the challenge of understanding the colossal thermoelectric effect in FeSb2 and the puzzles of the classic Kondo insulator FeSi.

I talked about the former yesterday at the cake meeting [take 7 minutes to convince everyone they should read a particular paper]. I noticed for the first time just how large the thermal conductivity is, actually comparable to diamond at low temperatures.

The red curve is FeSb2 and the black curve FeAs2, which is less correlated.

This is of interest for at least two reasons.

1. The large thermal conductivity is bad for thermoelectric applications as it will significantly reduce the thermoelectric figure of merit.

2. It needs to be explained theoretically, including the large difference between FeSb2 and FeAs2. [Presumably the phonons are similar in the two compounds].

3?. Does this make reliable thermoelectric measurements harder or easier?

For comparison below I show the temperature dependence of the  thermal conductivity of diamond and copper, taken from here. [n.b. the vertical scale is different by a factor of 100 compared to the above graph].

I welcome comments.

Keep it simple

KISS = Keep It Simple, Stupid!

"Make things as simple as possible, but no simpler."
paraphrase of Einstein, for the real quote and its evolution, see here.

A "principal object of theoretical research ... is to find the point of view from which the subject appears in its greatest simplicity." - J. W. Gibbs

This post is a mixture of rant, observation, and exhortation.
It is not just about theoretical model building but all of life! I also value simplicity in language, communication of ideas, administrative procedures, personal finances, software, email lists, meeting schedules, BibTex (arghh!), TV remote controls, .... But it seems that when it comes to things like grant applications, course profiles, .... there is a drive for greater complexity... The bigger the better. The more parameters the better...

I sometimes wonder if the value I place on simplicity is just a personality trait or preoccupation.  Or  is there some universal value that is being lost? It seems there are several issues. Do some people not do it because they think complicated is better? Or they are just lazy, or they just don't have the necessary ability to simplify? I take comfort that I am in the good company of Martin Gutzwiller, but he said he was "fighting a losing battle" and he died earlier this year.

Simplicity in science is hard work. Sometimes it requires brilliance. But other times it just requires some effort. Giving a simple physical picture for the results of a detailed computation may not be easy. But, shouldn't one at least make an attempt? When writing a paper first give a simple summary of the essence of the argument. When plotting a graph explain what are the relevant scales, e.g., if there is a maximum in resistivity versus temperature, describe the essential energy/temperature scale involved....
Then there is the whole topic of talks and seminars. Most need drastic simplification to have any chance of being comprehensible...

I should stress that I not against highly technical calculations or big computer simulations, per se. They can be incredibly valuable, particularly when they are used in conjunction with and enhance physical and chemical insight. Furthermore, good governance and accountability may need to be complicated. But, there has to be a balance.

Am I the only one concerned about this?

Extracting the quasi-particle weight from the imaginary time self energy

Generally it is a lot easier to numerical calculations in imaginary time than in real time. A Fourier transform then gives the value of correlation functions at Matsubara frequencies. It then becomes a challenge to analytically continue to real frequencies. For results with little numerical noise the most widely used method is Pade approximants, as introduced by Vidberg and Serene. For results with statistical noise (e.g. from a quantum Monte Carlo simulation) a common approach is to use Maximum entropy methods, as reviewed by Jarrell and Gubernatis.

In a Fermi liquid the quasi-particle weight Z is related to the real part of the self energy Sigma'(omega) by

How does one get this from the self energy at imaginary frequencies i omega_n?
It turns out one does not have to do the analytic continuation.
There is an exact identity one can use, as described in this paper, by Arsenault, Semon, and Tremblay.

[Minor correction: the Sigma in the middle of (12) should be Sigma'', the imaginary part.]

I had never seen this before and think it is very elegant.

Stokes-Einstein relation between viscosity and diffusion in liquids

The Stokes-Einstein equation

relates the diffusion constant D of a macroscopic particle of radius r undergoing a Brownian motion to the viscosity eta of the fluid in which it is immersed.
It is a beautiful and simple example of a fluctuation-dissipation relation.

But suppose now we think about one of the individual atoms or molecules in the fluid. It also undergoes Brownian motion and one can define a self-diffusion constant.
It is amazing to me that the Stokes-Einstein relation still holds for a wide range of liquids, temperatures, and pressures with r being of the order of the molecular radius.

The figure and table below are taken from this paper.

Can this relation be derived from microscopic theory?
Zwanzig gave a heuristic justification here.
Rah and Eu gave a derivation from stat. mech. here.

The Stokes-Einstein relation does break down as one approaches the glass temperature in a supercooled liquid, as for example shown here. The origin of that breakdown is controversial, as is many phenomena involving glasses.

Back of the envelope estimates in chemistry

Michelle Francl has a stimulating piece Take a number: Back-of-the-envelope calculations are an important part of chemistry in Nature Chemistry.

Francl asks her students, "Estimate the circumference of a benzene ring in metres".
This is an example of a Fermi problem.

Previously I posted about the importance of teaching solid state physics in a way that helps students get a feel for orders of magnitude. I don't think I could write a comparable post for physical chemistry. This is partly my lack of expertise and experience, but also I suspect that things in chemistry are not as clear. [One day I hope I will get asked to teach a course.]

For example, one thing I learnt and need to understand is that X-H bonds are shorter than X-X bonds.

Indeed, Francl says

I recently asked a few hundred of my closest chemical friends on Twitter and Facebook what should go on such a sheet for chemists, what they might encourage students to master. Schematics of periodic trends and the electromagnetic spectrum are obvious candidates for mappings, but the list of suggested anchors varied wildly with subfield. There are very few values that a majority of chemists cling to: room temperature is 300 K; the length of a single carbon–carbon bond is 154 pm; the atomic masses of C, H, N, O, S and Cl.

In response to Francl's article, Henry Rzepa says
Well, one of my own personal favourites is anchoring chemical timescales. From 10^-18 s (that of electron dynamics, and presumably the fastest processes in chemistry) to 10⁺¹⁸ (approximately the age of the universe). And (for a unimolecular process) this can be reduced to this equation:  
Ln(k/T) = 23.76 – ΔG^‡/RT 
I quoted this equation in a recent post, since it gives you the fastest possible chemical reaction if ΔG^‡ is set to zero (which of course is not a reaction but a vibration), but which gives you a good estimate of how fast a process will be for any given value of a barrier.

When it comes to condensed phase dynamics there are a multitude of different timescales, summarised in diagram below, taken from this review.

For me remembering that at room temperature, k_B T = 25 meV = 0.6 kcal/mol = "chemical accuracy" is useful. Basically, most electronic energy scales (ionic and covalent bond energies, energy barriers = activation energies) are of the order of eV. You see this in that most batteries [electrochemical cells] have voltages of a few volts.

What do you think are key orders of magnitude in chemistry?

My paper submission strategy

Getting papers published can be a slow, inefficient, and frustrating process. For what it worth here is the strategy and associated rationale that I have generally evolved over the years. My primary goals are:

• engage relevant people with what I am doing
• get constructive feedback on the paper and the science
• get the paper published as smoothly and quickly as possible.

Here are my usual steps:

1. get a local colleague to read the paper for feedback

2. put the paper on the arXiv [and write a post about it on this blog].

3. send the preprint to a few people who might be referees or be able to provide useful feedback

4. revise the paper in response to feedback, including another proof read

5. submit the paper to a journal, sometimes suggesting people who have provided positive feedback already as possible referees.

A few comments and rationale.

My target journals are mostly Physical Review B and Journal of Chemical Physics. About once a year I send something to PRL. For idealistic reasons, I abstain from the luxury journals and want to minimise publishing in journals from commercial publishers such as Elsevier. Going down the journal "food chain" involves continually reformatting a paper, wasting a lot of time.

If you publish in American Chemical Society journals it is not clear you can post on the arXiv.

Why not exchange steps 2 and 3? i.e. send it out for private comment before putting on the arXiv. I used to sometimes do that. However, I had a few instances where people would say things like, "we have some similar results, can we submit at the same time" or "we have some related experimental results can we publish together" or "lets combine your paper with ours" or "you really should also calculate XYZ ....". This can lead to significant time delays and (particularly in hindsight) debatable benefits. Ignoring their advice or requests can be awkward. If the paper is already on the arXiv it pre-empts some of this.

I welcome comments. What is your preferred strategy?