Quantifying vibronic entanglement

I just finished a paper, Quantum entanglement between electrons and vibrations in molecules, with Laura McKemmish, Noel Hush, and Jeff Reimers.

We consider a simple model Hamiltonian which describes two quantum states interacting with a single vibrational mode [alternatively known as the one mode spin-boson model, the Herzberg-Teller model, or the E x beta Jahn-Teller model].

A couple of things I learnt:
*Realistic model parameter values for six molecules including ammonia, benzene, and semibulvalene.
*The large entanglement which occurs in the strong coupling (adiabatic) limit can be quite "fragile". i.e., it can be destroyed by  a small asymmetry in energy. Compare the top left two boxes in the figure below which shows a colour-shaded plot of the entanglement as a function of the Hamiltonian parameters.

*In contrast, in a regime where all the energy scales are comparable, the entanglement is much more robust.

A curious side anecdote about this paper. Last week we first sent the paper to Physical Review A. However, an editor did not consider it would be "of interest to their readers" and so would not send it out for review. I found that rather disappointing. I wondered if that was because there was a passing reference to Penrose and Hameroff in the conclusion. So, we removed that reference and sent the paper to Journal of Chemical Physics. I would be curious to hear from "Phys. Rev. A readers" whether they think the paper is of interest.

Deconstructing climate change and energy options

Physics Today has a very helpful review of three important books by physicists about climate change and possible future options.

Beyond Smoke and Mirrors: Climate Change and Energy in the 21st Century by Burton Richter

Sustainable Energy - Without the Hot Air by David MacKay

Challenged by Carbon: the Oil Industry and Climate Change by Bryan Lovell.

Fermi liquid transport properties without quasi-particles

Today I encountered the following apparent puzzle. Suppose one has system with a self energy which is the sum of an impurity term and a marginal Fermi liquid self energy. One consequence is that the real part of the self energy is logarithmically divergent at low temperatures. Consequently, the quasi-particle weight vanishes for energies at the chemical potential.
If transport properties (such as the dc conductivity and thermal conductivity) are calculated from bubble diagrams ignoring vertex corrections then it seems the resulting expression only depends on the imaginary part (and not the real part) of the self energy. Consequently, at low temperatures the transport is dominated by impurity scattering and universal Fermi liquid properties such the Wiedemann-Franz law (and the Lorenz ratio) are obeyed.
Thus it seems one can have traditional Fermi liquid signatures without quasi-particles!

This was all stimulated by reading a nice 2002, PRL Heat Transport in a Strongly Overdoped Cuprate: Fermi liquid and a Pure d-wave BCS Superconductor. They observe that the Lorenz ratio has its universal value (to within about 1 %). I was wondering whether these observations at low temperatures had implications for recent work I did with Jure Kokalj, Consistent description of the metallic phase of overdoped cuprate superconductors as an anisotropic marginal Ferm liquid. My current view is that these experiments cannot be used to rule out a marginal Fermi liquid contribution to the self energy, but I welcome comments.

5 Papers every computational chemistry student should read

I have a dream. That every advisor (supervisor) who gets a student to perform a computational chemistry calculation will have them read the following five papers. The papers are from a range of eras and with different emphasis. But, a common theme is the importance of calculations aiding concept development and being aware of the limitations these calculations.
Reading these papers should be like reading the road rules before you get your drivers license.
I list the papers in chronological order.

Present state of molecular structure calculations
C.A. Coulson (1960)
Quantum chemistry and its unachieved missions
Jean-Paul Malrieu (1998)
Is my chemical universe localized or delocalized? is there a future for chemical concepts?
Sason Shaik (2007)
Predicting Molecules - More realism , please!
Roald Hoffmann, Paul Schleyer, and Fritz Schaefer (2008)
Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed
John P. Perdew, Adrienn Ruzsinszky, Lucian Constantin, Jianwei Sun, and Gabor Csonka (2009)

I welcome alternative suggestions. Later I may write more about the individual papers and why I think they are important.

Seeing how degenerate radicals can be

I have been slowly digesting a really nice combined theoretical and experimental paper The Lowest Singlet and Triplet States of the Oxyallyl Diradical which was featured on the cover of Angewandte Chemie in 2009 [For physicists this is the European counterpart to the prestigious JACS = Journal of the American Chemical Society].
[See also the commentary by Bettinger].

Here are a few interesting things I learnt:

• The ground state is a singlet but only 55 meV in energy below the lowest lying triplet. [In most organic molecules the energy difference is ~ 1-2 eV].
• C-C-C angle bending has a frequency of about 400 cm-1 and couples to the electronic transitions. 
• Another vibrational mode which couples strongly to electronic transitions is the C-O stretch [with a frequency of order 1700 cm-1].
• The singlet state is unstable to "disrotatory ring closure" to form cyclopropanone. 

The relevant valence bond structures are

and provide a natural framework to understand the above observations.

This paper is of particular interest to me because the oxyallyl diradical is a simple example of a methine dye [cf. green fluorescent protein, Malachite green] and a ketocyanine dye whose minimal quantum chemical description requires 4 electrons in 3 orbitals. [To physicists 4 electrons in a 3 site Hubbard model]. The paper though uses the framework of 4 electrons in 4 orbitals due to the analogue with trimethylenemethane (TMM) which actually has a triplet ground state. TMM is one of the simplest non-Kekule molecules.

Molecules of chocolate

The Journal of Chemical Education paper on chocolate based demonstrations discusses three key classes of molecules.
Triglyceride is a major component of cocoa butter. It is hydrophobic.

Serotonin is a major component of cocoa powder. It is is largely hydrophilic and so will dissolve in water.

Lecithin is an emulsifier [just like egg which leads to formation of a stable emulsion of oil and vinegar in a salad], an amphiphilic molecule, which promotes mixing of cocoa solids and cocoa butter.

  

Interlayer magnetoresistance in a pseudogap metal

I have been working through a really nice paper, Fermi surface of the electron-doped cuprate superconductor Nd_2–xCe_xCuO₄ probed by high-field magnetotransport by Mark Kartsovnik and collaborators.

The phase diagram of these electron-doped [in contrast to the more common hole-doped cuprates] materials is shown below. x is the Ce content. PG denotes a pseudogap phase.

(b) Shows the Fermi surface expected for x > 0.16 (e.g. from a tight binding model and DFT based calculations) and confirmed by Shubnikov de Haas (SdH) oscillations.

 (c) shows how this Fermi surface may be re-constructed due to a (pi,pi) superlattice potential (which might exist due to co-existing antiferromagnetic (AF) order.

I found the interlayer magnetoresistance measurements shown below particularly interesting. Each curve shows the interlayer resistivity as a function of magnetic field direction (theta= tilt angle from the normal to the layers) for a fixed magnetic field and temperature.

[Above some large angle the resistance goes to zero because the component of magnetic field perpendicular to the layers becomes less than the upper critical field needed to destroy the superconductivity].

What is interesting about these curves?

• They exhibit significant qualitative differences depending on the doping x, even over the narrow range 0.13 < x < 0.17.
• This is probably because the pseudogap has a big effect on the magnetoresistance.
• For x=0.13, 0.15 the dependence on the azimuthal direction (phi) of the magnetic field is very weak (and opposite in sign) compared to that for x=0.16, 0.17.

The only theory of the interlayer magnetoresistance in the presence of a pseudogap that I am aware of is a paper by Michael Smith and myself in 2009. Most of that paper focuses on the case of a field parallel to the layers and shows how the azimuthal angular dependence may reveal the anisotropy of the pseudogap. We did find that the pseudogap reduces the azimuthal anisotropy compared to the anisotropy seen in the normal phase due to anisotropy of Fermi surface properties. This is basically because the pseudogap suppresses large parts of the Fermi surface from contributing to the interlayer conductivity. That physics may be relevant for understanding the data shown above, but a detailed calculation is desirable.