Thursday, 19 May 2016

Entanglement Entropy of Electronic Excitations

There is more to excited states than meets the eye. Just looking at the orbitals will not tell you everything there is to know about the many-body wavefunctions. The purpose of my newest paper "Entanglement Entropy of Electronic Excitations," that just appeared in J. Chem. Phys., was to quantify the amount of information that is hidden from view. For this purpse, I used the idea of mutual information from quantum information theory.

The focus of this paper is the eigenvalue spectrum of the natural transition orbital (NTO) decomposition. There is information in the eigenvalue spectrum independent of the orbitals themselves. To illustrate the point, we can look at the first excited singlet state of two interacting ethylene molecules at 6.0 Å
and at 3.5 Å
The orbitals in both cases look similar but the eigenvalues λ1 and λ2 are different. For the larger separation both are equal at about 0.45. For the smaller separation, there is one dominant one at 0.86. Clearly, these are different wavefunctions, but what is the significance?

In the paper I am arguing that only the first case is consistent with the idea of a Frenkel exciton, i.e. two coupled local excitations. The second case can be seen as one homogeneous transition. This automatically means that there is admixture of charge transfer, since the orbitals are distributed evenly. And indeed when we apply our charge transfer measures, we find charge resonance character in the second case.

The whole formalism employed is somewhat abstract, unfortunately, and too much for one single blogpost. But the take home message is the following: Quantum and correlation effects appear even for rather simple excited state calculations. In critical cases these may mislead us when interpreting the calculations. Luckily, there is a solution to this conundrum - our wavefunction analysis tools TheoDORE and libwfa :)

Tuesday, 16 February 2016


If you are into large aromatic hydrocarbons, here is a new paper for you: "The Polyradical Character of Triangular non-Kekulé Structures, Zethrenes, p-Quinodimethane Linked Bisphenalenyl and the Clar Goblet in Comparison: An Extended Multireference Study," which just appeared in J. Phys. Chem. A. In this work we studied different bonding patterns for polycyclic hydrocarbons and how they lead to the formation of radical character. Some of the systems studied are based on phenalenyl:

In these cases the polyradical character derives from Ovchinnikov's rule. Simply speaking, in all these cases there are more "starred" atoms than "unstarred" atoms. Therefore, some of the "starred" atoms are always left out of the bonds and become radical centers.

For the other systems we studied, Clar's sextet rule comes into play. In an attempt to maximize the number of Clar sextets, the molecule creates empty valences somewhere else, leading to openshell character.

Wednesday, 10 February 2016

Wavefunction Overlaps

By using wavefunction overlaps you can run nonadiabatic dynamics without computing coupling vectors. This little trick gives you lots of freedom and allows you to run dynamics for any method as long as it gives you gradients. Different people have done that for TDDFT, we have added interfaces for coupled cluster and ADC, and for multireference methods with spin-orbit coupling. However, the one big problem about wavefunction overlaps is that computing them can get really expensive very quickly. Since the orbitals change between the two geometries, the Slater Condon rules do not apply anymore meaning that you have to compute one overlap determinant for every pair of Slater determinants in the expansion.

Fortunately, the situation is not quite as bad, as there are many repetitive terms. If you precompute those and reuse them, things get better. The first step was to identify those repetitive terms, the second one was to think of an algorithm that takes advantage of them, the third one was actually implementing it in a code that works. The result was quite nice: Typical calculations run a thousand times as fast as our previous code and produce exactly the same result. At the same time our formalism is completely general and allows you to do also other things than dynamics. More about that later ...

Read more about our algorithm in our new JCTC paper "Efficient and Flexible Computation of Many-Electron Wavefunction Overlaps". If you want to try it out yourself, wait for the new SHARC release or contact me.

Friday, 29 January 2016

TheoDORE 1.2 plus tutorial

The theoretical density, orbital relaxation and exciton analyis suite, conveniently abbreviated TheoDORE, goes into version 1.2. There is support for a number of different quantum chemical programs: Q-Chem, Columbus, Molcas, Turbomole, Orca, Gaussian, and various types of GAMESS. Aside from the charge transfer number analysis, the electron-hole correlation plots, and the natural transition orbitals, TheoDORE also lets you perform various kinds of population analysis. You can also process density matrices to get unpaired electrons, bond orders, and attachment/detachment densities. You can even get an approximate exciton size (even though the real thing is only available in Q-Chem). And everything is embedded in an ever improving user interface. So, check it out :)

There is also a new tutorial that should allow you to get started quickly and plot such nice things as these natural transition orbitals:

Wednesday, 20 January 2016

Many worlds of Surface Hopping

What happens during a surface hop in Surface Hopping dynamics? Does the wavefunction collapse or do you create a parallel universe?

Imagine the process of vision. We start with retinal in its excited state after it has absorbed a photon. In the next picosecond retinal has several distinct possibilities to hop to the ground state. Once such a hop occurrs, the molecule can isomerize, which can in turn change the configuration of the rhodopsin protein and ultimately trigger vision. In our simulations we need a random number generator to decide when the hop occurs. Why do we need a random number generator to simulate reality?

There are two equally disturbing answers to this question. Answer 1: Random wavefunction collapses happen, or as Einstein put it - God plays dice. Answer 2: The wavefunction never collapses. Everything we know of is just one big wavefunction. That means that for every possible quantum transition both branches are equally real (weighted by the transition probability). Effectively, we spawn a parallel universe with every quantum transition. In one branch of reality the hop occurs at 100 fs and triggers the isomerization, in another branch it happens at 200 fs. In yet another branch the isomerization does not occur and no nerve signal of vision is transmitted. All these branches exist in parallel. But if decoherence occured fast enough they do not know about each other and it seems like the wavefunction collapsed.

If you want to know more about parallel universes, read Max Tegmark's book "Our Mathemtatial Universe".

Looking back, I wrote a similar post before. The topic still captivates me ...