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 ...

Friday, 8 January 2016

User support

I am always happy about user requests for the various codes that I am involved with and I try to answer them quickly. Unless they annoy me. In the following, a short list of of rules that make it much more likely that I am not annoyed by a user request:
  • Use some polite words like "please" and "thank you".
  • Do not USE CAPITAL LETTERS to show which are the important parts. If not your whole e-mail is important, only send me the important parts.
  • Do not use bold face.
  • Why would you use more than one question mark in a row????
  • Tell me about what you are trying to do rather than just complaining that the code is not working.

Wednesday, 6 January 2016

More Conjugated Polymers

It looks like the exciton models we developed over the last years are actually reaching a level where "applied" people are becoming interested in them. I was very happy to have a joint project with S. Kraner from Dresden who wanted to examine universal properties of excitons in conjugated organic polymers. This collaboration lead to a new paper "Exciton size and binding energy limitations in one-dimensional organic materials" that just appeared in JCP.

The results showed that there is a quite universal relationship between molecular size and exciton size. The important point is, however, that the exciton size does not grow indefinitly with the molecular size. If the size of the π-system reaches about 40 Ang, no further enhancement of the exciton size occurs and a bound exciton remains.

Another point (and a reason why we had the pleasure to revise the manuscript quite a few times) is the fact that the results are strongly dependent on the exchange correlation functional. While the general trend of an exciton size limitation is present whenever you have some amount of Hartree-Fock exchange in the functional, the precise value differs, as discussed also in another recent paper by us. The reason is a correlation effect and ensuing dynamic charge transfer.