Thursday, 28 August 2014

Multireference spin-orbit configuration interaction - perturbational treatment

If you are interested in multireference methods and/or relativistic effects, here is a new paper for you: "Perturbational treatment of spin-orbit coupling for generally applicable high-level multi-reference methods" in J. Chem. Phys. What we did is taking the existing spin-orbit CI code in Columbus and extended it for quasi-degenerate perturbation theory, which is in fact just a fancy way of saying that we stop the MR-CI after the first iteration (using the non-relativistic solutions as initial guesses). Besides that we needed an interface translating the CI vectors between the non-relativistic and relativistic representations.

With this tool we could compare the perturbational treatment with the full SO-CI. The agreement of the relative energies was quite good. But there was a significant difference in the total energies, since spin polarization was missing in the perturbational model space. But this was a systematic error affecting all states more or less the same.

The main reason why we wanted the perturbational approach is that it allows for the computation of gradients and non-adiabatic interactions (assuming that the spin-orbit couplings are slowly varying). And then we can do non-adiabatic dynamics with it. So far the methodology is implemented in SHARC with an application in this paper.

And finally, since they always look cool, a representation of the Shavitt graph coding the SO-CI configurations:

Thursday, 31 July 2014

gmolden - exporting densities

For some reason I never realized that there was a program called gmolden that works just as normal molden but looks much cooler (with opengl graphics). You can download the precompiled executable from their homepage just as the normal one. And then, finally, you can have shiny molecules and orbitals in molden.

The reason why I went back to molden is that it lets you produce densities from orbitals and occupation data. In my case I wanted to compute hole/particle densities (which are similar to the attachment/detachment densities but for general wavefunctions not quite the same) as weighted sums over the natural transition orbitals.

And since I like to do my density plotting in VMD, I can also ask molden to export cube files, which I can open in VMD. And then I can plot at the hole density ...
... and the particle density ...
... the way I like to do this.

Sunday, 20 July 2014

Orbital relaxation - the natural difference orbitals

As another example for the wavefunction analysis tools from last post, let us look at dimethylaminobenzonitrile (DMABN), a prototype charge transfer molecule and analyze the S2 state. I will start with the natural transition orbitals (NTOs), the singular vectors of the transition density matrix. The S2 state of DMABN has only one pair of NTOs with any significant contribution. To the left the hole, to the right the particle NTO are shown. In this representation the state can be clearly identified as a ππ* state with some partial charge transfer character (going from the amino to the nitrile side).

The hole and particle densities, i.e. the weighted sums over all NTOs, closely resemble these primary NTOs:


For comparison, we can look at the attachment/detachment densities as computed from the difference density matrix:

These look notably different from the hole and particle densities! What you can see at first sight, is that they are "bigger" - there is more happening. While the hole and particle densities contain 0.84 electrons each, the integral over the attachment and detachment densities is 1.41 e. To get a more detailed look at this, we can analyze the natural difference orbitals (NDOs), the eigenvectors of the difference density. Here for example the first three detachment and attachment NDOs and their respective eigenvalues:

-0.9110.908
-0.0600.059
-0.0430.043

The first pair of NDOs corresponds to the NTOs as shown above. But aside from that, there are a number of additional contributions. The two most important ones are apparently polarizations of the σ-bonds: while the primary excitation process takes electrons from the π orbital at the amino N-atom, some of the electron density is restored through the σ-system. We can quantify this through a Mulliken analysis and find out that during the primary transition, the N-atom loses 0.33 e and gains 0.04, i.e. there is a primary charge shift of 0.29 e. By contrast the difference density tells us that 0.39 electrons are detached from N-atom and 0.19 are attached leading to a net charge shift of only 0.19 e on this atom. By construction the latter corresponds to the actual change in the Mulliken population. But, I guess also the former has a physical significance.

Anyway, I do not want to go into much more detail now. But I hope I could convince you that there is really a lot of exciting stuff happening with excited states (as the name suggests ...). And just looking at HOMOs and LUMOs is not going to help you with any of that. If you are interested, you can check out the two new papers (Part I, Part II), download the Wave Function Analysis Tools from my homepage, or use Columbus where some of these things are implemented as well. Unfortunately, the whole functionality is not released yet. But it will be made available soon within the ADC module of Q-Chem and as a separate C++ library. Let me know if you have any questions or any suggestions for applications.

Saturday, 12 July 2014

Analysis and visualization of excited states

My drive to create pretty orbital pictures lead to two new papers, which I quite like: "New tools for the systematic analysis and visualization of electronic excitations" Part I: Formalism and Part II: Applications. Actually, a number of interesting things happened on the way and people seem to like it so far.

One of the interesting points is the discrepancy between the transition and difference density matrices. Both should give you a compact representation of the transition - but not necessarily the same one ...

For example these are the hole and particle densities (computed from the 1-particle transition density matrix) of the first two singlet excited states of adenine (using Jan's extension of my VMD plotting script) deriving from a ππ* and a nπ* state.


For comparison the attachment/detachment densities (computed from the difference density)

 What you can see is that the attachment/detachment densites are "bigger" than the particle/hole densities. The difference is that many-body effects and orbital relaxation are only included in the latter case giving additional contributions. You can look at this in more detail by analyzing the individual orbitals these are composed of, the "natural difference orbitals". Maybe I'll show that in the next post. Or check out the articles - I think for the first 30 days you can even download them freely.

Sunday, 18 May 2014

Suitcases with wheels

More than 5000 years passed between the invention of the wheel and that of the wheeled suitcase, as Nassim N. Taleb points out in his book "Antifragility". By the time humanity sent a man to the moon we still had three decades left of straining our shoulders lugging around bags whenever we traveled. Quantum theory and relativity had been discovered for more than fifty years and the scientists uncovering the subtleties of these theories with ever more detail had to pick up and carry their suitcases when they wanted to go and discuss their findings at a conference. And then someone started putting wheels on a suitcase. This completely changed luggage carrying. Wherever you look, you'll find people dragging around their trolleys.

I think this is a big lesson for people like us who are supposed to be in the "invention business." The paradigm changing innovation may be right in front of our eyes, and it might have been there for a long time. It is just that we are too domain dependent to see it. "Interdisciplinarity" (in this case between the fields of luggage carrying and transportation) is an overused buzzword but it is a key element of efficient research. Let's build suitcases with wheels rather than reinvent the wheel.