ACS

Triet’s poster for the ACS in San Diego on Transient Absorption spectroscopy is looking great. It’s in the Sci-Mix section so take a look if you’re in the neighborhood. I’ll be speaking in three program items (all condensed into one day). Here’s what’s happening:

ched

Susi Lehtola Visit and Welcome Kevin & John

This week we were visited by Dr. Susi Lehtola from Martin Head-Gordon’s group at Berkeley. Susi’s doing a high performance implementation of PQ, PH etc. and seeing phenomenal speedups (>500x) over the old code. It looks like he’ll be only limited by orbital transformation time, and thus able to study huge systems. Of course the tradeoff is that vs. my original machine generated code (which was still large. ~200Kb files), Susi’s source files are so big they are making GCC squeal (who doesn’t wanna hear GCC squeal). John Herr and Kevin Koh have officially joined up as of a few hours ago welcome guys. IMG_20151119_165240

It’s working…

power

The RPA/TDDFT has many shortcomings, the most elementary being it’s inability to generate double excitations. Peaks are missing from the RPA spectrum and appear at the wrong energies. So here’s a difficult example where I’ve constructed a molecule which is strongly correlated (it’s bandgap is <1eV) and propagated it with our new EOM (ee2) & RPA. The exact transitions for this molecule occur at the red sticks. Despite the fact that it is based on the 1-RDM alone, is cheaper than Mp2, and despite the fact that it has no memory kernel, ee2 captures the missing states and double excitations. It provides a great improvement over RPA…

Halloween Stuff!

So much fun stuff has been going on that I’ve been neglecting to post. Let me summarize some developments:

  • Figures from Triet’s research will be featured in the Shamrock Series 5k.
  • Dr. Susi Lehtola will be visiting our group in November from Martin Head Gordon’s group in Berkeley.
  • I’ll be charing a session about dissipative states at ACS San Diego, and participating in a Forum in the Comp Section.
  • Finally my favorite: I have realized a correlated electronic dynamics which preserves positivity and yet changes natural orbital occupations! This is a the culmination of years of effort and thought. This methodology can be used to study dynamics in fractionally occupied, strongly correlated systems (a hard problem). The method can be considered an improvement to RPA, and like it’s parent it is non-linear, actually fifth order in the 1RDM. The non-linearity is what allows this 1RDM method to preserve positivity while avoiding any memory kernel. The Kernel is effectively time dependent, but that time dependence is just a time-local function of the instantaneous density matrix. People who are interested in non-adiabatic TDDFT functionals: take note! performance of this EOM for excitation energies will be published shortly. Here’s a teaser plot of the electronic entropy growing with time (fs) . This is a strongly correlated 4 electron system where orbital occupations in the exact state should be roughly ~(0,0,0,0,1,1,1,1)… Entropy

Postdoctoral Position Available.

Position requires proficiency in one of the standard computer programming languages used in science: C, C++, Fortran or Python, and a completed thesis on a topic relevant to quantum chemistry.

Student will have their choice of a broad range of topics in functional development, electronic or molecular dynamics, and correlation theory.

Interested parties should send their CV’s and best paper to john.parkhill@gmail.com.

Fun Math Problem.

I just finished a really fun elementary math problem that I needed for my work; thought I’d share the answer. The problem is this: suppose you have 8 positive numbers (p,q,r,s,t,u,v,w), all co-prime besides possibly being equal. How many different types of equality ensure:

p+q+r+s-t-u-v-w = 0          (1)

For example one solution is (p=t, q=u, r=v, s=w). The answer is related to a rotating-wave” or “secular” approximation for a many-particle density matrix in quantum dynamics. We can use sets of numbers which obey this condition to dramatically accelerate our many-body quantum dynamics calculations and treat correlation energy.

It turns out that the following expression of Kronecker deltas is 1 for every p,q,r,s… that satisfies (1) and zero otherwise, as you can easily verify. I’ll leave the derivation as an exercise to the reader :).

secularizer

Scientific Art.

The best part about this blog is we can post attractive but unconventional scientific stuff. This is a lovely “table-of-contents” style graphic that Triet has made about our recently developed realtime dynamics code. It nicely sums up our efforts in this area. The data is real too.

toc (1)

Lead Halide Perovskite (PbI3-CH3NH3) Under Impulsive Excitation

A broadband ‘light’ impulse of duration 0.07 atomic units is applied along the x-axis at time t=0. The electronic dynamics includes our dissipation theory, although this short time (~20fs) is not enough to watch the electron relax back to it’s ground state position. If you pay close attention to the atoms on the central line you can see the average ‘slosh’ of the density (on a timescale of about 1/frame which is roughly 1fs). The excitation is mostly due to rearrangement of the density onto lead from iodine. If you look at the surronding iodine atoms you can see their p-density rotate, responding to the central density oscillation, that’s what you’d call ‘dynamic screening’. (Click the image to animate)animated

Upcoming Meetings.

Want to hear about what we’re up to? We’re going to cover a pretty large swath of territory over the next few months. If you’re in the neighborhood we love to meet old and new friends.

Feb 19th: Notre Dame Physics Seminar

March 22nd – 26th: ACS National Meeting in Denver (Symposium for Highly Polarizable Systems)

May 26nd – 29th: Many Body Interactions Workshop

July 5th -12:  The Joint Heidelberg-Notre Dame Summer School in Computational Chemistry

July 13th-17th: Telluride Summer Schools

(also staying for  Nonequilibrium Phenomena, Nonadiabatic Dynamics and Spectroscopy”, July 2024, 2015) 

 

Relaxation movies with Jmol.

Probably the easiest but not the most attractive way to generate an animated gif of electron density during a relaxation process is the combination of Jmol with imagemagik. You run our code to generate a molden file with densities in sequential orbitals, and then run the following Jmol script after opening that molden file and dragging this into the script console. I have shamelessly adapted this script from Google:

print “Dumping densities... ”
for (var i = 1; i <= 1000; i = i+4)
 print i;
 var filename = "movie"+("00000"+i)[-4][0]+".jpg”;
 mo @i; 
 mo cutoff 0.000005
 mo translucent 0.3; 
 mo Fill noMesh noDots frontOnly frontlit;
 write IMAGE 600 400 JPG @filename;
 frank on; 
 select *; 
 set fontScaling false; 
end for

At that point in your Jmol has dumped .jpg’s into it’s directory which you can then convert into an animated gif by simply running the following command in that directory provided you have installed imagemagik. The animated .gif made below is the excess electron density (above the DFT ground state) caused by light irradiation along the x-axis of a hydrogen ring (click to see the animation in Chrome). “Energy” in the text of the plot is actually the time of the frame in atomic units. The occupancy of the excess electron is small because the applied field was ~0.0001 atomic units, and it oscillates while the excited states persists before it eventually decays to zero.

convert -delay 10 -loop 1 *.jpg animated.gif

animated

To equilibrate properly electronic relaxation rates depend on the density matrix!

In high dimensional systems very few exact results are known about quantum dynamics. One of the most important exact conditions we can try to satisfy is detailed balance, ie: dynamics should equilibrate to the correct statistical distribution, a Fermi distribution for electrons, at long times.

Lots of people are familiar with Surface Hopping, Redfield theory, and Ehrenfest dynamics, but actually you can’t use any of these methods to produce a Fermi distribution exactly. Based on our work simulating relaxation, we’ve actually been able to derive an equation of motion which does obey Fermi-Dirac statistics. In obtaining the derivation, we learned useful tricks that are going to help us treat mixed-states on the same footing as pure states. We’re super jazzed about these things.

There are cool experimental consequences, for example that non-radiative relaxation rates are not constant with time. You can check out the whole story on ArXiv for the time being:

PopulationsVsTime

http://arxiv.org/abs/1411.5324

Denver ACS Comp Symposium & Murray State

Daniel Lambrecht and I are putting the finishing touches on the schedule, and we’re very excited about the lineup. Thanks to all the fantastic speakers who submitted abstracts. We hope to have scheduling information for you soon. We’d both like to graciously thank Q-Chem for their support of our symposium as well.

Today I’m giving a talk at Murray State University in Murray Kentucky. I also want to thank Prof Kevin Miller for his hospitality here.

IMG_20141110_081931

A Symposium for Polarizable Systems

Daniel Lambrecht and myself are organizing a symposium at the Denver 2015 ACS on the subject of electronic structure methods for simulating highly polarizable systems. Please contact one of us if you are interested in contributing a talk. Here is the poster summary:

“There are widespread technological applications for molecules which can readily accept and transform small packets of energy. Optoelectronic materials, molecular electronics, and photocatalysis speak to the technological impact of modeling such systems. At the same time, any rational advancement involves a firm understanding of fundamental processes such as energy and electron transfer, electron and nuclear dynamics, and electron-phonon interactions.  Modeling the interactions of polarizable molecules with their environment therefore remains a challenge for modern electronic structure theory and represents an area of vibrant development. This symposium collects emerging methodologies for computing the properties of small-gap, polarizable materials in their ground and excited states. New phenomenological and ab-initio theories targeted at these systems are welcome contributions to this symposium, including developments in embedding approaches, excited state theories and electronic dynamics. State-of-the art applications of first principles approaches theory used to interpret, rationalize and guide experiment are also invited. The tools discussed are useful for studying charge and energy collection and transport on lengths ranging between atomic systems and the nanoscale.”

 

Data’s coming in.

Triet is a very good summer student, and she’s studying the classical noise that electrons experience after just 2 weeks of group history. The fluctuations she captured and plotted below will be used to characterize dephasing between electrons within a single molecule. Looking at the magnitude of these single electron energy fluctuations at 300K, we expect to be busy for a long time building dephasing models and understanding how they change photochemistry and excited state dynamics.

purrtyplot

Bath models made more cheaply and more physically

Readers familiar with the physics of open quantum systems have probably encountered a functional parametrization (ohmic, super-ohmic, etc.) for a thermal bath of linearly coupled, non-interacting harmonic oscillators. Physically motivating these models from the atomistic structure of a quantum material is a difficult and expensive semi-classical process, but the detailed structure of the bath can drastically alter short time population dynamics. The most satisfying procedure I am aware of consists of:

1) Performing a closed-dynamics (usually classical) simulation of quantum system and environment, somehow partitioning system and environment so you can monitor energy fluctuations of the system.

2) Taking the resulting energy fluctuation time-series constructing the real, symmetric classical correlation function.

3) Semi-classically extending this correlation function to obey the quantum conditions for causality and detailed balance while performing a Fourier transform to obtain the frequency dependent model for the harmonic bath.

In terms of wall-time, step 1) is most expensive because something like ab-initio MD needs to be run for a length time going as the inverse frequency of the slowest bath mode (40ps or so) while sampling the quantum Hamiltonian in the classical environment. In this recent work Thomas Markovitch reduced by a factor of roughly 8 the required MD simulation time, by exploiting a sparse l1 signal processing technique (super-resolution). As an added bonus the l1 technique decomposes the spectral density into an analytical form which yields an analytic non-Markovian bath kernel. This is a step towards “black-box” baths which are more than three parameters of an Ohmic function. (ArXiv)

sd_site1

Classical Force-Fields which Reproduce Equilibrium Quantum Distributions

Personal hero and noted banjo enthusiast Bill Miller often poses the following thought experiment to critique classical MD:

The zero point energy in the ~3000 wavenumber modes of water is more than 20 times larger than Kb*T at room temperature. If you gave these degrees of freedom their ZPE in classical MD that ZPE would leak into other modes, at the very least resulting in a high effective temperature.

In protein simulations this isn’t an immediate problem because high-frequency oscillators are frozen out by the SHAKE algorithm (to allow for large integrator timesteps) and given no zero point energy. Clearly it would be nicer to treat the quantum effects in the MD. People in this field know there are many, many ways to do this, usually based on some scheme to approximately integrate the path integral, but nothing as simple as running CHARMM or CPMD.

In this pre-print Ryan Alan and I propose an alternative: generate an effective force field which reproduces the density of the quantum system under the laws of classical statistical mechanics. We show such a potential exists, and that the map between the physical potential and the fictitious effective potential is unique. You can think of this like DFT for quantum MD, it takes a simulation which is easy to perform (classical MD/MC) and gives you the exact density. The catch is that you need to come up with this mapping that contains all the information about the difference between the quantum and classical effective potentials. (something like the problem of knowing the exact functional). We also numerically inverted that map for some low dimensional systems.

EFF

McClean’s Clock Variational Principle

In the time between finishing my post-doc and beginning the group I’ve been indulging my appetite for random quantum ideas outside of the electronic structure realm. Jarrod McClean came up with this pretty wild adaptation of quantum computing’s ancilla concept to do quantum dynamics. The approach (which we cast as a version of the quantum time-dependent variational principle) has some interesting features, and we eventually managed to do parallel in time dynamics with it. (arXiv)

clock