The Many-Body Expansion Combined with Neural Networks |

K. Yao J. Herr and J. Parkhill, JCP 2016 10.1063/1.4973380

The Many-Body Expansion Combined with Neural Networks |

K. Yao J. Herr and J. Parkhill, JCP 2016 10.1063/1.4973380

We have done a little cleanup of our Github and transitioned a bunch of private repositories to public repositories, and moved code from bitbucket onto github. I’ll be traveling a bit in the winter and early spring. Look for me at:

IPAM – MPSWS4 (San Diego December 5-8, 2016)

ACS San Francisco (April 2017)

ASAP in Journal of Physical Chemistry A:

Nonradiative Relaxation in Real-time Electronic Dynamics OSCF2: Organolead Triiodide Perovskite. Authors: Triet Nguyen-Beck, John Parkhill.

Narrated by John Parkhill. Watch it here!

“Black-Box, Real-Time Simulations of Transient Absorption Spectroscopy” will appear in JPCL. Authors: Triet S. Nguyen, Joong Hoon Koh, Susan Lefelhocz, John Parkhill.

A page announcing and collecting information for the Heidelberg@ND summer school is posted. This is a summer school opportunity for students interested in applying computational chemistry to experimental problems.

Kun’s Convolutional Neural Network functional will appear in JCTC (10.1021/acs.jctc.5b01011).

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.

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…

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
. 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)…*years of effort and thought*

Anyone can now read about Kun’s convolutional neural network approach to kinetic energy functionals.

John Herr and Kevin Koh will be rotating with the lab for a few weeks, learning python and generally getting started. Welcome John & Kevin.

Triet’s second paper: “Non-adiabatic Dynamics for Electrons at Second-Order: Real-time TDDFT and OSCF2” will appear in JCTC. DOI: 10.1021/acs.jctc.5b00262

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.

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 :).

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

Nguyen, Triet S.; Nanguneri, Ravindra; and Parkhill, John. The Journal of Chemical Physics, 142, 134113 (2015). DOI: http://dx.doi.org/10.1063/1.4916822

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)**

It’s unlikely that our research group would exist without the work of Father Theodore Hesburgh, a remarkably successful and dynamic personality who devoted his life to other people. We pay our respects (http://hesburgh.nd.edu/).

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 20–24, 2015)

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
```

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:

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.

Ravi’s work studying the short lived excitons in Perovskite solar absorbers is now available.

She’s gotten a lot done this year. (dropbox pdf link)

If you feel you have a strong background in electronic structure theory and would like a challenging postdoctoral opportunity in method development, feel free to email me your CV.

Best-

John

The group had a great time at the Midwest Theoretical Chemistry conference, thanks to Professors Shiozaki, Schatz Ratner, Seideman, Snurr, Szleifer, Reuter and Olvera!

Undergraduate Nahee Kim has received a College of Science Summer Undergraduate Research Fellowship. (on behalf of her and the group, thanks college of science)

Triet Nguyen got an NSF graduate fellowship.

CONGRATULATIONS!

Ravi is a UC Davis physics Ph.D. with a background studying metal oxides. He comes to us during a period of anomalously frigid weather in South Bend, but seems to be dealing with it cheerfully.

Kun is thinking about non-radiative relaxation, and temporarily desk-less until the group space is finished.

Couldn’t be happier for him! The blurb is pretty digestible for non-experts.

http://phys.org/news/2013-10-feynman-wasnt-quantum-dynamics-ground.html

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.”*