# Research

# Research interests

## Disorder in organic semiconductors

Organic semiconductors such as phthalocyanine are used in organic solar cells and organic light emitting diodes (OLEDs) that can be found in modern cell phones. Perhaps surprisingly, less is known about their properties that one might imagine. These compounds are used in thin films that lack long-range order. There are open questions about how the properties of these materials are different in thin films than in pure crystals, and whether existing simulation methods can capture any changes in the material properties in the different material phases.

The computational methods for studying molecules and materials on the nanoscale are not perfect, and are still undergoing heavy development. Multiscale, multiphysics simulations combining a variety of existing and new computational models will be needed to treated the wide range of physical and chemical phenomena that occur across the wide range of length scales that are relevant to the manufacture of organic solar cells.

We have investigated simple models of disorder using the widely used Anderson model.

## Anisotropic excitons and hydrogenic impurities in semiconductors

Together with the group of Professor Rhavindra Bhatt (Princeton), we are developing new parameters for the Hubbard model to describe hydrogenic impurity bands by fitting them to extremely accurate *ab initio* quantum chemistry data. This new empirical potential will allow for future investigations of possibly engineering materials with new band structures with tunable spin states.

We are currently looking into how these models can be applied to also model anisotropic excitons using quantum chemistry, which would allow for much more accurate calculations of excitation energies and excitonic band structure in indirect bandgap semiconductors such as silicon.

## Enabling atomistic simulations of electrochemistry

## Random matrix theory, free probability theory and their applications

Random matrix theory studies the relation between the probability distribution of the matrix elements to the resulting probability distribution of matrix properties such as eigenvalues and eigenvectors. Together with Professor Alberto Suárez (UAM) and Professor Alan Edelman (MIT), we have been investigating how to apply these ideas to a wide variety of problems in the computational sciences.

### Random matrix theory and the sampling problem

We have found that free probability can yield extremely accurate approximations to the spectral density of the Anderson model for a wide variety of lattices. We are investigating whether random matrix theory can aid in mapping the explicitly sampled "ab initio" data onto simpler model Hamiltonians such as the Anderson model discussed above.

### Big data applications to bus arrival spacings

We are investigating how well random matrix theory can model the real world distribution of bus arrivals in the Massachusetts Bay Transportation Authority (MBTA) network. Surprisingly, real world data collected from real-time GPS tracking data show shocking good agreement with the simple models. Our results point toward a hitherto unsuspected level of universality in the relationship between bus arrival timings and the spacings of eigenvalues in Gaussian unitary ensembles.

## Scientific visualization and big data challenges in scientific computing

Calculations for disordered systems and systems that are partially characterized require explicit sampling of molecular configurations that are compatible with the overall thermodynamics. Any detailed calculation of these systems becomes much more expensive as the number of electronic structure calculations is multiplied by the number of sampled configurations. I developed software tools to automate the collection of data from massively parallel electronic structure calculations on millions of sampled structures.

More research is needed to develop more efficient statistical tools to determine how many samples are enough to obtained converged predictions of experimental observables, and dynamically generate more samples as necessary.

## Other collaborations

I have also been fortunate to play some small supporting rôles in other scientific endeavors.

### Benchmarking coupled-cluster codes

I am currently assisting Professor Anna Krylov (USC) in the benchmarking of coupled cluster codes in the Q-Chem quantum chemistry package. In collaboration with my PhD advisor, Professor Todd Martínez (Stanford), we are currently comparing the relative performances of the Q-Chem and Molpro for a test suite of coupled cluster calculations.

### Dearomatization of organophosphine complexes at room temperature

The Buchwald research group have developed a range of organic phosphines which, when combined with palladium, form excellent catalysts for many difficult cross-coupling reactions in organic chemistry. They recently noticed that in some of their experiments, that the desired product not formed, but instead formed unusual palladium complexes containing modified phosphine ligands with partial loss of aromaticity.

I was roped in to assist with determining the mechanism and thermochemistry of this reaction in this particular class of ligands using density functional theory. The calculations corroborated experimental evidence that the driving force for this reaction was a change in the ligand field of the palladium(II) center from square planar to a less common trigonal planar configuration, which for this high field complex, resulted in an exergonic change.

Our work was published in the Journal of the American Chemical Society in 2012.

## Find me online

Mendeley profile

Google Scholar: TQYNuFAAAAAJ

ResearcherID: B-6707-2008

ORCID: 0000-0002-4357-6574