Our work makes use of a broad spectrum of ideas drawn from various areas of applied mathematics, condensed matter physics, quantum chemistry, solid mechanics, materials science and high performance scientific computing. Outlined below are some research problems that we have been working on.

## Research Projects

##### 1) First principles calculations of helical structures

The mathematical framework for classifying nanostructures shows that a vast class of these materials can be described as being helical, i.e., their spatial atomic arrangement possesses helical symmetries. Helical structures include important technological materials such as nanotubes (of any chirality), nanoribbons, nanowires and nanosprings; miscellaneous chiral structures encountered in chemistry; and examples from biology, including tail sheaths of viruses and many common proteins. Helical structures have been conjectured to be a fertile source of novel materials with unusual and attractive properties. For instance, collective or correlated electronic effects (such as those leading to ferromagnetism, ferroelectricity and superconductivity) can emerge in these materials. Also, helical structures are inherently chiral, and can serve as natural examples of materials systems in which unconventional transport phenomena can be observed.

In order to have predictive tools for studying helical structures, we have been developing a suite of rigorously formulated computational techniques that allow such materials to be simulated ab initio. The resulting tools allow for the ground state and excited state properties of helical structures to be calculated accurately and efficiently at the level of Kohn-Sham Density Functional Theory. We have been employing these tools for studying mechanical and electronic properties of various nanotube materials, as well as their response to imposed strains. This work has implications for the discovery and design of novel sensors, actuators and emergent quantum materials.

##### 2) Pushing the envelope of large scale first principles simulations of complex materials

Attractive as first principles calculations are, the solution of the equations of Density Functional Theory requires substantial computational resources while dealing with large and/or complex materials systems. In spite of active research in this area for several decades, first principles calculations (particularly, first principles molecular dynamics simulations) are still routinely limited to a few hundred atoms, unless simplifying assumptions about the nature of the system are made. We have been working towards overcoming some of these computational bottlenecks by designing and implementing novel mathematical and computational strategies. Our work (carried out with collaborators at Lawrence Berkeley National Lab, Georgia Tech. and Lawrence Livermore National Lab) has made it possible to carry out ab intio molecular dynamics simulations of non-insulating (i.e., metallic or semi-conducting) systems of unprecedented size, on large scale computational platforms.

As a result of these developments, it is now becoming possible for example, to carry out reliable large scale simulations of energy materials (such as Lithium ion batteries), refractory and structural materials (such as High Entropy Alloys), materials defects, and catalytic reactions. Such computational studies are expected to be instrumental in the design of next generation materials, as well as, energy storage/conversion devices. In particular, a vast number of problems of interest to engineers and mechanicians that have been outside the capabilities of existing first principles techniques, can be successfully attacked. Our current efforts (with collaborators at UCLA) include further algorithmic developments of the aforementioned techniques, as well as applications of these computational methods for simulations of specific materials systems of engineering interest.

##### 3) Understanding quantum properties of biomolecules

In recent years, there has been an emerging consensus that quantum effects (involving spin) in certain biomolecules may be critical to a variety of life processes. This includes magnetic field detection for animal migration, olfaction, metabolic and growth regulation in cells, and optimization of charge transport in proteins. Additionally, quantum simulations of the molecular processes responsible for these phenomena appear to suggest that the biomolecules at the heart of these processes are highly optimized to work within environmental parameters that closely match the surroundings in which they evolved (e.g., high sensitivity to low magnetic fields such as those associated with the Earth's). In particular, these molecules appear to function with utmost accuracy in wet and warm physiological environments, suggesting that they have evolved to resist or profit from the noise in their particular environment. These observations provide the motivation for investigating the properties of these molecules ab initio, so as to understand and harness their exceptional properties for technological applications.

Along these lines, together with collaborators from UCLA, we have been looking into the properties of certain nanoparticles of biological origin so as to understand their decoherence properties. A variety of computational tools (including first principles methods for studying cluster systems developed by our group) are being utilized for this. Our work is expected to have implications for the design of novel, room temperature quantum hardware.