### Focus # 1: First-principles force-fields for classical atomistic simulations

Multi-scale modeling connects quantum chemistry simulations that model individual electrons in a material to classical atomistic simulations. Classical atomistic simulations model a material as a collection of atoms (‘balls’) connected by bonds (‘springs’) to reach larger time and distance scales than feasible with quantum chemistry. Interaction models for classical atomistic simulations are called force fields. We develop methods to automatically parameterize force fields so the quantum chemistry accuracy can be transferred to classical atomistic simulations. To do this, we develop better methods to compute atoms-in-material properties for force-field parameterization: net atomic charges, electron cloud parameters, polarizabilities, dispersion coefficients, etc. Our methods are designed to work across an extremely broad range of material types, including both magnetic and non-magnetic materials, with or without periodic boundary conditions. Our methods are designed to work with many different chemical elements. Both accuracy and computational efficiency are major considerations. Our methods are designed to work with a high degree of automation with little-to-no required manual tweaking by the end user. Thus, our methods are ideally suited to study large material datasets.

##### Application Area # 1: Metal-Organic Frameworks

We received NSF funding to develop automated methods to construct polarizable, flexible force-fields to design membranes using metal-organic frameworks (MOFs) to purify (a) helium from natural gas sources and (b) hydrogen from solar water splitting. An example MOF is shown to the right. We compute gas adsorption isotherms using Monte Carlo simulations in RASPA software. We compute gas diffusion constants using molecular dynamics simulations in RASPA software. A key challenge is to develop accurate, reliable, and computationally efficient force fields for the thousands of known MOF crystal structures.

##### Application Area # 2: Biomolecules

Our group collaborates with other research groups to study biomolecules. This topic is still new to us, and we have only a small effort in this area. We believe there are significant opportunities to improve force-fields for biomolecular simulations using polarizabilities, net atomic charges, dispersion coefficients, and other atomistic descriptors extracted from quantum chemistry calculations.

### Focus # 2: Atom-in-Material Descriptors

We develop and use improved methods to quantify atom-in-material properties: bond orders, net atomic charges (see journal article), atomic spin moments (see journal article), atomic multipole moments, etc. These chemical descriptors are extremely useful to better understand chemical reactions, magnetic ordering of materials, charge transfer, and chemical bonding. Although the bond order concept has been around for more than 100 years, only recently has a comprehensive definition and method for computing it been developed in our group (see journal article). As one application, we studied 288 diatomic molecules (see journal article). We are developing improved methods to model long-range dispersion interactions in quantum chemistry calculations (see journal article).

### Focus # 3: Numerical Methods for Scientific Computing

Recently, I developed a failsafe conjugate residual (FCR) algorithm to solve any system of linear equations containing a non-singular Hermitian coefficients matrix. This has been applied to linear equation systems containing millions of unknown variables and billions of non-zero coefficients. This FCR algorithm has endless applications. We are using it to solve the polarizability equations for polarizable force-fields.

Currently, I am also developing a better computational algorithm to compute large matrix permanents.

### Focus # 4: Theoretical Models of Physical Forces and Space-Time Structure

I am developing improved theoretical models of nuclear structures, subatomic particles, and the dimensional structure of physical space.