This research concerns improved methods for the modeling of material systems. Many materials modeling problems rely heavily on quantum mechanical models. However, for quantum mechanics to be really useful, one has to couple it with either continuum models or molecular mechanics models. The success of such an approach has been well documented in chemistry applications. This project explores approaches based on quantum mechanics (density functional theory) coupled with molecular mechanics or continuum mechanics in modeling materials. Although the coupled quantum mechanics/molecular mechanics approach has enjoyed a considerable amount of success, winning the 2013 Nobel Prize in chemistry, its application to general material systems, particularly metallic systems, has been at issue for a long time. The problem comes from the non-local effect of the errors made at the interface between the molecular mechanics and quantum mechanics regions. This problem is particularly severe for metallic systems. This project tackles these important challenges in the modeling of material systems.
There are many technical hurdles that one needs to overcome. First of all, one needs to improve the efficiency of density functional theory (DFT) algorithms to be able to handle inhomogeneous systems, such as systems with point defects or a small portion of extended defects. The next hurdle is to derive classical models, based on either molecular mechanics or continuum theory, that are consistent with DFT. This means that the DFT models reduce to classical models in some limit. A third problem is to design coupling schemes that move smoothly from DFT to classical models. The current project will focus on the second and third problems, beginning with one-dimensional model problems. The investigation's starting point is the Fermi operator formulation of DFT. By making successive approximations on the Fermi operator formalism, the PI aim to arrive at a consistent DFT/molecular mechanics or DFT/continuum model coupling scheme.
