Executive Summary : | Density Functional Theory (DFT) allows us to write total energy, E[n], as an explicit functional of density, n(r). E[n] = Ts[n], Eext[n], Ecoul[n], and EXC[n], which are the non-interacting kinetic energy (KE), interaction energy of electron with external potential, classical Coloumb energy, and energy due to exchange and correlation, respectively. Ts[n] and EXC[n] have to be approximated since they do not have exact mathematical form as a density functional (DF). However, the search for accurate approximations for Ts[n] is still an active area of research. Machine learning-based methods, such as feed forward neural networks (FFNN), have been adopted for constructing KE density functionals. FFNNs are used to represent unknown mathematical functions accurately based on known functions, with the output being the unknown mathematical function.
This proposal proposes developing an orbital free (OF) DFT model by constructing KE density functionals using FFNNs. The FFNN-based KE DF is constructed by considering electron density as an input and expanding it in terms of basis functions. The coefficients of these basis functions serve as inputs to FFNN, which maps the inputs to any output depending on the different types of KE DFs chosen. OF DFT methods linearly scale with the number of electrons in the system, making it natural to choose OF DFT for larger systems if accurate forms of KE DFs are known. This proposal will lead to advancements in OF DFT methods, testing for 1 dimensional toy models like harmonic oscillators and later expanding to 2-dimensional and 3D models. |