Development of Effective Stochastic Kohn-Sham Potential Method using Random Matrix Theory for Performing DFT Calculations on Noisy Chemical Systems

In this work, we present the effective stochastic Kohn-Sham (ESKS) potential method to address the fundamental question of the impact of fluctuations in the external potential in the KS-DFT formulation. The functional relationship between the external potential and the electron density is central to the DFT formulation. Need for efficient treatment fluctuations in the external potential arises in chemical systems because of the presence of solvents and the existence of non-zero temperatures. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the effective stochastic Kohn-Sham potential was derived using functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESKS was obtained using the random-matrix theory method. The developed method was applied for calculations of the distribution of energies and quasiparticle gaps in atoms, molecules, and solvated quantum dots at non-zero temperatures.