Development of effective stochastic potential method using random matrix theory for calculation of ensemble-averaged quantum mechanical properties at non-zero temperatures

An ensemble-averaged description of quantum mechanical properties is computationally prohibitive because it requires performing many electronic structure calculations. In this work, the effective stochastic potential (ESP) method is presented for performing large-scale calculations of ensemble-averaged quantum mechanical properties, and alleviates the computational cost associated with the conformational sampling required to obtain these properties. The ESP method represents the thermal fluctuations in a chemical system as an effective stochastic potential, derived using random-matrix theory. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the deformation potential arising from non-zero temperature was obtained using an infinite-order central moment expansion of the distribution. The formal definition of the ESP was derived using a functional minimization approach to match the infinite-order expansion for the deformation potential. The ESP method was implemented using both HF and KS-DFT formalism, and ensemble-averaged ground and excited state energies will be presented.