Accelerate stochastic calculation of random-phase approximation correlation energy difference with atom-based correlated sampling

A kernel polynomial method (KPM) is developed to calculate the random phase approximation (RPA) correlation energy. In the method, RPA correlation energy is formulated in terms of the eigenvalues of a matrix that is the product between the Coulomb potential and Kohn-Sham (KS) linear response function. The integration over the eigenvalues is then calculated using KPM. Since it is often the energy difference between two systems that is of much interest in practice, another focus of this work is to develop a method to accelerate the convergence of such energy-difference calculations. The method is termed atom-based correlated sampling (ACS). The performance of ACS is examined by calculating the isomerization energy of acetone to 2-propanol and the energy of water-gas shift reaction. Using ACS, the convergences are accelerated by 3.6 and 4.5 times, respectively. Methods developed in this work are expected to be useful for calculating energy differences between systems that mainly differ in certain local regions, such as calculating adsorption energies of molecules on metal surfaces for surface catalysis.