Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis

We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring O(N-3) operations and O(N-2) memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-zeta quality basis.