Low-scaling analytical gradients for the direct random phase approximation using an atomic orbital formalism.

We present an atomic orbital formalism to obtain analytical gradients within the random phase approximation for calculating first-order properties. Our approach allows exploiting sparsity in the electronic structure in order to reduce the computational complexity. Furthermore, we introduce Cholesky decomposed densities to remove the redundancies present in atomic orbital basis sets, making our method a competitive alternative to canonical theories also for small molecules. The approach is presented in a general framework that allows extending the methodology to other correlation methods. Beyond showing the validity and accuracy of our approach and the approximations used in this work, we demonstrate the efficiency of our method by computing nuclear gradients for systems with up to 600 atoms and 5000 basis functions.