Divide-and-Conquer Method for Instanton Rate Theory.

Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around it. In the standard method, calculating the fluctuation terms involves the diagonalization of a large matrix, which can be unfeasible for large systems with a high number of ring-polymer beads. Here we present a method for computing the instanton fluctuations with a large reduction in computational scaling. This method is applied to three reactions described by fitted, analytic, and on-the-fly ab initio potential-energy surfaces and is shown to be numerically stable for the calculation of thermal reaction rates even at very low temperature.