Amount Awarded: $22,250
There is an increasing demand for computations in chemistry. While density-functional theory (DFT) is the workhorse of quantum chemistry, wave-function based methods are essential whenever high accuracy is needed. The coupled-cluster (CC) method has played a revolutionary role in establishing a new level of high accuracy in electronic structure calculations and quantum chemical simulations, and is today by far the most popular method. Despite this popularity, the mathematical analysis of CC formalisms is still in its infancy. In particular, there is no procedure for adaptive error improvement, i.e., a posteriori error estimation. The groups in Oslo and Berkeley specialize in quantum chemistry method development and analysis. The Berkeley group has in particular developed a posteriori error estimates for discontinuous Galerkin approximations of elliptic eigenvalue problems, while the Oslo group has developed a powerful mathematical framework for CC methods. The goal of this project is to elaborate a framework for a posteriori error analysis in CC theory. We believe this initial interdisciplinary effort could lead to long term and productive interactions between the groups, as well as produce analyses with potential great impact and opportunities for future research.