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Coupled cluster Green's function (GFCC) calculation has drawn much attention in the recent years for targeting the molecular and material electronic structure problems from a many body perspective in a systematically improvable way. However, GFCC calculations on scientific computing clusters usually suffer from expensive higher dimensional tensor contractions in the complex space, expensive interprocess communication, and severe load imbalance, which limits it's routine use for tackling electronic structure problems. Here we present a numerical library prototype that is specifically designed for large scale GFCC calculations. The design of the library is focused on a systematically optimal computing strategy to improve its scalability and efficiency. The performance of the library is demonstrated by the relevant profiling analysis of running GFCC calculations on remote giant computing clusters. The capability of the library is highlighted by computing a wide near valence band of a fullerene C60 molecule for the first time at the GFCCSD level that shows excellent agreement with the experimental spectrum.