Highly Accurate Random Phase Approximation Methods With Linear Time Complexity

摘要

One of the key challenges of electronic structure theory is to find formulations to compute electronic ground-state energies with high accuracy while being applicable to a wide range of chemical problems. For systems beyond the few atom scale often computations achieving higher accuracies than the so called double-hybrid density functional approximations become prohibitively expensive.udHere, the random phase approximation, which is known to yield such higher accuracy results has been developed from a theory applicable only to molecules on the tens of atoms scale into a highly accurate and widely applicable theory. To this end, a mathematical understanding has been developed that, without changing the computational complexity, allows to eliminate the error introduced by the resolution-of-the-identity approximation which had been introduced in the previous formulation.udFurthermore, in this work a new formulation of the random phase approximation for molecules has been presented which achieves linear-scaling of compute time with molecular size - thereby expanding the realm of molecules that can be treated on this level of theory to up to a thousand atoms on a simple desktop computer. udFinally, the theory has been matured to allow for use of even extensive basis sets without drastically increasing runtimes.udOverall, the presented theory is at least as accurate and even faster than the original formulation for all molecules for which compute time is significant and opens new possibilities for the highly accurate description of large quantum chemical systems.