2017/07/26 by Daniel Neuhauser, Roi Baer, Neuhauser, Daniel +3 · 2 citations
Physics and Astronomy · Chemistry · #Advanced Chemical Physics Studies #Spectroscopy and Quantum Chemical Studies #Advanced Physical and Chemical Molecular Interactions
paper · pdf · doi:10.48550/arxiv.1707.08296
The second-order Matsubara Green's function method (GF2) is a robust\ntemperature dependent quantum chemistry approach, extending beyond the\nrandom-phase approximation. However, till now the scope of GF2 applications was\nquite limited as they require computer resources which rise steeply with system\nsize. In each step of the self-consistent GF2 calculation there are two parts:\nthe estimation of the self-energy from the previous step's Green's function,\nand updating the Green's function from the self-energy. The first part formally\nscales as the fifth power of the system size while the second has a much\ngentler cubic scaling. Here, we develop a stochastic approach to GF2 (sGF2)\nwhich reduces the fifth power scaling of the first step to merely quadratic,\nleaving the overall sGF2 scaling as cubic. We apply the method to linear\nhydrogen chains containing up to 1000 electrons, showing that the approach is\nnumerically stable, efficient and accurate. The stochastic errors are very\nsmall, of the order of 0.1% or less of the correlation energy for large\nsystems, with only a moderate computational effort. The first iteration of GF2\nis an MP2 calculation that is done in linear scaling, hence we obtain an\nextremely fast stochastic MP2 (sMP2) method as a by-product. While here we\nconsider finite systems with large band gaps where at low temperatures effects\nare negligible, the sGF2 formalism is temperature dependent and general and can\nbe applied to finite or periodic systems with small gaps at finite\ntemperatures.\n