arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1707.08296physics.chem-phcond-mat.mes-hallcond-mat.mtrl-scicond-mat.str-elphysics.comp-ph
收藏

大电子系统关联能的随机自洽二阶格林函数方法

Stochastic self-consistent second-order Green's function method for correlation energies of large electronic systems

Daniel Neuhauser, Roi Baer, Dominika Zgid

摘要:

二阶松原格林函数方法(GF 2)是一种稳健的温度依赖量子化学方法,超越了随机相位近似。然而,到目前为止,GF 2应用程序的范围相当有限,因为它们需要随着系统规模急剧增加的计算机资源。在自洽GF ~ 2计算的每一步中,有两个部分:从前一步的格林函数估计自能和从自能更新格林函数。第一部分形式上按系统大小的五次幂缩放,而第二部分具有更温和的立方缩放。在这里,我们开发了一种GF 2(sGF 2)的随机方法,该方法将第一步的五次幂缩放减少到仅仅是二次的,使整体sGF 2缩放为三次的。我们将该方法应用于含有多达1000个电子的线性氢链,表明该方法在数值上是稳定的,有效的和准确的。的随机误差是非常小的,为0.1%或更少的大型系统的相关能量的顺序,只有一个温和的计算工作。GF 2的第一次迭代是在线性尺度下进行的MP2计算,因此我们获得了一个非常快速的随机MP2(sMP 2)方法作为副产品。虽然在这里,我们考虑有限的系统与大的带隙在低温下的影响是可以忽略不计的,sGF 2形式主义是温度依赖性和一般性的,可以应用于有限或周期性的系统在有限的温度下的小间隙。

英文摘要:

The second-order Matsubara Green's function method (GF2) is a robust temperature dependent quantum chemistry approach, extending beyond the random-phase approximation. However, till now the scope of GF2 applications was quite limited as they require computer resources which rise steeply with system size. In each step of the self-consistent GF2 calculation there are two parts: the estimation of the self-energy from the previous step's Green's function, and updating the Green's function from the self-energy. The first part formally scales as the fifth power of the system size while the second has a much gentler cubic scaling. Here, we develop a stochastic approach to GF2 (sGF2) which reduces the fifth power scaling of the first step to merely quadratic, leaving the overall sGF2 scaling as cubic. We apply the method to linear hydrogen chains containing up to 1000 electrons, showing that the approach is numerically stable, efficient and accurate. The stochastic errors are very small, of the order of 0.1% or less of the correlation energy for large systems, with only a moderate computational effort. The first iteration of GF2 is an MP2 calculation that is done in linear scaling, hence we obtain an extremely fast stochastic MP2 (sMP2) method as a by-product. While here we consider finite systems with large band gaps where at low temperatures effects are negligible, the sGF2 formalism is temperature dependent and general and can be applied to finite or periodic systems with small gaps at finite temperatures.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑