Kaltak Merzuk, Klimeš Jiří, Kresse Georg
University of Vienna, Faculty of Physics and Center for Computational Materials Science , Sensengasse 8/12, A-1090 Vienna, Austria.
J Chem Theory Comput. 2014 Jun 10;10(6):2498-507. doi: 10.1021/ct5001268. Epub 2014 May 13.
In this paper, we determine efficient imaginary frequency and imaginary time grids for second-order Møller-Plesset (MP) perturbation theory. The least-squares and Minimax quadratures are compared for periodic systems, finding that the Minimax quadrature performs slightly better for the considered materials. We show that the imaginary frequency grids developed for second order also perform well for the correlation energy in the direct random phase approximation. Furthermore, we show that the polarizabilities on the imaginary time axis can be Fourier-transformed to the imaginary frequency domain, since the time and frequency Minimax grids are dual to each other. The same duality is observed for the least-squares grids. The transformation from imaginary time to imaginary frequency allows one to reduce the time complexity to cubic (in system size), so that random phase approximation (RPA) correlation energies become accessible for large systems.
在本文中，我们确定了用于二阶莫勒-普莱塞特（MP）微扰理论的有效虚频和虚时网格。针对周期性系统比较了最小二乘积分和极小极大积分，发现极小极大积分在所考虑的材料中表现稍好。我们表明，为二阶开发的虚频网格在直接随机相位近似中的关联能计算方面也表现良好。此外，我们表明虚时轴上的极化率可以傅里叶变换到虚频域，因为时间和频率的极小极大网格是对偶的。对于最小二乘网格也观察到了相同的对偶性。从虚时到虚频的变换使得时间复杂度降低到立方级（与系统大小有关），从而对于大型系统也能够计算随机相位近似（RPA）关联能。
