Low Scaling Algorithms for the Random Phase Approximation: Imaginary Time and Laplace Transformations

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• 作者：Merzuk Kaltak ; Ji艡铆 Klime拧 ; Georg Kresse
• 刊名：Journal of Chemical Theory and Computation
• 出版年：2014
• 出版时间：June 10, 2014
• 年：2014
• 卷：10
• 期：6
• 页码：2498-2507
• 全文大小：427K
• 年卷期：v.10,no.6(June 10, 2014)
• ISSN：1549-9626

文摘

In this paper, we determine efficient imaginary frequency and imaginary time grids for second-order M酶ller鈥揚lesset (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.