報告題目💆🏻‍♀️：FCI Truncation for Solving the Electronic and Nuclear Schrödinger Equations

報告人🖥🕎：James S. M. Anderson

Postdoctoral Associate of Computational Materials Science Research Team, RIKEN (Supervisor: Seiji Yunoki)

報告時間：7月6日, 10:00-11:00

報告地點：閔行校區生物藥學樓4-200

聯系人🧵：魏冬青, 34204573; 徐沁, 34204348

Abstract

An important goal of contemporary electronic and nuclear structure is to be able obtain a desired accuracy from approximate solutions to the Schrödinger equation in the least time. The full  configuration interaction  (FCI)  method  provides the best possible wavefunction within a basis set. The approach prosed here involves selecting a subset of the solutions used in FCI (typically a subset of all possible Hartree-Fock solutions within a basis set). Results from Griebel and others [1-4] in the mathematics of complexity literature show that if the analytic solutions to a given Schrödinger equation have mixed bound derivatives then it is possible to obtain FCI accuracy with polynomial scaling (at least in the large basis set limit). The theorems from Griebel and others [1-4] indicate which solutions to include based on the number of nodes in each solution. We refer to this approach as the GK-CI method. This truncation of the FCI method does not require any physical intuition of orbitals (e.g. the Hartree-Fock solutions) and is not constructed from the typical excitation-hierarchy approach. In this presentation I will described the method as well as provide preliminary results from both electronic structure and nuclear structure calculations.[5]

[1] M. Griebel and S. Knapek, Constr. Approx. 16, 525 (2000).

[2] H. Bungartz and M. Griebel, Acta Numer. 13, 147 (2001).

[3] G. W. Wasilkowski and H. Wozniakowski, Found. Comput. Math. 5, 451 (2005).

[4] S. A. Smolyak, Dokl. Akad. Nauk, 4, 240 (1963).

[5] J. S. M. and P. W. Ayers, J. Chem. Phys. Submitted (2011).