Kollmar Christian, Neese Frank
Max Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany.
J Chem Phys. 2014 Oct 7;141(13):134106. doi: 10.1063/1.4896897.
The role of the static Kohn-Sham (KS) response function describing the response of the electron density to a change of the local KS potential is discussed in both the theory of the optimized effective potential (OEP) and the so-called inverse Kohn-Sham problem involving the task to find the local KS potential for a given electron density. In a general discussion of the integral equation to be solved in both cases, it is argued that a unique solution of this equation can be found even in case of finite atomic orbital basis sets. It is shown how a matrix representation of the response function can be obtained if the exchange-correlation potential is expanded in terms of a Schmidt-orthogonalized basis comprising orbitals products of occupied and virtual orbitals. The viability of this approach in both OEP theory and the inverse KS problem is illustrated by numerical examples.
在优化有效势（OEP）理论以及所谓的逆科恩-沙姆（KS）问题（即针对给定电子密度寻找局部KS势的任务）中，都讨论了描述电子密度对局部KS势变化响应的静态科恩-沙姆（KS）响应函数的作用。在对这两种情况下都要求解的积分方程的一般性讨论中，有人认为即使在有限原子轨道基组的情况下，也能找到该方程的唯一解。展示了如果交换关联势按照由占据轨道和虚轨道的轨道乘积组成的施密特正交基展开，如何获得响应函数的矩阵表示。数值示例说明了这种方法在OEP理论和逆KS问题中的可行性。
