直接求解密度矩阵（累积量）的理论方法和程序

In recent years there has been increasing interest in directly solving the contracted Shr?dinger equations for k-particle reduced density matrices (or their corresponding cumulants). Just like wavefunctions, reduced density matrices are not extensive (additively separable). However, the corresponding cumulants are of this important property, and scale linearly with respect to the number of electrons. Therefore, it is more appropriate to focus on cumulant-based formulations. This tempting project aimed to develop cumulant-based multi-configuration self-consistent field (MCSCF) theory and program. Due to limited time and great difficulties, the whole project has not yet been finished. However, significant progresses have been made in the formulations.

近年来，直接求解约化密度矩阵（或其累积量）的紧缩薛定愕方程成为多体理论的一个热点。像波函数一样，约化密度矩阵不是可加合量，但它的累积量却具有可加合性，即与电子数目成线性标度，因此应直接求解累积量的方程。本课题旨在发展基于累积量的多组态自洽场理论及程序，属探索性研究。由于时间关系和工作的难度，研究工作尚未完成，但在理论方面已取得一定进展。