电子结构计算是科学研究中的重要手段和工具，其中密度泛函理论是使用最广泛的计算模型。但是对强关联体系，密度泛函理论不能得到精确的模拟结果。为解决这个问题，我们研究电子的双密度函数和一阶约化密度矩阵。在多电子体系中，电子的相互作用能由电子双密度函数完全决定，而电子的动能由电子一阶约化密度矩阵完全决定。在传统的密度泛函理论模型中，这两个重要的物理量都没有被很好地近似，这也是导致密度泛函理论不适用于强关联体系计算的原因。我们将在强、弱关联两个极限下对这两个物理量进行理论分析，并结合数值实验，构建这两个物理量的精确的、可计算的模型。在此基础上，我们将设计新的密度泛函理论计算模型，它具有和传统密度泛函理论模型相同的计算量，而且对各种关联强度的体系都能得到精确的模拟结果。我们将进一步针对此模型设计高效的数值算法。

Electronic structure calculation is an important tool in scientific research, while density functional theory is the most widely used model. But for strongly correlated systems, density functional theory can not get accurate results. To solve this problem, we study the electron pair density and the first-order reduced density matrix. In many-electron system, the exact interaction energy between electrons is completely determined by the pair density, and the exact kinetic energy of electrons is completely determined by the first-order reduced density matrix. In standard density functional theory methods, these two important physical quantities are not well approximated, which is the reason why the density functional theory models do not apply to strongly correlated systems. We will analyze these two physical quantities under the strongly correlated and weakly correlated limits, together with numerical experiments to construct accurate and computable models of these two quantities. Based on these results, we will design a new density functional theory model, which has the same computational cost as standard density functional theory model, but can get accurate simulation results for both strongly correlated and weakly correlated systems. We will further design efficient numerical algorithms for this model.