求解多体Dirac-Coulomb方程是相对论量子化学的核心问题。基于我们最新发现的相对论Coalescence条件，本项目将开展多体Dirac-Coulomb方程显相关波函数方法的分析、设计和实现。围绕这个Coalescence条件，将寻找新的相对论显相关因子，研究负能态污染的去除方案以及设计相应代数特征值问题的快速迭代算法。为了验证和完善相对论显相关波函数方法，还将开展两体问题的数学理论研究，包括分析其谱结构和特征函数空间。从两电子之间距离趋于零的极限问题出发，将尝试解决"两体问题是否有平方可积特征函数"的公开问题。

How to solve the many-body Dirac-Coulomb equation efficiently and accurately is the core of relativistic quantum chemistry. Based on the new relativistic electronic coalescence condition discovered in our group, we will analyze, develop and implement the explicitly correlated wavefunction method for the many-body Dirac-Coulomb equation. Centering on such relativistic coalescence condition, we will construct new correlation factors, compare the strategies for removing the contaminations of negative energy states and study efficient iterative methods for resulting algebraic eigenvalue problems. In order to verify and improve the explicitly correlated wavefunction method, we will analyze rigorously the two-body problem and investigate both the spectral structure and the space for eigenfunctions. Finally, we will try to answer the open problem "Does the two-body operator have square integrable eigenfunctions?" with the help of corresponding limit problem as the distance of electrons goes to zero.