基于全相对论狄拉克方程的杂化密度泛函理论、程序与应用

对重元素体系进行电子结构计算通常有两类困难：1）相对论效应；2）多体效应，尤其是d/f电子的强关联效应。对相对论效应的精确处理原则上应基于狄拉克方程而非薛定谔方程，前者因自身波函数包含四个分量而会使实际计算量大幅增加，此点限制了其在第一性原理计算中的应用。在过去的研究中，申请人基于数值原子基组发展了一种高效的精确二分量相对论理论，采用冻结正电子自由度的方式来仅仅处理电子部分的贡献，从而能够以二个分量的小规模计算量获取四个分量的精度，使四分量全相对论方法得以应用于大型体系。另一方面，杂化泛函相较于传统的LDA及GGA泛函能够更好地处理d/f电子体系的多体效应，并得到了广泛应用，但其基本理论仍是基于非相对论的薛定谔方程。本项目希望在现有的全相对论理论和程序框架中引入以HSE06为代表的杂化泛函，以期能够发展一种同时处理相对论效应和强关联效应的理论方法，从而促进对重元素体系的计算应用。

The treatment of relativistic effects and many body effects (especially the strong correlation in d/f electron systems) has been the two main challenges in the electronic structure calculations of systems containing heavy elements. For relativistic effects, the exact treatment should be in principle based on the Dirac equation instead of the Schrӧdinger equation, the former of which contains four components in its wavefunction and therefore requires much larger computation in real application. In the previous research, we have developed a high-efficiency exact two-component (X2C) relativistic method based on numerical atomic basis sets: by decoupling the contribution of electrons and positrons, the X2C theory can finally treat the electron-only two-component Hamiltonian with affordable computation while achieving the same precision as traditional time-consuming four-component methods. On the other hand, hybrid density functional has been prevalently used nowadays due to its better description on many body effects – compared to the traditional LDA and GGA functionals. A limitation is that its theoretical framework is nonrelativistic and one-component. In this project, we aim to develop a fully relativistic hybrid density functional theory based on the aforementioned X2C framework, so as to treat both relativistic effects and strong correlation in one shot. We hope the new project provides a better way for the calculation of heavy element systems and thus promotes the corresponding application research.