基于多参考态组态相互作用的自旋－轨道耦合计算方法和程序实现

Relativistic effect and electron correlation are two important issues in electronic structure theory. This project will develop a new program package to calculate spin-orbit coupling effect using multi-reference configuration interaction (MRCI) and its approximated methods such as internally contracted MRCI (icMRCI) and multi-reference second order perturbation theory (MRPT2). Firstly, the integral-graphic hybrid driven technique will be employed to develop a highly efficient icMRCI algorithm. A parallel icMRCI program will be developed to improve the computational efficiency further. Also, MRCI will be applied in newly introduced electron-nuclear general mean field configuration interaction (EN-GMFCI) theory. Then, the sf-X2C+so-DKHn Hamiltonian will be used to treat the relativistic effect; the state interaction scheme will be used based on MRCI/icMRCI/MPRT2 to calculate SOC effect in a perturbative manner. The graphic unitary group approach will be employed to calculate SOC matrix element. Finally, a new SOC-MRCI/icMRCI algorithm will be introduced to include SOC effect variationally. A spin-orbit coupling MRCI program package will be developed that can be used not only in weak relativistic system such as organic molecules but also in strong relativistic system such as compounds with heavy 5p and 6p elements.

相对论效应和电子相关是电子结构理论研究的两个基本问题。本项目致力于研究基于精确MRCI和近似MRCI方法如内收缩的MRCI、MRPT2等的自旋轨道耦合(SOC)计算方法和程序，从而在不同层次来考虑SOC效应。首先，通过积分－图形混合驱动和并行化提高现有内收缩MRCI的计算效率，并将MRCI用于电子－原子核广义平均场组态相互作用理论(EN-GMFCI)；其次，基于sf-X2C+so-DKHn自旋分离的哈密顿，发展利用MRCI/icMRCI/MRPT2波函数的态－态相互作用微扰计算SOC效应的程序，图形酉群理论将被用以计算SOC矩阵元；最后，研究在MRCI级别变分包含SOC效应的SOC-MRCI/icMRCI算法和程序。最终形成一个适用于从弱相对论效应的有机分子到强相对论效应5p、6p重元素体系的基于MRCI的自旋轨道耦合计算程序包。

电子相关与相对论效应是精确的量子化学计算中的两个重要问题，在分子光谱、分子激发态过程及自旋翻转的化学反应研究中至关重要。多组态电子相关理论如多组态自洽场(Multi-configurational self-consistent field -- MCSCF)及多参考态组态相互作用（multi-reference configuration interaction -- MRCI）是处理化学中强关联体系电子相关的有效方法。对于相对论效应，常常先对哈密顿进行自旋分离，利用自旋独立(Spin-Free --SF)的哈密顿考虑相对论效应，再利用自旋轨道耦合(Spin-orbital coupling -- SOC)处理自旋部分的贡献。本项目将多组态方法与SF+SOC方法相结合，发展了基于多组态波函数的相对论量子化学计算理论及程序。首先，利用空穴-粒子对称的图形酉群方法(hole-particle symmetry in graphical unitary group approach – HP-GUGA)带来的对组态空间分类的优势，提出了灵活多收缩的MRCI计算方法并开发了计算程序；其次，发展了在U(n)群框架下计算自旋轨道耦合矩阵元的理论，导出了计算SOC矩阵元的工作方程；再次，推导了HP-GUGA方法中SOC计算所需的片段因子，并基于此实现了完全活性空间组态相互作用(complete active space configuration interaction -- CASCI)和MRCI波函数自旋轨道耦合计算程序；最后，项目还探索了非波恩-奥本海默近似框架下的相关能计算问题，发展了电子-原子核广义平均场方法（Electron-nuclear general mean field）及广义平均场组态相互作用(General mean field configuration interaction - GMF-CI)，并给出了分子体系中原子核-电子、原子核-原子核的相关能的定义。本项目的发展的软件已经集成国产量子化学软件包BDF与Xi’an-CI中。