Zhang Ning, Liu Wenjian
Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China.
J Chem Theory Comput. 2024 Oct 22;20(20):9003-9017. doi: 10.1021/acs.jctc.4c00967. Epub 2024 Oct 2.
In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments ( , , 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 ( , , 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.
在仅基于物理论据进行相对论哈密顿量统一构建（文献[具体文献1]、[具体文献2]、[文献编号084111]）的同时，本文通过编程技术（例如C++ 中的模板元编程和多态性）实现了相对论波函数方法的统一实现。也就是说，一旦构建哈密顿矩阵的代码准备就绪，其余部分可以从用于非相对论对应物的现有模板自动生成。将二次量子化的相对论哈密顿量分解为拓扑结构与计算无自旋组态态函数（CSF）之间基本耦合系数所需的图相同的图，有助于实现这一点。此外，时间反演和二元双点群对称性都可以很容易地纳入分子积分和哈密顿矩阵元中。由于两者之间的简单关系，后者可以首先在（随机选择的）自旋相关行列式的空间中进行评估，然后转换到自旋相关CSF的空间。作为一个示例，我们在此考虑带选择和微扰校正的无对四分量相对论迭代组态相互作用（4C-iCIPT2），它是无自旋iCIPT2（文献[具体文献3]、[具体文献4]、[文献编号949]）的自然扩展，并且如数值示例所示，可以在正能量态流形（PES）内提供近乎精确的数值结果。
