Pauli旋量表示中的高效四分量Dirac-Coulomb-Gaunt Hartree-Fock
Efficient Four-Component Dirac-Coulomb-Gaunt Hartree--Fock in Pauli Spinor Representation
摘要：
四分量Dirac Hartree-Fock是一种精确的平均场方法，用于处理相对论效应很重要的分子系统。然而，两电子相互作用的计算成本和复杂性使得这种方法不太常见，即使我们可以考虑狄拉克-哈特里-福克哈密顿量的电子结构的“地面真理”，除非明确的量子电动力学效应。能够计算这些影响，然后是至关重要的低标度方法的设计准确的预测计算光谱学和性质的重元素复合物，必须包括相对论效应，甚至定性的准确性。在这项工作中，我们提出了一个泡利四元数形式的最大组件和自旋分离计算的Dirac-库仑-冈特Hartree-Fock基态，与最小的浮点运算计数算法。这种方法还允许人们明确地从两体相互作用中分离不同的自旋物理，例如自旋自由，自旋轨道和自旋自旋贡献。此外，我们使用这种形式主义来检查周期表中的相对论趋势，并分析原子金和金二聚体系统的基组依赖性。
英文摘要：
Four-component Dirac Hartree--Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction makes this method less common, even though we can consider the Dirac Hartree--Fock Hamiltonian the "ground truth" of electronic structure, barring explicit quantum-electrodynamical effects. Being able to calculate these effects is then vital to the design of lower scaling methods for accurate predictions in computational spectroscopy and properties of heavy element complexes that must include relativistic effects for even qualitative accuracy. In this work, we present a Pauli quaternion formalism of maximal component- and spin-separation for computing the Dirac-Coulomb-Gaunt Hartree--Fock ground state, with a minimal floating-point-operation count algorithm. This approach also allows one to explicitly separate different spin physics from the two-body interactions, such as spin-free, spin-orbit, and the spin-spin contributions. Additionally, we use this formalism to examine relativistic trends in the periodic table, and analyze the basis set dependence of atomic gold and gold dimer systems.
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