An atomic mean-field (AMF) spin-orbit (SO) approach within exact two-component theory (X2C) is reported, thereby exploiting the exact decoupling scheme of X2C, the one-electron approximation for the scalar-relativistic contributions, the mean-field approximation for the treatment of the two-electron SO contribution, and the local nature of the SO interactions. The Hamiltonian of the proposed SOX2CAMF scheme comprises the one-electron X2C Hamiltonian, the instantaneous two-electron Coulomb interaction, and an AMF SO term derived from spherically averaged Dirac-Coulomb Hartree-Fock calculations of atoms; no molecular relativistic two-electron integrals are required. Benchmark calculations for bond lengths, harmonic frequencies, dipole moments, and electric-field gradients for a set of diatomic molecules containing elements across the periodic table show that the SOX2CAMF scheme offers a balanced treatment for SO and scalar-relativistic effects and appears to be a promising candidate for applications to heavy-element containing systems. SOX2CAMF coupled-cluster calculations of molecular properties for bismuth compounds (BiN, BiP, BiF, BiCl, and BiI) are also presented and compared with experimental results to further demonstrate the accuracy and applicability of the SOX2CAMF scheme.

中文翻译：

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精确两分量理论中的原子平均场自旋轨道方法，用于对自旋轨道耦合进行非扰动处理

报道了精确的两成分理论（X2C）中的原子平均场（AMF）自旋轨道（SO）方法，从而利用了X2C的精确去耦方案，即标量相对论贡献的单电子近似值，即均值场近似用于处理双电子SO的贡献以及SO相互作用的局部性质。拟议的SOX2CAMF方案的哈密顿量包括单电子X2C哈密顿量，瞬时两电子库仑相互作用以及从原子的球均Dirac-Coulomb Hartree-Fock计算得出的AMF SO项；不需要分子相对论两电子积分。基准长度计算，包括键长，谐波频率，偶极矩，周期表中包含元素的一组双原子分子的电场梯度和电场梯度表明，SOX2CAMF方案可为SO和标量相对论效应提供平衡的处理，似乎是应用到包含重元素的系统中的有希望的候选者。还介绍了铋化合物（BiN，BiP，BiF，BiCl和BiI）的分子特性的SOX2CAMF耦合簇计算，并与实验结果进行了比较，以进一步证明SOX2CAMF方案的准确性和适用性。