Spin‐Orbit Coupling in All‐Electron Mixed Basis Approach
Spin‐Orbit Coupling in All‐Electron Mixed Basis Approach
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DOI：
10.1002/andp.201900060
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发表时间：
2019-05
影响因子：
2.4
通讯作者：
Takeru Nakashima;K. Ohno
中科院分区：
文献类型：
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作者：
Takeru Nakashima;K. Ohno
在自旋轨道耦合（SOC）的评价中，在有效势非球对称的原子间区域，使用L·S公式是无效的。这一问题在LCAO、LMTO和APW方法中出现，而平面波伪势和PAW方法不能处理核心轨道的自旋轨道分裂（SOS）。为了避免这些问题，采用平面波和原子轨道作为基集的全电子混合基方法。对于PWs可以采用一般形式S·∇V × p，而对于AOs可以采用标准形式L·S， AOs可以很好地定域在球势区的非重叠原子球内，由对数径向网格上的数值径向函数和解析三次谐波组成。给出了自旋极化系统SOC的AO-AO、PW-AO和PW-PW矩阵元素的显式公式。特别地，AO-AO矩阵被明确地推导为p， d和f轨道。该方法应用于X射线光电子能谱中核能级和价能级的SOS。计算结果与已有的实验数据吻合良好，表明了该方法的有效性。
In the evaluation of the spin‐orbit coupling (SOC), the use of the L · S formula is invalid in the interatomic region where the effective potential is not spherically symmetric. This problem occurs in the LCAO, LMTO, and APW methods, while the plane‐wave pseudopotential and PAW methods cannot treat the spin‐orbit splitting (SOS) of core orbitals. To avoid these problems, the all‐electron mixed basis approach is adopted, which uses both plane waves (PWs) and atomic orbitals (AOs) as a basis set. The general form S · ∇V × p can be used for PWs, while the standard form L · S can be used for AOs, which are well localized inside the non‐overlapping atomic sphere in the spherical potential region and composed of the numerical radial function on a logarithmic radial mesh and analytic cubic harmonics. The explicit formula of the AO–AO, PW–AO, and PW–PW matrix elements of the SOC for spin‐polarized systems is presented. In particular, the AO–AO matrices are explicitly derived for p, d, and f orbitals. The method is applied to the SOS of core and valence levels in X‐ray photoelectron spectra. The results are in excellent agreement with the available experimental data, which suggests the validity of the present method.