Origin-independent calculation of quadrupole intensities in X-ray spectroscopy
Origin-independent calculation of quadrupole intensities in X-ray spectroscopy
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DOI：
10.1063/1.4766359
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发表时间：
2012-11-28
影响因子：
4.4
通讯作者：
Jacob, Christoph R.
中科院分区：
文献类型：
--
作者：
Bernadotte, Stephan;Atkins, Andrew J.;Jacob, Christoph R.
对于电磁光谱中紫外和可见光范围内的电子激发，通常在偶极近似下计算强度，该偶极近似假定振荡电场在跃迁的长度尺度上是恒定的。对于硬X射线光谱学中使用的短波长，偶极近似可能不够充分。特别是，对于金属K边X射线吸收光谱(XAS)，有必要包括更高阶的贡献。在X射线光谱学的量子化学方法中，到目前为止，这些所谓的四极强度是通过包括依赖于电-四极矩和磁偶极跃迁矩平方的贡献来计算的。但是，产生的四极强度取决于坐标系原点的选择。在这里，我们表明，为了获得一个与原点无关的理论，我们必须一致地在波矢中包含所有同阶的贡献。这导致了两个额外的贡献，分别取决于电偶极和电八极以及电偶极和磁四极跃迁矩的乘积。我们在含时密度泛函理论中实现了这种与原点无关的XAS中四极强度的计算，并证明了它在计算过渡金属络合物的金属和配体K边XAS谱中的有效性。(C)2012年美国物理研究所。[http://dx.doi.org/10.1063/1.4766359]
For electronic excitations in the ultraviolet and visible range of the electromagnetic spectrum, the intensities are usually calculated within the dipole approximation, which assumes that the oscillating electric field is constant over the length scale of the transition. For the short wavelengths used in hard X-ray spectroscopy, the dipole approximation may not be adequate. In particular, for metal K-edge X-ray absorption spectroscopy (XAS), it becomes necessary to include higher-order contributions. In quantum-chemical approaches to X-ray spectroscopy, these so-called quadrupole intensities have so far been calculated by including contributions depending on the square of the electric-quadrupole and magnetic-dipole transition moments. However, the resulting quadrupole intensities depend on the choice of the origin of the coordinate system. Here, we show that for obtaining an origin-independent theory, one has to include all contributions that are of the same order in the wave vector consistently. This leads to two additional contributions depending on products of the electric-dipole and electric-octupole and of the electric-dipole and magnetic-quadrupole transition moments, respectively. We have implemented such an origin-independent calculation of quadrupole intensities in XAS within time-dependent density-functional theory, and demonstrate its usefulness for the calculation of metal and ligand K-edge XAS spectra of transition metal complexes. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4766359]