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 whole molecule. For the short wavelengths used in X-ray spectroscopy, this dipole approximation breaks down and 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 X-ray absorption spectroscopy (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.
Intensities of all fine-structure resolved rovibrational electric quadrupole absorption lines in $^{16}$O$_2$($X^{3}Σ^{-}_{g}$) calculated with a new $\textit{ab initio}$ quadrupole moment curve
Cavity ring-down spectroscopy of CO$_2$ near $λ$ = 2.06 $μ$m: Accurate transition intensities for the Orbiting Carbon Observatory-2 (OCO-2) "strong band"
CO的$λ$ = 2.06 $μ$ m吸收带被广泛用于大气二氧化碳的遥感，使其与许多重要的自上而下的碳通量测量相关。在这些测量中采用的检索算法中使用的前向模型需要越来越精确的线强度和线形状的数据，从中可以计算吸收截面。为了克服现有谱线表的精度限制，我们使用稳频腔衰荡光谱测量了$^{12}$ C $^{16}$ O $_2$吸收带中的39个跃迁。测量谱线强度，估计的相对组合标准不确定度为$u_r$ = 0.08%。我们使用两种理论模型1预测测量强度的$J$依赖性：具有Herman-Wallis旋转振动校正的一维光谱模型和逐线从头计算偶极矩表面模型[Zak et al. JQSRT 2016;177：31-42]。对于第二种方法，我们只拟合一个因子来重新调整理论积分带强度，使其与测量强度一致。我们发现，后一种方法产生了同样充分的代表性的拟合$J$依赖的强度数据，并提供了最物理的一般表示的结果。我们推荐的积分带强度值等于7.183 $\times$ 10 $^{-21}$ cm分子$^{-1}$ $\pm$ 6 $\times$ 10 $^{-24}$ cm分子$^{-1}$，该值基于重新标度的从头算模型，对应于拟合的标度因子1.0069 $\pm$ 0.0002。将文献强度值与我们的结果进行比较，发现系统偏差范围为$-$ 1.16%至+0.33%。
Beyond the Electric Dipole Approximation: Electric and Magnetic Multipole Contributions Reveal Biaxial Water Structure from SFG Spectra at the Air-Water Interface
