Accurate Core-Excited States via Inclusion of Core Triple Excitations in Similarity-Transformed Equation-of-Motion Theory

Abstract

The phenomenon of orbital relaxation upon excitation of core electrons is a major problem in the linear-response treatment of core-hole spectroscopies. Rather than addressing relaxation through direct dynamical correlation of the excited state via equation-of-motion coupled cluster theory (EOMEE-CC), we extend the alternative similarity-transformed equation-of-motion coupled cluster theory (STEOMEE-CC) by including the core−valence separation (CVS) and correlation of triple excitations only within the calculation of core ionization energies. This new method, CVS-STEOMEE-CCSD+cT, significantly improves on CVS-EOMEE-CCSD and unmodified CVS-STEOMEE-CCSD when compared to full CVS-EOM-CCSDT for Kedge core-excitation energies of a set of small molecules. The improvement in both absolute and relative (shifted) peak positions is nearly as good as that for transition-potential coupled cluster (TP-CC), which includes an explicit treatment of orbital relaxation, and CVS-EOMEE-CCSD*, which includes a perturbative treatment of triple excitations.

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations

“…As the XABOOM benchmark set contains molecules of up to 18 atoms, the calculations using higher-order methods would be unfeasible. On top of that, spectral properties, such as oscillator strengths, are not available for such approaches. , The performance of the reference methods has been extensively tested against experimental measurements with great success; ,,,, unfortunately, the comparisons against higher-order methods are very limited. The performance of CVS-EOM-CCSD was tested by Matthews et al , using CC methods including triple excitations as a reference.…”

“…On top of that, spectral properties, such as oscillator strengths, are not available for such approaches. , The performance of the reference methods has been extensively tested against experimental measurements with great success; ,,,, unfortunately, the comparisons against higher-order methods are very limited. The performance of CVS-EOM-CCSD was tested by Matthews et al , using CC methods including triple excitations as a reference. As shown, the excitation energies are systematically overestimated by around 1.5 eV.…”

“…Later, an effective implementation for the frozen-core equation-of-motion CC singles and doubles (fc-CVS-EOM-CCSD) was also presented by Coriani and co-workers, where the CVS approximation was fully utilized. Due to its excellent results and performance, the method quickly became popular in the community and is considered as a standard approach for medium-sized molecules. − It is also noteworthy that the CVS approximation was combined with the emerging similarity-transformed EOM-CCSD method, while implementations for higher-order EOM-CC approaches, including triple excitations, were also presented by Matthews et al , …”

“…Due to its excellent results and performance, the method quickly became popular in the community and is considered as a standard approach for medium-sized molecules. 30−36 It is also noteworthy that the CVS approximation was combined with the emerging similaritytransformed EOM-CCSD method, 37 while implementations for higher-order EOM-CC approaches, including triple excitations, were also presented by Matthews et al 38,39 Nowadays, time-dependent (TD) density functional theory (DFT) is the method of choice for extended molecular systems as its computational costs are relatively low. 40−42 The formalism was extended to core excitations by Stener and co-workers, 43 and its performance was comprehensively discussed in excellent reviews.…”

Theoretical Investigation of the X-ray Stark Effect in Small Molecules

“…Among such spectroscopic techniques, high-resolution x-ray based spectroscopies have emerged as powerful probes for determining the local structure of atoms and molecules, particularly in the soft x-ray regime (roughly 100–1000 eV). − Since x-ray absorption spectroscopy (XAS) and x-ray photoelectron spectroscopy (XPS) involve the excitation of core level electrons, these are excellent techniques for studying the local environment on a submolecular scale. The challenges and recent advances in the methods for simulating x-ray spectra are presented in a recent review article by Norman et al In this article, we are especially interested in the application of equation-of-motion coupled cluster (EOM-CC) techniques, for which many theoretical methods are being developed to increase the accuracy and efficiency of simulating XAS and XPS of molecules. − Additionally, theoretical methods are being developed to simulate other x-ray spectroscopies, such as x-ray two photon absorption, x-ray circular dichroism spectra, and resonant inelastic x-ray scattering . Further, x-ray based spectroscopies provide elemental specificity, which is not possible in vibrational or UV–vis spectroscopies.…”