From synchrotrons for XFELs: the soft x-ray near-edge spectrum of the ESCA molecule

Abstract

A predictive understanding of soft x-ray near-edge absorption spectra of small molecules is an enduring theoretical challenge and of current interest for x-ray probes of molecular dynamics. We report the experimental absorption spectrum for the ESCA molecule (ethyl trifluoroacetate) near the carbon 1s absorption edge between 285-300 eV. The ESCA molecule with four chemically distinct carbon sites has previously served as a theoretical benchmark for photoelectron spectra and now for photoabsorption spectra. We report a simple edge-specific approach for systematically expanding standard basis sets to properly describe diffuse Rydberg orbitals and the importance of triple excitations in equation-of-motion coupled-cluster calculations of the energy interval between valence and Rydberg excitations.

Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac–Coulomb(−Gaunt) Hamiltonian

“…This formulation is naturally combined with the frozen-core approximation separating valence and core spaces. However, one may argue that it introduces at the same time an additional error from neglecting core correlation. , …”

“…Besides the original CC-CVS approach, we have also investigated other approximations: Further restricting the definition of the projectors to also drop excited configurations with two core indices (ND, for “No Doubly core hole determinants”); this corresponds to the method suggested, e.g., in ref , obtaining Freezing the core in the ground-state calculation, thus retaining only the valence orbitals, typically defined as the orbitals with the highest principal quantum number n (FC-V); this essentially corresponds to using eq while setting ϵ CV to a fairly high value (for example, in the atom of Xe, ϵ 4d < ϵ CV < ϵ 5s ). Freezing all core orbitals, except for those that are to be targeted in the EOM step (FC-V-except); for example, this means treating a core spinor k , that should make up the most important core-excited configurations for state μ, different from other core spinors in the ground-state calculation. This corresponds to setting projectors for ground and excited states such that This approach is equivalent to the one of Sorensen et al The definition of the core/valence spaces follows that of the CVS definition/threshold, that is, only the core orbitals with the same or lower energy than the ones belonging to the edge under investigation are frozen (FC-f). This is the same approach adopted in ref , and it corresponds to setting projectors for ground and excited states such that Further restricting the number of frozen-core spinors to only those below the ones of the edge of interest (FC-fpMO frozen corefollow previous MO).…”

“…Freezing all core orbitals, except for those that are to be targeted in the EOM step (FC-V-except); for example, this means treating a core spinor k , that should make up the most important core-excited configurations for state μ, different from other core spinors in the ground-state calculation. This corresponds to setting projectors for ground and excited states such that This approach is equivalent to the one of Sorensen et al…”

“…Because of the availability of different Hamiltonians in Dirac , we also investigate the performance of two-component approaches with respect to the four-component one. We refer to, e.g., refs − for other examples of relativistic EOM-CC implementations, and to refs , , , , , , , , , for other examples of CVS-EOM-CC implementations. We also wish to underline that the literature on the theoretical approaches for core spectroscopy is vast and rapidly increasing, and the studies cited in the previous paragraphs cannot be considered exhaustive.…”

Photon-In/Photon-Out X-ray Free-Electron Laser Studies of Radiolysis

“…Interpretation of ultrafast X-ray spectroscopic measurements is invariably linked with theory, which, for understanding structural dynamics of core-excited matter, is an ongoing challenge as described in some recent reviews [73,74]. There are already challenges at a very basic level, e.g., to predict the X-ray absorption spectrum of ground-state species with sub-eV accuracy [75] and to locate the positions of double-hole states [76]. Here, advances in equation-of-motion coupled-cluster (EOM-CC) approaches [77,78] have allowed a systematic convergence after application of the core-valence separation scheme [79] within the EOM-CC framework [80].…”