Soft X-ray Spectroscopy Simulations with Multiconfigurational Wave Function Theory: Spectrum Completeness, Sub-eV Accuracy, and Quantitative Reproduction of Line Shapes

Abstract

Multireference methods are known for their ability to accurately treat states of very different nature in many molecular systems, facilitating high-quality simulations of a large variety of spectroscopic techniques. Here, we couple the multiconfigurational restricted active space self-consistent field RASSCF/RASPT2 method (of the CASSCF/CASPT2 methods family) to the displaced harmonic oscillator (DHO) model, to simulate soft X-ray spectroscopy. We applied such an RASSCF/RASPT2+DHO approach at the K-edges of various second-row elements for a set of small organic molecules that have been recently investigated at other levels of theory. X-ray absorption near-edge structure (XANES) and X-ray photoelectron spectroscopy (XPS) are simulated with a sub-eV accuracy and a correct description of the spectral line shapes. The method is extremely sensitive to the observed spectral shifts on a series of differently fluorinated ethylene systems, provides spectral fingerprints to distinguish between stable conformers of the glycine molecule, and accurately captures the vibrationally resolved carbon K-edge spectrum of formaldehyde. Differences with other theoretical methods are demonstrated, which show the advantages of employing a multireference/multiconfigurational approach. A protocol to systematically increase the number of core-excited states considered while maintaining a contained computational cost is presented. Insight is eventually provided for the effects caused by removing core–electrons from a given atom in terms of bond rearrangement and influence on the resulting spectral shapes within a unitary orbital-based framework for both XPS and XANES spectra.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Accurate X-ray Absorption Spectroscopy

“…Nowadays, most quantum chemistry methods can be used to extract core excitation states. Currently, the best accuracy is provided by many electron wave function methods, such as complete active space self-consistent field with multi-configurational perturbation theory, 1 coupled cluster, [2][3][4][5] restricted active space self-consistent field, 6 or linear-response methods like the algebraic diagrammatic construction, 7,8 linear-response complete-active space self-consistent field, 9 and Bethe-Salpeter equation (BSE) formalism, 10 just to mention a few. Still, their applicability is usually hindered by their computational cost.…”

Ab Initio Calculations of XUV Ground and Excited States for First-Row Transition Metal Oxides

“…Some of these methods, including static exchange, transition potential DFT (TP-DFT), and the core–valence separation (CVS) approximation, were specifically designed for the simulation of X-ray spectroscopies. However, appropriate integration of both core-excited and valence-excited states has proven difficult. − Other approaches, including time-dependent DFT (TDDFT) methods, multiconfigurational wave function theory, and coupled cluster methods, are more generalizable and can be used to predict X-ray transitions. − ,− Real time TDDFT (RT-TDDFT) has been used to successfully evaluate photoexcited perturbations to X-ray edges for a variety of materials, including α-Fe 2 O 3 and α-Cr 2 O 3 . − The strength of RT-TDDFT methods is that they can determine the spectral response from a single time propagation . That said, RT-TDDFT methods are computationally expensive, which makes computing picosecond and longer time scales photodynamics or back-extracting information from measured dynamics difficult.…”

“…A commonly used and highly successful approach for modeling the M 2,3 edge in XUV spectra has been a semiempirical atomic multiplet theoretical approach, the Charge Transfer Multiplet program for X-ray Absorption Spectroscopy (CTM4XAS). ,,,− This method has been successfully applied to transition metal oxide spectra, but the method is not ab initio and does not accurately capture the many-body effects that are important in solids. Incorporating excited state effects and dynamics into CTM4XAS calculations also requires assumptions about changes in oxidation state and crystal field parameters to align simulations with experiment. ,,,,− …”

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Accurate X-ray Absorption Spectroscopy

“…Nowadays, most quantum chemistry methods can be used to extract core excitation states. Currently, the best accuracy is provided by many electron wave function methods, such as complete active space self-consistent field with multi-configurational perturbation theory, coupled cluster, − restricted active space self-consistent field, or linear-response methods like the algebraic diagrammatic construction, , linear-response complete-active space self-consistent field, and Bethe–Salpeter equation (BSE) formalism, just to mention a few. Still, their applicability is usually hindered by their computational cost.…”