Density Functional Theory Based Methods for the Calculation of X-ray Spectroscopy

Abstract

Conspectus The availability of new light sources combined with the realization of the unique capabilities of spectroscopy in the X-ray region has driven tremendous advances in the field of X-ray spectroscopy. Currently, these techniques are emerging as powerful analytical tools for the study of a wide range of problems encompassing liquids, materials, and biological systems. Time-resolved measurements add a further dimension to X-ray spectroscopy, opening up the potential to resolve ultrafast chemical processes at an atomic level. X-ray spectroscopy encompasses a range of techniques which provide complementary information, and these include X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES), and resonant inelastic X-ray scattering (RIXS). In many studies, the interpretation of the experimental data relies upon calculations to enable the nature of the underlying molecular structure, electronic structure, and bonding to be revealed. Density functional theory (DFT) based methods are some of the most widely used methods for the simulation of X-ray spectra. In this Account, we focus on our recent contributions to the simulation of a range of X-ray spectroscopic techniques using DFT and linear-response time-dependent density functional theory (TDDFT) and show how these methods can provide a computational toolkit for the simulation of X-ray spectroscopy. The importance of the exchange-correlation functional for the calculation of XAS is discussed, and the introduction of short-range corrected functionals is described. The application of these calculations to study large systems through the use of efficient implementations of TDDFT will be highlighted, with the use of these methods illustrated through studies of ionic liquids and transition metal complexes. The extension of TDDFT to calculate XES through the use of a reference determinant for the core-ionized state will be described, and the factors that affect the accuracy of the computed spectra discussed. The application of these approaches will be illustrated through the study of a range of organic molecules and transition metal complexes, which also show how going beyond the dipole approximation in determining the transition intensities can be critical. The application of these approaches to the simulation of the RIXS spectrum of water will also be described, highlighting how ultrafast dynamics on the femtoscale time scale are evident in the measured spectra. In these calculations, the description of the core-ionized and core-excited states becomes increasingly important, and the role of the basis set in accurately describing these states will be explored.

Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory

“…However, computations of core-excited states are very challenging as they require simulating electronic transitions with energies much higher than the ionization threshold, using large uncontracted basis sets, and incorporating orbital relaxation, electron correlation, and relativistic effects. 4,[23][24][25][26][27] For this reason, most of the currently available methods for the simulations of XPS introduce simplifications based on the assumption that the ground-state electronic structure is well described using a single (reference) electronic configuration. These single-reference methods developed using a variety of theoretical approaches [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] can be used to simulate the XPS spectra of weakly-correlated molecules and materials, but may be unreliable for chemical systems that exhibit strong electron correlation.…”

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].…”

Core-hole delocalization for modeling X-ray spectroscopies: A cautionary tale

“…53 In TDDFT, the approximate nature of the exchange and correlation (xc) functional leads to self-interaction errors (SIE) 29,[55][56][57] that are exacerbated in the case of coreexcitations (due to the high densities in the core region). This has spurred the design of a plethora of tailored xcfunctionals, 29,56,58 which can yield improved absolute energies, but not necessarily improved relative energies. 28 Among correlated ab initio methods for excited states, of interest here are the algebraic diagrammatic construction (ADC) scheme for the polarization propagator, and coupled cluster (CC) theory.…”