Environment Effects on X-Ray Absorption Spectra With Quantum Embedded Real-Time Time-Dependent Density Functional Theory Approaches

Abstract

In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods' performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@ ${\left({\left(H_{2}O\right)}_8\right)}^{-}$ , X = F, Cl). We observe that for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L₁ edges, and is capable of reproducing the splitting of the 1s¹ (n + 1)p¹ final states (n + 1 being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the 1s¹ (n + 2)p¹ states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent. The BOMME results, on the other hand, provide a faithful qualitative representation of the spectra in all energy regions considered, though its intrinsic approximation of employing a lower-accuracy exchange-correlation functional for the environment induces non-negligible shifts in peak positions for the excitations from the halide to the environment. Our results thus confirm that QM/QM embedding approaches are viable alternatives to standard real-time simulations of X-ray absorption spectra of species in complex or confined environments.

Keywords: X-ray absorption spectroscopy; block-orthogonalized manby-miller embedding; frozen density embedding; halides; real-time propagation; time-dependent density functional theory.

FIGURE 1

Structure for snapshot 1 of the fluoride-water droplet system taken from Bouchafra et al. (Bouchafra et al., 2018a; Bouchafra et al., 2018b) (A) and the model used in this work (B), in which the halide and the eight nearest water molecules making up its first solvation shell were extracted from the 50-water droplet.

FIGURE 2

Simulated K-edge spectra for the fluoride model system, over the roughly 30 eV interval starting at the free ion edge peak. It should be noted that here the peak heights (in arbitrary units) for each family of models: free ion (=iso), FDE, BOMME, and supermolecule (super) have been scaled, with a height of 1 assigned to the most intense transition.

FIGURE 3

Simulated K-edge spectra for the chloride model system, over the roughly 30 eV interval starting at the free ion edge peak. It should be noted that here the peak heights (in arbitrary units) for each family of models: free ion (=iso), FDE, BOMME, and supermolecule (=super) have been scaled, with a height of 1 assigned to the most intense transition.

FIGURE 4

Details on the three main energy ranges for the K-edge spectra of F⁻ (A,C,E) and Cl⁻ (B,D,F) model systems selected from the spectra shown in Figures 2, 3.

FIGURE 5

Simulated L₁-edge spectra for the fluoride model system in the edge region (contrary to the K edge, no peaks of appreciable intensity have been observed at higher energies). It should be noted that here the peak heights (in arbitrary units) for each family of models: free ion (=iso), FDE, BOMME, and supermolecule (super) have been scaled, with a height of 1 assigned to the most intense transition.