Simulation of X-ray absorption spectra with orthogonality constrained density functional theory

Abstract

Orthogonality constrained density functional theory (OCDFT) is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree–Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine.

Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states

“…Recently, there have been increasing interest in so-called ∆SCF methods [18][19][20][21][22][23] as an alternative to the linear-response mean-field approaches such as CI singles (CIS) and timedependent density functional theory (TDDFT) 24 . In this category, the most popular approach is based on the maximum overlap method (MOM) developed by Gilbert and Gill 22 .…”

Theoretical X‐ray spectroscopy of transition metal compounds

“…They differ in the construction of occupied and virtual MOs involved in the excitation and in setting their occupation numbers, see Reference and references therein. Exemplarily, one should mention the application of a multiple hole/particle algorithm within orthogonality constrained DFT to the calculation of K ‐edge spectra . Moreover, state‐following algorithms can be applied to avoid the variational collapse without explicit setting the orthogonality constraint.…”

Extended Koopmans' theorem at the second‐order perturbation theory

“…This is generally referred to as the Δ method. [ 1–10 ] In practice, however, it is often difficult, if not impossible, to converge to the desired ionized state. Furthermore, because the magnitude of IPs is typically much smaller than the total energies per se, it is well‐known that the Δ method suffers from the imbalanced treatments of the initial and the final states.…”

“…In principle, IPs can be straightforwardly obtained at any level of theory via calculations of the ground-and excited-state energies of the (N−1)-electron system with respect to the ground-state energy of the N-electron system.This is generally referred to as the Δ method. [1][2][3][4][5][6][7][8][9][10] In practice, however, it is often difficult, if not impossible, to converge to the desired ionized state. Furthermore, because the magnitude of IPs is typically much smaller than the total energies per se, it is well-known that the Δ method suffers from the imbalanced treatments of the initial and the final states.These problems can be effectively circumvented in the direct methods, where IPs are computed without relying on explicit total energy evaluations of the initial and the final states for their differences.…”