Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn–Sham Approach

We
present the use of the recently developed square gradient minimization
(SGM) algorithm for excited-state orbital optimization to obtain spin-pure
restricted open-shell Kohn–Sham (ROKS) energies for core excited
states of molecules. The SGM algorithm is robust against variational
collapse and offers a reliable route to converging orbitals for target
excited states at only 2–3 times the cost of ground-state orbital
optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V
functionals is found to predict the K-edge of C, N, O, and F to a
root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective
at predicting L-edge spectra of third period elements, provided a
perturbative spin–orbit correction is employed. This high accuracy
can be contrasted with traditional time-dependent density functional
theory (TDDFT), which typically has greater than 10 eV error and requires
translation of computed spectra to align with experiment. ROKS is
computationally affordable (having the same scaling as ground-state
DFT and a slightly larger prefactor) and can be applied to geometry
optimizations/ab initio molecular dynamics of core excited states,
as well as condensed phase simulations. ROKS can also model doubly
excited/ionized states with one broken electron pair, which are beyond
the ability of linear response based methods.