  We formulate a one-center non-orthogonal configuration interaction singles
(1C-NOCIS) theory for the computation of core excited states of an initial
singlet state with two unpaired electrons. This model, which we refer to as
1C-NOCIS two-electron open-shell (2eOS), is appropriate for computing the
K-edge near-edge X-ray absorption spectra (NEXAS) of the valence excited states
of closed-shell molecules relevant to pump-probe time-resolved (TR) NEXAS
experiments. With inclusion of core hole relaxation effects and explicit spin
adaptation, 1C-NOCIS 2eOS requires mild shifts to match experiment, is free of
artifacts due to spin contamination, and can capture the high-energy region of
the spectrum beyond the transitions into the singly occupied molecular orbitals
(SOMO). Calculations on water and thymine illustrate the different key features
of excited-state NEXAS, namely the core-to-SOMO transition as well as shifts
and spin-splittings in the transitions analogous to those of the ground state.
Finally, simulations of the TR-NEXAS of acetylacetone after excitation onto its
pi to pi-star singlet excited state at the carbon K-edge - an experiment
carried out recently - showcases the ability of 1C-NOCIS 2eOS to efficiently
simulate NEXAS based on non-adiabatic molecular dynamics simulations.
