Fig. 1. Schematic illustrations of the two-step RIXS process |i → |t → |f (for electronic states and soft X-ray regime) in a system with inversion symmetry, with color coded electronic inversion parities g (gerade, blue) and u (ungerade, red). (a) Static RIXS with the electronic GS as initial state (GS-RIXS): only g → u → g RIXS processes are allowed, with zero or positive energy loss. (b) Pump–probe RIXS (LMCT-RIXS for Fe(CN)₆^3–): the optical pump pulse inverts the initial inversion parity from g to u, with u → g → u RIXS process for the pumped species (here the energetically lowest state of u symmetry). The state manifolds for the GS-RIXS and LMCT-RIXS processes are thereby separated, with no possibility for negative energy losses. (c) Excited-state RIXS after excited-state dynamics (Quartet-RIXS after inter-system crossing for Fe(CN)₆^3–): non-adiabatic transition(s) populates an excited state with g parity. Both the unpumped and newly populated excited species have g → u → g RIXS processes, with overlapping state manifolds that allows for negative energy loss, denoted as anti-Stokes RIXS (AS-RIXS).