Energy level shifts in two-step spin–orbit coupling ab initio calculations

We point out a problem with two-step spin–orbit ab initio calculations in which the energy levels of spin–orbit free Hamiltonians are shifted as a means to including dynamic correlations at low cost in small spin–orbit configuration interaction calculations. The usual shifts driven by the energy order of the states can lead to anomalous results when avoided crossings exist with significant change of wave function character, which take place at different nuclear positions in the configurational spaces of the first and the second steps. In these cases, the shifts of the spin–orbit free energy levels must be assigned according to the characters of the wave functions.