It is found to be lower in energy than the 1πu MO, both experimentally and from more sophisticated computational models, so that the expected order of filling is the 3σg before the 1πu. Hence the approximation to ignore the effects of further interactions is valid.
This passage discusses the energy levels of a system, specifically comparing the lower-energy state to the 1πu MO. It emphasizes that neglecting further interactions is justified because the observed energy level aligns with the expected order of electron filling.