Sera

Hi all, I hope I got the right forum for this I'm reading the original paper on Restricted Open Shell Kohn-Sham ('Molecular dynamics in low-spin excited states', Frank et al) right now and am confused. It says there "Due to spin symmetry, a minimum of two determinants is necessary for the description of the wave function of non-degenerate excited singlet states of a closed-shell system." What exactly is concluded from spin symmetry? What exactly do they even mean with spin symmetry - that the wave function needs to stay an eigenfunction of the spin operator? How is that connected to symmetry? The term 'symmetry adapted orbital' also is frequently mentioned and I'm not really sure what is meant by that. If there's someone in here who could help me with that, I'd be very thankful.