The electronic spectra of alpha and beta solid O2 were calculated in a
full many-body approach for a cluster consisting of four O2 molecules
with periodic boundary conditions. Only the partially occupied pi orb
itals (sixteen spin-orbitals, eight electrons) were included. The lowe
st 81 many-body states, which correspond to neutral, unexcited molecul
es, describe accurately the magnetic excitations of the solids. The tw
o phases have very different spectra resulting, even at very low tempe
ratures, in a large difference in the (magnetic) entropy. The calculat
ed entropy difference at 23.9 K (the alpha-beta phase transition tempe
rature) agrees surprisingly well with the experimentally measured heat
of transformation.