Hund's multiplicity rule for some atoms and molecular fragments a quantumchemical UHF interpretation

Seven atoms(neutral,cationic,anionic),and five species of molecular fragment(with the two nuclear electronics,heteronuclear two electronics,two electronic multi-cores,multi-core multi-electronics) were taken as examples,their structures were optimized by UHF/6-311++G(3df,2p) method for their vertical and adiabatic process in the transition process.Single point energy(ES,ET) for low and high spin state with the same electronic configuration were calculated and compared with their highest occupied orbital energy(eS-HOMO;eT-HOMO).Our Results showed that the equtations ΔeHOMO=eS-HOMO-ΔeT-HOMO0,and ΔES-T≈ΔeHOMO0 are independent for vertical,or adiabatic process,or bond length.