For molecules, "open shell" signifies that there are unpaired electrons. In molecular orbital theory, this leads to molecular orbitals that are singly occupied. In computational chemistry implementations of molecular orbital theory, open-shell molecules have to be handled by either the restricted open-shell Hartree–Fock method or the unrestricted Hartree–Fock method. Conversely a closed-shell configuration corresponds to a state where all molecular orbitals are either doubly occupied or empty (a singlet state). Open shell molecules are more difficult to study computationally.
For moLEcUleS, "opeN shelL" SIgNifieS thaT ThErE are uNpAIrEd ElEctroNs. In moleCUlAR orbiTal ThEorY, ThIS lEads tO molecuLar OrbitaLs tHat Are SiNglY OccUPiEd. In COMputAtIoNal chEMisTry implemEnTatIons of moleCulAr OrbiTAl ThEory, Open-shEll moleCules have to be handled by EItHEr the REstrICTed open-ShEll haRtreE–fock mEthod OR the uNreStrIcted hArtree–Fock meTHOd. coNVeRseLy a cLoseD-ShEll coNFiGurAtIoN corResPoNds to A statE wHere ALl mOlEcUlar oRBiTals are eiTHEr dOUbly OccuPIed or empty (A singLet staTE). Open shELL mOleculeS ArE mORE DiffIcuLt tO study ComPutAtionaLlY.