Display omitted •UB3LYP-D3 + COSMO calculations yielded meta-stable structures of S2 state of CaMn4O5 cluster in PSII.•Relative stability was investigated by hybrid-DFT and DLPNO-CC methods.•Broken-Symmetry (BS) solutions for all pattern of spin configurations were constructed and evaluated sets of effective exchange integrals J as magnetic coupling parameters. Full geometry optimization of all S2 intermediates in OEC (oxygen-evolving complex) of PSII (photosystem II) were carried out by using UB3LYP-D3/Def2-TZVP with COSMO solvation effects. Our detail calculations yielded meta-stable structures of six (=3 × 2 (HS (high-spin), IS (intermediate-spin)) intermediates for W1 = W2 = H2O and eight (=4 × 2 (HS, IS)) intermediates for W1 = OH− or W2 = OH−, and were named to H2O and OH models, respectively. In the next step, relative stability among these intermediate structures were investigated by hybrid-DFT and DLPNO-CC methods. UB3LYP methods show that right (R)-opened structures (open-cubane) are more stable than left (L)-opened structures (closed-cubane) by about 3.5 kcal/mol, though decreasing of DFT-weights suppresses such energy gaps. DLPNO-CCSD(T0) methods promote stabilization of (L)-structures and finally reproduce near degeneration or more stable (L)-structure. All pattern of spin configurations in four Mn(III) and Mn(IV) ions were assumed and BS (broken-symmetry) solutions were successfully obtained to find the most stable spin structures. This complete sets of all spin conformations enabled us evaluate sets of effective exchange integrals J as magnetic coupling parameters. The calculated J values for the spin Hamiltonian elucidated one g2 (S = 1/2) and two g4 (S = 5/2) molecular structures in the S2 state in accord with the recent EXAFS results.