HEISENBERG-MODEL OF TETRAMERIC MANGANESE CLUSTER OF S2 CENTER OF PHOTOSYSTEM-II

The Heisenberg exchange model of the mixed-valence [Mn3(III)Mn(IV)] and [Mn3(IV)Mn(III)] clusters - the prototypes of the manganese active center of Photosystem II in the S2 state - is developed. The proposed approach gives us the generalized solutions of the exchange problem. The exchange model H(A) = -2 [J12S1S2 + J(a)(S1S3 + S2S3) + J(b)(S1S4 + S2S4) + J34s3s4] describes the system with fixed intermediate spin S12, the states with different S34 are mixed. The Heisenberg model H(B) = -2[J.2S1S2+J(alpha)(S1S3 + s1S4) + J(beta)(S2S3 + S2S4) + J34s3s4] describes the manganese clusters with mixing of the spin states with different intermediate spins S12 (S and S34 are fixed). The two Heisenberg models H(A) and H(B) have analytical solutions for the exchange energy for the states with S = 1/2. These analytical solutions give the results of different Kambe models with fixed intermediate spins in the particular cases. The exchange matrices (S= 1/2) for the general exchange model H= - 2(J]2S1S2 + J13S1S3+J23s2S3 + J14S1S4 + J24S2S4 + J34S3S4) were obtained by using the technique of irreducible tensor operators. The general model explains the splittings and the transformation of spin levels of complex manganese clusters: trapezoid, T-type, bent structures, and strongly distorted tetrahedron models, which do not allow the Kambe solutions of the exchange problem and also the solutions in the generalized models H(A) and H(B). The states of the general model are characterized by the net spin S and by the exchange mixture of the inter-mediate spins. Double exchange leads to the formation of the exchange-resonance states.