Heisenberg model of tetrameric manganese cluster of S 2 center of Photosystem II

Abstract

The Heisenberg exchange model of the mixed-valence [Mn 3(III)Mn(IV)] and [Mn 3(IV)Mn(III)] clusters — the prototypes of the manganese active center of Photosystem II in the S 2 state — is developed. The proposed approach gives us the generalized solutions of the exchange problem. The exchange model H A = −2[ J 12 s 1 s 2+ J a( s 1 s 3+ s 2 s 3)+ J b( s 1 s 4+ s 2 s 4)+ J 34 s 3 s 4] describes the system with fixed intermediate spin S 12, the states with different S 34 are mixed. The Heisenberg model H B=−2[ J 12 s 1 s 2+ J α( s 1 s 3+ s 1 s 4)+ J β( s 2 s 3+ s 2 s 4) + J 34 s 3 s 4] describes the manganese clusters with mixing of the spin states with different intermediate spin S 12 ( S and S 34 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 12 s 1 s 2+ J 13 s 1 s 3+ J 23 s 2 s 3+ J 14 s 2 s 4+ J 34 s 3 s 4) 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 intermediate spins. Double exchange leads to the formation of the exchange-resonance states.