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Subject classification: 13; 22.9 Institute of Chemistry, Academy of Sciences of the Moldavian SSR, Kishinev On the Insufficiency of the Heisenberg Model of Exchange Interaction for Polynuclear Clusters BY B.S. TSUKERBLAT, M. I. BELINSKII, and A . V. ABLOV At present there is no rigorously substantiated framework of the applicability of the Heisenberg-Dirac-Van Vleck (HDVV) Hamiltonian (1) to polynuclear many-electronio systems. On the other hand a great number of experiments cannot be explained on the base of the HDVV model. As a striking instance crystals containing 3* [ Cr30(CH2COO)6(H20)~+-type clusjers with three octahedrally coordinated C r ions in the corners of on equilateral triangle can be mentioned (1 to 7). The antiferromagnetic intramolecular interaction fi = J spin degeneracy, however the energy levels of thz states with the same total spins (2D (ll2), 4D(3'2) etc.) coincide (Fig. la) in contrast with the experimental data on the temperature dependence of heat capacity C(T) , the magnetic susceptibility (3 to 6) being indicative of the splitting of the ground and excited states. The numerous attempts to interpret the experimental data by introducing the additional exchange parameter J 3 8 (3, 5, 6), should be admitted to be incorrect because they contradict the X-ray data (2, 4). In the present note we show that to explain the above mentioned experiments one does not demand the complicate HDW model 3. S. (S = 3/2) removes the 64-fold 0.. 1 J A

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The theory of double exchange is generalized to mixed valence (MV) trinuclear clusters. The results obtained by quantum-theoretical calculations of exchange and resonance splittings are compared to the results of the model theory which takes account of Heisenberg and double exchange. The comparison demonstrates unambiguously the coincidence of transfer parameters and the model double exchange parameters. The double exchange parameters of trinuclear MV clusters depend on total and intermediate spins as well as individual ion spin. The common effect of electron (or hole) migration and interion exchange interaction on the magnetic properties of ae'-d"-d" + 1 (n = 0, 1, 2, 3, 4, 5) and am-ae'-d H-1 (n = 1, 2, 3, 4) MV trimers is considered. Heisenberg and double exchange form exchange-resonance multiplets which are characterized by irreducible representations F of Dab symmetry group of MV clusters. Double exchange splits Heisenberg multiplets but does not mix the states of different S. Level correlation diagrams for MV trimer clusters are plotted. The level trends and magnetic behaviour of MV trimers differ significantly from the classical Anderson-Hasegawa model obtained for dimeric MV clusters. In MV dimers strong double exchange (]p] >> I J[) leads to ferromagnetic ground state (Sss ---Sn~ ) irrespective of the signs for p and J. In MV trimers several types of magnetic behaviour are possible depending on the signs and values for J and p parameters. In antiferromagnetic clusters (J < 0) with the migrating electron (p < 0) or hole (p > 0) strong double exchange reduces antiferromagnetic Heisenberg-type ordering and leads to ferromagnetic spins alignment (S~=S .... when [pl>>lJ[). In antiferromagnetic trimers, a~-ff'-d ~+1 (p > 0) and dm-a~-a ~-t ~ < 0), the level with Sgs = Smin i$ the ground state irrespective of the value of p/J. In ferromagnetic exchange clusters (J > 0) with the migrating hole strong double exchange disorders the ferromagnetic spin ordering of the MV system.