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Using an efficient numerical scheme that exploits spatial symmetries and spinparity, we have obtained the exact low-lying eigenstates of exchangeHamiltonians for the high nuclearity spin clusters, Mn_{12}, Fe_8 and V_{15}.The largest calculation involves the Mn_{12} cluster which spans a Fock spaceof a hundred million. Our results show that the earlier estimates of theexchange constants need to be revised for the Mn_{12} cluster to explain thelevel ordering of low-lying eigenstates. In the case of the Fe_8 cluster,correct level ordering can be obtained which is consistent with the exchangeconstants for the already known clusters with butterfly structure. In theV_{15} cluster, we obtain an effective Hamiltonian that reproduces exactly, theeight low-lying eigenvalues of the full Hamiltonian.Comment: Revtex, 12 pages, 16 eps figures; this is the final published versio

Properties of low-lying states in some high-nuclearity Mn, Fe, and V clusters: Exact studies of Heisenberg models