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We have carried out Density Matrix Renormalization Group (DMRG) calculations on the ground state of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian. The PPP model includes long-range electron correlations which are required for physically realistic modeling of conjugated polymers. We have obtained the ground state energy as a function of the dimerization δ and various correlation functions and structure factors for δ = 0. From energetics, we find that while the nature of the Peierls' instability in polyacene is conditional and strong electron correlations enhance the dimerization.The cis form of the distortion is favoured over the trans form. However, from the analysis of correlation functions and associated structure factors, we find that polyacene is not susceptible to the formation of a bond order wave (BOW), spin density wave (SDW) or a charge density wave (CDW) in the ground state. PACS numbers : 31.25.Qm, 71.10.Fd, 71.30.+h, 71.45.-d 1 Introduction The question whether an infinitely long linear polyene (polyacetylene, PA) would have equal bond lengths or not has been debated ever since it was known that benzene has equal bond lengths while 1,3,5-hexatriene has alternating short (double) and long (single) bonds. Addressing this issue, Lennard-Jones [1] and Coulson [2] predicted a ground state with uniform bond lengths. Later work by Labhart [3], Ooshika [4], Longuet-Higgins and Salem [5] established that the ground state would have bond-alternation i.e. the infinite polyene would have alternate long and short bonds. Experimentally, such a dimerization would qualitatively explain the finite optical gap obtained by extrapolation of optical data for linear polyenes [6]. Earlier, Peierls established a more general result, known as the Peierls' instability or Peierls' distortion [7] for a partially filled one-dimensional band. Peierls' demonstrated that lattice vibrations couple to electrons in the band leading to the opening of a gap at the Fermi surface, making the material insulating. The Hückel model solution of Longuet-Higgins and Salem pertain to the specific case of Peierls' distortions in a half-filled extended system. Longuet-Higgins and Salem showed that for an infinite polyene chain, the total electronic energy per carbon atom as a function of the distortion δ in the chain, within a Hückel model [8] is proportional to δ 2 ln |δ| [5].The elastic strain energy of the system is proportional to δ 2 , the proportionality constant depending directly on the lattice stiffness and inversely on the electron-phonon coupling constant. The algebraic forms of the strain and electronic energies guarantee that the gain in electronic energy always exceeds the strain energy and the ground state would correspond to nonzero δ. The distortion of the polyene chain is termed unconditional as the distorted state is always more stable than the undistorted state for any value of the

Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians 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 space of a hundred million. Our results show that the earlier estimates of the exchange constants need to be revised for the Mn 12 cluster to explain the level ordering of low-lying eigenstates. In the case of the Fe 8 cluster, correct level ordering can be obtained which is consistent with the exchange constants for the already known clusters with butterfly structure. In the V 15 cluster, we obtain an effective Hamiltonian that reproduces exactly, the eight low-lying eigenvalues of the full Hamiltonian.PACS numbers: 75.50.Xx, 61.46.+w I. INTRODUCTIONThe synthesis of high nuclearity transition metal complexes has provided a new dimension to the field of nanomagnetism.1 Many interesting phenomena have been observed in these systems. Amongst the most exciting are the observation of quantum resonance tunneling and quantum interference 2 in some of these clusters. For example, in the case of the Mn 12 cluster, the ground state with total spin S G = 10 of the exchange Hamiltonian, under the influence of a large single ion anisotropy gives rise to a manifold of doubly degenerate states with nonzero M s values, with M s = ±10 being the lowest energy states. The application of a magnetic field splits the degeneracy of the M s = ±10 states. Varying the magnetic field brings states with |M s | = 10 closer in energy to the higher of the two states with |M s | = 10. The weak spin dipolar interactions that exist in the system can connect these nearly degenerate states with different M s values, leading to tunneling between the states. This is reflected in experiments as jumps in magnetization in the magnetization vs magnetic field plots, whenever the resonance condition is satisfied and as plateaus for offresonance field values. Similar plateaus are also observed in the V 15 cluster 3 , although the reason for the plateaus in this system is qualitatively different. The quantum interference phenomena observed in the Fe 8 cluster is because the paths connecting the M s = +10 and M s = −10 could interfere in the presence of a magnetic field, leading to an oscillation in the tunneling probabilities. 4These clusters, at a very basic level are characterized by multidentate ligands interconnecting the transition metal ions. In the clusters, a given magnetic ion has exchange interactions of either sign with several of its neighbors. Thus, these magnetic clusters often correspond to spin frustrated systems. Because of the rather complex exchange pathways which exist in these systems, it is 1 difficult to predict a priori even the sign of the exchange constant, let alone its magnitude.5 Since the site symmetry at the magnetic ions is also usually low because of the multidentate ligands in the system, the orbital degeneracy would be lifted ...

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