Theoretical studies on effective spin interactions, spin alignments and macroscopic spin tunneling in polynuclear manganese and related complexes and their mesoscopic clusters

Theoretical efforts to investigate molecular magnetic materials are reviewed mainly from the viewpoint of our interest. Ab initio calculations of effective exchange interactions between spins are performed for H-H, W-I-Ie-H and simplified models of binuclear manganese and related complexes by using the spin unrestricted Hartree-Fock (UHF) and spin-polarized density functional (DFT), and UHF plus DFT hybrid methods. The scope and limitation of these broken-symmetry approaches are briefly discussed in relation to several computational schemes of effective exchange integrals (J(ab)). The calculated J(ab) values for the three systems are summarized for comparison of the computational methods. The natural orbitals (UNO or DNO) of the UHF and DFT solutions for magnetic clusters are determined by diagonalizing their first-order density matrices. They are used for MO-theoretical interpretation of superexchange interactions. The effective spin Hamiltonians such as the Heisenberg model are constructed for polynuclear complexes assuming the calculated and experimental effective exchange integrals. The macroscopic quantum tunneling (MQT) and coherence (MQC) of spins in the manganese oxide clusters are analyzed using the Heisenberg model, and the tunneling rate of spins is calculated by the coherent state path integral method. The topological rules for MQT and MQC are derived from this analysis. The path integral formulations are extended to tunneling probabilities for clusters of clusters and spin lattices with mesoscopic size. The resulting ideas are also applied to the molecular design of mesoscopic clusters of clusters in intermediate and strong correlation regimes. The active control of spins are finally discussed from the viewpoint of functionalities in molecular and biological materials, and technological applications of mesoscopic molecular magnets to quantum computing. (C) 2000 Elsevier Science S.A. All rights reserved.