Recently, the synthesis, crystallographic structure, and Mossbauer characterization of the first example of an [(Fe(IV)TAML)(2)O](2-) (TAML = tetra-amido microcyclic ligand) complex were reported. Here, we elucidate the prominent structural, electronic, and magnetic properties of this complex on the basis of density functional theory (DFT) calculations. While the torsion between the molecular halves is caused by hydrogen bonding between the TAML moieties, the bending of the Fe-O-Fe unit is an intrinsic property of the bridge, The values for the Fe-57 isomer shift and quadrupole splitting obtained with DFT are in good agreement with experimental results and indicate that the irons have intermediate spin states (S-1 = S-2 = 1). The iron spins are coupled by strong antiferromagnetic exchange to yield a ground state with system spin S = 0. The Fe-O distances in the excited S > 0 states are significantly longer than in the ground state. Since the wave function of the ground state, in which the iron spins are antiferromagnetically coupled to give system spin S = 0, is a linear combination of Slater determinants that cannot be treated with existing DFT codes, the Fe-O distance for the S = 0 state has been estimated by extrapolation from the optimized geometries for the ferromagnetic state (S = 2) and the broken symmetry state to be 1.748 angstrom, in good agreement with the crystallographic distance 1.728 angstrom. To accommodate the spin-dependent reorganization energies, the conventional bilinear spin Hamiltonian has been extended with a biquadratic coupling term: (H) over capH(ex) = c' + j(0)(S) over cap (1) center dot (S) over cap (2) + j(1)((S) over cap (1) center dot (S) over cap (2))(2). A computational scheme is presented for estimating the exchange parameters, yielding the values j(0) = 199 cm(-1) and j(1) = -61 cm(-1) for [((FeB)-B-IV*)(2)O](2-). Two mechanisms for biquadratic exchange are discussed.