The origin of the pair-delocalized ground state of spin S = 1/2, observed in the chemically symmetric, mixed-valence [Fe4S4](3+) cores in the high-potential iron protein (HiPIP) and its synthetic analogues, is analyzed in the framework of an effective Hamiltonian model, comprising terms for excess-electron transfer (leading to double-exchange coupling of the paramagnetic Fe(III) cores), vibronic coupling (trapping the excess electron), and Heisenberg-Dirac-Van Vleck exchange. The adiabatic potential surfaces of the system d(5)-d(5)-d(5)-d(6) are determined, and their extremal points, corresponding to definite electron distributions, are ascertained. The electron distributions depend essentially on the ratio of the transfer parameter and vibronic trapping energy, beta/(lambda(2)/2 kappa). For small ratios, the excess electron is site-trapped; for ratios of larger magnitude (greater than or equal to 1), the delocalization behavior depends on the nature of the electronic state considered. The transfer Hamiltonian has for beta < 0 an orbitally nondegenerate ground state of high spin (S = 19/2), in which the excess electron is uniformly distributed over the four sites. However, for beta > 0, the transfer interaction stabilizes a highly orbital- and spin-degenerate electronic ground state, including spin levels ranging from S = 1/2 to 17/2. The degeneracy is removed by vibronic interaction, leading to broken-symmetry, pair-delocalized states which appear in the energy order E(1/2) < E(3/2) < ... . Inhomogeneous HDVV exchange, arising from differences in the coupling parameters for ferrous-ferric (J) and ferric-ferric (J(1)) interactions, has little effect on the composition of the broken-symmetry states but has a great impact on state energy. The spin structures of the two lowest broken-symmetry states of the total Hamiltonian are similar to those inferred from spectroscopic studies of HiPIP and synthetic analogues thereof.