A quantum admixture model for the d(5) configuration of the high-spin <----> low spin (HS <-> LS) transition ((6)A(1) <-> T-2(2)) Fe(III) complex molecules has been established by using the UCFC scheme. The analysis shows that there exists an indirect spin-orbital coupling interaction between the high-spin and low-spin states via the intermediate-spin states. This interaction may be described approximately by two small matrices (the order is 25 and 14, respectively) of the Hamiltonian, which involves the electron-electron repulsion, the ligand-field; the spin-orbit coupling, and the Zeeman interactions. By diagonalizing these matrices, the electronic and magnetic structures of the Fe(III) molecules in the spin-transition region can be derived. The results show a sensitive dependence on the ratio Delta Dq/zeta. Here zeta is the spin-orbit coupling coefficient and Delta Dq Dq - Dq(0), while Dq(0) is the ligand-field strength at the spin-transition point. From this model a reasonable explanation for the temperature-dependent magnetic moment of the Fe(III) in [Fe(3-OEt-SalAPA)(2)]ClO4. C6H6 molecules has been given.