The single-molecule magnets (SMMs) [Mn4O3X(OAc)(3)(dbm)(3)] (X = Br, Cl, OAc, and F) were investigated by a detailed inelastic neutron scattering (INS) study. Up to four magnetic excitations between the zero-field split levels of the lowest S = 9/2 cluster ground-state have been resolved. From the determined energy-level diagrams and the relative INS intensities we can show that the inclusion of a rhombic term in the zero-field splitting (ZFS) Hamiltonian is essential in these compounds. On the basis of the Hamiltonian: (H) over cap (ZFS) = D[(S) over cap (2)(z) - 1/3S(S + 1)] + E((S) over cap (2)(x) - (S) over cap (2)(y)) + B-4(0)(O) over cap (0)(4), the following sets of parameters are derived: For X = Cl: D = -0.529 cm(-1), \E\ = 0.022 cm(-1), and B-4(0) = -6.5 x 10(-5) cm(-1); for X = Br: D = -0.502 cm(-1), \E\ = 0.017 cm(-1), and B-4(0) = -5.1 x 10(-5) cm(-1); for X = OAc: D = -0.469 cm(-1), \E\ = 0.017 cm(-1), and B-4(0) = -7.9 x 10(-5) cm(-1); and for X = F: D = -0.379 cm(-1) and B-4(0) = -11.1 x 10-5 cm(-1). The wave functions derived from the energy analysis are in excellent agreement with the relative intensities of the observed INS transitions. The observed temperature maxima of the out-of-phase component of the variable frequency AC magnetic susceptibility T-max[chi"] correlate very well with the energy splittings determined by INS. Direct information about the rate of quantum tunneling is contained in the cluster wave functions derived in this study. The difference in the quantum tunneling between X = Cl and Br is shown to be directly related to differences in the rhombic anisotropy parameter \E\.