Density functional theory (DFT) and the valence bond configuration interaction (VBCI) model have been applied to the oximato-based Mn^III₃O single-molecule magnets (SMMs), allowing one to correlate the Mn^III -Mn^III exchange coupling energy (J) with the bridging geometry in terms of two structural angles: the Mn-O-N-Mn torsion angle (γ) and the MN₃ out-of-plane shift of O (angle δθ). Using DFT, a two-dimensional (γ, δθ) energy surface of J is derived and shown to yield essentially good agreement with the reported J values deduced from magnetic susceptibility data on trigonal oximato-bridged MN₃ SMMs. VBCI is used to understand and analyze the DFT results. It is shown that the exchange coupling in these systems is governed by a spin-polarization mechanism inducing a pronounced and dominating ferromagnetic exchange via the oximato bridge as opposed to kinetic exchange, which favors a weaker and antiferromagnetic exchange via the bridging oxide. In the light of these results, a discussion of the exchange coupling in the Mn₆ family of the SMM with a record demagnetization barrier is given.