We have examined the distance and orientation dependence of the energy splitting, Delta E(pi*), between the two lowest-lying unoccupied molecular orbitals of a pair of tetracyanoethylene (TCNE) molecules bridged by a stack of noncovalently bonded benzene rings; the stack length ranged from one to six benzene molecules. The distance between ring planes was fixed at 3.4 Angstrom, while the orientation of the rings and of the TCNE molecules was varied. The magnitude of the splitting energy was found to decay exponentially with increasing stack length, r; Delta E(pi*) = A exp(-0.5 beta(e)r), with the damping factor, beta(e), ranging in value from 1.1 to 1.6 Angstrom(-1), as might be anticipated for instances where the "tunneling energy" lies several electron volts away from the frontier orbitals of the pi-electron stack, Both ab initio and semiempirical computations predict a weak dependence of the coupling upon the orientation of the rings. The ab initio HF/3-21G calculations give beta(e) values approximately 20% smaller than those values found in semiempirical computations using ct-stacks in which the separation between adjacent benzene molecules (3.4 Angstrom) is typical of stacked aromatic systems. This is due to the improved capability of the 3-21G basis set to treat the nearest-neighbor inter-ring orbital interactions, compared to the more contracted complete neglect of differential overlap (CNDO) basis set. Comparison to calculations with a more extended basis shows the 3-21C basis is accurate for rings separated by up to 4.0 Angstrom, but for larger separations, ab initio calculations require the use of diffuse functions to properly describe the exponential decay of the interaction.