The synthesis and physical characterization of ore-bridged [Cr-2(tmpa)(2)(mu-O)(X)](eta+) complexes (tmpa = tris(2-pyridylmethyl)amine) containing a variety of complementary ligands (X = CO32-, PhPO(4)(2-), HS-) are described, with the objective of understanding factors underlying variations in the antiferromagnetic coupling constant J. We also present the crystal structure of [(tmpa)Cr(mu-O)(mu-CO3)Cr(tmpa)] (ClO4)(2) . 2H(2)O, for comparison with previous findings on [(tmpa)Cr(mu-O)(mu-CH3CO2)Cr(tmpa)](ClO4)(3). The carbonate-bridged complex crystallizes in the monoclinic space group P2(1)/c with a = 11.286(10) Angstrom, b = 18.12(2) Angstrom, c = 20.592(12) Angstrom, beta = 95.99(5)degrees, and V = 4190 Angstrom(3) and Z = 4. Asymmetric tmpa ligation pertains, with apical N atoms situated trans to bridging oxo and acido O atoms. Key structural parameters include Cr-O-b bond lengths of 1.818(6) and 1.838(6) Angstrom, Cr-OCO2 distances of 1.924(7) and 1.934(7) Angstrom, and a bridging bond angle of 128.3(3)degrees. Several attempts to prepare ore, amido-bridged dimers were unsuccessful, but the nearlinear [Cr(tmpa)(N(CN)(2))]O-2(ClO4)(2) . 3H(2)O complex was isolated from the reaction of dicyanamide ion with [Cr(tmpa)(OH)](4+)(2). In contrast to the behavior of analogous diiron(III) complexes, antiferromagnetic coupling constants of [Cr-2(tmpa)(2)(mu-O)(X)](eta+) dinuclear species are highly responsive to the X group. Considering the complexes with X = CO32-, PhPO(4)(2-), HS-, SO42-, and RCO(2)(-) (10 R substituents), we find a reasonably linear, empirical relationship between J and oxo bridge basicity, as measured by pK(a), (Cr(OH)Cr) values in aqueous solution. While there is no theoretical basis for such a correlation between solid-state and solution-phase properties, this relationship demonstrates that CrOCr pi-bonding contributes significantly to antiferromagnetic exchange. Thus, J tends to become less negative with increasing mu-O2- basicity, showing that greater availability of a bridging oxo group lone pair toward the proton,with decreasing CrOCr pi-interaction, reduces the singlet-triplet gap.