In this study, part 1 of a series examining the electronic structure of the coenzyme vitamin B12 and related derivatives, we present a study of the electronic structure of Co(DH)2(L)(R) (DH = dimethylglyoxime; L = NH3, py, 2-NH2py, 5,6-dimethylbenzimidazole; R = CH3, i-C3H7, 5’-deoxyadenosyl) as model systems for the vitamin B12 coenzyme. We have optimized 12 DH derivatives with varying degrees of steric bulkiness and sigma donor capability of the axial ligands. Our goal was to determine which factors may contribute to structural changes in the equatorial ligand and in the Co-axial bonds and to validate the use of the model system in understanding the function of coenzyme B12. In the model systems, we were able to demonstrate the effects upon the Co-axial bonds as a result of (a) puckering of the DH ligand, (b) trans-steric interactions, and (c) trans-electronic influence. By constraining the DH ligand to initially remain planar and then allowing full relaxation of the equatorial ligand, we were able to determine how puckering of the equatorial ligand alone affected the Co-axial bonds. We found that upon relaxation, the nitrogens of the glyoxime rings bend predominantly toward the nitrogen-bound axial ligand, while the carbons of the glyoxime rings could be displaced in either direction depending on the steric bulkiness of the axial ligands. The Co was displaced toward the alkyl group, where the amount of displacement depended upon the steric bulkiness of the axial ligands. Puckering of the equatorial ligand alone did not cause an elongation of the Co-C bond, even though there was a lengthening of the Co-N(ax) bond upon distortion of the DH ligand. To examine the trans-steric influence, we substituted the axial groups with bulky substituents. Bulky axial ligands induced conformation changes in the equatorial ligand with a slight elongation of the Co-alkyl bond. The Co-C(ax) bond length increased with an increase in the bulkiness of R as well as L. The longest Co-C(ax) and Co-N(ax) bonds were found in R = adenosyl and L = 2-NH2py. To examine the trans-electronic influence upon the axial bond, we varied the basicity of L and the sigma donor character of R. There was no structural evidence that the Co-alkyl bond weakened as a result of a decrease in the basicity of L. Comparison of overlap populations in the alkyl derivatives with planar equatorial ligands and fixed average Co-C and C-N(ax) bond lengths indicated little variation in the electronic contributions from the alkyl groups, even though they possessed different sigma-donating strengths. Although the DH derivatives have provided useful information for modeling the alkyl-cobalt bond in the coenzyme, our results indicate that there is very little structural changes in the equatorial ligand that significantly influence the alkyl-cobalt bond.