As demonstrated in previous spectroscopic studies of 1,3-dioxole [J. Am. Chem. Soc., 1993, 115, 12132-12136] and 1,3-benzodioxole [J. Am. Chem. Soc., 1999, 121, 5056-5062], analysis of the ring-puckering potential energy function (PEF) of a "pseudo-four-membered ring" molecule can provide insight into understanding the magnitude of the anomeric effect. In the present study, high-level CCSD/cc-pVTZ and somewhat lower-level MP2/cc-pVTZ ab initio computations have been utilized to calculate the PEFs for 1,3-dioxole and 1,3-benzodioxole and 10 related molecules containing sulfur and selenium atoms and possessing the anomeric effect. The potential energy parameters derived for the PEFs directly provide a comparison of the relative magnitudes of the anomeric effect for molecules possessing OCO, OCS, OCSe, SCS, SCSe, and SeCSe linkages. The torsional potential energies produced by the anomeric effect for these linkages were estimated to range from 5.97 to 1.91 kcal/mol. The ab initio calculations also yielded the structural parameters, barriers to planarity, and ring-puckering angles for each of the 12 molecules studied. Based on the refined structural parameters for 1,3-dioxole and 1,3-benzodioxole, improved PEFs for these molecules were also calculated. The calculations also support the conclusion that the relatively low barrier to planarity of 1,3-benzodioxole results from competitive interactions between its benzene ring and the oxygen atom p orbitals.