Relative Interacting Atomic Energy Analysis of the Anomeric Effect in Cyclic and Acyclic O–C–X Systems

The conformational preferences of 2-substituted cyclic and acyclic ethers, arising from the anomeric effect, have been analyzed using the Relative Interacting Atomic Energy (RIAE) analysis within Molecular Electron Density Theory framework, using the M06-2X/6-311G(d,p) level. Comparison of the equatorial-axial energy differences of substituted tetrahydropyrans and cyclohexanes enables the proposal of the anomeric τ index, which quantifies the excess axial stabilization of the tetrahydropyrans relative to the corresponding cyclohexane references and provides an operational estimate of the contribution associated with the O–C–X motif. The RIAE analysis reveals two distinct patterns in the distribution of the atomic energy contributions associated with anomeric stabilization, dominated by either intra-atomic or interatomic terms, which correlate with the period of the X atom. Accordingly, the studied compounds can be classified into two groups: Group I, comprising compounds with second-period X elements (X = N, O, and F), in which axial stabilization is dominated by favorable intra-atomic energy contributions within the basin of the anomeric carbon; and Group II, comprising compounds with third- and fourth-period X elements (X = S, Cl, and Br), in which stabilization is primarily associated with favorable interatomic energy contributions between the ether oxygen and the anomeric carbon atoms. This atomic energy-based analysis provides a complementary interpretation of the X-dependent conformational trends and identifies analogous energy contribution patterns in the cyclic and acyclic systems examined.