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.