ORIGINAL RESEARCH Hyperconjugative interactions are the main responsible for the anomeric effect: a direct relationship between the hyperconjugative anomeric effect, global hardness and zero-point energy Davood Nori-Shargh 1 • Seiedeh Negar Mousavi 2 • Rose Tale 1 • Hooriye Yahyaei 3 Received: 13 April 2016 / Accepted: 17 June 2016 Ó Springer Science+Business Media New York 2016 Abstract The correlations between the global hardness (g), hyperconjugative anomeric effect, Pauli exchange-type repulsions, electrostatic model associated with dipole– dipole interaction and structural parameters in 2-fluorote- trahydropyran, -thiopyran, -selenopyran (1–3) and their chloro- (4–6) and bromo-analogs (7–9) were investigated by means of the conventional and range-corrected func- tionals and natural bond orbital (NBO) interpretation. By deletion of the HC-exo-AE and HC-endo-AE, the equatorial conformations of compounds 1–9 become more stable than their corresponding axial forms, revealing that anomeric relationships in compounds 1–9 have the hyperconjugative anomeric effect origins while the electrostatic model associated with dipole–dipole interaction does not play a determining role on the variations of the anomeric rela- tionships in these compounds. The anomeric relationships in compounds 1–3 have no Pauli exchange-type repulsions origin, but it has a significant impact on the conformational preferences in compounds 4–6 and 7–9. A canonical molecular orbital interpretation was conducted to investi- gate the correlations between the linear combinations of natural bond orbitals in the HOMOs, LUMOs and the global hardness (g) values. There is a direct relationship between the hyperconjugative anomeric effect, global hardness (g) and zero-point energies in compounds 1–3, 4– 6 and 7–9. The harder axial conformations with the greater hyperconjugative anomeric effect and zero-point energy values are more stable than their corresponding equatorial forms. Keywords Hyperconjugative anomeric effect Á Global hardness Á Pauli exchange-type repulsions Á Zero-point energy Á NBO Á 2-Halotetrahydropyrans Introduction The important properties of the molecules such as the hardness (g), softness (S) and electronegativity (v) can be determined from the energy gaps, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) [1–6]. The electronic clouds can be distorted in the soft molecules that possess the small HOMO–LUMO gaps. Therefore, the polarizability in the soft molecules is high. The molecules with the large HOMO–LUMO gaps have small ability to the electronic clouds distortions. The hardness is defined as the resistance toward the deformation of electronic clouds of the mole- cules. In the hard species, the electronic cloud is strongly held by the nucleus. Based on the maximum hardness principle which has pointed out by Pearson [4], molecules arrange themselves to be as hard as possible. It has to be noted that the max- imum hardness principle has been successfully applied to the study of some chemical and physical transformations but there are various exceptions to this principle [7–9]. Electronic supplementary material The online version of this article (doi:10.1007/s11224-016-0791-0) contains supplementary material, which is available to authorized users. & Davood Nori-Shargh nori_ir@yahoo.com; D-norishargh@iau-arak.ac.ir 1 Department of Chemistry, Arak Branch, Islamic Azad University, Arak, Iran 2 Department of Nanochemistry, Faculty of Pharmaceutical Chemistry, Pharmaceutical Science Branch, Islamic Azad University (IAUPS), Tehran, Iran 3 Department of Chemistry, Zanjan Branch, Islamic Azad University, Zanjan, Iran 123 Struct Chem DOI 10.1007/s11224-016-0791-0