Natural bond orbital (NBO), nuclear magnetic resonance (NMR) analysis and hybrid-density functional theory based method (B3LYP/Def2-TZVPP) were used to investigate the correlation between the nucleus-independent chemical shifts [NICS, as an aromaticity criterion], σ Al(1)-X2(b) → σ*Al(3)-X₄(b) electron delocalizations and the dissociation energies of Al₂F₆, Al₂Cl₆, Al₂Br₆ and Al₂I₆ to 2AlX₃ (X = F, Cl, Br, I). The results obtained showed that the dissociation energies of Al₂F₆, Al₂Cl₆, Al₂Br₆ and Al₂I₆ decrease from Al₂F₆ to Al₂I₆. Like aromatic molecules, these compounds have relatively significant negative NICSiso(0) values. Clearly, based on magnetic criteria, they exhibit aromatic character and make it possible to consider them as σ-delocalized aromatic species, such as Möbius σ-aromatic species. The σ-aromatic character which is demonstrated by their NICSiso(0) values decreases from Al₂F₆ to Al₂I₆. The NICSiso values are dominated by the in-plane σ₂₂ (i.e., σyy, the plane containing halogen atoms bridged) chemical shift components. The increase of the NICSiso values explains significantly the decrease of the corresponding dissociation energies of Al₂F₆, Al₂Cl₆, Al₂Br₆ and Al₂I₆. Importantly, the NBO results suggest that in these compounds the dissociation energies are controlled by the stabilization energies associated with σ Al(1)-X2(b) →σ*Al(3)-X4(b) electron delocalizations. The decrease of the stabilization energies associated with σ Al(1)-X₂(b) →σ*Al(3)-X4(b) electron delocalizations is in accordance with the variation of the calculated NICSiso values. The correlations between the dissociation energies of Al₂F₆, Al₂Cl₆, Al₂Br₆ and Al₂I₆, σ Al(1)-X₂(b) →σ*Al(3)-X4(b) electron delocalizations, natural atomic orbitals (NAOs) and NICSiso values have been investigated.

The structural properties of ethene (1) and tetrahydridodimetallenes M(2)H(4) [M = Si (2), Ge (3), and Sn (4)] have been examined by means of CCSD(T)/Def2-TZVPP, MP4(SDTQ)/Def2-TZVPP, and B3LYP/Def2-TZVPP levels of theory and natural bond orbital analysis (NBO) interpretations. The results obtained showed the expected planar ground state structure for compound 1 (D(2h) symmetry) but trans-bent ground state structures for compounds 2-4 (C(2h) symmetry). The distortions of the high-symmetry configurations of compounds 2-4 are due to the pseudo Jahn-Teller effect (PJTE), which is the only source of instability of high-symmetry configurations in nondegenerate states. The distortions are due to the mixing of the ground A(g) and excited B(2g) states [i.e., HOMO(B(3u)) → LUMO + 3(B(1u)) for compound 1, HOMO(B(3u)) → LUMO + 2(B(1u)) for compound 2, and HOMO(B(3u)) → LUMO + 1(B(1u)) for compounds 3 and 4]. Importantly, the higher-lying B(1g), B(2u), and B(2g) states are not involved in the PJT interactions. The energy gaps between reference states (Δ) in the undistorted configurations decrease from compound 1 to compound 4, and the PJT stabilization energies increase. Therefore, the primary force constant of the ground state in the Q((b2g)) direction (K(0)) decreases from compound 1 to compound 4. This fact can be justified by the valence isoelectronic systems of these compounds (having similar vibronic coupling constants, F). For the purpose of more chemical transparency, the NBO results were analyzed, and their relation to the PJT interactions has been revealed. The NBO analysis showed that stabilization energy associated with π(M-H) (b(u)) → σ*(M═M) (b(u)) electron delocalization (i.e., the mixing of the distorted b(u) molecular orbitals along the b(2g) bending distortions) increases from compound 1 to compound 4. Also, by using the hybridized orbitals obtained, an n parameter is defined. The NBO results revealed that the n values in the mean hybrid orbitals (sp(n)) increase from compound 1 to 4. The correlations between the PJT stabilization energies, bond orders, n values, π(M-M) → σ*(M═M) electron delocalizations, and structural parameters of compounds 1-4 have been investigated.

Complete basis set CBS-4, hybrid-density functional theory (hybrid-DFT: B3LYP/6-311+G**) based methods and natural bond orbital (NBO) interpretations have been used to examine the contributions of the hyperconjugative, electrostatic, and steric effects on the conformational behaviors of trans-2,3-dihalo-1,4-diselenane [halo = F (1), Cl (2), Br (3)] and trans-2,5-dihalo-1,4-diselenane [halo = F (4), Cl (5), Br (6)]. Both levels of theory showed that the axial conformation stability, compared to its corresponding equatorial conformation, decreases from compounds 1 → 3 and 4 → 6. Based on the results obtained from the NBO analysis, there are significant anomeric effects for compounds 1-6. The anomeric effect associated with the electron delocalization is in favor of the axial conformation and increases from compounds 1 → 3 and 4 → 6. On the other hand, dipole moment differences between the axial and equatorial conformations [Δ(μ(eq)-μ(ax)] decrease from compounds 1 → 3. Although Δ(μ(eq)-μ(ax)) parameter decreases from compound 1 to compound 3, the dipole moment values of the axial conformations are smaller than those of their corresponding equatorial conformations. Therefore, the anomeric effect associated with the electron delocalizations (for halogen-C-Se segments) and the electrostatic model associated with the dipole-dipole interactions fail to account for the increase of the equatorial conformations stability on going from compound 1 to compound 3. Since there is no dipole moment for the axial and equatorial conformations of compounds 4-6, consequently, the conformational preferences in compounds 1-6 is in general dictated by the steric hindrance factor associated with the 1,3-syn-axial repulsions. Importantly, the CBS-4 results show that the entropy difference (∆S) between the equatorial axial conformations increases from compounds 1 → 3 and 4 → 6. This fact can be explained by the anomeric effect associated with the electron delocalization which affects the C₂-Se bond orders and increase the rigidity of the corresponding rings. The Gibbs free energy difference values between the axial and equatorial conformations (i.e. ΔG(ax-ax) and ΔG(eq-eq)) of compounds 1 and 4, 2 and 5 and also 3 and 6 have been calculated. The correlations between the anomeric effect, electrostatic model, ΔG(eq-ax), ΔG(ax-ax), ΔG(eq-eq), bond orders, dipole-dipole interactions, structural parameters and conformational behaviors of compounds 1-6 have been investigated.

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2-Methoxytetrahydropyran (1), -thiopyran (2) and -selenopyran (3) have been chosen as model compounds to investigate the origin of the anomeric effect (AE). The impacts of the hyperconjugation, electrostatic and steric interactions on the conformational preferences of compounds 1 -3 have been analysed by means of complete basis set-4, hybrid-density functional theory (B3LYP/6-311 þ G**) based methods and natural bond orbital (NBO) interpretation. Both levels of theory showed that the axial conformations of compounds 1 -3 are more stable than their equatorial conformations. The Gibbs free energy difference (G eq -G ax ) values (i.e. DG eq -ax ) between the axial and equatorial conformations increase from compound 1 to compound 2 but decrease from compound 2 to compound 3. Based on the NBO results obtained, the AE associated with the electron delocalisation [i.e. S(endo-AE eq þ exo-AE eq ) 2 S(endo-AE ax þ exo-AE ax )] increase slightly from compound 1 to compound 2 but decrease from compound 2 to compound 3. Similar trend is also observed for the differences between the calculated total steric exchange energy values [i.e. D(TSEE) eq -ax ]. On the other hand, the calculated differences between the dipole moment values of the axial and equatorial conformations [i.e. D(m eq -m ax )] decrease from compound 1 to compound 3. These findings led to the proposal that the AE associated with the electron delocalisation (the hyperconjugation effect) is more significant for the explanation of the conformational preferences of compounds 1 -3 than the electrostatic model. The correlations between the AE associated with the electron delocalisation, bond orders, TSEE, DG eq -ax , dipole-dipole interactions, structural parameters and conformational behaviours of compounds 1 -3 have been investigated.

Contrary to the published conclusions in the literature concerning the origin of the generalized anomeric relationships in open-chain nonplanar systems, its origin has remained an open question. In order to explore the origin of the generalized anomeric relationships in open-chain nonplanar systems, we assessed the roles and contributions of the effective factors on the conformational properties of methyl propargyl ether (1), methyl propargyl sulfide (2), and methyl propargyl selenide (3) by means of the G3MP2, CCSD(T), MP2, LC-ωPBE, and B3LYP methods and natural bond orbital (NBO) interpretations. We examined the contributions of the hyperconjugative interactions on the conformational preferences of compounds 1-3 by the deletions of the orbitals overlapping from the Fock matrices of the gauche- and anti-conformations. The trend observed for energy changes in the Fock matrices justify the variations of the gauche-conformations preferences going from compound 1 to compound 3, revealing that the hyperconjugative interactions are solely responsible for the generalized anomeric relationships in compounds 1-3. Accordingly, the conclusions published in the literature concerning the origin of the generalized anomeric effect in the acyclic nonplanar compounds should be revised by these findings. The Pauli exchange type repulsions (PETR) are in favors of the gauche-conformations and the variations of the PETR differences between the gauche- and anti-conformations of compounds 1-3 correlate well with their gauche-conformations preferences, revealing that the generalized anomeric relationships in compounds 1-3 have also the Pauli exchange-type repulsions origin. The resemblance between the preorthogonal natural bond orbitals (that are involved in the hyperconjugative interactions) and their corresponding molecular orbitals have been investigated.

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