A theoretical conformational study on the structural parameters involved in the ring strain of exo-unsaturated four-membered heterocycles, Y = CCH2CH2X
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Abstract:
The effect of ring-puckering angle on the structural parameters (bond lengths and angles) involved in the ring strain of a series of four-membered heterocycles (1–16) was theoretically demonstrated by using the ab initio methods MP2 and HF, and the DFT methods PBE1PBE, B3LYP, SVWN5 with 6-31+G(d,p) as basis set. The results revealed that the bonds within the ring (C–X and C–C) are the most sensitive to puckering angle changes. The variation of the C–X and C=Y bond lengths as function of puckering angle are determined by a balance between the 1,3 repulsive interactions and the electronic nature of the heteroatoms X and Y. Particularly, for azetidines and phosphetanes, the C–X and C=Y bond lengths exhibit a major increase at axial conformations. In general, the C–C bond length decreases with the puckering angle for all heterocycles. While the heteroatom–H bonds (in the ring skeleton) are very sensitive to geometric changes, exhibiting an increasing behaviour for equatorial conformations and a decreasing behaviour for axial conformations highly puckered (ϕ > −20°). The C–X–C angle decreases monotonically with the puckering angle, increasing the Baeyer strain on the studied molecules. Finally, all methods predicted a similar behaviour for the studied parameters as function of the puckering angle, although some smaller differences in the predictions of their respective values, especially at HF level, were observed.Keywords:
Molecular geometry
Heteroatom
Ring strain
Based on the helical and rotational symmetries and Tersoff potential, the structural parameters, i.e., bond lengths and bond angles, have been investigated for armchair single-wall carbon nanotubes. The bond lengths and bond angles are determined for several radii tubes of various lengths. Results for armchair tubes show that one bond length is greater than that of the graphite while the other is smaller. Furthermore, the tube length is found to have significant effects on these bond lengths and bond angles. We have also recalculated the variation of these bonds under hydrostatic pressure. With the application of pressure, the bond lengths compress and the larger bond length decreases faster with pressure in comparison to the shorter one. As a consequence, at some critical pressure the bond lengths become equal. An analysis regarding the cross-sectional shape of the nanotubes and its pressure dependence has also been done. At some particular pressure, the first transition from circular to elliptical cross section takes place. For (10,10) tube the first transition pressure is found to be equal to $2.2\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$.
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We have studied bond length and bond angle of a series of phenols. For present study the molecular modelling and geometry optimization of all the compounds were carried out with MOPAC software using MINDO/3 methods. We have conclude that the order of bond lengths between C-O, C-C, C-H and O-H atoms have been changed by changing the position of the substituents i.e., from ortho to para substitution. The C-C-C band angles have the same value while the C-C-O and C-O-H band angles differ from their normal values on substitution.
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We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zigzag single-wall nanotubes in detail. The bond lengths and bond angles are determined for several radii tubes by using a theoretical procedure based on the helical and rotational symmetry for atom coordinates generation, coupled with Tersoff potential for interaction energy calculations. Results show that the structure of zigzag tubes is governed by two bond lengths. One bond length is found to have a value equal to that of graphite, while the other one is larger. Furthermore, the tube length is found to have significant effect only on larger bond length in zigzag tubes. With the application of the pressure, only the larger bond length compresses, the other one remaining practically constant. At some critical pressure, this bond length becomes equal to constant bond length. This behavior of bond lengths is different from those of armchair tubes. An analysis regarding the cross sectional shape has also been done. At some higher pressure, transition from circular to oval cross section takes place. This transition pressure is found to be equal 2.06GPa for (20,0) tube. Some comparison with chiral tubes has also been made and important differences on bond length behavior have been observed.
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MINDO
Molecular geometry
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The effect of ring-puckering angle on the structural parameters (bond lengths and angles) involved in the ring strain of a series of four-membered heterocycles (1–16) was theoretically demonstrated by using the ab initio methods MP2 and HF, and the DFT methods PBE1PBE, B3LYP, SVWN5 with 6-31+G(d,p) as basis set. The results revealed that the bonds within the ring (C–X and C–C) are the most sensitive to puckering angle changes. The variation of the C–X and C=Y bond lengths as function of puckering angle are determined by a balance between the 1,3 repulsive interactions and the electronic nature of the heteroatoms X and Y. Particularly, for azetidines and phosphetanes, the C–X and C=Y bond lengths exhibit a major increase at axial conformations. In general, the C–C bond length decreases with the puckering angle for all heterocycles. While the heteroatom–H bonds (in the ring skeleton) are very sensitive to geometric changes, exhibiting an increasing behaviour for equatorial conformations and a decreasing behaviour for axial conformations highly puckered (ϕ > −20°). The C–X–C angle decreases monotonically with the puckering angle, increasing the Baeyer strain on the studied molecules. Finally, all methods predicted a similar behaviour for the studied parameters as function of the puckering angle, although some smaller differences in the predictions of their respective values, especially at HF level, were observed.
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Heteroatom
Ring strain
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