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Hyperconjugation can be used to rationalize a variety of chemical phenomena, including the anomeric effect, the gauche effect, the rotational barrier of ethane, the beta-silicon effect, the vibrational frequency of exocyclic carbonyl groups, and the relative stability of substituted carbocations and substituted carbon centred radicals, and the thermodynamic Zaitsev's rule for alkene stability.
Figure 9: The C–H bonding orbital is mixing with the C–X anti-bonding orbital through hyperconjugation. Figure 10: In an E 2 mechanism molecules generally prefer an anti-periplanar geometry because it aligns molecular orbitals and sets up the molecule to move electrons in a C–H bonding orbital into a π C-C bonding orbital.
In differential geometry, conjugate points or focal points [1] [2] are, roughly, points that can almost be joined by a 1-parameter family of geodesics. For example, on a sphere, the north-pole and south-pole are connected by any meridian. Another viewpoint is that conjugate points tell when the geodesics fail to be length-minimizing.
Negative hyperconjugation is seldom observed, though it can be most commonly observed when the σ *-orbital is located on certain C–F or C–O bonds. [ 3 ] [ 4 ] In negative hyperconjugation, the electron density flows in the opposite direction (from a π- or p-orbital to an empty σ * -orbital) than it does in the more common ...
Qalculate! supports common mathematical functions and operations, multiple bases, autocompletion, complex numbers, infinite numbers, arrays and matrices, variables, mathematical and physical constants, user-defined functions, symbolic derivation and integration, solving of equations involving unknowns, uncertainty propagation using interval arithmetic, plotting using Gnuplot, unit and currency ...
The gauche effect is very sensitive to solvent effects, due to the large difference in polarity between the two conformers.For example, 2,3-dinitro-2,3-dimethylbutane, which in the solid state exists only in the gauche conformation, prefers the gauche conformer in benzene solution by a ratio of 79:21, but in carbon tetrachloride, it prefers the anti conformer by a ratio of 58:42. [9]
In many common bonds of this type, the bonding orbital is shifted towards two of the three atoms instead of being spread equally among all three. Example molecules with 3c–2e bonds are the trihydrogen cation (H + 3) and diborane (B 2 H 6). In these two structures, the three atoms in each 3c-2e bond form an angular geometry, leading to a bent ...
For example, consider the generalized hypergraph consisting of two edges and , and zero vertices, so that = {} and = {}. As this loop is infinitely recursive, sets that are the edges violate the axiom of foundation .
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