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An example of modest stereoselectivity is the dehydrohalogenation of 2-iodobutane which yields 60% trans-2-butene and 20% cis-2-butene. [5] Since alkene geometric isomers are also classified as diastereomers, this reaction would also be called diastereoselective.
[1] [2] Stereocenters are also referred to as stereogenic centers. A stereocenter is geometrically defined as a point (location) in a molecule; a stereocenter is usually but not always a specific atom, often carbon. [2] [3] Stereocenters can exist on chiral or achiral molecules; stereocenters can contain single bonds or double bonds. [1]
The sum on k includes all the values of k in the Brillouin zone (or any other primitive cell of the reciprocal lattice) that are consistent with periodic boundary conditions on the crystal. This includes N different values of k, spread out uniformly through the Brillouin zone.
The reaction most often occurs at an aliphatic sp 3 carbon center with an electronegative, stable leaving group attached to it, which is frequently a halogen (often denoted X). The formation of the C–Nu bond, due to attack by the nucleophile (denoted Nu), occurs together with the breakage of the C–X bond.
The last equation shows that the resulting vector has the x and y components in phase and oriented exactly in the direction, as we had intended, justifying the representation of any linearly polarized state at angle as the superposition of right and left circularly polarized components with a relative phase difference of .
Expanding [] using its Taylor series, the n-point correlation function becomes a sum of interaction picture correlation functions which can be evaluated using Wick's theorem. A diagrammatic way to represent the resulting sum is via Feynman diagrams , where each term can be evaluated using the position space Feynman rules.
Zero field splitting (ZFS) describes various interactions of the energy levels of a molecule or ion resulting from the presence of more than one unpaired electron. In quantum mechanics , an energy level is called degenerate if it corresponds to two or more different measurable states of a quantum system.
The condition of zero divergence is satisfied whenever a vector field v has only a vector potential component, because the definition of the vector potential A as: = automatically results in the identity (as can be shown, for example, using Cartesian coordinates): = =