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A conjugated system has a region of overlapping p-orbitals, bridging the interjacent locations that simple diagrams illustrate as not having a π bond. They allow a delocalization of π electrons across all the adjacent aligned p-orbitals. [3] The π electrons do not belong to a single bond or atom, but rather to a group of atoms.
In fact, all cyclic conjugated hydrocarbons with a total of 4n π-electrons share this molecular orbital pattern, and this forms the basis of Hückel's rule. Dewar reactivity numbers deriving from the Hückel approach correctly predict the reactivity of aromatic systems with nucleophiles and electrophiles .
Whereas a normal conjugated system such as a polyene typically has alternating single and double bonds along consecutive atoms, a cross-conjugated system has an alkene unit bonded to one of the middle atoms of another conjugated chain through a single bond. In classical terms, one of the double-bonds branches off rather than continuing ...
In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct § Topological equivalence of flows, are important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterative function can be determined, then that ...
Köhler illumination addresses this by ensuring the image of the light source is perfectly defocused in the sample plane and its conjugate image planes. In a ray diagram of the illumination light path, this can be seen as the image-forming rays passing parallel through the sample. Köhler illumination requires several optical components to ...
Typically, the more conjugated (longer) the pi-system is, the longer the wavelength of photon can be captured. In other words, with every added adjacent double bond we see in a molecule diagram, we can predict the system will be progressively more likely to appear yellow to our eyes as it is less likely to absorb yellow light and more likely to ...
The molecule must have a complete conjugated π-electron system within the ring. The molecule must have 4n π-electrons where n is any integer within the conjugated π-system. This differs from aromaticity only in the fourth criterion: aromatic molecules have 4n +2 π-electrons in the conjugated π system and therefore follow Hückel’s rule ...
In molecules with alternating double bonds and single bonds, p-orbital overlap can exist over multiple atoms in a chain, giving rise to a conjugated system. Conjugation can be found in systems such as dienes and enones. In cyclic molecules, conjugation can lead to aromaticity. In cumulenes, two double bonds are adjacent.