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Two pi bonds are the maximum that can exist between a given pair of atoms. Quadruple bonds are extremely rare and can be formed only between transition metal atoms, and consist of one sigma bond, two pi bonds and one delta bond. A pi bond is weaker than a sigma bond, but the combination of pi and sigma bond is stronger than either bond by itself.
A molecule with no rings can be represented as a tree with a number of bonds equal to the number of atoms minus one (as in dihydrogen, H 2, with only one sigma bond, or ammonia, NH 3, with 3 sigma bonds). There is no more than 1 sigma bond between any two atoms. Molecules with rings have additional sigma bonds, such as benzene rings, which have ...
Griffith and Orgel used the electrostatic principles established in crystal field theory to describe transition metal ions in solution and used molecular orbital theory to explain the differences in metal-ligand interactions, thereby explaining such observations as crystal field stabilization and visible spectra of transition metal complexes.
For example, a bond between two s-orbital electrons is a sigma bond, because two spheres are always coaxial. In terms of bond order, single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds contain one sigma bond and two pi bonds. However, the atomic orbitals for bonding may be hybrids.
In number theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function. In applied mathematics , σ( T ) denotes the spectrum of a linear map T . In complex analysis , σ is used in the Weierstrass sigma-function .
the Pi function, i.e. the Gamma function when offset to coincide with the factorial; the complete elliptic integral of the third kind; the fundamental groupoid; osmotic pressure; represents: Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter; the prime-counting function
According to the frontier molecular orbital theory, the sigma bond in the ring will open in such a way that the resulting p-orbitals will have the same symmetry as the HOMO of the product. [4] For the 5,6-dimethylcyclohexa-1,3-diene, only a disrotatory mode would result in p-orbitals having the same symmetry as the HOMO of hexatriene.
Sigmatropic rearrangements are concisely described by an order term [i,j], which is defined as the migration of a σ-bond adjacent to one or more π systems to a new position (i−1) and (j−1) atoms removed from the original location of the σ-bond. [3]