Production flow analysis

In chemistry, variable hybridization is an extension of orbital hybridization and is the mixing of atomic orbitals into hybrid orbitals that allow chemical bonds to form. It allows for a quantitative depiction of bond formation when the geometric results deviate from ideal bond angles and bond length.

Only bonding with 4 equivalent substituents results in 4 Template:Serif hybridized orbitals. When looking at molecules with different substituents we can rationalize the quantitative results using variable hybridization to explain the differences in bond angles and bond length between different atoms. In molecules like methyl fluoride, the HCF angle is greater than the HCH bonds, 110.200° and 108.733° respectively. Also, the carbon–hydrogen bond length is 1.0870Å whereas the carbon–fluorine bond length is longer at 1.3830Å. These differences can be attributed to more Template:Serif character in the C−F bonding and less Template:Serif character in the C−H bonding orbitals. The bond directed towards a more electronegative substituent tends to have higher Template:Serif character as stated in Bent's rule.

To determine the degree of hybridization of each bond one can utilize the hybridization parameter (Template:Mvar). Utilizing the relationship of the square of the hybridization parameter equals the hybridization index (Template:Mvar) one can find the degree of hybridization Template:Serif.

$\ n=\lambda ^{2}$

The fractional s character can be found using the equation:

$\sum _{i}{\frac {i}{1+\lambda _{i}^{2}}}=1$

The fractional Template:Serif character can be found using the equation:

$\sum _{i}{\frac {\lambda _{i}^{2}}{1+\lambda _{i}^{2}}}=1,2or3$

These hybridization parameters can then be related to physical properties like bond angles. Using the two bonding atomic orbitals Template:Mvar and Template:Mvar we are able to find the magnitude of the interorbital angle. The orthogonality condition implies the relation known as Coulson's theorem:

$\ 1+\lambda _{i}\lambda _{j}\cos \theta _{i}=0$

For two identical ligands the following equation can be utilized:

$\ 1+\lambda _{i}^{2}\cos \theta _{ii}=0$

The hybridization index cannot be measured directly in any way. However, one can find it indirectly by measuring specific physical properties. NMR coupling constants can be used to provide a measure of bonding density around the nucleus of a bonding carbon atom. This can then be used to find the hybridization due to the fact that there is Template:Serif character around the nuclei of the bonding electrons. The relationship can be shown with the following equation.

$\ J={\frac {500}{1+\lambda _{i}^{2}}}$

Where Template:Mvar is the NMR spin-spin coupling constant of ¹³C and H.

The ¹³C NMR spectroscopy has been useful in determining quantitative Template:Serif and Template:Serif character in cycloalkanes, showing as you go from cyclopropane to cyclooctane the Template:Serif character increases.

References

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