en>Lbertolotti at 17:02, 12 July 2013

2013-07-12T17:02:56Z

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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 [[substituent]]s results in 4 {{serif|sp3}} hybridized orbitals. When looking at [[molecule]]s 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]] [[bond length|length]] is 1.0870Å whereas the [[carbon–fluorine bond]] length is longer at 1.3830Å.<ref>National Institute of Science and Technology. List of Experimental Data for CH3F. [http://cccbdb.nist.gov/exp2.asp?casno=593533 (accessed May 10, 2013).]</ref> These differences can be attributed to more {{serif|s}} character in the C−F bonding and less {{serif|s}} character in the C−H bonding orbitals. The bond directed towards a more [[electronegativity|electronegative]] substituent tends to have higher {{serif|p}} character as stated in [[Bent's rule]].

To determine the degree of hybridization of each bond one can utilize the '''hybridization parameter''' ({{mvar|λ}}). Utilizing the relationship of the square of the hybridization parameter equals the hybridization index ({{mvar|n}}) one can find the degree of hybridization {{serif|sp''n''}}.<ref>Carroll, F. A. ''Perspectives on Structure and Mechanism in Organic Chemistry'', 2nd ed.; John Wiley & Sons: New Jersey, 2010.</ref><ref>Mislow, K. ''Introduction to Stereochemistry''; W.A. Benjamin Inc: New York. 1965.</ref>
<ref>Anslyn, A.V., Dougherty, D.A. ''Modern Physical Organic Chemistry'' 3rd ed; University Science: California. 2006.</ref>

:<math>\ n = \lambda^2</math>

The fractional s character can be found using the equation:

: <math>\sum_{i} \frac{i}{1+ \lambda_i^2} = 1</math>

The fractional {{serif|p}} character can be found using the equation:

:<math>\sum_{i} \frac{\lambda_i^2}{1+\lambda_i^2} = 1,2 or 3</math>

These hybridization parameters can then be related to physical properties like bond angles. Using the two bonding atomic orbitals {{mvar|i}} and {{mvar|j}} we are able to find the magnitude of the interorbital angle. The orthogonality condition implies the relation known as [[Charles Coulson|Coulson's]] theorem:<ref>[http://isites.harvard.edu/fs/docs/icb.topic776365.files/lecture%202.pdf Kwan, E.E. Lecture notes Chem 106 (Harvard University)]</ref>

:<math>\ 1 + \lambda_i \lambda_j \cos \theta_i = 0</math>

For two identical ligands the following equation can be utilized:

:<math>\ 1 + \lambda_i^2 \cos \theta_{ii} = 0</math>

The hybridization index cannot be measured directly in any way. However, one can find it indirectly by measuring specific physical properties. [[J-coupling|NMR coupling constant]]s 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 {{serif|s}} character around the nuclei of the bonding electrons. The relationship can be shown with the following equation.

:<math>\ J = \frac {500}{1 + \lambda_i^2}</math>

Where {{mvar|J}} is the [[NMR]] [[J-coupling|spin-spin coupling]] constant of 13C and H.

The 13C NMR spectroscopy has been useful in determining quantitative {{serif|s}} and {{serif|p}} character in [[cycloalkane]]s, showing as you go from cyclopropane to cyclooctane the {{serif|s}} character increases.<ref>Carroll, F. A. ''Perspectives on Structure and Mechanism in Organic Chemistry'', 2nd ed.; John Wiley & Sons: New Jersey, 2010.</ref><ref>Anslyn, A.V., Dougherty, D.A. ''Modern Physical Organic Chemistry'' 3rd ed; University Science: California. 2006.</ref><ref>Ferguson, L.N. ''Highlights of Alicyclic Chemistry'', Part 1; Franklin Publishing Company, Inc.: Palisade, NJ, 1973.</ref>

== References ==

{{reflist}}

[[Category:Chemical bonding]]
[[Category:Quantum chemistry]]

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en>Lbertolotti at 17:02, 12 July 2013