Isovalent hybridization
In
Only bonding with 4 equivalent
The bond length between similar atoms also shortens with increasing s character. For example, the C−H bond length is 110.2 pm in ethane, 108.5 pm in ethylene and 106.1 pm in acetylene, with carbon hybridizations sp3 (25% s), sp2 (33% s) and sp (50% s) respectively.
To determine the degree of hybridization of each bond one can utilize a hybridization parameter (λ). For hybrids of s and p orbitals, this is the coefficient multiplying the p orbital when the hybrid orbital is written in the form . The square of the hybridization parameter equals the hybridization index (n) of an spn orbital.[2][3][4] .
The fractional s character of orbital i is , and the s character of all the hybrid orbitals must sum to one, so that
The fractional p character of orbital i is , and the p character of all the hybrid orbitals sums to the number of p orbitals involved in the formation of hybrids:
These hybridization parameters can then be related to physical properties like bond angles. Using the two bonding atomic orbitals i and j we are able to find the magnitude of the interorbital angle. The orthogonality condition implies the relation known as Coulson's theorem:[5]
For two identical ligands the following equation can be utilized:
The hybridization index cannot be measured directly in any way. However, one can find it indirectly by measuring specific physical properties. Because nuclear spins are coupled through bonding electrons, and the electron penetration to the nucleus is dependent on s character of the hybrid orbital used in bonding,
- and ,[6]
where 1JX-Y is the one-bond
constant between nuclei X and Y and χS(α) is the s character of orbital α on carbon, expressed as a fraction of unity.As an application, the 13C-1H coupling constants show that for the cycloalkanes, the amount of s character in the carbon hybrid orbital employed in the C-H bond decreases as the ring size increases. The value of 1J13C-1H for cyclopropane, cyclobutane and cyclopentane are 161, 134, and 128 Hz, respectively. This is a consequence of the fact that the C-C bonds in small, strained rings (cyclopropane and cyclobutane) employ excess p character to accommodate their molecular geometries (these bonds are famously known as 'banana bonds'). In order to conserve the total number of s and p orbitals used in hybridization for each carbon, the hybrid orbital used to form the C-H bonds must in turn compensate by taking on more s character.[2][4][7] Experimentally, this is also demonstrated by the significantly higher acidity of cyclopropane (pKa ~ 46) compared to, for instance, cyclohexane (pKa ~ 52).[4][8][9]
References
- ^ "Listing of experimental geometry data for CH3F (Methyl fluoride). See table Internal coordinates". Computational Chemistry Comparison and Benchmark DataBase. National Institute of Standards and Technology. 21 August 2020. Retrieved 4 February 2021.
- ^ a b Carroll, F. A. Perspectives on Structure and Mechanism in Organic Chemistry, 2nd ed.; John Wiley & Sons: New Jersey, 2010.
- Mislow, K. Introduction to Stereochemistry; W.A. Benjamin Inc: New York. 1965.
- ^ a b c Anslyn, A.V., Dougherty, D.A. Modern Physical Organic Chemistry 3rd ed; University Science: California. 2006.
- ^ Coulson, C.A. Valence (2nd ed., Oxford University Press 1961) p.204
- )
- ^ Ferguson, L.N. Highlights of Alicyclic Chemistry, Part 1; Franklin Publishing Company, Inc.: Palisade, NJ, 1973.
- ^ Evans, David A. (4 November 2005). "The Evans pKa Table" (PDF). The Evans Group. Archived from the original (PDF) on 19 June 2018. Alt URL
- ^ These pKa values were estimated by Streitwieser by measuring the rates of deuterium exchange.