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In particular, Pauling introduced the concept of hybridisation, where atomic s and p orbitals are combined to give hybrid sp, sp 2, and sp 3 orbitals. Hybrid orbitals proved powerful in explaining the molecular geometries of simple molecules like methane, which is tetrahedral with an sp 3 carbon atom and bond angles of 109.5° between the four ...
The angle between any two bonds is the tetrahedral bond angle of 109°28' [3] (around 109.5°). Pauling supposed that in the presence of four hydrogen atoms, the s and p orbitals form four equivalent combinations which he called hybrid orbitals. Each hybrid is denoted sp 3 to indicate its composition, and is directed along one of the four C–H ...
As such, the predicted shape and bond angle of sp 3 hybridization is tetrahedral and 109.5°. This is in open agreement with the true bond angle of 104.45°. The difference between the predicted bond angle and the measured bond angle is traditionally explained by the electron repulsion of the two lone pairs occupying two sp 3 hybridized orbitals.
This would result in the geometry of a regular tetrahedron with each bond angle equal to arccos(− 1 / 3 ) ≈ 109.5°. However, the three hydrogen atoms are repelled by the electron lone pair in a way that the geometry is distorted to a trigonal pyramid (regular 3-sided pyramid) with bond angles of 107°.
Only bonding with 4 equivalent substituents results in exactly sp 3 hybridization. For molecules with different substituents, we can use isovalent hybridization to rationalize the differences in bond angles between different atoms. In the molecule methyl fluoride for example, the HCF bond angle (108.73°) is less than the HCH bond angle (110.2 ...
Linus Pauling explained the importance of orbital overlap in the molecular bond angles observed through experimentation; it is the basis for orbital hybridization. As s orbitals are spherical (and have no directionality) and p orbitals are oriented 90° to each other, a theory was needed to explain why molecules such as methane (CH 4) had ...
If the edge length of the cube is chosen as 2 units, then the two bonds OA and OB correspond to the vectors a = (1, –1, 1) and b = (1, 1, –1), and the bond angle θ is the angle between these two vectors. This angle may be calculated from the dot product of the two vectors, defined as a ⋅ b = ‖ a ‖ ‖ b ‖ cos θ where ‖ a ...
Molecular geometries can be specified in terms of 'bond lengths', 'bond angles' and 'torsional angles'. The bond length is defined to be the average distance between the nuclei of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds.