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Chemist Linus Pauling first developed the hybridisation theory in 1931 to explain the structure of simple molecules such as methane (CH 4) using atomic orbitals. [2] Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and a fourth weaker bond ...
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 ( λ ) {\displaystyle (\lambda )} multiplying the p orbital when the hybrid orbital is written in the form ( s + λ p ) {\displaystyle (s+\lambda p)} .
The hybrid can certainly be normalized, as it is the sum of two normalized wavefunctions. Orthogonality must be established so that the two hybrid orbitals can be involved in separate covalent bonds. The inner product of orthogonal orbitals must be zero and computing the inner product of the constructed hybrids gives the following calculation.
Molecular orbitals are of three types: bonding orbitals which have an energy lower than the energy of the atomic orbitals which formed them, and thus promote the chemical bonds which hold the molecule together; antibonding orbitals which have an energy higher than the energy of their constituent atomic orbitals, and so oppose the bonding of the ...
See illustration of a cross-section of these nested shells, at right. The s orbitals for all n numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus (having a wave node at the nucleus).
Both models are of value and represent the same total electron density, with the orbitals related by a unitary transformation. In this case, we can construct the two equivalent lone pair hybrid orbitals h and h' by taking linear combinations h = c 1 σ(out) + c 2 p and h' = c 1 σ(out) – c 2 p for an appropriate choice of coefficients c 1 and ...
Figure 5: Molecular orbital diagram depiction of frontier orbitals in methane and a basic ML 6 metal complex. As seen above, when a fragment is formed from CH 4, one of the sp 3 hybrid orbitals involved in bonding becomes a nonbonding singly occupied frontier orbital. The frontier orbital’s increased energy level is also shown in the figure.
The other sp-hybrid radiates into the center of the structure forming a large bonding molecular orbital at the center of the cluster. The remaining two unhybridized orbitals lie along the tangent of the sphere like structure creating more bonding and antibonding orbitals between the boron vertices. [9] The orbital diagram breaks down as follows: