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In chemistry, isovalent or second order hybridization is an extension of orbital hybridization, the mixing of atomic orbitals into hybrid orbitals which can form chemical bonds, to include fractional numbers of atomic orbitals of each type (s, p, d). It allows for a quantitative depiction of bond formation when the molecular geometry deviates ...
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 ...
The seven f-orbitals are atomic orbitals with an angular momentum quantum number ℓ = 3. often expressed like = () The angular part of the f-orbitals are the cubic harmonics (). In many cases different linear combinations of spherical harmonics are chosen to construct a cubic f-orbital basis set.
The lower energy orbitals will be d z 2 and d x 2-y 2, and the higher energy orbitals will be d xy, d xz and d yz - opposite to the octahedral case. Furthermore, since the ligand electrons in tetrahedral symmetry are not oriented directly towards the d-orbitals, the energy splitting will be lower than in the octahedral case.
The three dumbbell-shaped p-orbitals have equal energy and are oriented mutually perpendicularly (or orthogonally). The p-orbitals oriented in the z-direction (p z) can overlap end-on forming a bonding (symmetrical) σ orbital and an antibonding σ* molecular orbital. In contrast to the sigma 1s MO's, the σ 2p has some non-bonding electron ...
In the case of water, with its 104.5° HOH angle, the OH bonding orbitals are constructed from O(~sp 4.0) orbitals (~20% s, ~80% p), while the lone pairs consist of O(~sp 2.3) orbitals (~30% s, ~70% p). As discussed in the justification above, the lone pairs behave as very electropositive substituents and have excess s character.
Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, such as a specific bond or lone pair on a specific atom. They can be used to relate molecular orbital calculations to simple bonding theories, and also to speed up post-Hartree–Fock electronic structure calculations by taking ...
Since the nature of the overlapping orbitals are different in H 2 and F 2 molecules, the bond strength and bond lengths differ between H 2 and F 2 molecules. In methane (CH 4 ), the carbon atom undergoes sp 3 hybridization, allowing it to form four equivalent sigma bonds with hydrogen atoms, resulting in a tetrahedral geometry.