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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 ...
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 ...
Hybridisation of s and p orbitals to form effective sp x hybrids requires that they have comparable radial extent. While 2p orbitals are on average less than 10% larger than 2s, in part attributable to the lack of a radial node in 2p orbitals, 3p orbitals which have one radial node, exceed the 3s orbitals by 20–33%. [19]
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.
For the hydrogen fluoride molecule, for example, two F lone pairs are essentially unhybridized p orbitals of π symmetry, while the other is an sp x hydrid orbital of σ symmetry. An analogous consideration applies to water (one O lone pair is in a pure p orbital, another is in an sp x hybrid orbital).
A MO with δ symmetry results from the interaction of two atomic d xy or d x 2-y 2 orbitals. Because these molecular orbitals involve low-energy d atomic orbitals, they are seen in transition-metal complexes. A δ bonding orbital has two nodal planes containing the internuclear axis, and a δ* antibonding orbital also has a third nodal plane ...
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.