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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 ...
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).
For a given value of the azimuthal quantum number ℓ, the possible values of the magnetic quantum number m ℓ are the integers from m ℓ =-ℓ to m ℓ =+ℓ, including 0. In addition, the spin quantum number m s can take two distinct values. The set of orbitals associated with a particular value of ℓ are sometimes collectively called a ...
As with s orbitals, this phenomenon provides p, d, f, and g orbitals at the next higher possible value of n (for example, 3p orbitals vs. the fundamental 2p), an additional node in each lobe. Still higher values of n further increase the number of radial nodes, for each type of orbital.
The block names (s, p, d, and f) are derived from the spectroscopic notation for the value of an electron's azimuthal quantum number: sharp (0), principal (1), diffuse (2), and fundamental (3). Succeeding notations proceed in alphabetical order, as g, h, etc., though elements that would belong in such blocks have not yet been found.
The top two PIOs sums to over 90% of the overall orbital contribution. The first PIO pair is between the d z2 orbital of the metal and the pi orbital of ethylene. The second PIO pair is between the d xz orbital of the metal and the π* orbital of ethylene. Principal interacting orbitals in the Zeise's salt.
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 oxygen atomic orbitals are labeled according to their symmetry as a 1 for the 2s orbital and b 1 (2p x), b 2 (2p y) and a 1 (2p z) for the three 2p orbitals. The two hydrogen 1s orbitals are premixed to form a 1 (σ) and b 2 (σ*) MO. Mixing takes place between same-symmetry orbitals of comparable energy resulting a new set of MO's for water: