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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 ...
A molecular orbital diagram, ... The 1b 1 MO is a lone pair, while the 3a 1, 1b 2 and 2a 1 MO's can be localized to give two O−H bonds and an in-plane lone pair. [30]
The symmetry properties of molecular orbitals means that delocalization is an inherent feature of molecular orbital theory and makes it fundamentally different from (and complementary to) valence bond theory, in which bonds are viewed as localized electron pairs, with allowance for resonance to account for delocalization.
Molecular orbital theory was seen as a competitor to valence bond theory in the 1930s, before it was realized that the two methods are closely related and that when extended they become equivalent. Molecular orbital theory is used to interpret ultraviolet–visible spectroscopy (UV–VIS). Changes to the electronic structure of molecules can be ...
Valence bond theory complements molecular orbital theory, which does not adhere to the valence bond idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can extend over the entire molecule. Although both theories describe chemical bonding, molecular ...
The combination of IBO analysis with other computational methods, such as natural bond orbital (NBO) analysis for a Ti-catalyzed pyrrole synthesis [20] or natural localized molecular orbital (NLMO) analysis for an intramolecular cycloaddition of a phosphaalkene to an arene has likewise led to insightful results regarding the specifics of the ...
Example of a localized Wannier function of titanium in barium titanate (BaTiO3) Although, like localized molecular orbitals, Wannier functions can be chosen in many different ways, [3] the original, [1] simplest, and most common definition in solid-state physics is as follows.
This VIF theory also connected both delocalized and localized molecular orbital schemes into a unified form in an elegant way. Chemical deductions are made from a VIF picture with the application of two pictorial rules. These are linear transformations applied to the VIF structural formula as a quantum operator.