Chemical localized orbitals

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

Manning, P. P., Proc. Roy. Soc. London) A225, 136, 244, The molecular orbital theory of chemical valency. XVII. Higher approximations. XVIII. Localized orbitals in conjugated molecules."... 

Stabilization of the systems due to homoconjugation is discussed. 13C and nB NMR chemical shifts of the compounds were also calculated using the individual gauge for localized orbitals (IGLO) method <2000JOC5956>. 

A new reservoir of comets may have formed at around 5 AU in a local orbit around Jupiter or at least perturbed by its gravitational attraction. A comet close to Jupiter would simply have been captured, delivering its chemical payload to the ever-increasing gas giant. Some comets would merely have been deflected towards the inner terrestrial planets, delivering a similar payload of water and processed molecules. Cometary impacts such as the spectacular collision of the comet Shoemaker-Levy 9 with Jupiter would have been common in the early formation phase of the solar system but with a much greater collision rate. Calculations of the expected collision rate between the Earth and potential small comets deflected from the snow line may have been sufficient to provide the Earth with its entire... 

The natural localized orbitals introduced in Section 1.5 provide a useful alternative to the canonical delocalized MOs (CMOs) that are usually employed to analyze chemical bonding. The NAO and NBO basis sets may be regarded as intermediates in a succession of basis transformations that lead from starting AOs /, to the final canonical MOs , ... 

In atomic theory or molecular orbital theory, the chemical potential is related to the orbital energy [5,6]. In the case of one or two electrons in the same orbital, the local orbital energy s is equal to the local chemical potential ... 

Localized Orbitals, Chemical Intuition and Molecular Quantum Mechanics... 

Since rigorous theoretical treatments of molecular structure have become more and more common in recent years, there exists a definite need for simple connections between such treatments and traditional chemical concepts. One approach to this problem which has proved useful is the method of localized orbitals. It yields a clear picture of a molecule in terms of bonds and lone pairs and is particularly well suited for comparing the electronic structures of different molecules. So far, it has been applied mainly within the closed-shell Hartree-Fock approximation, but it is our feeling that, in the future, localized representations will find more and more widespread use, including applications to wavefunctions other than the closed-shell Hartree-Fock functions. 

The following presentation is limited to closed-shell molecular orbital wave-functions. The first section discusses the unique ability of molecular orbital theory to make chemical comparisons. The second section contains a discussion of the underlying basic concepts. The next two sections describe characteristics of canonical and localized orbitals. The fifth section examines illustrative examples from the field of diatomic molecules, and the last section demonstrates how the approach can be valuable even for the delocalized electrons in aromatic ir-systems. All localized orbitals considered here are based on the self-energy criterion, since only for these do the authors possess detailed information of the type illustrated. We plan to give elsewhere a survey of work involving other types of localization criteria. 

What has been said applies to approximate as well as to ab-initio molecular orbital wavefunctions,i.e. those obtained by solving the self-consistent-field equations exactly. Hence, the localized orbital approach also offers an attractive tool for bridging the gap between rigorous quantitative calculations and qualitative chemical intuition. The experience gained so far has shown that interpretations suggested by the localized orbital picture correspond closely to intuitive chemical thinking. 

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