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Orbital overlap can lead to bond formation. The general principle for orbital overlap is that, the greater the greater the over between orbitals, the greater is the bond strength. Linus Pauling explained the importance of orbital overlap in the molecular bond angles observed through experimentation; it is the basis for orbital hybridization.
Overlapping generations are found in species that live for many years, and reproduce many times. Many birds, for instance, have new nests every (couple of) year(s). Therefore, the offspring will, after they have matured, also have their own nests of offspring while the parent generation could be breeding again as well.
Pi bonds result from overlap of atomic orbitals that are in contact through two areas of overlap. Most orbital overlaps that do not include the s-orbital, or have different internuclear axes (for example p x + p y overlap, which does not apply to an s-orbital) are generally all pi bonds. Pi bonds are more diffuse bonds than the sigma bonds.
The interatomic overlap matrix elements , should be rather small or neglectable. If they are large it is again an indication that the tight binding model is of limited value for some purposes. Large overlap is an indication for too short interatomic distance for example.
The current definition of an overlapping gene varies significantly between eukaryotes, prokaryotes, and viruses. [2] In prokaryotes and viruses overlap must be between coding sequences but not mRNA transcripts, and is defined when these coding sequences share a nucleotide on either the same or opposite strands.
Mulliken charges arise from the Mulliken population analysis [1] [2] and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used as variables in linear regression (QSAR [3]) procedures. [4]
The localized orbital corresponding to one O-H bond is the sum of these two delocalized orbitals, and the localized orbital for the other O-H bond is their difference; as per Valence bond theory. For multiple bonds and lone pairs, different localization procedures give different orbitals.
The possible orbital symmetries are listed in the table below. For example, an orbital of B 1 symmetry (called a b 1 orbital with a small b since it is a one-electron function) is multiplied by -1 under the symmetry operations C 2 (rotation about the 2-fold rotation axis) and σ v '(yz) (reflection in the molecular