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The overlap matrix is a square matrix, used in quantum chemistry to describe the inter-relationship of a set of basis vectors of a quantum system, such as an atomic orbital basis set used in molecular electronic structure calculations. In particular, if the vectors are orthogonal to one another, the
Double bonds for these heavier elements, when they exist, are often weak due to poor orbital overlap between the n>2 orbitals of the two atoms. Although such compounds are not intrinsically unstable, they instead tend to dimerize or even polymerize. [1]
The s orbital is normalized and so the inner product s | s = 1. Also, the s orbital is orthogonal to the p i and p j orbitals, which leads to two terms in the above equaling zero. Finally, the last term is the inner product of two normalized functions that are at an angle of ω ij to each other, which gives cos ω ij by definition.
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 type of bonding can be explained in terms of orbital hybridisation. In ethylene each carbon atom has three sp 2 orbitals and one p-orbital. The three sp 2 orbitals lie in a plane with ~120° angles. The p-orbital is perpendicular to this plane. When the carbon atoms approach each other, two of the sp 2 orbitals overlap to form a sigma bond.
In chemistry, primarily organic and computational chemistry, a stereoelectronic effect [1] is an effect on molecular geometry, reactivity, or physical properties due to spatial relationships in the molecules' electronic structure, in particular the interaction between atomic and/or molecular orbitals. [2]
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 .