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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
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.
where F is the Fock matrix (which depends on the coefficients C due to electron-electron interactions), C is a matrix of coefficients, S is the overlap matrix of the basis functions, and is the (diagonal, by convention) matrix of orbital energies. In the case of an orthonormalised basis set the overlap matrix, S, reduces to the identity matrix.
where is the so-called Fock matrix (which is a function of ), is a matrix of coefficients, is the overlap matrix of the basis functions, and is the (diagonal, by convention) matrix of orbital energies. Unlike restricted Hartree–Fock theory for closed shell molecules, the form of the Fock matrix is not unique.
Overlapping probes or probes in very close proximity can be used. This gives an unbiased analysis with high resolution. Besides these advantages, tiling arrays show high reproducibility and with overlapping probes spanning large segments of the genome, tiling arrays can interrogate protein binding sites, which harbor repeats.
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.
For a wave function = where ,, …, are a linearly independent, orthogonal set of basis orbitals, the weight of a constituent orbital would be since the overlap integral, , between two wave functions , would be 1 for = and 0 for . In valence bond theory, however, the generated structures are not necessarily orthogonal with each other, and ...
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]