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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
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 CI procedure leads to a general matrix eigenvalue equation: H c = e S c , {\displaystyle \mathbb {H} \mathbf {c} =\mathbf {e} \mathbb {S} \mathbf {c} ,} where c is the coefficient vector, e is the eigenvalue matrix, and the elements of the hamiltonian and overlap matrices are, respectively,
The off-diagonal Hamiltonian matrix elements are given by an approximation due to Wolfsberg and Helmholz that relates them to the diagonal elements and the overlap matrix element. [2] = + K is the Wolfsberg–Helmholz constant, and is usually given a value of 1.75. In the extended Hückel method, only valence electrons are considered; the core ...
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.
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.
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 ...