Orbital overlap
In chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space. Orbital overlap can lead to bond formation. The importance of orbital overlap was emphasized by Linus Pauling to explain the molecular bond angles observed through experimentation and is the basis for the concept of orbital hybridization. Since s orbitals are spherical (and have no directionality) and p orbitals are oriented 90° to each other, a theory was needed to explain why molecules such as methane (CH4) had observed bond angles of 109.5°. Pauling proposed that s and p orbitals on the carbon atom can combine to form hybrids (sp3 in the case of methane) which are directed toward the hydrogen atoms. The carbon hybrid orbitals have greater overlap with the hydrogen orbitals, and can therefore form stronger C–H bonds.
A quantitative measure of the overlap of two atomic orbitals on atoms A and B is their overlap integral, defined as
where the integration extends over all space. The star on the first orbital wavefunction indicates the complex conjugate of the function, which in general may be complex-valued.
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 overlap matrix will be diagonal. In addition, if the basis vectors form an orthonormal set, the overlap matrix will be the identity matrix. The overlap matrix is always n×n, where n is the number of basis functions used. It is a kind of Gramian matrix.
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