The overlap matrix is a square matrix used in computational chemistry, to describe the inter-relationship of a set of basis vectors of a quantum system. 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.
In general, the overlap matrix is defined as:
where
is the j-th basis ket (vector), and
- Ψj
is the j-th wavefunction, defined as
.
See also
References
Quantum Chemistry: Fifth Edition, Ira N. Levine, 2000