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Overlap matrix

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. 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:

\mathbf{S}_{jk}=\left \langle b_j|b_k \right \rangle=\int \Psi_j^* \Psi_k d\tau


\left |b_j \right \rangle

is the j-th basis ket (vector), and


is the j-th wavefunction, defined as

\Psi_j(x)=\left \langle x | b_j \right \rangle.

See also


Quantum Chemistry: Fifth Edition, Ira N. Levine, 2000

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Overlap_matrix". A list of authors is available in Wikipedia.
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