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Fock matrix



In quantum mechanics, the Fock matrix is a matrix approximating the single-electron energy operator of a given quantum system in a given set of basis vectors.

Additional recommended knowledge

It is most often formed in computational chemistry when attempting to solve the Roothaan equations for an atomic or molecular system. The Fock matrix is actually an approximation to the true Hamiltonian operator of the quantum system. It includes the effects of electron-electron repulsion only in an average way. Importantly, because the Fock operator is a one-electron operator, it does not include the electron correlation energy.

The Fock matrix is defined by the Fock operator. For the restricted case which assumes closed-shell orbitals and single-determinantal wavefunctions, the Fock operator for the first electron is given by:

\hat F(1) = \hat H^{core}(1)+\sum_{j=1}^{n}[2\hat J_j(1)-\hat K_j(1)]

where:

\hat F(i)

is the Fock operator for the i-th electron in the system,

{\hat H}^{core}(i)

is the core Hamiltonian for the i-th electron,

n

is the total number of orbitals in the system (equal to UNIQ19b50e422c8f0149-math-00000005-QINU, where N is the number of electrons),

\hat J_j(i)

is the Coulomb operator, defining the repulsive force between the j-th and i-th electrons in the system,

\hat K_j(i)

is the exchange operator, defining the effect of exchanging the two electrons.

See also

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