Chemistry:Coulomb operator

Short description: Quantum mechanical operator used in the field of quantum chemistry

The Coulomb operator, named after Charles-Augustin de Coulomb, is a quantum mechanical operator used in the field of quantum chemistry. Specifically, it is a term found in the Fock operator. It is defined as:

${\hat{J}}_j(1)f_i(1)=f_i(1)\int {|{\phi }_j(2)|}^2\frac{1}{r_{12}}d{r}_2$

where

${\hat{J}}_j(1)$ is the one-electron Coulomb operator defining the repulsion resulting from electron j,

$f_i(1)$ is the one-electron wavefunction of the $i^{th}$ electron being acted upon by the Coulomb operator,

${\phi }_j(2)$ is the one-electron wavefunction of the $j^{th}$ electron,

$r_{ij}$ is the distance between electrons $(i)$ and $(j)$.

See also

• Core Hamiltonian
• Exchange operator