Chemistry:Coulomb operator
From HandWiki
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:[1]
- [math]\displaystyle{ \widehat J_j (1) f_i(1)= f_i(1) \int { \left | \varphi_j(2) \right | }^2 \frac{1}{r_{12}}\,dr_2 }[/math]
where
- [math]\displaystyle{ \widehat J_j (1) }[/math] is the one-electron Coulomb operator defining the repulsion resulting from electron j,
- [math]\displaystyle{ f_i(1) }[/math] is the one-electron wavefunction of the [math]\displaystyle{ i^{th} }[/math] electron being acted upon by the Coulomb operator,
- [math]\displaystyle{ \varphi_j(2) }[/math] is the one-electron wavefunction of the [math]\displaystyle{ j^{th} }[/math] electron,
- [math]\displaystyle{ r_{ij} }[/math] is the distance between electrons [math]\displaystyle{ (i) }[/math] and [math]\displaystyle{ (j) }[/math].
See also
- Core Hamiltonian
- Exchange operator
References
- ↑ Ramachandran, K. I. (2008). Computational chemistry and molecular modeling : principles and applications. G. Deepa, K. Namboori. Berlin: Springer. pp. 107. ISBN 978-3-540-77304-7. OCLC 272298712. https://www.worldcat.org/oclc/272298712.
 |  |
