Editing Hartree–Fock method (section)

===Total energy=== 
The optimal total energy <math> E_{HF} </math> can be written in terms of molecular orbitals.

:<math> E_{HF} = \sum_{i=1}^{N} \hat h_{ii} + \sum_{i=1}^{N} \sum_{j=1}^{N/2} [2\hat J_{ij} - \hat K_{ij}] + V_{\text{nucl}} </math>

<math>\hat J_{ij}</math> and <math>\hat K_{ij}</math> are matrix elements of the Coulomb and exchange operators respectively, and <math>V_{\text{nucl}}</math> is the total electrostatic repulsion between all the nuclei in the molecule.

The total energy is not equal to the sum of orbital energies.

If the atom or molecule is [[closed shell]], the total energy according to the Hartree-Fock method is
: <math>E_{HF} = 2 \sum_{i=1}^{N/2} \hat h_{ii} + \sum_{i=1}^{N/2} \sum_{j=1}^{N/2} [2\hat J_{ij} - \hat K_{ij}] + V_{\text{nucl}}.</math><ref name= Levine>Levine, Ira N. (1991). Quantum Chemistry (4th ed.). Englewood Cliffs, New Jersey: Prentice Hall. p. 402-3. {{ISBN|0-205-12770-3}}.</ref>