Hartree Fock Method Symmetric Energy Expression

[arsc]

Hello.

I just wonder why the energy expression of Hartree Fock method is symmetric. I tried to find out the reason on the Internet but I could only find that: since the Hartree Fock energy expression is symmetric, it is variational.

In Hartree Fock method, the repulsive energy between different electrons is averaged, so does that mean the amount of contribution of different electrons to the repulsive energy is indistinguishable which leads to the symmetric energy expression?

Thank you for your reply

 

[azntoon]

in advance.The Hartree Fock energy expression is symmetric because of the variational principle. The variational principle states that the energy of a system is minimized when the wave function of the system is varied. By making the energy expression symmetric, it ensures that the wave function of the system can be varied more easily. By making sure that the wave function of the system can be varied more easily, the energy can be more accurately determined. Thus, the symmetry of the Hartree Fock energy expression ensures that the energy of the system is minimized.