Hello Hiroshi Kawabata, the term 1/2 that you're referring to is related to the Coulomb (classical electrostatic) interaction energy between the electrons in a molecular system.

In the context of density functional theory (DFT), this term represents the classical electrostatic interaction between electron pairs. It's calculated by integrating the electron density times the Poisson equation (or the solution of the Poisson equation) over the whole space. Mathematically, it's expressed as:

1/2 = 1/2 ∫ρ(r) * V_coulomb(r) dr

where ρ(r) is the electron density at position r and V_coulomb(r) is the Coulomb potential generated by the electron density at position r. The factor of 1/2 is included to avoid double counting the interactions since each electron pair is interacting with one another.

The other terms you mentioned (Ex, Ec, N-N, E-N, and KE) represent exchange energy, correlation energy, nuclear-nuclear repulsion energy, electron-nuclear attraction energy, and kinetic energy, respectively. These are all components of the total energy calculated by DFT for a molecular system. Regards,

Dear Hiroshi Kawabata,

Yes, correct. The general abbreviation for the term 1/2 is typically denoted as E_Coulomb or E_C, representing the Coulomb (classical electrostatic) interaction energy between the electrons in a molecular system.

As for the other energy components you've mentioned, here are their respective abbreviations:

Regards,

You're welcome Hiroshi Kawabata