Pair-energy double counting in Hartree orbital sums
= Pair-energy double counting in Hartree orbital sums
For Hartree direct integrals $J_{ij}$ and orbital <eigenvalues> $\epsilon_i$, the product-state <energy> is $E=\sum_i\epsilon_i-\sum_{i<j}J_{ij}$. Each pair enters two orbital mean fields but only once in the total interaction <energy>. Orbital energies are therefore not independent additive particle energies.