Mulliken notation for two-electron integrals

If we abbreviate the diagonal matrix elements of the one-electron part of the Hamiltonian with respect to as Hkk and use the Mulliken notation for two-electron integrals, we get the following expectation values Eavsq for Papsg, Ejf for and Eo for the single Slater determinant. In all cases we limit ourselves to a closed-shell state and we assume the coefficients to be real. 

We use the Mulliken notation for two-electron integrals over (real-valued) Gaussian atomic basis functions in the following ... 

---