1. We use a S C R I P T font for quantities that symbolize general many-electron operators.
2. To simplify the notation, atomic units have been used here and throughout the presentation.
3. since Hel does not differentiate with respect to the nuclear coordinates it commutes with Ψnuc (R).
4. Here, and throughout the presentation, we use ‘n’ to represent the number of electrons in a many-electron system.
5. We will be using this “shadowed” font whenever we refer to a matrix or vector in n dimensions.