Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 24 / a / i

For clamped nuclei and SI units, the many-electron electronic Hamiltonian isThe terms are electron kinetic energy, electron–nucleus attraction, and electron–electron repulsion. The nuclear kinetic operator is omitted in the Born-Oppenheimer approximation. The nuclear repulsionis a constant at fixed separation and is added to electronic energies to form the total potential curve. Some conventions include it in ${\hat{H}}_e$ as a constant; the electronic-energy convention used below excludes it so that the two one-electron energies can be compared without double-counting nuclear repulsion.