Cancellations Occurring in the Calculation of Transition Energies by a Perturbation Development of Configuration Interaction Matrices

Two theorems are demonstrated: (1) The coefficients of most of the (2n+1) excited configurations in the nth- order correction to any well separated monoexcited state are multiplied by a factor 2−½, equal to the coefficients of most of the 2n excited configurations in the nth order correction to the wavefunction of the ground state; (2) while the calculation of the nth-order correction to the energy of any state implies (2n)-uple summations over the molecular orbitals, the nth-order correction to the transition energy between the ground and a monoexcited state only implies (2n−1)-uple summations over the molecular orbitals. These two theorems are only valid when n is smaller than the number of particles in the system.