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

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Abstract
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.