Hypervirial relations as constraints in calculations of electronic excitation properties: the random phase approximation in configuration interaction language

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Abstract
Off-diagonal hypervirial relations (for example, the equivalence of the dipole length and dipole velocity forms of the electronic transition moment for exact wavefunctions) are imposed upon two approximate configuration interaction (CI) representations of the ground and excited states of interest in an atomic or molecular system. It is shown that, if the ground state is approximated by the exact Hartree-Fock function correlated by double excitations and the excited state is represented by mono-excited CI, the hypervirial constraint on the transition moments leads directly to the random phase approximation (RPA) equations. No second-quantized formulation or assumed excitation operator is invoked. The same constraint, applied to an uncorrelated ground state, leads to non-variational mono-excited CI schemes, which are related to Hartree-Fock instability conditions. The methods are illustrated by 5–31/G computations of the chiroptical properties, in dipole length, velocity and acceleration forms, of two low-lying excitations of ethylene distorted as in trans-cyclooctene. The results are discussed and compared with recent large-scale calculations and with experiment.