7.2.3 Random Phase Approximation (RPA)

The Random Phase Approximation (RPA), ¹²⁸ Bouman T. D., Hansen A. E.
Int. J. Quantum Chem. Symp.
(1989), 23, pp. 381. Link ^{, 442} Hansen A. E., Voight B., Rettrup S.
Int. J. Quantum Chem.
(1983), 23, pp. 595. Link also known as time-dependent Hartree-Fock (TD-HF) theory, is an alternative to CIS for uncorrelated calculations of excited states. It offers some advantages for computing oscillator strengths, e.g., exact satisfaction of the Thomas-Reike-Kuhn sum rule, and is roughly comparable in accuracy to CIS for singlet excitation energies, but is inferior for triplet states. RPA energies are non-variational, and in moving around on excited-state potential energy surfaces, this method can occasionally encounter singularities that prevent numerical solution of the underlying equations, ²³³ Cordova F. et al.
J. Chem. Phys.
(2007), 127, pp. 164111. Link whereas such singularities are mathematically impossible in CIS calculations.