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# 7.2.3 Random Phase Approximation (RPA)

(December 20, 2021)

The Random Phase Approximation (RPA), 123 Bouman T. D., Hansen A. E.
Int. J. Quantum Chem. Symp.
(1989), 23, pp. 381.
, 416 Hansen A. E., Voight B., Rettrup S.
Int. J. Quantum Chem.
(1983), 23, pp. 595.
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, 223 Cordova F. et al.
J. Chem. Phys.
(2007), 127, pp. 164111.
whereas such singularities are mathematically impossible in CIS calculations.