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(June 30, 2021)

The Random Phase Approximation (RPA),
^{
121
}
Int. J. Quantum Chem. Symp.

(1989),
23,
pp. 381.
Link
^{,}
^{
405
}
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,
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219
}
J. Chem. Phys.

(2007),
127,
pp. 164111.
Link
whereas such singularities are mathematically impossible in CIS calculations.