We present a derivation
of real-time (RT) time-dependent orbital-optimized
Møller–Plesset (TDOMP2) theory and its biorthogonal companion,
time-dependent non-orthogonal OMP2 theory, starting from the time-dependent
bivariational principle and a parametrization based on the exponential
orbital-rotation operator formulation commonly used in the time-independent
molecular electronic structure theory. We apply the TDOMP2 method
to extract absorption spectra and frequency-dependent polarizabilities
and first hyperpolarizabilities from RT simulations, comparing the
results with those obtained from conventional time-dependent coupled-cluster
singles and doubles (TDCCSD) simulations and from its second-order
approximation, TDCC2. We also compare our results with those from
CCSD and CC2 linear and quadratic response theories. Our results indicate
that while TDOMP2 absorption spectra are of the same quality as TDCC2
spectra, including core excitations where optimized orbitals might
be particularly important, frequency-dependent polarizabilities and
hyperpolarizabilities from TDOMP2 simulations are significantly closer
to TDCCSD results than those from TDCC2 simulations.
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