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In this work we present a derivation of the real-time time-dependentorbital-optimized M{\o}ller-Plesser TDOMP2 and its biorthogonal companion,time-dependent non-orthogonal OMP2 (TDNOMP2), theory starting from thetime-dependent bivariational principle and a parametrization based on theexponential orbital-rotation operator formulation commonly used intime-independent molecular electronic-structure theory. We apply the TDOMP2method to extract absorption spectra and frequency-dependent polarizabilitiesand first hyperpolarizabilities from real-time simulations, comparing theresults with those obtained from conventional time-dependent coupled-clustersingles and doubles (TDCCSD) simulations and from its second-orderapproximation TDCC2. We also compare with results from CCSD and CC2 linear andquadratic response theory. Our results indicate that while TDOMP2 absorptionspectra are of the same quality as TDCC2 spectra, frequency-dependentpolarizabilities and hyperpolarizabilties from TDOMP2 simulations aresignificantly closer to TDCCSD results than those from TDCC2 simulations.

Linear and nonlinear optical properties from TDOMP2 theory