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Favorably scaling numerical time-dependent many-electron techniques such astime-dependent density functional theory (TDDFT) with adiabaticexchange-correlation potentials typically fail in capturing highly correlatedelectron dynamics. We propose a method based on natural orbitals, i.e., theeigenfunctions of the one-body reduced density matrix, that is almost asinexpensive numerically as adiabatic TDDFT, but which is capable of describingcorrelated phenomena such as doubly excited states, autoionization, Fanoprofiles in the photoelectron spectra, and strong-field ionization in general.Equations of motion (EOM) for natural orbitals and their occupation numbershave been derived earlier. We show that by using renormalized natural orbitals(RNO) both can be combined into one equation governed by a hermitian effectiveHamiltonian. We specialize on the two-electron spin-singlet system, known asbeing a "worst case" testing ground for TDDFT, and employ the widely used,numerically exactly solvable, one-dimensional helium model atom (in a laserfield) to benchmark our approach. The solution of the full, nonlinear EOM forthe RNO is plagued by instabilities, and resorting to linear response is not anoption for the ultimate goal to study nonperturbative dynamics in intense laserfields. We therefore make two rather bold approximations: we employ theinitial-state-"frozen" effective RNO Hamiltonian for the time-propagation andtruncate the number of RNO to only two per spin. Surprisingly, it turns outthat even with these strong approximations we obtain a highly accurate groundstate, reproduce doubly-excited states, and autoionization.

Time-dependent renormalized natural orbital theory applied to the two-electron spin-singlet case: ground state, linear response, and autoionization