Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent problems is being investigated only since recently. Correlated two-particle systems are of particular importance because the structure of the two-body reduced density matrix expanded in natural orbitals is known exactly in this case. However, in the time-dependent case the natural orbitals carry time-dependent phases that allow for certain time-dependent gauge transformations of the first kind. Different phase conventions will, in general, lead to different equations of motion for the natural orbitals. A particular phase choice allows us to derive the exact equations of motion for the natural orbitals of any (laser-) driven two-electron system explicitly, i.e., without any dependence on quantities that, in practice, require further approximations. For illustration, we solve the equations of motion for a model helium system. Besides calculating the spin-singlet and spin-triplet ground states, we show that the linear response spectra and the results for resonant Rabi flopping are in excellent agreement with the benchmark results obtained from the exact solution of the time-dependent Schrödinger equation. PACS numbers: 31.15.ee, 31.70.Hq,

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is based on the equations of motion for the so-called natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix. Exact TDRNOT can be formulated for any time-dependent two-electron system in either spin configuration. In this paper, the method is tested against high-order harmonic generation (HHG) and Fano profiles in absorption spectra with the help of a numerically exactly solvable one-dimensional model He atom, starting from the spin-singlet ground state. Such benchmarks are challenging because Fano profiles originate from transitions involving autoionizing states, and HHG is a strong-field phenomenon well beyond linear response. TDRNOT with just one natural orbital per spin in the helium spin-singlet case is equivalent to time-dependent HartreeFock or time-dependent density functional theory (TDDFT) in exact exchange-only approximation. It is not unexpected that TDDFT fails in reproducing Fano profiles due to the lack of doubly excited, autoionizing states. HHG spectra, on the other hand, are widely believed to be well-captured by TDDFT. However, HHG spectra of helium may display a second plateau that originates from simultaneous HHG in He + and neutral He. It is found that already TDRNOT with two natural orbitals per spin is sufficient to capture this effect as well as the Fano profiles on a qualitative level. With more natural orbitals (6-8 per spin) quantitative agreement can be reached. Errors due to the truncation to a finite number of orbitals are identified.

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is tested on nonsequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI of atoms in strong laser fields is a prime example of non-perturbative, highly correlated electron dynamics. As such, NSDI is an important "worst-case" benchmark for any timedependent few and many-body technique beyond linear response. It is found that TDRNOT reproduces the celebrated NSDI "knee," i.e., a many-order-of-magnitude enhancement of the double ionization yield (as compared to purely sequential ionization) with only the ten most significant natural orbitals (NOs) per spin. Correlated photoelectron spectra-as "more differential" observables-require more NOs.

The quantum effciency for the photodimerization of rruns-cinnamic acid in the solid state is independent of intensity and is found to have a value approaching two. Thus, the reaction involves one excited and one un-excited molecule.During the exposure, a dimer film developing on the surface of the cinnamic acid Jayer