We present a reproducible ab-initio method to produce benchmark tests between time-dependent Schrödinger equation (TDSE) in the single-active-electron approximation (SAE) and time-dependent density functional theory (TDDFT) in the highly nonlinear multiphoton and tunneling regime of strong-field physics. To this end we compare results for high-order harmonic generation from valence shells in atoms using the SAE-TDSE approach and TDDFT calculations. As key to the benchmark comparison we obtain an analytic form of SAE potentials based on density functional theory, which we applied for different atoms and ions. The ionization energies of atomic ground and excited states, as well as the energies of inner shells, for the SAE potentials agree well with experimental data. Using these potentials we find remarkable agreement between the results of the two independent numerical approaches (TDDFT and SAE-TDSE) for the high-order harmonic yields in helium, demonstrating the accuracy of the SAE potentials as well as the predictive power of SAE-TDSE and TDDFT calculations for the nonperturbative and highly nonlinear strong-field process of high harmonic generation in the ultraviolet and visible wavelength regime. Finally, as another application of the SAE potentials, high harmonic spectra from outer and inner valence shells are calculated and it is shown that unphysical artifacts in the SAE-spectra from the individual shells are removed once all the amplitudes are considered.

We analyze the role of the difference between the central frequencies of the spectral distributions of the vector potential and the electric field of a short laser pulse. The frequency shift arises when the electric field is determined as the derivative of the vector potential to ensure that both quantities vanish at the beginning and end of the pulse. We derive an analytical estimate of the frequency shift and show how it affects various light induced processes, such as excitation, ionization and high harmonic generation. Since observables depend on the frequency spectrum of the electric field, the shift should be taken into account when setting the central frequency of the vector potential to avoid potential misinterpretation of numerical results for processes induced by few-cycle pulses.

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.