Photoionization processes have been examined from a theoretical perspective with the aim of increasing the number of the describable phenomena involved in such processes. This aim has been achieved by the implementation of several algorithms based on the use of B-splines as basis functions to treat both correlation effects and non-perturbative photoionization regime.
The first part of the thesis is dedicated to correlation effects within the bound states. Since a standard DFT method does not permit to study any correlation effect, we present a single channel approach that uses Configuration Interaction (CI) to describe both the neutral initial state and ionic final state. More specifically, this method applies a Complete Active Space Self-Consistent Field (CASSCF) procedure to treat such correlation effects. Ionization potentials are further improved by n-electron valence state perturbation theory (NEVPT2). Dyson orbitals are used in this context to calculate the dipole transition moments. The most frequent evidence of electron correlation is the presence of additional bands, called satellite bands, in the photoelectron spectra. The structure and the position of satellite bands in some diatomic molecules has been studied. For all the considered molecules, dynamical photoionization observables have been calculated for the first ionization states, by comparing the results so obtained to those ones got by standard DFT method, Dyson orbital approach and HF method. The formalism has been also applied to the O_3 molecule within a collaboration that aimed to obtain the time-resolved photoelectron spectrum of this molecule.
In the second part of the thesis, the implementation of an algorithm to calculate two-electron integrals in the LCAO B-spline basis with the aim to treat all the many-electron effects is illustrated. This has been done to fully express the final wavefunction within the so called Close-Coupling (CC) formalism that permits to also describe correlation effects involving continuum states. In particular, two-electron integrals have been calculated by solving the Poisson equation relative to the first charge density and integrating the resulting potential with the second charge density. The results are compared to the corresponding integrals obtained by using MOLPRO quantum chemistry package.
The third part of the thesis presents a method to treat the non-perturbative phenomena by solving Time-Dependent Schrödinger Equation (TDSE). In this method, time-evolution is discretized in subintervals sufficiently small so that the Hamiltonian approximately becomes time-independent. The final wavepacket, derived by time propagation, is then projected onto the continuum states calculated with the DFT method. Photoelectron spectra and MFPADs are obtained for several systems, such as hydrogen atom, H_2^+, NH_3 and H_2 O.
