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This thesis is focused on the application of an efficient ab initio numerical method based on algebraic diagrammatic construction (ADC) theory to the calculation of many-electron dynamics in atomic and molecular systems, in the absence or presence of (non-)perturbative laser fields. The first part of the research applies the ADC method to the calculation of Penning ionisation widths. Along with the numerical method, an analytical formula for PI is also derived in the asymptotic regions. The calculations show the exact region of inter-molecular distances, where the electron transfer mechanism in PI is the dominant one. It also shows that the regime of the energy transfer mechanism in PI cannot be reached in collisions even when approaching zero collisional temperature, but might be realised in He droplet environment. The second part of the research applies the ADC method to the calculations of high harmonic generation (HHG) spectra with counter-rotating bi-circular fields in B-spline basis. B-spline basis set is able to accurately describe the strongly oscillating continuum orbitals, such as in the case of HHG processes. Such a task poses a challenge to Gaussian-type basis which will easily run into linear dependence problems for high energy and high resolution calculations. The calculations show that, for He, Ne and Ar, the difference between the intensities of left- and right-circularly polarised harmonics is present at single atom level. The dominant polarisation shifts from left to right around the ionisation potential of the atom. The calculated spectra also suggest that changing the relative intensity of the driving \omega_0 and 2\omega_0 pulses, or varying the time delay between them has limited control over the intensity difference in the spectra at single atom level. Open Access

The excited state non-adiabatic dynamics of polyatomic molecules, leading to the coupling of structural and electronic dynamics, is a fundamentally important yet challenging problem for both experiment and theory. Ongoing developments in ultrafast extreme vacuum ultraviolet (XUV) and soft X-ray sources present new probes of coupled electronic-structural dynamics because of their novel and desirable characteristics. As one example, inner-shell spectroscopy offers localized, atom-specific probes of evolving electronic structure and bonding (via chemical shifts). In this work, we present the first on-the-fly ultrafast X-ray time-resolved absorption spectrum simulations of excited state wavepacket dynamics: photo-excited ethylene. This was achieved by coupling the ab initio multiple spawning (AIMS) method, employing on-the-fly dynamics simulations, with high-level algebraic diagrammatic construction (ADC) X-ray absorption cross-section calculations. Using the excited state dynamics of ethylene as a test case, we assessed the ability of X-ray absorption spectroscopy to project out the electronic character of complex wavepacket dynamics, and evaluated the sensitivity of the calculated spectra to large amplitude nuclear motion. In particular, we demonstrate the pronounced sensitivity of the pre-edge region of the X-ray absorption spectrum to the electronic and structural evolution of the excited-state wavepacket. We conclude that ultrafast time-resolved X-ray absorption spectroscopy may become a powerful tool in the interrogation of excited state non-adiabatic molecular dynamics.