Time-dependent Schrödinger equation for coherent electron dynamics in poly-electronic atoms
The energetics of chemically relevant processes is largely affected by the way electrons manage to avoid each other, thus reducing their mutual repulsion, a phenomenon called correlation. The need to go beyond independent-particle models is also the reason why an accurate theoretical description of many-electron systems is so hard to achieve. As a consequence, correlation is firmly at the center of any investigation of atomic and molecular reactivity.
Photoionization with controlled sequences of sub-femtosecond pulses is a good way to monitor the dynamical manifestation of correlated motion since electrons respond to the sudden ejection of one of them on a characteristic timescale of few tens of attosecond to a few femtoseconds. To reproduce theoretically the outcome of similar processes, it is necessary to integrate numerically the time-dependent Schroedinger equation (TDSE), the equation of motion of isolated quantum systems, in a very big configuration space. We achieve this in practice by running large simulations on parallel supercomputers.
The objective of this short-term scientific mission is to adapt a parallel solver for the TDSE to the output of the multi-reference Hartree-Fock close-coupling program developed in Stockholm, which provides bound and single ionization states for arbitrary atoms, as well as the radiative transition amplitudes between them.
The parallel solver is based on a second-order split-exponential propagator on a spectral basis. The action of the exponential of the dipole non-diagonal interaction on the propagating state vector is achieved with an iterative Krylov space method implemented using the PETSc parallel library. The close-coupling multi-reference Hartree-Fock representation of the single-ionization space for arbitrary atoms and ions, provided by the Stock package developed in Stockholm, was interfaced with the parallel solver and a first simulation for the ionization of the Ne+ ion was successfully carried out.
This result is a step towards a theoretical reproduction of realistic attosecond pump-probe experiments that takes quantitatively into account the parent-ion rearrangement following a photoionization event. During this visit, we extended to the time domain the Stockholm atomic-structure program with a parallel solver for the TDSE. We also planned the upgrade of the program that computes the scattering states used to extract asymptotic photoelectron distributions from time-dependent wave packets.