Posts Tagged ‘TDSE’
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.
Time-dependent atomic photoionisation with a Multi-Configuration-Hartree-Fock close-coupling approach
This STSM concerned the collaboration between the COST nodes in Stockholm and Madrid to build a new program to solve the timedependent Schrodinger equation (TDSE) for arbitrary poly-electronic atoms under the action of pulsed fields.
The program under construction extends a Multi-Conguration-Hartree-Fock (MCHF) atomic-structure package to include the coupling to an ionized electron. It is based on close-coupling ionization states built from MCHF parent-ion states coupled to radial B-splines. Prior to the STSM, the package could already reproduce photoionization cross sections for arbitrary atoms with both the initial bound state and the final continuum states described
at the MCHF level as detailed in a recent publication [Carette, Dahlstrom, Argenti
and Lindroth 2013 Phys. Rev. A 87 023420].
As a result of the STSM:
- The inclusion of the K-matrix package for the calculation of multichannelsingle-ionisation scattering states to resolve energetically and angularly the partial photoelectron spectra encoded in the electronic wave packetsobtained from simulations of pump-probe experiments on atoms was started. A similar integration technique was already successfully demonstrated in 2010 [Argenti et al. 2013, Phys. Rev. A 87 053405].
- The user friendly setup of the package was tested
- The benchmarking of neon- and argon photoionization, and especially the issue of how to obtain a correct energy position of the so-called Cooper minima in argon was discussed.