H2+ in external XUV pulses. Calculations by using the exact prolate spheroidal coordinates
In recent years new and efficient numerical codes have been developed in order to solve the time-dependent Schrödinger equation (TDSE) for single or few-electron atomic and molecular systems. By applying the implemented algorithms on high performance computing platforms, exact solutions to the interaction of such systems with external and intense laser fields are obtained. For larger systems this laser field initiated dynamics is described in a simplified manner in the framework of the Born-Oppenheimer approach, where the nuclear dynamics is restricted to a few relevant electronic levels. A crucial part of these approaches is the calculation of high precision stationary electronic wave functions and the transition dipole moments between them.
The work of the STSM implied the development of an efficient algorithm for the calculation of the bound electronic eigenstates of H2+ for various internuclear distances. In the implemented approach we have discretized the electronic Hamiltonian in prolate spheroidal coordinates using finite difference (FD) discretization. The eigenstates were obtained via the direct diagonalization of the discretized Hamiltonian, and they were sorted according to their symmetry properties. The symmetry properties of each eigenstate was identified by counting the radial and angular nodal planes in prolate spheroidal coordinates (See figure below). After the convergence of the eigenstates (of the electronic wave functions) was carefully checked, the accurate transition dipole moments were also calculated.
In the next step the obtained ab initio electronic energy levels and transition moments will be included in the numerical code developed by the group of prof. Fernando Martin, and the combined electronic and nuclear dynamics of H2+ under the influence of ultrashort laser pulses will be studied.
In the existing approach of the host group the electronic wave functions are obtained by using one center partial wave expansion, which has the disadvantage of slow convergence, and low precision at large internuclear distances. During the present STSM this drawback was eliminated by the present approach.