Towards explicit electronic quantum dynamics in a pre-Born-Oppenheimer context
Dirigée par Daniel Pelaez-Ruiz et Bérenger Gans
This PhD thesis provides the framework for electronic quantum dynamics in a pre-Born-Oppenheimer context, employing the multiconfiguration time-dependent Hartree (MCTDH) method in first-quantization.
This paves the way to the explicit simulation of few-electrons processes, such as inter-particle Coulombic decay, which are ubiquitous but remain poorly understood. In this respect, it is well established that nuclear dynamics have an impact on the efficiency and the final state of the processes. Consequently any simulation should be able to take into account inter-particle interactions and to represent on the same footing, bound and continuum states, in principle for all particles, electrons and possibly nuclei.
Arguably the major bottleneck, being a grid-based method, is the expression of quantities, in terms of high-dimensional tensors, the so called « curse of dimensionality », is handled by using a sum-of-products form. Cartesian coordinates are chosen to avoid imposing any artificial constraints and because the kinetic-energy operators have a simple and general form.
In this work we have achieved an efficient way of generating and representing the Coulomb interactions in Cartesian coordinates in analytical and separable form. A pairwise range-separated representation is developed by leveraging exact symmetries resulting in a low-rank sum of products of analytical one-dimensional factors. Furthermore, the influence of mode-partitions on the compressibility of the Coulomb potential is also studied for particle-based, coordinate-based and fully-separated representation. Exchange symmetry of the fermionic/bosonic (spatial) wavefunction is adapted to different mode-partitions, where particle exchange acts within several (logical) modes rather than by permutation of complete particle modes.
This theoretical and methodological work has been complemented by the development of software tools for the analysis, representation and visualization of multidimensional objects such as real and complex wavefunctions in a atomic/molecular context.