Our article sheds light on the control of the motion of the ionized electrons during double ionization. To first order, the field only drives the electron into the same direction (front-to-back motion). In this paper, our goal was to achieve the opposite, back-to-back motion, where both electrons are ejected into opposite directions. This is only possible via an interplay between the inter-particle forces and the potential. By extensive usage of four different control procedures (local control, derivative-free optimizations of basis expansions, Krotov method, and control of the classical equations of motions), we could identify pulse characteristics that lead to the desired back-to-back motion. Additionally, we were able to identify a simple, classical two-step mechanism. Besides these new physical results, this contribution also discusses new methodologies for using local control procedures for this difficult system and employs a new method to efficiently propagate the wavefunction in time [H. R. Larsson, B. Hartke and D. J. Tannor, J. Chem. Phys., 145, 204108 (2016)].

During my postdoctoral studies in the group of Prof. G. Chan (Caltech), I explored new ways to apply the density matrix renormalization group (DMRG) to bigger systems. In this article we explore a class of simple, qualitative wavefunctions, the minimal matrix product state (MMPS), which combines projection operators and the DMRG in order to yield a low-scaling method for quick explorations of the potential energy landscape of strongly correlated systems. Without jeopardizing low computational cost, MMPSs generalize well-established methods such as the projected Hartree-Fock-Bogoliubov (HFB)/antisymmetrized geminal power (AGP) method and the generalized valence bond (GVB) method. For the systems we studied, we show that MMPSs give correct qualitative behavior across the whole PES, often significantly improving aforementioned ansätze.

During my postdoctoral studies in the group of Prof. G. Chan (Caltech), as side project, I worked on the computation of vibrational spectra using tree-tensor network states (TTNS). There, I applied methods developed in the condensed matter community to molecular systems. Compared to established approaches for computing vibrational spectra, such as the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method, the new approach is faster and much more robust and the diagrammatic language from condensed matter physics I use gains much more insights. I am currently working on using the TTNS method to compute high-lying vibrational states of the Zundel ion.

The main project of my PhD studies (in the groups of Prof. B. Hartke and Prof. D. Tannor) was the exploitation of sparsity in vibrational and electronic wavefunctions. Exploiting the sparsity means pruning of the underlying basis. This is similar to selected CI techniques for electronic structure calculations. Particularly successful was the application of dynamical pruning to the multiconfiguration time-dependent Hartree (MCTDH) method. While simple static pruning has already been studied 20 years ago by Worth [1], the conclusions from this mainly was that even static pruning requires too much bookkeeping such that this approach has quickly been abandoned. Due to this experience, many MCTDH developers advised me against developing methods based on pruning. Instead, I started working on a completely new MCTDH implementation with pruning. This was successful and the developed methods were applied to up to 24-dimensional systems and were up to 50 times faster than conventional MCTDH and competitive with state-of-the-art but more complicated multilayer MCTDH. The reasons for this speedup are newly developed algorithms, an efficient implementation, and a dynamical pruning instead of a simple static one. Furthermore, I applied, also for the first time, dynamical pruning both to the orbitals and the underlying grid representation. This means that the used basis changes at each time step at two different levels.

The main project of my PhD studies (in the groups of Prof. B. Hartke and Prof. D. Tannor) was the exploitation of sparsity in vibrational and electronic wavefunctions. Exploiting the sparsity means pruning of the underlying basis. This is similar to selected CI techniques for electronic structure calculations. However, here, pruning was used for solving the time-dependent Schrödinger equation. Since the wavefunction changes with time, also the sparsity pattern changes such that the pruning has to be done dynamically. In this publication, for the first time, I could show that pruning actually is faster than conventional methods. This was only possible by developing new algorithms adapted to the pruned basis and by identifying certain requirements the employed basis has to fulfill, most importantly orthogonality, in order to achieve an efficient algorithm. The developed algorithms deal with the update of the sparsity pattern and with the computation of the action of an operator onto a wavefunction. This can be understood as a transformation of sparse, high-dimensional tensors. Parts of the algorithms I developed are now used in the group of Prof. T. Carrington (Queen’s University) [1], who is one of the lead-developers of methods based on pruning.

During my Master’s studies (in the group of Prof. M. Bonitz, Kiel University), I performed electron dynamics simulations utilizing a time-dependent multireference configuration interaction (TD-MR-CI) method. This method reduces the computational effort by considering only a selection of relevant configurations needed to describe the wavefunction, based on physical insights into the problem. With the help of a well-chosen coordinate system and a careful optimization of tensor transformations appearing in this method (more than 50,000 basis functions can be used), I could improve the methodology such that I was able to unravel correlation effects that occur during ionization dynamics of LiH in strong and short laser fields. In particular, I could show that, for intermediate field intensities, qualitatively wrong results are predicted if methods that are too simple are employed that take no correlation into account. My code is now used in the group of Prof. L. Madsen (Aarhus University) [1] [2].

In my Bachelor’s studies (in the group of Prof. B. Hartke, Kiel University), I performed global optimization of the reactive force field ReaxFF. The development of force fields that are able to describe any chemical reactions is a highly complex task and the optimization of the parameters of the force fields is very demanding, due to the sheer number of parameters (up to 300), their strong and partially non-obvious interdependencies, and the complicated, highly nonlinear and rugged function that needs to be globally optimized. Analytic derivatives with respect to the parameters are typically not available. Despite these challenges, I successfully performed global optimization of ReaxFF for systems containing containing Si, O and H. My optimized force field outperformed that of the lead developer of ReaxFF.