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Ultrafast dynamics in chemical systems provide a unique access to fundamental processes at the molecular scale. A proper description of such systems is often very challenging because of the quantum nature of the problem. The concept of matrix product states (MPS), however, has proven its performance in describing such correlated quantum systems in recent years for a wide range of applications. In this work, we continue the development of the MPS approach to study ultrafast electron dynamics in quantum chemical systems. The method combines time evolution schemes, such as fourth-order Runge–Kutta and Krylov space time evolution, with MPS, in order to solve the time-dependent Schrödinger equation efficiently. This allows for describing electron dynamics in molecules on a full configurational interaction (CI) level for a few femtoseconds after excitation. As a benchmark, we compare MPS-based calculations to full CI calculations for a chain of hydrogen atoms and for the water molecule. Krylov space time evolution is in particular suited for the MPS approach, as it provides a wide range of opportunities to be adjusted to the reduced MPS dimension case. Finally, we apply the MPS approach to describe charge migration effects in iodoacetylene and find direct agreement between our results and experimental observations.

Efficient mass transfer and light utilization are essential for high photocatalytic production rates. Here, we present a hierarchical three-dimensional (3D)-printed aerogel photocatalyst that unites both aspects by taking inspiration from the light scattering in clouds during photochemical processes and from mass transfer in plants during photosynthesis. We combine the geometric freedom of additive manufacturing with computational fluid dynamics and Monte Carlo simulations to guide the implementation of a self-supported aerogel in a continuous gas flow reactor. Here, 3D microstructuring reduced the pressure drop of a monolithic aerogel by 5 orders of magnitude without compromising the gas permeation and the light-harvesting efficiency of the intrinsic nanoporous material. We match the macroscopic thickness with the ultraviolet (UV) light penetration depth and show that the 3D aerogel of 1.1 mm thickness improves photocatalytic hydrogen production rates relative to the nanoparticle powder by a factor of five from 1.3 to 6.6 μmol g–1h–1for TiO2and from 30.0 to 141.8 μmol g–1h–1for Au/TiO2, respectively. Ultimately, our approach can be applied for other nanomaterials to boost the overall performance of a variety of photochemical processes and reactor designs.

The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple system is made strongly non-integrable in the classical regime by the introduction of particle interactions. In particular, we present a two-particle classical system contained in a d-dimensional billiard with hard walls. Similarly, a corresponding two-dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields.

The energy level structure of an interacting system of electrons is analysed. The model chosen describes electrons in a semiconductor quantum dot system, whose energy levels could be accessed via finite-bias transport experiments. We find that the normalized level spacing of the system exhibits significant departures from Poisson statistics, and that these are strongly dependent on magnetic field, and quantum numbers of the level sequence.

We present calculations of the tunneling characteristics of quantum dot systems with few electrons, making explicit consideration of electronic correlations introduced by Coulomb interactions. These are shown to strongly affect the many-particle overlap matrix elements which describe the addition or removal of single electrons to the system. We show that the main features of the differential conductance of quantum dots observed in recent experiments in the nonlinear regime can be attributed to effects introduced by these electronic correlations. Copyright 1994, 1999 Academic Press