Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavorable scaling with increasing molecular size. Tensor decomposition techniques can overcome such challenges by decomposing unattainably large numerical representations of chemical problems into smaller, tractable ones. In the first two decades of this century, algorithms based on such tensor factorizations have become state-of-the-art methods in various branches of computational chemistry, ranging from molecular quantum dynamics to electronic structure theory and machine learning. Here, we consider the role that tensor decomposition schemes have played in expanding the scope of computational chemistry. We relate some of the most prominent methods to their common underlying tensor network formalisms, providing a unified perspective on leading tensor-based approaches in chemistry and materials science.
A sol-gel process for the synthesis of a multi-component oxide material from the system SiO2-ZrO2-Al2O3underwent optimization and up-scaling. Initially, on a laboratory scale, components including precursors, catalysts, and additives were methodically evaluated to ensure a safe and efficient transition to larger volumes. Subsequently, the equipment for the whole setup of the sol-gel process was strategically selected. Leveraging insights from these optimizations, the process was successfully scaled-up to pilot-scale operation, conducting hydrolysis, condensation reactions, gelation, aging, and drying within a single, integrated conical dryer system for an 80 L batch. A visual test and FTIR spectroscopy were applied for process control and monitoring.
Two applications of a radical trap based on a homolytic substitution reaction (SH2') are presented for the trapping of short-lived radical intermediates in organic reactions. The first example is a photochemical cyanomethylation catalyzed by a Ru complex. Two intermediate radicals in the radical chain propagation have been trapped and detected using mass spectrometry (MS), along with the starting materials, products and catalyst degradation fragments. Although qualitative, these results helped to elucidate the reaction mechanism. In the second example, the trapping method was applied to study the radical initiation catalyzed by a triethylboronoxygen mixture. In this case, the concentration of trapped radicals was sufficiently high to enable their detection by nuclear magnetic resonance (NMR). Quantitative measurements made it possible to characterize the radical flux in the system under different reaction conditions (including variations of solvent, temperature and concentration) where modelling was complicated by chain reactions and heterogeneous mass transfer.
Large-scale distillation is a challenge in many respects. Particularly difficult is the purification by distillation of a compound with limited thermal stability. This article describes various aspects of these difficulties with some possible solutions. Special emphasis is placed on the collaboration of different disciplines to find pragmatic solutions to these challenges. The purification of diketene in quantities of several 1000 ta-1 is an excellent example to illustrate the different requirements. Although the distillation of diketene has been carried out by several companies for many years, there are still some aspects that deserve special attention.