Scheme 2. Substrate scope of the aryl migration reaction with reaction Conditions B. Scheme 3. Further elaborations.Figure 2. DFT study on the selectivity of radical formation. Angewandte Chemie Communications 626

The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light-harvesting and spin transport, and so forth. In recent years, time-dependent density matrix renormalization group (TD-DMRG) has emerged as a general, numerically accurate and efficient method for highdimensional full-quantum dynamics. This review will cover the fundamental algorithms of TD-DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD-DMRG by benchmarking with the current state-of-the-art methods for simulating quantum dynamics of the spin-boson model and the Frenkel-Holstein(-Peierls) model. As applications of TD-DMRG to real-world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface.

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Interactive molecular dynamics in virtual reality (IMD-VR) simulations provide a digital molecular playground for students as an alternative or complement to traditional molecular modeling kits or 2D illustrations. Previous IMD-VR studies have used molecular mechanics to enable simulations of macromolecules such as proteins and nanostructures for the classroom setting with considerable success. Here, we present the InteraChem molecular visualizer, intended for reactive IMD-VR simulation using semiempirical and ab initio methods. InteraChem visualizes not only the molecular geometry but also (1) isosurfaces such as molecular orbitals and electrostatic potentials and (2) two-dimensional graphs of time-varying simulation quantities such as kinetic/potential energy, internal coordinates, and user-applied force. Additionally, InteraChem employs speech recognition to facilitate user interaction and introduces a novel “atom happiness” visualization using emojis to indicate the energetic feasibility of a particular bonding arrangement. We include a set of accompanying exercises that we have used to teach chemical reactivity in small molecular systems.