Mapping variable ring polymer molecular dynamics (MV-RPMD) is an approximate quantum dynamics method based on imaginary-time path integrals for simulating electronically nonadiabatic photochemical processes. By employing a mapping protocol to transform from a discrete electronic state basis to continuous Cartesian phase-space variables, the method captures electronic state transitions coupled to nuclear motion using only classical MD trajectories. In this work, we extend the applicability of MV-RPMD to simulations of photoinduced excited electronic state dynamics in nonadiabatic systems with multiple avoided crossings. We achieve this by deriving a new electronic state population estimator in the phase space of electronic variables that is exact at equilibrium and numerically accurate in real time. Further, we introduce an efficient constraint protocol to initialize an MV-RPMD simulation to a particular electronic state. We numerically demonstrate the accuracy of this estimator and constraint technique in describing electronic state dynamics from an initial nonequilibrium state in six model systems, three of which describe photodissociation.

We present a mean field ring polymer molecular dynamics method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. Our approach involves calculating a transition state theory (TST) estimate to the rate using an exact path integral in discrete electronic states and continuous Cartesian nuclear coordinates. A dynamic recrossing correction to the TST rate is then obtained from real-time dynamics simulations using mean field ring polymer molecular dynamics. We employ two different reaction coordinates in our simulations and show that, despite the use of mean field dynamics, the use of an accurate dividing surface to compute TST rates allows us to achieve remarkable agreement with Fermi's golden rule rates for nonadiabatic ET in the normal regime of Marcus theory. Further, we show that using a reaction coordinate based on electronic state populations allows us to capture the turnover in rates for ET in the Marcus inverted regime.

We investigate the mechanisms of condensed phase proton-coupled electron transfer (PCET) using Mapping-Variable Ring Polymer Molecular Dynamics (MV-RPMD), a recently developed method that employs an ensemble of classical trajectories to simulate nonadiabatic excited state dynamics. Here, we construct a series of system-bath model Hamiltonians for the PCET, where four localized electron-proton states are coupled to a thermal bath via a single solvent mode, and we employ MV-RPMD to simulate state population dynamics. Specifically, for each model, we identify the dominant PCET mechanism, and by comparing against rate theory calculations, we verify that our simulations correctly distinguish between concerted PCET, where the electron and proton transfer together, and sequential PCET, where either the electron or the proton transfers first. This work represents a first application of MV-RPMD to multi-level condensed phase systems; we introduce a modified MV-RPMD expression that is derived using a symmetric rather than asymmetric Trotter discretization scheme and an initialization protocol that uses a recently derived population estimator to constrain trajectories to a dividing surface. We also demonstrate that, as expected, the PCET mechanisms predicted by our simulations are robust to an arbitrary choice of the initial dividing surface.

Success of the shrimp aquaculture industry requires technological advances that increase production and environmental sustainability. Indoor, superintensive, aquaculture systems are being developed that permit year-round production of farmed shrimp at high densities. These systems are intended to overcome problems of disease susceptibility and of water quality issues from waste products, by operating as essentially closed systems that promote beneficial microbial communities (biofloc). The resulting biofloc can assimilate and detoxify wastes, may provide nutrition for the farmed organisms resulting in improved growth, and may aid in reducing disease initiated from external sources. Nuclear magnetic resonance (NMR)-based metabolomic techniques were used to assess shrimp health during a full growout cycle from the nursery phase through harvest in a minimal-exchange, superintensive, biofloc system. Aberrant shrimp metabolomes were detected from a spike in total ammonia nitrogen in the nursery, from a reduced feeding period that was a consequence of surface scum build-up in the raceway, and from the stocking transition from the nursery to the growout raceway. The biochemical changes in the shrimp that were induced by the stressors were essential for survival and included nitrogen detoxification and energy conservation mechanisms. Inosine and trehalose may be general biomarkers of stress in Litopenaeus vannamei. This study demonstrates one aspect of the practicality of using NMR-based metabolomics to enhance the aquaculture industry by providing physiological insight into common environmental stresses that may limit growth or better explain reduced survival and production.

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Electronic structure calculations at the correlated molecular orbital theory and density functional theory levels have been used to generate a reliable set of clustering energies for up to three water molecules in carbon dioxide clusters up to n = 12. The structures and energetics are dominated by Lewis acid-base interactions with hydrogen-bonding interactions playing a lesser energetic role. The actual binding energies are somewhat larger than might be expected. The correlated molecular orbital MP2 method and density functional theory with the ωB97X exchange-correlation functional provide good results for the energetics of the clusters, but the B3LYP and ωB97X-D functionals do not. Seven CO(2) molecules form the first solvent shell about a single H(2)O with four CO(2) molecules interacting with the H(2)O via Lewis acid-base interactions, two CO(2) interacting with the H(2)O by hydrogen bonds, and the seventh CO(2) completing the shell. The Lewis acid-base and weak hydrogen bond interactions between the water molecules and the CO(2) molecules are strong enough to disrupt the trimer ring configuration for as few as seven CO(2) molecules. Calculated (13)C NMR chemical shifts for mCO(2)·(H(2)O)(n) show little change with respect to the number of H(2)O or CO(2) molecules in the cluster. The O-H stretching frequencies do exhibit shifts that can provide information about the interactions between water and CO(2) molecules.

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There has always been a need for engaging assessments in online learning environments, though the COVID-19 pandemic further emphasized this need. Instructors across science, technology, engineering, and mathematics (STEM) disciplines have begun to implement escape room activities as effective and engaging learning tools in their classrooms.