Grid Cells Form a Global Representation of Connected Environments.

The firing patterns of grid cells in medial entorhinal cortex (mEC) and associated brain areas form triangular arrays that tessellate the environment [1, 2] and maintain constant spatial offsets to each other between environments [3, 4]. These cells are thought to provide an efficient metric for navigation in large-scale space [5-8]. However, an accurate and universal metric requires grid cell firing patterns to uniformly cover the space to be navigated, in contrast to recent demonstrations that environmental features such as boundaries can distort [9-11] and fragment [12] grid patterns. To establish whether grid firing is determined by local environmental cues, or provides a coherent global representation, we recorded mEC grid cells in rats foraging in an environment containing two perceptually identical compartments connected via a corridor. During initial exposures to the multicompartment environment, grid firing patterns were dominated by local environmental cues, replicating between the two compartments. However, with prolonged experience, grid cell firing patterns formed a single, continuous representation that spanned both compartments. Thus, we provide the first evidence that in a complex environment, grid cell firing can form the coherent global pattern necessary for them to act as a metric capable of supporting large-scale spatial navigation

Prediction of kinetic product ratios: investigation of a dynamically controlled case

Of the various factors influencing kinetically controlled product ratios, the role of nonstatistical dynamics is arguably the least well understood. In this paper, reactions were chosen in which dynamics played a dominant role in product selection, by design. Specifically, the reactions studied were the ring openings of cyclopropylidene to allene and tetramethylcyclopropylidene to tetramethylallene (2,4-dimethylpenta-2,3-diene). Both reactions have intrinsic reaction coordinates that bifurcate symmetrically, leading to products that are enantiomeric once the atoms are uniquely labeled. The question addressed in the study was whether the outcomes─that is, which product well on the potential energy surface was selected─could be predicted from their initial conditions for individual trajectories in quasiclassical dynamics simulations. Hybrid potentials were developed based on cooperative interaction between molecular mechanics and artificial neural networks, trained against data from electronic structure calculations. These potentials allowed simulations of both gas-phase and condensed-phase reactions. The outcome was that, for both reactions, prediction of initial selection of product wells could be made with >95% success from initial conditions of the trajectories in the gas phase. However, when trajectories were run for longer, looking for “final” products for each trajectory, the predictability dropped off dramatically. In the gas-phase simulations, this drop off was caused by trajectories hopping between product wells on the potential energy surface. That behavior could be suppressed in condensed phases, but then new uncertainty was introduced because the intermolecular interactions between solute and bath, necessary to permit intermolecular energy transfer and cooling of the hot initial products, often led to perturbations of the initial directions of trajectories on the potential energy surface. It would consequently appear that a general ability to predict outcomes for reactions in which nonstatistical dynamics dominate remains a challenge even in the age of sophisticated machine-learning capabilities

Meso-1, 2-Bis (Methylazo)-1, 2-Diphenylethane

The title compound, meso-1,2-bis(methyldiazenyl)-1,2-diphenylethane, C16H18N4, is arranged in a disordered manner around an inversion point. The N—N atom distances in the azo group of 1.192 (8) and 1.195 (8) Å, and the C—C atom distances in the ethylene moiety at 1.512 (8) and 1.503 (8) Å in the two models [refined to 51.7 (6) and 48.3 (6)% occupancies] were not significantly different

Final Report on Research Conducted under Grant DE-FG02-98ER14857

Work in the Carpenter laboratory under the aegis of grant DE-FG02-98ER14857 concerned the formation, properties, and reactions of organic free radicals known or believed to be important in hydrocarbon combustion. Both computational and experimental methods were employed in these studies

Re-evaluating the transition state for reactions in solution

In this microreview we revisit the early work in the development of Transition State Theory, paying particular attention to the idea of a dividing surface between reactants and products. The correct location of this surface is defined by the requirement that trajectories not recross it. When that condition is satisfied, the true transition state for the reaction has been found. It is commonly assumed for solution‐phase reactions that if the potential energy terms describing solvent‐solute interactions are small, the true transition state will occur at a geometry close to that for the solute in vacuo. However, we emphasize that when motion of solvent molecules occurs on a time scale similar or longer than that for structural changes in the reacting solute the true transition state may be at an entirely different geometry, and that there is an important inertial component to this phenomenon, which cannot be described on any potential energy surface. We review theories, particularly Grote‐Hynes theory, which have corrected the Transition State Theory rate constant for effects of this kind by computing a reduced transmission coefficient. However, we argue that searching for a true dividing surface with near unit transmission coefficient may sometimes be necessary, especially for the common situation in which the rate‐determining formation of a reactive intermediate is followed by the branching of that intermediate to several products

Evidence for nonstatistical dynamics in the Wolff rearrangement of a carbene

Two 13C-labeled isomers of the formal Diels−Alder adduct of acetylmethyloxirene to tetramethyl 1,2,4,5-benzenetetracarboxylate have been synthesized. Flash vacuum thermolysis of these adducts leads to various isotopic isomers of acetylmethylketene, the ratios of which have been determined by NMR. The surprising finding that the principal product comes from methylpyruvoyl carbene rather than its more stable isomer diacetylcarbene is explained by MPWB1K density functional calculations, which show that the reactant probably undergoes a unimolecular rearrangement to a norcaradiene derivative prior to its fragmentation. Coupled-cluster calculations on the methylpyruvoyl carbene show that it is capable of undergoing three unimolecular isomerizations. The fastest is 1,2-acetyl migration to give acetylmethylketene directly. The next is rearrangement via acetylmethyloxirene to diacetylcarbene and thence by Wolff rearrangement to acetylmethylketene. The least-favorable reaction is degenerate rearrangement via 1,3-dimethyl-2-oxabicyclo[1.1.0]butan-4-one (the epoxide of dimethylcyclopropenone). The combined experimental and computational results indicate that Wolff rearrangement of the diacetylcarbene occurs with a 2.5:1 ratio of the methyl groups despite the fact that they are related by a twofold axis of symmetry in the carbene. Preliminary molecular dynamics simulations are consistent with this conclusion. Taken together, the results suggest that the Wolff rearrangement is subject to the same kind of nonstatistical dynamical effects detected for other kinds of thermally generated reactive intermediates

Photochemical synthesis of oligomeric amphiphiles from alkyl oxoacids in aqueous environments

The aqueous phase photochemistry of a series of amphiphilic α-keto acids with differing linear alkyl chain lengths was investigated, demonstrating the ability of sunlight-initiated reactions to build molecular complexity under environmentally relevant conditions. We show that the photochemical reaction mechanisms for α-keto acids in aqueous solution are robust and generalizable across alkyl chain lengths. The organic radicals generated during photolysis are indiscriminate, leading to a large mixture of photoproducts that are observed using high-resolution electrospray ionization mass spectrometry, but these products are identifiable following literature photochemical mechanisms. The alkyl oxoacids under study here can undergo a Norrish Type II reaction to generate pyruvic acid, increasing the diversity of observed photoproducts. The major products of this photochemistry are covalently bonded dimers and trimers of the starting oxoacids, many of which are multi-tailed lipids. The properties of these oligomers are discussed, including their spontaneous self-assembly into aggregates

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

We examine the phase space structures that govern reactiondynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories

Sur un théorème de Poncelet et sa généralisation par M. Horvarth

Most chemical transformations (reactions or conformational changes) that are of interest to researchers have many degrees of freedom, usually too many to visualize without reducing the dimensionality of the system to include only the most important atomic motions. In this article, we describe a method of using Principal Component Analysis (PCA) for analyzing a series of molecular geometries (e.g., a reaction pathway or molecular dynamics trajectory) and determining the reduced dimensional space that captures the most structural variance in the fewest dimensions. The software written to carry out this method is called PathReducer, which permits (1) visualizing the geometries in a reduced dimensional space, (2) determining the axes that make up the reduced dimensional space, and (3) projecting the series of geometries into the low-dimensional space for visualization. We investigated two options to represent molecular structures within PathReducer: aligned Cartesian coordinates and matrices of interatomic distances. We found that interatomic distance matrices better captured non-linear motions in a smaller number of dimensions. To demonstrate the utility of PathReducer, we have carried out a number of applications where we have projected molecular dynamics trajectories into a reduced dimensional space defined by an intrinsic reaction coordinate. The visualizations provided by this analysis show that dynamic paths can differ greatly from the minimum energy pathway on a potential energy surface. Viewing intrinsic reaction coordinates and trajectories in this way provides a quick way to gather qualitative information about the pathways trajectories take relative to a minimum energy path. Given that the outputs from PCA are linear combinations of the input molecular structure coordinates (i.e., Cartesian coordinates or interatomic distances), they can be easily transferred to other types of calculations that require the definition of a reduced dimensional space (e.g., biased molecular dynamics simulations)