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Quantum Chemical Analysis of Polyamic Acids and Polyimides
Published in Michael I. Bessonov, Vladimir A. Zubkov, Polyamic Acids and Polyimides, 2020
The calculations were carried out by the MNDO method within the framework of transition state theory. The geometries of transition states were found by NRP and iterative NRP procedures (see Section II) and also by the reaction coordinate (RC) procedure.81 The reaction coordinate is a geometrical variable that changes markedly during a reaction and is used to follow the course of the reaction. In the RC procedure used here for the study of cyclization of ionic forms, the total energy ET is minimized with respect to every molecular coordinate (other than the reaction coordinate) when moving along a reaction coordinate. For example, in the case of the imide ring formation, the reaction coordinate qi is the distance between the nitrogen atom and the carbon atom of the carboxyl group.
Introduction: Background Material
Published in Nassir H. Sabah, Neuromuscular Fundamentals, 2020
In general, a reaction cannot proceed unless reacting molecules possess a minimum energy known as the activation energy, Ea, of the reaction (Figure 1.14). The horizontal coordinate, representing the progress of the reaction along a reaction pathway, is referred to as the reaction coordinate. It is usually a geometric parameter, such as bond length or bond angle, that changes during the conversion of one or more reactants into one or more products. A simple classical example is the breaking of a covalent bond in the dissociation of a hydrogen molecule into two hydrogen atoms.
Enzyme Catalysis
Published in Harvey W. Blanch, Douglas S. Clark, Biochemical Engineering, 1997
Harvey W. Blanch, Douglas S. Clark
Transition state theory provides a more detailed picture of enzymatic catalysis. In this theory, the mechanism of interaction of reactants is not considered; the important criterion is that colliding molecules must have sufficient energy to overcome a potential energy barrier (the energy of activation) to react. The reaction is described along a reaction coordinate, against which is plotted the energies of the reactants, transition state species and products. The activation energy may be obtained from values of the reaction rate determined at various
A bonding evolution theory study on the catalytic Noyori hydrogenation reaction
Published in Molecular Physics, 2019
Julen Munárriz, Ruben Laplaza, Víctor Polo
All DFT theoretical calculations were performed using the Gaussian09 programme package [29]. B3LYP method [30,31] has been employed including the D3 dispersion correction scheme developed by Grimme [32] using the Becke–Johnson damping [33] for both energies and gradient calculations; in conjunction with the ‘ultrafine’ grid. The def2-SVP basis set [34] has been selected for all atoms for geometry optimisations, performing single-point calculations with def2-TZVP basis set to refine energy results. The nature of the stationary points has been confirmed by analytical frequency analysis; minima and transition states were characterised by zero and one imaginary frequencies, respectively. Transition states were characterised by the calculation of reaction paths following the intrinsic reaction coordinate (force constants were calculated for each point along the reaction pathway). The ELF study was performed with TopMod programme [35] using the corresponding mono determinantal B3LYP-D3BJ/def2-TZVP wave functions in a tridimensional grid of 300 points in each direction. ELF plots were represented using the Chimera software [3,36,37]. The topological partition of the ELF gradient field yields basins of attractors that can be identified as corresponding to atomic cores, bonds, and lone pairs. In molecular systems, two types of basins can be found: (i) core basins surrounding nuclei and (ii) valence basins that are characterised by the number of core basins sharing the boundary, also called the synaptic order. The ELF topology depends on control space parameters, in this case, the reaction pathway as traced by following the intrinsic reaction coordinate connecting stationary points. In this way, the reaction pathway is divided into a sequence of structural stability domain (SSD) of the ELF topology, characterised by catastrophe or turning points.