An analytical computation of Christoffel symbols for reaction coordinate and trajectory treatments under internal coordinates

1991 ◽  
Vol 6 (1) ◽  
pp. 77-90 ◽  
Author(s):  
Holger Dachsel ◽  
Wolfgang Quapp
Keyword(s):  
Reaction Coordinate ◽  
Analytical Computation ◽  
Internal Coordinates ◽  
Christoffel Symbols

Force field for in-plane vibrations of terephthalonitrile

1989 ◽  
Vol 54 (1) ◽  
pp. 18-27 ◽  
Author(s):  
Juan F. Arenas ◽  
Juan I. Marcos ◽  
Francisco J. Ramírez
Keyword(s):  
Experimental Data ◽  
Force Field ◽  
Normal Coordinates ◽  
Internal Coordinates ◽  
Isotopic Shifts ◽  
Quadratic Force Field ◽  
Semi Empirical

The general quadratic force field for the in-plane vibrations of terephthalonitrile was calculated by the semi-empirical MINDO/3 method. This force field was refined to the frequencies observed experimentally for terephthalonitrile and isotopic shifts of terephthalonitrile-[15N2]. The refined frequencies reproduce the experimental data with errors less than 0.5%. The normal coordinates and the force field in internal coordinates were also calculated from the refined field.

Bimolecular Reactions, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Saddle Point ◽  
Transition State Theory ◽  
Classical Mechanics ◽  
Small Degree ◽  
State Theory ◽  
Reaction Coordinate ◽  
Partition Functions ◽  
Bimolecular Reactions ◽  
Activated Complex

This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

Location-thinking, value-thinking, and graphical forms: combining analytical frameworks to analyze inferences made by students when interpreting the points and trends on a reaction coordinate diagram

2021 ◽  
Author(s):  
Alexander P. Parobek ◽  
Patrick M. Chaffin ◽  
Marcy H. Towns
Keyword(s):  
Reaction Rate ◽  
Research Study ◽  
Reaction Rates ◽  
Reaction Coordinate ◽  
Structured Interviews ◽  
Chemistry Students ◽  
Qualitative Research Study ◽  
The Impact ◽  
Analytical Frameworks ◽  
Chemical Representations

Reaction coordinate diagrams (RCDs) are chemical representations widely employed to visualize the thermodynamic and kinetic parameters associated with reactions. Previous research has demonstrated a host of misconceptions students adopt when interpreting the perceived information encoded in RCDs. This qualitative research study explores how general chemistry students interpret points and trends on a RCD and how these interpretations impact their inferences regarding the rate of a chemical reaction. Sixteen students participated in semi-structured interviews in which participants were asked to interpret the points and trends along provided RCDs and to compare relative reaction rates between RCDs. Findings derived from this study demonstrate the diversity of graphical reasoning adopted by students, the impact of students’ interpretations of the x-axis of a RCD on the graphical reasoning employed, and the influence of these ideas on inferences made about reaction rate. Informed by analytical frameworks grounded in the resources framework and the actor-oriented model of transfer, implications for instruction are provided with suggestions for how RCDs may be presented to assist students in recognizing the critical information encoded in these diagrams.

scholarly journals On the 3D → 2D Isomerization of Hexaborane(12)

Chemistry ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 28-38
Author(s):  
Josep M. Oliva-Enrich ◽  
Ibon Alkorta ◽  
José Elguero ◽  
Maxime Ferrer ◽  
José I. Burgos
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Transition States ◽  
Three Dimensional ◽  
Reaction Coordinate ◽  
Intrinsic Reaction Coordinate ◽  
Limiting Factor ◽  
Two Dimensional ◽  
Axis Of Rotation

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).

The Energy Gap as a Universal Reaction Coordinate for the Simulation of Chemical Reactions

2009 ◽  
Vol 113 (22) ◽  
pp. 7867-7873 ◽  
Author(s):  
Letif Mones ◽  
Petr Kulhánek ◽  
István Simon ◽  
Alessandro Laio ◽  
Monika Fuxreiter
Keyword(s):  
Chemical Reactions ◽  
Energy Gap ◽  
Reaction Coordinate

New solutions to the problems of chain orientation and chain continuity in structure analysis of fibrous polymers. A reconsideration of the structure of polyisobutene

2007 ◽  
Vol 40 (1) ◽  
pp. 10-15 ◽  
Author(s):  
Attilio Immirzi ◽  
Davide Alfano ◽  
Consiglia Tedesco
Keyword(s):  
New York ◽  
Degrees Of Freedom ◽  
Structure Refinement ◽  
General Interest ◽  
Structural Refinement ◽  
X Ray Diffraction ◽  
Chain Orientation ◽  
Crystalline Polymers ◽  
Internal Coordinates ◽  
Fibrous Polymers

Two points of general interest in structural refinement of polymers based on internal coordinates are discussed: the chain orientation and the chain continuity. Using a proprietary computer program, based on revised approaches to these questions, the structure of polyisobutene has been reconsidered, using new X-ray diffraction measurements (Fuji image plate) and performing a structure refinement based on internal coordinates. Three refinement schemes, with a decreasing number of degrees of freedom, have been considered, with the conclusion that the distortion from the 83regular helix, claimed by Tadokoro [(1979).Structure of Crystalline Polymers, p. 136. New York: Wiley-Interscience], is confirmed, though lower than supposed. The new procedures implemented for chain orientation and chain continuity work excellently.

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