Rotational transition states: relative equilibrium points in inelastic molecular collisions

2003 ◽  
Vol 36 (7) ◽  
pp. 1319-1335 ◽  
Author(s):  
L Wiesenfeld ◽  
A Faure ◽  
T Johann
Keyword(s):  
Equilibrium Points ◽  
Relative Equilibrium ◽  
Transition States ◽  
Rotational Transition ◽  
Molecular Collisions

Non-linear dynamics of the photodissociation of nitrous oxide: Equilibrium points, periodic orbits, and transition states

2011 ◽  
Vol 134 (24) ◽  
pp. 244302 ◽  
Author(s):  
Frederic Mauguiere ◽  
Stavros C. Farantos ◽  
Jaime Suarez ◽  
Reinhard Schinke
Keyword(s):  
Nitrous Oxide ◽  
Periodic Orbits ◽  
Equilibrium Points ◽  
Transition States ◽  
Linear Dynamics ◽  
Non Linear

Study of molecular collisions using a new interpolation scheme

1979 ◽  
Vol 57 (1) ◽  
pp. 69-72 ◽  
Author(s):  
G. K. Johri ◽  
Suresh C. Mehrotra
Keyword(s):  
Perturbation Theory ◽  
Line Width ◽  
Transition Probabilities ◽  
Rotational Transition ◽  
Time Dependent ◽  
Interpolation Scheme ◽  
Molecular Collisions ◽  
First Time

An interpolation scheme as suggested, by Mehrotra and Boggs in their time-dependent perturbation theory is applied for the first time to the study of strong collisions and to evaluate the collision induced transition probabilities when their absolute values are more than one. This approximation is used to compute the line width parameter of the rotational transition J = 1 → 2 of the OCS–OCS system.

EQUILIBRIUM POINTS AND THEIR STABILITY IN THE RESTRICTED FOUR-BODY PROBLEM

2011 ◽  
Vol 21 (08) ◽  
pp. 2179-2193 ◽  
Author(s):  
A. N. BALTAGIANNIS ◽  
K. E. PAPADAKIS
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Relative Equilibrium ◽  
Center Of Mass ◽  
Basins Of Attraction ◽  
Equilibrium Solutions ◽  
Velocity Surface ◽  
Four Body Problem ◽  
The Stability ◽  
Zero Velocity Surface

We study numerically the problem of four bodies, three of which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle, while the fourth is infinitesimal. The fourth body does not affect the motion of the three bodies (primaries). The allowed regions of motion as determined by the zero-velocity surface and corresponding equipotential curves as well as the positions of the equilibrium points are given. The existence and the number of collinear and noncollinear equilibrium points of the problem depend on the mass parameters of the primaries. For three unequal masses, collinear equilibrium solutions do not exist. Critical masses associated with the existence and the number of equilibrium points, are given. The stability of the relative equilibrium solutions in all cases is also studied. The regions of the basins of attraction for the equilibrium points of the present dynamical model for some values of the mass parameters are illustrated.

scholarly journals Hindered rotational barriers in conjugated donor–acceptor substituted systems: calculations vs. experiments

2020 ◽  
Vol 22 (3) ◽  
pp. 1214-1221
Author(s):  
Mark Sigalov ◽  
Vladimir Lokshin ◽  
Nina Larina ◽  
Vladimir Khodorkovsky
Keyword(s):  
Transition States ◽  
Rotational Transition ◽  
Rotational Barriers ◽  
Donor And Acceptor ◽  
Donor Acceptor

Calculation of a barrier to rotation within push–pull derivatives requires considering at least three states: ground, donor and acceptor rotational transition states.

scholarly journals Photodissociation transition states characterized by chirped pulse millimeter wave spectroscopy

2019 ◽  
Vol 117 (1) ◽  
pp. 146-151 ◽  
Author(s):  
Kirill Prozument ◽  
Joshua H. Baraban ◽  
P. Bryan Changala ◽  
G. Barratt Park ◽  
Rachel G. Shaver ◽  
...  
Keyword(s):  
Transition State ◽  
Millimeter Wave ◽  
Transition States ◽  
Rotational Transition ◽  
Bimolecular Reaction ◽  
Parent Molecule ◽  
Chirped Pulse ◽  
Millimeter Wave Spectroscopy ◽  
Population Distributions ◽  
Elimination Mechanism

The 193-nm photolysis of CH2CHCN illustrates the capability of chirped-pulse Fourier transform millimeter-wave spectroscopy to characterize transition states. We investigate the HCN, HNC photofragments in highly excited vibrational states using both frequency and intensity information. Measured relative intensities ofJ= 1–0 rotational transition lines yield vibrational-level population distributions (VPD). These VPDs encode the properties of the parent molecule transition state at which the fragment molecule was born. A Poisson distribution formalism, based on the generalized Franck–Condon principle, is proposed as a framework for extracting information about the transition-state structure from the observed VPD. We employ the isotopologue CH2CDCN to disentangle the unimolecular 3-center DCN elimination mechanism from other pathways to HCN. Our experimental results reveal a previously unknown transition state that we tentatively associate with the HCN eliminated via a secondary, bimolecular reaction.

Hyperconjugation in hydrocarbons: Not just a “mild sort of conjugation”

2013 ◽  
Vol 85 (5) ◽  
pp. 921-940 ◽  
Author(s):  
Judy I-Chia Wu ◽  
Paul von Ragué Schleyer
Keyword(s):  
Bond Strength ◽  
Transition States ◽  
Substituent Effects ◽  
Rotational Transition ◽  
Electron Delocalization ◽  
Geometrical Features

This article emphasizes two underappreciated aspects of hyperconjugation in hydrocarbons, two-way hyperconjugation and hyperconjugation in tight spaces. Nonplanar polyenes [e.g., cyclooctatetraene (D2d), biphenyl (D2), styrene (C1)], the nonplanar rotational transition states (TSs) of planar polyenes (e.g., perpendicular 1,3-butadiene), as well as the larger nonplanar Hückel or Möbius annulenes, are stabilized by effective σ-electron delocalization (involving either the C–C or C–H bonds) via two-way hyperconjugation. The collective consequence of two-way hyperconjugation in molecules can be nearly as stabilizing as π-conjugation effects in planar polyenes. Reexamination of the σ- vs. π-bond strength of ethylene results in surprising counterintuitive insights. Strained rings and cages (e.g., cyclopropane and tetrahedrane derivatives, the cubyl cation, etc.) can foster unexpectedly large hyperconjugation stabilizations due to their highly deformed ring angles. The thermochemical stabilities of these species rely on a fine balance between their opposing destabilizing geometrical features and stabilizing hyperconjugative effects in tight spaces (adjustable via substituent effects). We hope to help dispel chemists’ prejudice in viewing hyperconjugation as merely a “mild” effect with unimportant consequences for interpreting the structures and energies of molecules.

scholarly journals On the dynamics of a particle inside a U – shaped rotating thin tube

2018 ◽  
Vol 27 (2018) ◽  
pp. 41-46
Author(s):  
Dumitru Deleanu
Keyword(s):  
Energy Balance ◽  
Governing Equation ◽  
Equilibrium Points ◽  
Relative Equilibrium ◽  
Equation Of Motion ◽  
Energy Balance Method ◽  
Analytical Technique ◽  
Strongly Nonlinear ◽  
Thin Tube ◽  
Nonlinear Motion

In this paper the problem of the strongly nonlinear motion of a particle on a rotating parabola is generalized for an arbitrary U-shaped curve. The governing equation of motion is deducted and then particularized on three cases, namely quadratic parabola, quartic parabola and cosine curve. Each case is numerically investigated for various small and large parameters and the results are contrasted with those provided by a relatively new analytical technique called energy balance method. The importance of the relative equilibrium points on the particle’s dynamics is highlighted.

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