Unimolecular Dissociation from a Dense Set of States

1996 ◽  
Vol 100 (19) ◽  
pp. 7962-7971 ◽  
Author(s):  
F. Remacle ◽  
R. D. Levine
Keyword(s):  
Unimolecular Dissociation ◽  
Dense Set

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

Generic rotation sets

2020 ◽  
pp. 1-13
Author(s):  
SEBASTIÁN PAVEZ-MOLINA
Keyword(s):  
Dynamical System ◽  
Convex Body ◽  
Probability Measures ◽  
Topological Dynamical System ◽  
Continuous Vector ◽  
Rotation Set ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Uniquely Ergodic ◽  
Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

scholarly journals Structure theorems in tame expansions of o-minimal structures by a dense set

2020 ◽  
Vol 239 (1) ◽  
pp. 435-500 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Ayhan Günaydin ◽  
Philipp Hieronymi
Keyword(s):  
Structure Theorems ◽  
Dense Set

Unimolecular dissociation rates by a semiclassical analysis of quantum resonance lifetimes

1987 ◽  
Vol 133 (6) ◽  
pp. 531-537 ◽  
Author(s):  
Vincenzo Aquilanti ◽  
Simonetta Cavalli ◽  
Gaia Grossi
Keyword(s):  
Unimolecular Dissociation ◽  
Semiclassical Analysis ◽  
Quantum Resonance

Microcanonical rates for the unimolecular dissociation of the ethyl radical

1999 ◽  
Vol 110 (12) ◽  
pp. 5485-5488 ◽  
Author(s):  
Thomas Gilbert ◽  
Thomas L. Grebner ◽  
Ingo Fischer ◽  
Peter Chen
Keyword(s):  
Unimolecular Dissociation ◽  
Ethyl Radical

Time-dependence of the isotope effects in the unimolecular dissociation of tertiary amine molecular ions

1991 ◽  
Vol 26 (10) ◽  
pp. 875-881 ◽  
Author(s):  
Steen Ingemann ◽  
Els Kluft ◽  
Nico M. M. Nibbering ◽  
Colin E. Allison ◽  
Peter J. Derrick ◽  
...  
Keyword(s):  
Time Dependence ◽  
Tertiary Amine ◽  
Isotope Effects ◽  
Molecular Ions ◽  
Unimolecular Dissociation

The C—Br bond dissociation energy in halogenated bromomethanes

1951 ◽  
Vol 209 (1096) ◽  
pp. 110-131 ◽  
Keyword(s):  
Bond Dissociation Energy ◽  
Dissociation Energy ◽  
Methyl Bromide ◽  
Frequency Factor ◽  
Unimolecular Dissociation ◽  
Bond Dissociation Energies ◽  
Kcal Mole ◽  
Fast Reaction ◽  
Bond Dissociation ◽  
Dissociation Energies

The pyrolyses of methyl bromide and of the halogenated bromomethanes, CH 2 CI. Br, CH 2 Br 2 , CHCl 2 .Br, CHBr 3 , CF 3 Br, CCI 3 . Br and CBr 4 , have been investigated by the ‘toluene-carrier' technique. It has been shown that all these decompositions were initiated by the unimolecular process R Br → R + Br. (1) Since all these decompositions were carried out in the presence of an excess of toluene, the bromine atoms produced in process (1) were readily removed by the fast reaction C 6 H 5 .CH 3 + Br → C 6 H 5 . CH 2 • + HBr. Hence, the rate of the unimolecular process (1) has been measured by the rate of formation of HBr. The C—Br bond dissociation energies were assumed to be equal to the activation energies of the relevant unimolecular dissociation processes. These were calculated by using the expression k ═ 2 x 10 13 exp (- D/RT ). The reason for choosing this particular value of 2 x 10 13 sec. -1 for the frequency factor of these reactions is discussed. The values obtained for the C—Br bond dissociation energies in the investigated bromomethanes are: D (C—Br) D (C—Br) compound (kcal./mole) compound (kcal./mole) CH 3 Br (67.5) CHBr 3 55.5 CH 2 CIBr 61.0 CF 3 Br 64.5 CH 2 Br 2 62.5 CCI 3 Br 49.0 CHCl 2 Br 53.5 CBr 4 49.0 The possible factors responsible for the variation of the C—Br bond dissociation energy in these compounds have been pointed out.

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