Chemical reaction cross sections and rate constants

Induced Magnetism of the MoS2 Monolayer during the Transition Metal (Fe/Ni) Bombardment Process: A Nonadiabatic Ab Initio Collision Dynamics Investigation

“…The spots of destination are chosen at the point x 2 R (Å) along radius R , where x holds a value in the range of [0, 1] with a discrete step of 0.1. The probability of locating the destination point on a circular surface (considered as a cross section) of radius R is proportional to x 2 , which was described in a theoretical work by Kuppermann and Greene . For convenience, we name D as the case X being fired perpendicularly to the surface; C1, C2, ..., C10 and B1, B2, ..., B10 as the cases in which X is aimed toward the so-defined B or C spots on the projected Mo–S vector and the bisecting vector of two Mo–S bonds, respectively.…”

“…The probability of locating the destination point on a circular surface (considered as a cross section) of radius R is proportional to x 2 , which was described in a theoretical work by Kuppermann and Greene. 45 For convenience, we name D as the case X being fired perpendicularly to the surface; C1, C2, ..., C10 and B1, B2, ..., B10 as the cases in which X is aimed toward the so-defined B or C spots on the projected Mo−S vector and the bisecting vector of two Mo−S bonds, respectively. In total, 42 trajectories of X−MoS 2 (X = Fe/ Ni) collision are investigated in this study.…”

A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

“…The collision frequency of one electron with a background of target molecules of density n BG can be expressed as ν c = n BG σ(v r ) v r r , where v r is the relative velocity between the considered electron and the population of target species, and • r denotes the integration over the distribution of relative velocities. 53 In classical gas dynamics, the collision frequency is often expressed by assuming a Maxwellian distribution of relative velocities, resulting in ν c = n σ v th , with v th = (8k B T /(πm)) 1/2 the thermal velocity.…”

Social Distancing During the COVID-19 Pandemic: An Analogy to Explain Collision Cross-Sections in Chemical Kinetics

“…We now turn to a more chemically intuitive application of our previously discussed concept of the collision cross-section. Let us consider once more the reaction from eq , in which A and B collide to yield a product, P. The rate of this elementary step can then be expressed as given by eq , as a second-order reaction with a rate constant k : Equation is written considering changes in concentration as a function of time . It can be rewritten in terms of the change in the absolute number of molecules ( N A , N B , N P ) per unit time, leading to eq , which is more convenient for our subsequent discussion: The relationship between the rate constant, k , and the collision cross-section, σ, is as follows: For the interested reader, we now proceed with the demonstration of this relationship by following a simplified scheme (a thorough mathematical derivation of the general problem is presented in ref ).…”