Transmission coefficient, calculation

We use the effective mass approximation. The structure potential is approximated b y a c onsequence o f rectangular quantum barriers a nd wells. Their widths and potentials are randomly varied with the uniform distribution. The sequence of the parameters is calculated by a random number generator. Other parameters, e.g. effective masses of the carriers, are assumed equal in different layers. To simplify the transmission coefficient calculations, we approximate the electric field potential by a step function. The transmission coefficient is calculated using the transfer matrix method [9]. The 1-V curves of the MQW stmctures along the x-axis (growth direction) a re derived from the calculated transmission spectra... 

The applications of this stochastic picture to the trans-gauche isomerization of -alkanes and the boat-chair isomerization of cyclohexane have demonstrated the usefulness of this approach. In both cases, the transmission coefficients calculated from stochastic dynamics agreed quite well with those from the (later) molecular dynamics calculations, given that there can be an uncertainty in the correct value of the collision frequency to use in comparing with the full molecular dynamics in solution. Stochastic dynamics therefore can allow the rapid calculation of reaction dynamics over a wide range of solvent densities and/or viscosities. 

For gas-phase reactions, Eq. (5-40) offers a route to the calculation of rate constants from nonkinetic data (such as spectroscopic measurements). There is evidence, from such calculations, that in some reactions not every transition state species proceeds on to product some fraction of transition state molecules may return to the initial state. In such a case the calculated rate will be greater than the observed rate, and it is customaiy to insert a correction factor k, called the transmission coefficient, in the expression. We will not make use of the transmission coefficient. 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

If insulation panels are not of uniform construction (as in the case of a wall containing a window) the average sound-insulation value must be derived for use in calculations. The total transmission coefficient for the composite panel will equal the sum of the individual coefficient times their respective areas divided by the total area. Thus ... 

Some gas phase data suggest that a certain fraction of the transition states for some reactions are reflected back to products. One can multiply the right side of Eq. (7-55) by k, the transmission coefficient, to account for this, in which case k < 1. We shall ignore this factor k, taking it as unity. Indeed, we shall ignore a large body of experimental research on gas phase reactions and the theoretical calculations on them. 

Approximate calculation of the integral over 8 in Eq. (34.27) shows that the ejfective electron transmission coefficient for nonadiabatic reactions is equal to... 

As these functions cannot be normalized, it is sufficient here to pose A[2 = 1 and calculate the relative probability densities in each succeeding step. Then, R = 1512 represents the reflection coefficient and T = F 2 the transmission coefficient Assuming that the particle cannot remain trapped within the hairier, the relation... 

Equation (SI) can be verified by calculation of R = B 2 from the simultaneous equations for the coefficients and substitution in Eq. (80). The result represented by Eq. (81) shows that the transmission coefficient decreases as the height V or the thickness t of the barrier increases. 

The use of Eq. (5-10) to evaluate the reaction rate is characterised by the calculation of Hessians for a large number of points along the MEP which are required to locate the free energy maximum and also to evaluate the curvature required for evaluation of the transmission coefficient. In view of the associated computational expense, high-level electronic structure calculations are not feasible and alternative strategies, one of which is to use a semi-empirical method, are usually employed [81]. 

Effect of diagonal-off-diagonal dynamic disorder (D-off-DDD). The polarization fluctuations and the local vibrations give rise to variation of the electron densities in the donor and the acceptor, i.e., they lead to a modulation of the electron wave functions A and B. This leads to a modulation of the overlapping of the electron clouds of the donor and the acceptor and hence to a different transmission coefficient from that calculated in the approximation of constant electron density (ACED). This modulation may change the path of transition on the potential energy surfaces. 

Equations (50) and (51) show that for 0 < 6 < 1 the potential well for the electron near the donor site is more shallow than that in the initial equilibrium configuration. This leads to the fact that the radius of the electron density distribution in the transitional configuration is greater than in the initial equilibrium one (Fig. 3). A similar situation exists for the electron density distribution near the acceptor site. This leads to an increased transmission coefficient as compared to that calculated in the approximation of constant electron density (ACED). 

Fig. 11 The scattering properties of a five branches - four electrodes molecular bridge, (a) Detailed atomic structure of the molecule. A central perylene branch was included to mimic an internal measurement branch, (b) EHMO-ESQC calculated T12(E) transmission coefficient (plain) and predicted T12(E) transmission coefficient (dashed), applying the intramolecular circuit rules discussed for the four molecular fragments given in Fig. 12. The dashed (dotted) line is the Ti2(E) variation for the single molecular branch, as presented in the inset, to show the origin of the destructive interference...

Nuclear frequency factors are calculated directly from the calculated molecular vibrational frequencies and the reorganizational energies, and these, in conjunction with the calculated Hab values lead to values for the electronic transmission coefficient, Kep... 

The calculation of the transmission coefficient for adiabatic electron transfer modeled by the classical Hamiltonian Hajis based on a similar procedure developed for simulations of general chemical reactions in solution. The basic idea is to start the dynamic trajectory from an equilibrium ensemble constrained to the transition state. By following each trajectory until its fate is determined (reactive or nonreactive), it is possible to determine k. A large number of trajectories are needed to sample the ensemble and to provide an accurate value of k. More details... 

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