Energy transfer probability density

INTERMOEECUEAR ENERGY TRANSFER PROBABILITY DENSITY FUNCTION... 

One of the most important and elusive quantities in molecular djmamics calculations of reacting system is the intermolecular energy transfer probability density function P(E ,E) which is used in master equation calculations of reaction rate coefficients [1]. 

Trajectory calculations together with ab initio inter and intramolecular potential are efficient and productive in producing detailed information on the mechanism of binary and termoleeular collisions and provide numerical values of collisional energy transfer quantities such as the average energy transferred in a collision, the average lifetime of binary and temaiy collision complex, the energy transfer probability density function, supercollisions and the second virial coefficient. 

A representation of the cascading process is shown in Figure 2 for the hypothetical stepladder situation in which only constant AE increments are allowed. More complex transition probabihty models utilize statistical descriptions of the energy transfer probability density [P(AE)]. For such cases individual collisions probe a range of AE values, but the average energy transfer increment ( ) remains constant. 

Moreover, it has to be kept in mind that bond valence maps (or more precisely, bond valence sum mismatch maps) use bond valence units scale rather than an energy scale, and attempts to link energy or probability density to the bond valence mismatch were difficult to achieve in a general transferable way as the calculation of effective bond valence mismatches according to Eq. 1 requires scaling between bond valence terms and cation-cation (or anion-anion) repulsions or (for open structures) to discriminate between sites of identical bond valence sum based on the degree to which the equal valence rule is fulfilled. 

Recently, we have studied the effect of the surface density of states on the charge-transfer probability, in the case where the surface possesses localized states created by surface perturbations or the presence of adatoms. For the tight-binding linear chain these perturbations or adatoms are taken into account by changing the electronic energy of the end atom of the chain to a, which differs from the energy a of the other atoms in the chain. This difference can lead to the formation of a localized surface state, whose energy is... 

There is a probability N 8R do for a collision specified by energy transfer T to the translational motion of the struck atom. N is the volume density of atoms, and one approximation for do is given by Equation 9. If a collision occurs, the particle has a probability F(x — 5x, E — T,ri ) of obtaining a total projected range, x. Therefore, N 5R do F(x — 5x, E — T,r ) is the contribution from this specified collision to the total probability for the projected range, x. When this term space is integrated over all collisions, the total contribution becomes ... 

It is clear from eq. (15) that a modification of the density of phonon states in nanocrystals influences the efficiency of energy transfer. Because the energy transfer rate depends also on the distance between the donor and acceptor, the transfer in very small nanocrystals is restricted. This restriction may be understood based on the fact that the hopping length and the transfer probability are restricted for a donor to find a matching acceptor in the neighborhood of the nanoparticle. 

This would seem to imply that the Kassel model for energy transfer is not too bad for this complex molecule. If we correct the probable values of Table XI. 2 to the high frequency factor and the lower gas density at 450 C, we obtain a value of about 13 oscillators, also in agreement. 

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