Transition probabilities, extended sampling

A consideration of the transition probabilities allows us to prove that microscopic reversibility holds, and that canonical ensemble averages are generated. This approach has greatly extended the range of simulations that can be perfonned. An early example was the preferential sampling of molecules near solutes [77], but more recently, as we shall see, polymer simulations have been greatly accelerated by tiiis method. 

Langer and Doltsinis [45] have calculated nonadiabatic surface hopping trajectories for 10 different initial configurations sampled from a ground state AIMD runs at 100 K. They later extended their study to a total of 16 trajectories [41, 42], From a mono-exponential fit to the 5) population a lifetime of 1.3 ps is obtained (see Table 10-1 the average transition probability and its standard deviation leads to the interval [0.6...1.1...3.5] ps. Thus methylation appears to result in a slightly longer excited state lifetime. 

We shall now discuss a model we shall use for the description of optical transitions in amorphous semiconductors. The basic difference compared to crystals is the non-conservation of the k-vector. This is due to the change of the character of the wave-functions, some of which become localized over a certain volume V(E) rather than extended over the whole volume of the sample as in crystals. When the wavefunctions are localized, the transition probabilities between states localized at different sites are reduced by a factor depending on the overlap of the wavefunctions of the initial and final states. The effects of conelation were considered by Stem (1971), Dow and Hopfield (1971) and Sak (1972). We shall neglect the correlation and consider only transitions between states of which one is localized and the other extended, or of which both are weakly localized so that the over-... 

The phenomenon of vacancy ordering is often observed in the transition metal carbides. " While in the group 4 carbides the tendency towards carbon ordering is weak and can be observed only by extended annealing of 5-TCi samples at comparably low temperatures (<800 °C), the tendency becomes more pronounced in the group 5 and 6 carbides. By the ordering of vacancies at low temperatures, even the metal atom positions are affected. In some cases, however, such ordered structures probably cannot be regarded as equilibrium phases nor can an impurity influence on the stabihty of the structures be ruled out. 

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