Potential basin

After having established the present-day hydrocarbon migration characteristics in a basin, evaluation of these characteristics leads to the selection of areas where preferred migration of hydrocarbons takes place, and, consequently, provides insight into the potential basin-wide distribution of hydrocarbons. 

Identification of the potential basins to which any point on a classical trajectory belongs is made with use of the so-called quenching technique due to Stillinger and Weber [18],... 

As described in the preceding section, our model molecule has four local minima [16]. (See Fig. 1.) As the energy is increased from the solid-like phase, trajectories begin to get out of the potential basin of PBP structure and travel around the other basins. We would like to explore how the dynamics of structural change proceeds with time. To this end, we define a simple indicator that can detect the structural transitions with high sensitivity. Let be a position vector from the octh to ith particles. Suppose a triangle plane that is expanded by two... 

First of all we show, in Table I, the accumulated residence time for trajectories to reside in the four possible basins (denoted by t a a = PBP, COCT, 1ST, and SKEW) at three typical energies, — 13.505e and — 11,505e, which are sampled from the coexistence and liquid-like regions, respectively. The residence times have been obtained by applying periodically the so-called quenching technique [18] with which to search for the local minima of the potential basins. 

Figure 16. The entropy Sst relevant to the size of four potential basins in phase space. Say( ) represents entropy in terms of the accumulated residence time 1 (E). The dotted curve without a mark symbol represents a Lindeman index.

This figure also shows the Lindemann index as a reference. Since classical trajectories are practically confined in one of the potential basins below E = —14.0s, 5dy( ) is truncated at this energy. 

Figure 17. Decay of the number of surviving trajectories of the M4 cluster staying in the initial potential basin. The lower curve represents the dynamics constrained to the Eckart subspace under no influence of the gauge field, while the upper one indicates the true dynamics under the influence of the gauge field. Number of the sample trajectories is 5000 and their internal energy is set to / 5 6. for the respective dynamics.

In the case of symmetric exchange reactions one most consider transmission coefficients as shown in Section VI, if there exists a potential basin in the potential surface between two equivalent activated complex sites. 

The existence of the basin leads then to two different activated states for the forward and the reverse reactions, respectively. The assumption is made that, once the system wanders around in the potential basin, its chances of decomposing in the two different ways are independent of the direction from which the system entered the basin. This is equivalent to setting the sum of the transmission coefficients, resulting from the basin in the surface, for the forward and backward reactions equal to unity, i.e., xf -Kr 2= 1. Then... 

Fig. 3.7 Oscillatory behavior of the total ion signal solid line arising from the wave packet confined in the inner potential basin. Broken line the total ion signal based on the Pranck-Condon approximation. (Reprinted with permission from Y. Arasaki et al., J. Chem. Phys. 112, 8871 (2000)).

It is obvious that the lowest excited state in the initial geometry range (of the short OH distance) is tt — tt state. On the other hand, the lowest excited state in the right-hand side potential basin (beyond the potential barrier and of a longer OH distance) is of the Rydberg-state nature. More precisely, the main electronic configuration of the four low-ljdng (adiabatic) excited states beyond the potential barrier are... 

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