Equi-energy curves

The qualitative interpretation of the ISM method can be illustrated by Figure 11.18. Figure 11.18a shows the equi-energy curves that pertain to the transfer of H between methyl and methane and ethyl and ethane. The curves nearly overlap, but the slightly weaker C-H bond in ethane is characterized by a smaller force constant and leads to a somewhat smaller barrier. The calculated barriers are 14.6 and 14.3 kcal/mol, respectively. The methyl-ethane reaction, shown in Figure 11.18b, is exothermic and there is a much more substantial shift in the curves. The calculated barrier is 12.4 kcal, compared with the experimental value of 11.5. Thus, the calculation moves the barriers in the right direction, although it does not reproduce the entire effect that is observed experimentally. 

In order to theoretically predict the MSAPCA, it is necessary to pinpoint the lowest minimum in the Gibbs energy curve. Mathematically, to identify the lowest minimum among multiple minima is possible only by checking aU minima one by one. Therefore, no analytical way exists to immediately recognize the most stable equi-hbrium state of a wetting system. Nevertheless, a useful approach... 

Fig. 14 Absolute truncation error of the reduced potential energy of the Ewald summation as a function of a/(s) = exp(s-2)/s-2 at a = 0.3R- and b a at s = 3.0 from simulation with i cut and cut evaluated according to Eqs. 26 and 27, respectively, and the same equi-librium configuration of System IV as in Fig. 12 (symbols). The corresponding estimated truncation errors of the real-space and reciprocal-space terms of the reduced potential energy according to Eqs. 21 and 22. respectively (solid curves), and the values of cut are also shown. In a, the function g(s) = o.4/(s) is given (dotted line)...

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