Fluctuating potential energy curves

Physisorption or physical adsorption is the mechanism by which hydrogen is stored in the molecular form, that is, without dissociating, on the surface of a solid material. Responsible for the molecular adsorption of H2 are weak dispersive forces, called van der Waals forces, between the gas molecules and the atoms on the surface of the solid. These intermolecular forces derive from the interaction between temporary dipoles which are formed due to the fluctuations in the charge distribution in molecules and atoms. The combination of attractive van der Waals forces and short range repulsive interactions between a gas molecule and an atom on the surface of the adsorbent results in a potential energy curve which can be well described by the Lennard-Jones Eq. (2.1). 

Figure 16.5 shows the variation in nuclear deformation calculated for the fission barrier of 298114 Qf particular interest are the small local fluctuations at small deformation. The minimum of 8 MeV at zero deformation constrains the nucleus to a spherical shape. Spontaneous fission is a very slow process in this situation since it involves tunneling through the 8 MeV barrier. These local fluctuations in the potential energy curve in Figure 16.S result from adding corrections for shell effects to a liquid drop model. The resistance to deformation associated with closed shell nuclei produces much longer half-lives to spontaneous fission than would be expected from calculations based on a standard liquid drop model.

Fig. 5.13 Dynamically fluctuating potential curves of the two low lying states of LiF under control laser. Upper panel the extreme positions reached by the effective potential energy curves f) and V2 R,t). Lower panel time evolution of the dynamical...

Figure 3. Autocorrelation curves (bold continuous lines) of the mean energy fluctuation of total and potential energy for mode m, and their corresponding exponential and damped oscillatory fits (thin dotted lines).

In sum, the free-energy curves of the species involved in the reaction provide a good description of the thermodynamics of methyl formate hydrolysis in an aqueous medium. These curves, which are constructed on the basis of the solute-solvent interaction energies with the solvent fluctuation being chosen as reaction coordinate, respond acceptably to the activation barrier of this process. Also, to obtain reasonable results for this reaction in solution one must take into account a mechanism that includes the assistance of various water molecules. It was also observed that the activation barrier depends appreciably on other factors, in particular, the basis set used to describe the systems, the components of the interaction energy used in the fits of the potential functions, and the procedure employed to construct and move the curves. 

Since there is a short-range order in a liquid the local potential curve U(x) in its nearest surroundings resembles a periodic character (Figure 9.32). Atoms settle down in points of potential energy minimum. In a settled state an atom oscillates with an amplitude significantly smaller than the interatomic distance d. It was found experimentally that the frequency of these fluctuations have the same order as in solids, namely Vg 10 sec and the oscillation period Tq = (1/Vq) 10 sec. In order... 

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