Deep potential energy

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

L. Sun, K. Song, and W. L. Hase, A Sn2 Reaction that Avoids its Deep Potential Energy Minimum, Science, 2002, 296, 875. 

Theoretical studies of dication 92 have shown it to reside in a deep potential energy well, with a gas-phase barrier to deprotonation estimated to be about 42 kcal/mol (MP4/6-311G level).45... 

The classical trimethylene diradical model for cyclopropane stereomutations featured a deep potential energy well for the intermediate and internal rotations about 10 times faster than ring closure Improved experimental estimates for the heat of formation for the singlet trimethylene diradical, and for the energy required for the isomerizations of l,2-d2-cyclopropanes, place the diradical in an extremely shallow energy well, one on the order of only 1 kcal moP deep The classical model can never accommodate k + k. k i ratios less than 2, and several substituted cyclopropanes exhibit such ratios. Thus the model, at least in its original form, seems thermochemically flawed and unable to accommodate experimental data for some systems. 

Again, it appears as if 56 lies in a deep potential energy well (see Scheme 5.6). The computed barrier (CCSD(T)/cc-pVQZ//M06-2x/cc-pVDZ) for the [1,2]-H shift to form benzaldehyde 57 is 28.8 kcal mol and the alternative exit channel leading to benzene and CO has an even higher barrier of 55.0 kcal mol . ... 

Carpenter and Borden made two important conclusions that raise significant concerns about the traditional physical organic notions of reaction mechanisms. First, nonstatistical dynamics can occur even when intermediates exist in relatively deep potential energy wells, not just on flat caldera-like surfaces. Second, multiple products can be formed from crossing a single TS. The steepest descent path from a TS can only link to a single product, but reactions can follow nonsteepest descent paths that reach different products. 

Once the H atoms have reached the bottom of the deep potential energy vell... 

After the disjoining pressure of the double layer under the effect of hydrodynamic pressing forces (see Figs. 10.7 and 10.8) has been overcome, a subsequent detachment of the particle displaced to the rear pole of a bubble is hindered only at a sufficiently deep potential energy minimum. Even when the bubble is charged opposite to the particle, this minimum may be insufficiently deep if the a-film is thick enough (see Appendix lOD). The question about the depth of the primary minimum is very complex (cf Derjaguin Kudryavtseva 1964, Martynov Muller 1972, Overbeek 1977). 

HI of, HI ay, and so on, inside the bracket of Eq. (2.9) can be safely neglected because the ratio H a is much smaller than unity. A schematic representation of the van der Waals interaction between two approaching particles is shown in Figure 2.3. It is the exceedingly deep potential energy well observed at small distance of separation between two interactive particles that is responsible for the loss of colloidal stability. The attractive van der Waals force decreases rapidly with increasing distance of separation. 

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