Minimum in the potential

The examples of ArF (193 nm), KrF (248 nm), XeF (351 nm), KrCl (222 nm), XeCl (308 nm) and XeBr (282 nm) indicate the range of wavelengths from excimer lasers. Because the ground states of these molecules are not totally repulsive but very weakly bound, there is a very shallow minimum in the potential curve, as illustrated in Figure 9.15. In the case of XeF the potential energy minimum is relatively deep, about 1150 cm and supports a few vibrational levels. As a result the laser may be tuned over several transitions. 

The first ab initio smdy of an interaction polarizability was that of O Brien et al. (1973) on a pair of helium atoms. They obtained /0(r) for the range r = 3.5ao through lOao- The experimentally determined value of is negative, which suggests that the incremental mean pair polarizability must be negative around the minimum in the potential curve. 

Plotting U as a function of L (or equivalently, to the end-to-end distance r of the modeled coil) permits us to predict the coil stretching behavior at different values of the parameter et, where t is the relaxation time of the dumbbell (Fig. 10). When et < 0.15, the only minimum in the potential curve is at r = 0 and all the dumbbell configurations are in the coil state. As et increases (to 0.20 in the Fig. 10), a second minimum appears which corresponds to a stretched state. Since the potential barrier (AU) between the two minima can be large compared to kBT, coiled molecules require a very long time, to the order of t exp (AU/kBT), to diffuse by Brownian motion over the barrier to the stretched state at any stage, there will be a distribution of long-lived metastable states with different chain conformations. With further increases in et, the second minimum deepens. The barrier decreases then disappears at et = 0.5. At this critical strain rate denoted by ecs, the transition from the coiled to the stretched state should occur instantaneously. 

Rough quantitative calculations of the energy of interaction of the electron pairs and the phonon can be made with use of the force constants for the bonds19 and the changes in the position of the minimum in the potential functions for a bond, as given by the foregoing values of the change in effective radius. 

The contribution to the classical energy of activation by the normal mode in Figure 5, /ikQ nt, is the energy difference between the minimum in the potential energy curve of the reactants and the intersection point. It is given by equation (53). When contributions from all of the trapping vibrations, j, are included, X is given by equation (22) or a more complex expression like equation (16a) when the force constants differ considerably. 

The minimum in the potential energy surface corresponding to a tricoordinated... 

IR results show that the tricarbonyl complex is not formed. To check this result modelling was performed. It was not possible to reach a minimum in the potential energy surface for the tricarbonyl Nin complex with a nickel dicoordinated to the cluster the structure evolves toward a dicarbonyl complex. Even if a ligand displacement of the silica surface is assumed by adding a third CO molecule as shown by the reaction ... 

The occurrence of a reactive minimum in the potential energy surface of the first excited state makes the ortho photocycloaddition an allowed reaction if that minimum is accessible. 

Repulsion due to overlapping of electron clouds (Born repulsion) predominates at very small distances when the particles come into contact, and so there is a deep minimum in the potential energy curve which is not shown in Figures 8.2-8.4. 

The molecular size of a solvent can be characterized in several ways. One of them is to assign the solvent a molecular diameter, as if its molecules were spherical. From a different aspect, this diameter characterizes the cavity occupied by a solvent molecule in the liquid solvent. From a still further aspect, this is the mean distance between the centers of mass of two adjacent molecules in the liquid. The diameter plays a role in many theories pertaining to the liquid state, not least to those treating solvent molecules as hard spheres, such as the scaled particle theory (SPT, see below). Similar quantities are the collision diameters a of gaseous molecules of the solvent, or the distance characterizing the minimum in the potential energy curve for the interaction of two solvent molecules. The latter quantity may be described, e.g., according to the Lennard-Jones potential (Marcus 1977)... 

Straight self-consistent field calculations have been carried out on the interaction of water with neon and argon.30 Here it is possible to obtain some of the attractive contribution to the intermolecular force since there will be an inductive second-order interaction caused by the large dipole of the water molecule. Such interactions appear at the SCF level and the authors find a minimum in the potential at an O -Ne distance of 3.63 A, with a binding energy of 0.71 kJ mol-1. There is a shallower minimum in the case of argon. Calculations at a similar level of sophistication have been carried out on the H2----He system,31 primarily, however, from the... 

The interatomic distances are primarily determined by the position of the minimum in the potential energy function describing the interactions between the atoms in the crystal. The question is then, what are the sizes of the atoms and ions The extension of electron density for an atom or an ion is not rigorously defined no exact size can be... 

Encounter complex An intermolecular ensemble formed by molecular entities in contact or separated by a distance small compared to the diameter of solvent molecules and surrounded by several shells of solvent molecules the innermost shell is the solvent cage . If one of the species is excited, the excitation usually takes place prior to formation of the encounter complex. During the lifetime of the encounter complex the reactants can collide several times to form colHsion complexes, and then undergo structural and electronic changes. If the interaction between the reactants leads to a minimum in the potential energy and one of the entities is electronically excited, the encounter complex may represent an exciplex or excimer. 

Potential Functions. Near the minimum in the potential-energy curve of a dia-tomie moleeule, the harmonic-oscillator model is usually quite good. Therefore the foree constant h can be calculated from the relation... 

Contact and solvent-separated ion pairs can be distinguished in anionic systems the interionic distance of the former is usually 1-3 A, which increases to 4 or even 7 A in solvent-separated ion pairs [21]. There is apparently no further minimum in the potential energy diagram. The reactivity of solvent-separated ion pairs and free ions in anionic systems are similar, being a few orders of magnitude more reactive than contact ion pairs. In contrast, contact ion pairs in cationic systems are separated by 4-6 A, and therefore resemble the solvent-separated species of anionic systems in terms of structure, as well as their relative reactivity and ability to dissociate. The existence of solvent-separated ion pairs in cationic polymerization is questionable and has not yet been proven spectroscopically. 

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