TURN, description

As we shall see, in molecules as well as atoms, the interplay between the quantum description of the internal motions and the corresponding classical analogue is a constant theme. However, when referring to the internal motions of molecules, we will be speaking, loosely, of the motion of the atoms in the molecule, rather than of the fiindamental constituents, the electrons and nuclei. This is an extremely fundamental point to which we now turn. 

A charge transfer contribution is often identified in perturbative descriptions of intennolecular forces. This, however, is not a new effect but a part of the short-range induction energy. It is possible to separate the charge transfer part from the rest of the induction energy [80]. It turns out to be relatively small and often negligible. Stone [28] has explained clearly how charge transfer has often been a source of confusion and error. 

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

We now turn to a mean-field description of these models, which in the language of the binary alloy is the Bragg-Williams approximation and is equivalent to the Ciirie-Weiss approxunation for the Ising model. Botli these approximations are closely related to the van der Waals description of a one-component fluid, and lead to the same classical critical exponents a = 0, (3 = 1/2, 8 = 3 and y = 1. 

Instead of devoting more space to copolymers, we turn next to stereoregular polymers, in which many of the descriptions of microstructure developed in Sec. 7.6 can also find application. 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

Although the above description has concentrated on separation from a smooth surface, separation also occurs at sharp edges. Where separation is undesirable for a process reason, it can often be eliminated by redirecting the flow using turning vanes, ie, forcing it to hug the surface. 

Definiteness. Adequate description or definiteness requites that the patent claims provide an outline of those elements which are integral to the appHcation s invention. In turn, the specification acts as a dictionary wherein the reader can interpret and understand the elements in the patent claims. Complementary to the requirement of definiteness is the requirement that the appHcation must disclose the entire invention. The appHcant cannot make a claim of right to the invention where essential elements of the invention are not disclosed in the patent. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

The description of the physical characteristics of ventilation noise is based on more reliable knowledge than the description of the human effect. Misconceptions about the levels and frequency characteristics of ventilation noise are still common. This in turn has sometimes led to wrong suggestions about the measures that should be taken in order to eliminate the effects of a ventilation noise exposure. 

It turns out that a rather simple description of this nonlinear relaxation in terms of a single relaxation time,, depending on the final average chain length Loo, is suggested by a scaling plot of L t) for different L o, as shown in Fig. 18 for an initial exponential MWD. It is evident from Fig. 18 that the response curves, L o — L t), for different L o may be collapsed onto a single master curve, 1 - L t)lLoo = /(V Loo) measured in units of a... 

A basis set is the mathematical description of the orbitals within a system (which in turn combine to approximate the total electronic wavefunction) used to perform the theoretical calculation. Larger basis sets more accurately approximate the orbitals by imposing fewer restrictions on the locations of the electrons in space. In the true quantum mechanical picture, electrons have a finite probability of existing anywhere in space this limit corresponds to the infinite basis set expansion in the chart we looked at previously. 

The pyrites and marcasite structures can be thought of as containing 82 units though the variability of the interatomic distance and other properties suggest substantial deviation from a purely ionic description. Numerous higher polysulfides S have been characterized, particularly for the more electropositive elements Na, K, Ba, etc. They are yellow at room temperature, turn dark red on being heated, and may be thought of as salts of the polysulfanes... 

---