Motion, molecular

Quack M 1995 Molecular infrared spectra and molecular motion J. Mol. Struct. 347 245-66 

Marquardt R and Quack M 1989 Molecular motion under the Influence of a coherent Infrared-laser field infrared Phys. 29 485-501 

This section will concentrate on the motions of atoms within molecules— internal molecular motions —as comprehended by the revolutionary quantum ideas of the 20th century. Necessarily, limitations of space prevent many topics from being treated in the detail they deserve. Some of these are treated in more detail in 

The view of this author is that knowledge of the internal molecular motions, perhaps as outlined in this chapter, is likely to be important in achieving successfiil control, in approaches that make use of coherent light sources and quantum mechanical coherence. However, at this point, opinions on these issues may not be much more than speculation. 

The preceding sections were concerned with the description of molecular motion. An ambitious goal is to proceed further and influence molecular motion. This lofty goal has been at the centrepiece of quantum dynamics in the past decade and is still under intense investigation [182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193 and 194]. Here we will only describe some general concepts and schemes. 

This is a comprehensive survey of algebraic methods for internal molecular motions. 

Neuhauser D and Rabitz H 1993 Paradigms and algorithms for controlling molecular motion Acc. Chem. Res. 26 496 

Gusev A A and Suter U W 1995 Relationship between helium transport and molecular motions in a glassy polycarbonate Macromolecules 28 2582- 4 

The principal dilTerence from liquid-state NMR is that the interactions which are averaged by molecular motion on the NMR timescale in liquids lead, because of their anisotropic nature, to much wider lines in solids. Extra infonnation is, in principle, available but is often masked by the lower resolution. Thus, many of the teclmiques developed for liquid-state NMR are not currently feasible in the solid state. Furthemiore, the increased linewidth and the methods used to achieve high resolution put more demands on the spectrometer. Nevertheless, the field of solid-state NMR is advancing rapidly, with a steady stream of new experiments forthcoming. 

Both infrared and Raman spectroscopy provide infonnation on the vibrational motion of molecules. The teclmiques employed differ, but the underlying molecular motion is the same. A qualitative description of IR and Raman spectroscopies is first presented. Then a slightly more rigorous development will be described. For both IR and Raman spectroscopy, the fiindamental interaction is between a dipole moment and an electromagnetic field. Ultimately, the two 

Conservation laws at a microscopic level of molecular interactions play an important role. In particular, energy as a conserved variable plays a central role in statistical mechanics. Another important concept for equilibrium systems is the law of detailed balance. Molecular motion can be viewed as a sequence of collisions, each of which is akin to a reaction. Most often it is the momentum, energy and angrilar momentum of each of the constituents that is changed during a collision if the molecular structure is altered, one has a chemical reaction. The law of detailed balance implies that, in equilibrium, the number of each reaction in the forward direction is the same as that in the reverse direction i.e. each microscopic reaction is in equilibrium. This is a consequence of the time reversal syimnetry of mechanics. 

The axis labels (p,q,r) are chosen In order not to confuse this axis system with other systems, such as the molecule fixed axes (x,y,z) discussed below, used to describe molecular motion. 

In equilibrium statistical mechanics, one is concerned with the thennodynamic and other macroscopic properties of matter. The aim is to derive these properties from the laws of molecular dynamics and thus create a link between microscopic molecular motion and thennodynamic behaviour. A typical macroscopic system is composed of a large number A of molecules occupying a volume V which is large compared to that occupied by a molecule  

Classically, the nuclei vibrate in die potential V(R), much like two steel balls coimected by a spring which is stretched or compressed and then allowed to vibrate freely. This vibration along the nuclear coordinated is our first example of internal molecular motion. Most of the rest of this section is concerned with different aspects of molecular vibrations in increasingly complicated sittiations. 

Even with these complications due to anliannonicity, tlie vibrating diatomic molecule is a relatively simple mechanical system. In polyatomics, the problem is fiindamentally more complicated with the presence of more than two atoms. The anliannonicity leads to many extremely interestmg effects in tlie internal molecular motion, including the possibility of chaotic dynamics. 

We begm tliis section by looking at the Solomon equations, which are the simplest fomuilation of the essential aspects of relaxation as studied by NMR spectroscopy of today. A more general Redfield theory is introduced in the next section, followed by the discussion of the coimections between the relaxation and molecular motions and of physical mechanisms behind the nuclear relaxation. 

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