Larger Molecules

An electrocyclic reaction, on the other hand, can be depicted using a VB-picture, but its stereochemistry cannot be deduced from such a treatment (Fig. 3.2). 

Generally, a VB-treatment is used to teach chemistry (because it is more succinct and less complicated than MO-theory) until cases (like electro-cyclic reactions) are treated that cannot be understood properly within simple VB-theory. This need not be the case, but is usually a good compromise for teaching chemical bonding and reactivity effectively. 

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The estimation of surface area from solution adsorption is subject to many of the same considerations as in the case of gas adsorption discussed in Chapter XVII, but with the added complication that larger molecules are involved. 

The resonance vector analysis has been used to explore all of the questions raised above on the fate of the polyad numbers in larger molecules, the most thoroughly investigated case so far probably being C2FI2- This molecule has been very extensively probed by absorption as well as stimulated emission pumping and dispersed fluorescence teclmiques [, 53, 70 and 71], the experimental spectra have been analysed in... 

There are also approaches [, and M] to control that have had marked success and which do not rely on quantum mechanical coherence. These approaches typically rely explicitly on a knowledge of the internal molecular dynamics, both in the design of the experiment and in the achievement of control. So far, these approaches have exploited only implicitly the very simplest types of bifiircation phenomena, such as the transition from local to nonnal stretch modes. If fiittlier success is achieved along these lines m larger molecules, it seems likely that deliberate knowledge and exploitation of more complicated bifiircation phenomena will be a matter of necessity. 

This section has focused mainly on the internal dynamics of small molecules, where a coherent picture of the detailed mtemal motion has been emerging from intense efforts of many theoretical and experimental workers. A natural question is whether these kinds of issues will be important m the dynamics of larger molecules, and whether their investigation at the same level of detail will be profitable or tractable. 

Larger molecules generally caimot be studied in quite the same way, as an electric discharge merely breaks them up into smaller molecules or atoms. In such a case excited states are usually produced by optical excitation using light of the same or higher energy. Many modem fluorimeters are made with two... 

In this case, the scattering serves as a means for counting the number of molecules (or particles, or objects) per unit volume (N/V). It is seen that the polarizability, a, will be greater for larger molecules, which will scatter more. If we take the Clausius-Mosotti equation [16] ... 

With relatively simple spectra, it is usually possible to extract the individual coupling constants by inspection, and to pair them by size in order to discover what atoms they coimect. However, the spectra of larger molecules present more of a challenge. The multiplets may overlap or be obscured by the presence of several unequal but similarly sized couplings. Also, if any chiral centres are present, then the two hydrogens in a... 

The reaction of an atom with a diatomic molecule is the prototype of a chemical reaction. As the dynamics of a number of atom-diatom reactions are being understood in detail, attention is now being turned to the study of the dynamics of reactions involving larger molecules. The reaction of Cl atoms with small aliphatic hydrocarbons is an example of the type of polyatomic reactions which are now being studied [M, 72, 73]. 

Related results of promotion (catalysis) and inliibition of stereonuitation by vibrational excitation have also been obtained for the much larger molecule, aniline-NHD (CgH NHD), which shows short-time chirality and stereonuitation [104. 105]. This kind of study opens the way to a new look at kinetics, which shows coherent and mode-selective dynamics, even in the absence of coherent external fields. The possibility of enforcing coherent dynamics by fields ( coherent control ) is discussed in chapter A3.13. 

Eqnation (B3.4.1) is general and applies to both scattering and bonnd state spectroscopy. Scattering will be considered first. For shnplicity, the discnssion rises the collinear model for the A -l- BC AB -l- C reaction (i.e. assuming all particles lie on a line). This model is easy to visualize and embodies most elements of tlnee-dimensional (3D) scattering of larger molecules. 

The mean field teclmique is one of the most robust and simple methods used to handle larger molecules in gas and liquid enviromnents [M, 134. 135 and 136]. The basic premise of all mean-field methods is that the fiill wavefiinction represents N very weakly coupled modes (2 ) and can be approximated as... 

The mathematical form of the PEF is in almost every case a compromise between speed and accuracy. As computer power continually increases, ideally following Moore s Law, and the cost/performance ratio is getting better, one might think that there is no longer a need to sacrifice accuracy to save computational time. This is not really true, because in direct proportion to the CPU speed is the rise in the scientists interest in calculating larger and larger molecules (in fact, their interest always rises faster than the CPU speed). 

For a larger molecule wdth V nuclei and n electrons, we unite... 

SEMIEMPIRICAL CALCULATIONS ON LARGER MOLECULES The spin eigenfunctions are orthogonal... 

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