Seleetion rules

Eleetron energy-loss speetroseopy is used for obtaining speetroseopie data as a eonvenient substitute for optieal speetroseopy, and, taking advantage of diflferenees in seleetion rules, as an adjimet to optieal speetroseopy. In addition, eleetron speetroseopy has many applieations to ehemieal and stnietural analysis of samples in the gas phase, in the solid phase, and at the solid-gas interfaee. 

B. Seleetion Rules on the Vibrational Quantum Number in the Harmonie Approximation... 

The derivation of these seleetion rules proeeeds as before, with the following additional eonsiderations. The transition dipole moment s itrans eomponents along the lab-fixed axes must be related to its moleeule-fixed eoordinates (that are determined by the nature of the vibrational transition as diseussed above). This transformation, as given in Zare s text, reads as follows ... 

The produet of these 3-j symbols is nonvanishing only under eertain eonditions that provide the rotational seleetion rules applieable to vibrational lines of symmetrie and spherieal top moleeules. 

These seleetion rules are derived by realizing that in addition to k = 1, one has ... 

The absorption that is "missing" from the figure below lying slightly below 2900 em is the Q-branch transition for whieh E = E it is absent beeause the seleetion rules forbid it. 

Beyond sueh eleetronie symmetry analysis, it is also possible to derive vibrational and rotational seleetion rules for eleetronie transitions that are El allowed. As was done in the vibrational speetroseopy ease, it is eonventional to expand if (R) in a power series about the equilibrium geometry of the initial eleetronie state (sinee this geometry is more eharaeteristie of the moleeular strueture prior to photon absorption) ... 

This expression is appropriate for an ensemble of moleeules that ean be in various initial states i with probabilities pi. The eorresponding result for transitions that originate in a partieular state (i) but end up in any of the "allowed" (by energy and seleetion rules) final states reads ... 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

In eonsequenee, the symmetry seleetion rules on (with the corresponding values) are... 

The seleetion rules derived above pertained to electronic transitions, where the positions of the nuelei were fixed in space. Now a change of the vibrational states of the molecule will be eonsidered, while the electronic state is assumed to be unchanged. The vibrations of a molecule are related to its vibrational levels (each of them corresponding to an irreducible representation) and the eorresponding vibrational wave functions, and the IR spectrum results from transitions between sueh levels. Fig. C.6 shows the energy levels of three normal modes. 

The resulting set of lines together forms a distinctive band envelope, whieh depends on the symmetry of the vibration concerned because the rotational seleetion rules are different for different vibrational symmetries. In some cases, the individual lines making up the envelope can be resolved (Section 7.3.2). 

In the previous chapters, IR spectroscopy of polymers was discussed. In this ehap-ter, a complementary teehnique that also measures the vibrational energy levels, Raman spectroseopy, will be examined. As discussed in Chapter 2, there is a fundamental differenee in the IR and Raman techniques. IR spectroscopy depends on a change in the permanent dipole moment of the chemieal bond or molecule with the vibrational normal mode in order to produce absorption. Raman spectroscopy, on the other hand, depends on a change in the induced dipole moment or polarization to produce Raman scattering. This difference in the physical nature of the seleetion rules may seem minor, but it plays a major role in the manner in which the two vibrational techniques are used for the study of polymers. 

The seleetion of the eontrol IC is very important. If the wrong ehoiee is made, it eould result in supply instability and waste valuable time. The designer should understand the subtle differenee between the various forms of eontrol. In general, forward-mode topologies usually have voltage-mode eontrollers, and boost-mode topologies usually have eurrent-mode eontrol. This is not a roek-solid rule sinee every method of eontrol ean be used for every topology, with mixed results. 

The seleeted seale-up rule is applied to determine the agitator speed N2 from the equation ... 

The mobile phase is usually seleeted by trial-and-error guided by prior experience or by performing preliminary analytieal separations of the sample in a saturated ehamber. PLC separations will be inferior to analytical TLC separations using the same mobile phase beeause of the thieker layer, larger particle size, and overloaded sample eonditions used for PLC. A good general rule is that analytical TLC should achieve separations with least 0.1 Rf value difference if the PLC separations are to be adequate with the transferred mobile phase. Isocratic development is usually used, but gradient development has been applied in certain situations for increased resolution. 

Seleet and orient the minimum number of eonstitutional units necessary to represent the polymer strueture [1] where there is a ehoiee, seleetion is based on the seniority rules of [1]. Struetures are written to be read from left to right. 

The solvent used is also important and the sueeess of reasolutiar depends much on the proper selection of the solvent. There is no hard and fast rule in the seleetion of the solvent. Generally water, alcohols, acetone and ethyl oxalates have been chosen as solvents. In some cases the seleetion of the solvent becomes very difficult and the diastereomers are then separated by several fi actional... 

Walas has provided handy rules of thumb to foeus equipment seleetion and design on reasonable eommereial eapabilities. The artiele is published here unehanged. 

In the United States, most Seleet grades are deseribed by names (Superior, Prime) or by letters and combinations of letters (B BTR, C BTR, D) depending on the species and grading rules under whieh the timber is graded. The specifications... 

Rule 8. Decreasing conformational states of a template inereases seleetivity. 

Supervisors may have reasons for observing certain employees. For example, repeat offense is an example of a area where a job would be seleeted because of individual needs. The supervisor should select the repeat offender for tegular platmed safety observations. Such observations can show reasons why some employees have more accidents than others. Another area selected for observation includes chronically unsafe employees. These may be workers who take uimecessaiy chances, violate safety rules, and develop improper working methods. Workers suspected of being physically or mentally incapable of safe work may also fit into the area of individual needs. 

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