Qualitative description

The physical reasons for the benefits of EOR on recovery are discussed in Section 8.7, and the following gives a qualitative description of how the techniques may be applied to manage the production decline period of a field. 

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... 

For homogeneous particles, it represents the number of distances within the particle. For inhomogeneous particles, it has to take into account the different electron density of the volume elements. Thus it represents the number of pairs of difference in electrons separated by the distance r. A qualitative description of shape and internal structure of the... 

It is particularly desirable to use MCSCF or MRCI if the HF wave function yield a poor qualitative description of the system. This can be determined by examining the weight of the HF reference determinant in a single-reference Cl calculation. If the HF determinant weight is less than about 0.9, then it is a poor description of the system, indicating the need for either a multiple-reference calculation or triple and quadruple excitations in a single-reference calculation. 

An area of great interest in the polymer chemistry field is structure-activity relationships. In the simplest form, these can be qualitative descriptions, such as the observation that branched polymers are more biodegradable than straight-chain polymers. Computational simulations are more often directed toward the quantitative prediction of properties, such as the tensile strength of the bulk material. 

In practice, such a fractionation experiment could be carried out by either lowering the temperature or adding a poor solvent. In either case good temperature control during the experiment is important. Note that the addition of a poor solvent converts the system to one containing three components, so it is apparent that the two-component Flory-Huggins model is at best only qualitatively descriptive of the situation. A more accurate description would require a... 

The molecular orbital (MO) approach to the electronic structure of diatomic, and also polyatomic, molecules is not the only one which is used but it lends itself to a fairly qualitative description, which we require here. 

The pyrazole ring is particularly difficult to cleave and, amongst the azoles, pyrazoles together with the 1,2,4-triazoles are the most stable and easiest to work with. This qualitative description of pyrazole stability covers the neutral, anionic and cationic aromatic species. On the other hand, the saturated or partially saturated derivatives can be considered as hydrazine derivatives their ring opening reactions usually involve cleavage of the N—C bond and seldom cleavage of the N—N bond. It should be noted, however, that upon irradiation or electron impact the N—N bond of pyrazoles can be broken. 

Although the Hiickel method has now been supplanted by more complete treatments for theoretical analysis of organic reactions, the pictures of the n orbitals of both linear and cyclic conjugated polyene systems that it provides are correct as to symmetry and the relative energy of the orbitals. In many reactions where the n system is the primary site of reactivity, these orbitals correctly describe the behavior of the systems. For that reason, the reader should develop a familiarity with the qualitative description of the n orbitals of typical linear polyenes and conjugated cyclic hydrocarbons. These orbitals will be the basis for further discussion in Chapters 9 and 11. 

Late Toxicity - Where there is evidence that a chemical can cause cancer, mutagenic effects, teratogenic effects, or delayed injury to vital organs such as the liver or kidney, a qualitative description of the chemical is given. The term implies long-term or chronic effects due to exposure to the chemical. 

The uncertainties in human error rates may be within the stated uncertainty bounds, but such is not demonstrated from sparse experiments. Both the qualitative description of the human interaction logic and the quantitative assessment of those actions rely on the virtually untested judgment of experts. 

From the early work of Taylor [63T01] connecting dislocation behavior to observed viscoplastic shock-compression response, numerous studies have attempted to relate conventional dislocation dynamics models to experimental observations. Theory and observations consistently require unusually large numbers of mobile dislocations. Although qualitatively descriptive, progress to date on dislocation models has not proven to provide quantitative descriptions to the observations in metals. 

Does the method provide a qualitative description of the technical system N N N N Y N N... 

Semi-empirical and ab initio methods differ in the trade-off made between computational cost and accuracy of result. Semi-empirical calculations are relatively inexpensive and provide reasonable qualitative descriptions of molecular systems and fairly accurate quantitative predictions of energies and structures for systems where good parameter sets exist. 

However, it is also impirrtant to emphasize that orbitals are actually mathematical conv enience.s and not physical quantities (despite how real models may make them seem). While the energy, electron density, and optimized geonipctry are physical obseivables, the orbitals are not. In fact, several different sets of orbitals can lead to the same energy. Nevertheless, orbitals are very irseful in qualitative descriptions of bonding and reactivity. 

The simplest description of an excited state is the orbital picture where one electron has been moved from an occupied to an unoccupied orbital, i.e. an S-type determinant as illustrated in Figure 4.1. The lowest level of theory for a qualitative description of excited states is therefore a Cl including only the singly excited determinants, denoted CIS. CIS gives wave functions of roughly HF quality for excited states, since no orbital optimization is involved. For valence excited states, for example those arising from excitations between rr-orbitals in an unsaturated system, this may be a reasonable description. There are, however, normally also quite low-lying states which essentially correspond to a double excitation, and those require at least inclusion of the doubles as well, i.e. CISD. 

The more important physical aspects of the flow of gas -containing systems are analyzed for a uni-phase and a biphase flow. Equations are developed for a qualitative description of these systems. 

For a theoretical consideration of the metal-silicon interaction in silylene complexes, the fragment orbital description proves to be very useful [148], This approach has been extensively used in the organometallic chemistry of carbon and allows a basic understanding of the interrelations also by means of a qualitative description. 

The van der Waals equation gives a correct qualitative description, but it does not do well in quantitatively predicting r, except at low pr. 

The approach discussed above can provide a qualitative description of the effect of external fields on bond-breaking processes. For example, consider the H2 molecule (HA — HB) in the presence of an Li+ ion 3 A away from HB on the A-B axis. To study this problem, we assume that there is no charge migration to the Li location (so that Pc = 0) and that fiAC = pBC = 0 since the Li+ ion is sufficiently far from HA and HB. In this case, we can write the H matrix as... 

Needless to remind that Equation (2.29) is a very approximate expression which can be expected to provide only a qualitative description and not a quantitative fit to actual promotional kinetic data. 

This qualitative description of the interactions in the metal is compatible with quantum mechanical treatments which have been given the problem,6 and it leads to an understanding of such properties as the ratio of about 1.5 of crystal energy of alkali metals to bond energy of their diatomic molecules (the increase being the contribution of the resonance energy), and the increase in interatomic distance by about 15 percent from the diatomic molecule to the crystal. 

With this qualitative description for guidance, the underlying physical processes can now be examined in greater detail. 

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