Structure effects quantitative treatment

QEUC, see Quasi-molecular enlarged unit cell Quadricyclene, 20 323 valence isomerization of, 20 304 Quadricyclene, isomerization of, 24 146, 148 Quadrupolar interactions, 33 205-209 Quadrupole splitting, 26 126, 134, 140-142 Qualitative studies of simple reactions, 32 116 Quantitative treatment, structure effects, 29 155-162... 

The quantitative treatment of the electron-transfer paradigm in Scheme l by FERET (equation (104)) is restricted to the comparative study of a series of structurally related donors (or acceptors). Under these conditions, the reactivity differences due to electronic properties inherent to the donor (or acceptor) are the dominant factors in the charge-transfer assessment, and any differences due to steric effects are considered minor. Such a situation is sufficient to demonstrate the viability of the electron-transfer paradigm to a specific type of donor acceptor behavior (e.g. aromatic substitution, olefin addition, etc.). However, a more general consideration requires that any steric effect be directly addressed. 

The old and lasting problem of heterogeneous catalysis, the mechanism of alkene hydrogenation, has also been approached from the viewpoint of structure effects on rate. In 1925, Lebedev and co-workers (80) had already noted that the velocity of the hydrogenation of the C=C bond decreases with the number of substituents on both carbon atoms. The same conclusion can be drawn from the narrower series of alkenes studied by Schuster (8J) (series 52 in Table IV). Recently authors have tried to analyze this influence of substituents in a more detailed way, in order to find out whether the change in rate is caused by polar or steric effects and whether the substituents affect mostly the adsorptivity of the unsaturated compounds or the reaetivity of the adsorbed species. Linear relationships have been used for quantitative treatment. 

A quantitative treatment of the Jahn-Teller effect is more challenging (46). A major issue is that many theoretical models explicitly or implicitly assume the Bom—Oppenheimer approximation which, for octahedral Cu(II) systems in the vibronic coupling regime, cannot be correct (46,51). Hitchman and co-workers solved the vibronic Hamiltonian in order to model the temperature dependence of the molecular structure and the attendant spectroscopic properties, notably EPR spectra (52). Others, including us, take a more simphstic approach (53,54) but, in either case, a similar Mexican hat potential energy description of the principal features of the Jahn-Teller effect in homoleptic Cu(II) complexes emerges (Fig. 13). 

Our objective in this work is to present surveys of the methods now available for the quantitative treatment of steric effects in the design of bioactive molecules. Commonly, this consists in the modification of a lead compound by structural changes which result in a set of bioactive substances. The bioactivity is determined and then related to structure. This is generally carried out by means of multiple linear regression analysis using a correlation equation of the type... 

Structure-property relationships for metal-free organic magnetic materials, 45, 93 Substitution, aromatic, a quantitative treatment of directive effects in, 1, 35 Substitution, nueleophilic vinylic, 7, 1... 

We have indicated that interference and reinforcement effects depend both on the positions of atoms in a structure and the number of electrons associated with each atom. A quantitative treatment of these effects makes use of the important structure-factor equation which represents the addition of waves (sine and cosine functions) from each atom within a unit cell. All waves are of the same lengths but amplitudes and phases may differ. The structure-factor equation, to be given here but not derived, deals with the relative intensities of the reflected rays rather than with the absolute amplitudes or intensities of reflected rays (which depend on the amplitudes and intensities of the x-rays used as a source). The relative intensity, /, of a ray of indices hkl, from a set of planes hkl, is... 

For the quantitative treatment of substituent effects in such reactions, Brown proposed (Brown and Okamoto, 1957) a new Hammett-type structure-reactivity relationship, the Brown equation (1), in terms of substituent constant instead of a in the original Hammett equation. 

When the major catalytic surface is in the interior of a solid particle, the resistance to transport of mass and energy from the external surface to the interior can have a significant effect on the global rate of reaction. Quantitative treatment of this problem is the objective in Chap. 11. It is sufficient here to note that this treatment rests on a geometric model for the extent and distribution of void spaces within the complex porous structure of the particle. It would be best to know the size and shape of each void space in the particle. In the absence of this information the parameters in the model should be evaluated from reliable and readily obtainable geometric properties. In addition to the surface area, three other properties fall into this classification void volume, the density of the solid material in the particle, and the distribution of void volume according to void size (pore-volume distribution). The methods of measurement of these four properties are considered in Secs. 8-5 to 8-7. 

Taft RW, Murray JS. Some effects of molecular structure on hydrogen-bonding interactions. some macroscopic and microscopic views from experimental and theoretical results. In Politzer P, Murray JS, eds. Quantitative Treatments of Solute/Solvent Interactions. Amsterdam Elsevier, 1994 55-82. 

Qualitative explanations advanced prior to 1952 were reviewed by Stuart in his book of that date. Le F vre et al. (1956) attempted an a priori quantitative treatment of anomalous anisotropy in centro-symmetric non-polar structures along lines used previously for atomic polarizations (Le Fevre and Rao, 1954, 1955). The expression reached for the mK of a CX4 molecule involved link moments pcx, c—x and i x, stretching and bending force constants, effective charges on atoms, and the rates of change of b% x and with elongation or contraction... 

---