Constant Correlations

Studies by the group directed by Mayoral have been limited to Diels-Alder reactions of type A. When water was not included, the rate constants correlate with the solvent hydrogen-bond-donating capacity Upon inclusion of water the solvophobidty parameter, Sp, contributed significantly in... 

The solvophobic model has been used to deduce a functional form for a Henry s constant correlation based on molecular coimectivity index and polarizabiHty (42). Accurate predictions are reported over a span of seven log units in Henry s constant. A reHable solvophobic model of aqueous solubiHty has also been reported (45,46). 

Various Langmiiir-Hinshelwood mechanisms were assumed. GO and GO2 were assumed to adsorb on one kind of active site, si, and H2 and H2O on another kind, s2. The H2 adsorbed with dissociation and all participants were assumed to be in adsorptive equilibrium. Some 48 possible controlling mechanisms were examined, each with 7 empirical constants. Variance analysis of the experimental data reduced the number to three possibilities. The rate equations of the three reactions are stated for the mechanisms finally adopted, with the constants correlated by the Arrhenius equation. 

Calculations have been done at the STO-3G and 4-3IG levels, and the resulting substituent constants correlate well with empirical values derived from ground-state structural parameters, such as C-NMR chemical shifts and IR absorption frequencies. 

Base hydrolysis is much faster, at any significant hydroxide ion concentration, than aquation but, as is apparent from Table I the two reactions exhibit comparable ranges of rate constants. Indeed the two sets of rate constants correlate very well, over more than nine orders of magnitude, with a slope close to unity for a correlation plot. 

In a qualitative sense, the rate constants correlate with the change in degree of steric hindrance provided by the increasing bulk of the substituents. We can relate those changes,... 

These studies show that when the accumulation of HOCs occurs solely by respiration or dermal absorption, BMO and SPMD rate constants correlated very well, but that concentrations in SPMDs are often higher than those in BMOs. However, good correlations between the fingerprints or patterns of HOC residues in BMO tissues and SPMDs would not be expected to hold, when diet plays a major role in the uptake of compounds with high TfowS (see Eq. 7.5). For example, Peven et al. (1996) compared the accumulation of organic contaminants by transplanted... 

Intrinsic Binding Constants, Correlation Functions, and Corresponding Free Energies (in kcal/mol) for Various Carboxylic Acids ... 

It has been found that the chemical shift of the benzylidene carbon, Sct, in ring-substituted benzaldoximes (Scheme 2) correlates well with Hammett a constants. On the other hand, it is known that the chemical shift of that atom in the NMR spectra of benzaldoximes depends mainly on the substituents inductive effect and its resonance effect is of reduced importance. Multiparameter correlations of Scr with the inductive and resonance substituents constants are of better quality. It is known that the chemical shifts of para-substituted benzaldoximes are linearly dependent on Hammett a constants. Correlations between the NMR chemical shifts of the oximino oxygen and a, a and aj substituent constants for substituted benzaldoximes are poor. These results show that coplanarity of Ar—CH=NOH creates difficulties in transmission of the substituents effect, especially the resonance effect, to the CH=NOH group. ... 

The expectation that the k rate constants correlate with thermochemical bond-energy data in this radical process has indeed found quantitative support through the determination of the activation parameters, on running the H-abstraction experiments by BTNO from selected substrates at various temperatures. From the Arrhenius equation (logfe = log A — Ei /RT), log A and were obtained (Table 7). 

For a series of /lara-substituted A-acetoxy-A-butoxybenzamides (104), rate constants correlated with Hammett a+ with a /O-value of —1.452, is also consistent with nitre-... 

In addition to these limited procedures a number of experimental methods (vibrational spectroscopy, dipole moment measurements, electron diffraction, NMR, etc.) have been employed to determine the relative stabilities of these complexes.11,23 Intense effort has been directed towards establishing some kind of correlation between NMR parameters and stability of the borane complexes. The chemical shifts alone rarely show good correlation. However, complexation shifts (the chemical shift difference between the free and complexed borane or ligand) and various spin-spin coupling constants correlate better with calorimetric data, especially for ligands or boranes belonging to structurally similar series (Table 2).10,24... 

Original model (with Ergun constants correlation of [43]). 

According to eq. (3.15), the magnitude of one-bond car bon-13 —nitrogen-15 coupling constants correlates with the product of s characters of the hybrid orbitals overlapping in the C-N bond [135] ... 

The failure of the empirical NMR coupling constant correlation is actually not very surprising. These correlations have a reputation of breaking down in highly strained hydrocarbons24, of which [l.l.l]propellane surely is a prime example, and do not do particularly well even in bicyclo[l. 1.0]butane. 

As with arene-amine radical ion pairs, the ion pairs formed between ketones and amines can also suffer a-deprotona-tion. When triplet benzophenone is intercepted by amino acids, the aminium cation radical can be detected at acidic pH, but only the radical formed by aminium deprotonation is detectable in base (178). In the interaction of thioxanthone with trialky lamines, the triplet quenching rate constant correlates with amine oxidation potential, implicating rate determining radical ion pair formation which can also be observed spectroscopically. That the efficiency of electron exchange controls the overall reaction efficiency is consistent with the absence of an appreciable isotope effect when t-butylamine is used as an electron donor (179). 

Note that in Table 2.5 all alkyl groups have small negative a values. It has been argued that these values, which often do not give good rate and equilibrium constant correlations, should properly be zero for all alkyl groups. For a review see note 4(a), p. 60. But also S. Fliszar, J. Amer. Chem. Sac., 94, 1068 (1972). 

Gorman, WG and Hall, GD., Dielectric constant correlations with solubility paramdteffeprm. 

Kato, Y. and Ohuchi, T. Studies on solubilizing agents IV. Dielectric constant correlations with drug solubility in mixtures of glycols and their derivatives with wafi kugaku Zashi, 92, 25263,1972. 

Mg(DOPMR)2-H2(DOP) [Mg(DOP )+-(R)2-[H2(DOP )] - Solvent acetone, CH2C12, DMF or alkyl-acetates X, = 532 or 588 nm the charge-recombination rate constant correlates with the reverse of the solvent relaxation times [196]... 

The e j rate constants correlate better with normal o- values derived from electrophilic substitution than with a para values obtained from data of nucleophilic reactions. This is not surprising in view of the fact that the e]fq reactions constitute an interaction of an electron with the 77-orbitals of the ring, as in electrophilic substitution, rather than with effects on electron distribution and polarizability of a certain substituent. 

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