Linear scaling relationships correlate

Linear scaling relationships correlate the heat of adsorption of molecules with the heat of adsorption of a descriptor, generally of the heteroatom of the molecule. Abild-Pedersen et al. [41] observed that the heat of adsorption of AH fragments correlates... 

It is clear from perusal of the data in Table VI that there is no overall general correlation between pJCR and /c0H or kH2o e.g., although the 2-benzyl-5-nitroquinolinium and 9-phenyl-10-methylacridinium cations have similar pKR values, the values of k0H for these two cations differ by a factor of 105. However, within series of very closely structurally related cations, useful linear rate-equilibrium correlations do exist.39 Thus, Fig. 4 displays linear relationships between log k0H and pXR+ for quinolinium and isoquinolinium cations. The correlation lines in this figure are given by Eqs. (30) and (31). These correlations cover six units of the p KR + scale and a... 

The effects of substituents on the symmetrically disubstituted diarylethyl tosylates, [27(X = Y)j, can be described accurately in terms of the Y-T relationship with p = -4.44 and r = 0.53. The Y-T plot against the Y-T o scale with an appropriate r of 0.53 gives an excellent linear correlation for the whole set of substituents, indicating a uniform mechanism for all of them. When Y X, the overall solvolysis rate constant corresponds to the sum of the rate constants, + kj, and hence k cannot be employed directly in the Y-T analysis. The acetolysis of monosubstituted diphenylethyl tosylates gave a non-linear Y-T correlation, which is ascribed to a competitive X-substituted aryl-assisted pathway and the phenyl-assisted k pathway. By application of an iterative non-linear least-squares method to (9), where the terms k and ks are now replaced by k and k, respectively, the substituent effect on k can be dissected into a k correlation with p = -3.53, Ta = 0.60, and an... 

For the 1000m scale, the correlation between simulated t and P (Gutters and Shuttle, 2000) is well approximated by a power fit /3= 3416z , Although the relationship is strictly non-linear, it is sufficiently close to linear so that we write P = kT with k =3416 1/m. Using the distribution of T as obtained from DFN simulations, we compare in Figure lb the CCDF and CDF of P directly obtained from simulation with P approximated by P =34I6z, where CCDF and CDF of rare those from DFN simulations. 

Kamlet, M. J., A. Solomonovici, and R. W. Taft. 1979. Linear Solvation Energy Relationships. 5. Correlations between Infrared Ar Values and the (3 Scale of Hydrogen Bond Acceptor Basicities. J. Am. Chem. Soc. 101, 3734. 

This area is a development in the usage of NDDO models that emphasizes their utility for large-scale problems. Structure-activity relationships (SARs) are widely used in the pharmaceutical industry to understand how the various features of biologically active molecules contribute to their activity. SARs typically take the form of equations, often linear equations, that quantify activity as a function of variables associated with the molecules. The molecular variables could include, for instance, molecular weight, dipole moment, hydrophobic surface area, octanol-water partition coefficient, vapor pressure, various descriptors associated with molecular geometry, etc. For example, Cramer, Famini, and Lowrey (1993) found a strong correlation (r = 0.958) between various computed properties for 44 alkylammonium ions and their ability to act as acetylcholinesterase inhibitors according to the equation... 

For reviews of solvent polarity scales, see Abraham Grellier Abboud Doherty Taft Can. J. Chem. 1988,66. 2673-2686 Kamlet Abboud Taft Prog. Phys. Org. Chem. 1981,13,485-630 Shorter Correlation Analysis of Organic Reactivity Wiley New York, 1982, pp. 127-172 Reichardt, Ref. 386 Reichardt Dimroth, Ref. 386 Abraham Prog. Phys. Org. Chem. 1974, II, I -87 Koppel Palm, in Chapman Shorter Advances in Linear Free Energy Relationships, Plenum New York, 1972, pp. 203 280 Ref. 384. See also Chastrette Carrclto Tetrahedron 1962,38, 1615 Chastrette Rajzmann Chanon Purcell J. Am. Chem. Soc. 1965,107, 1. 

There is a linear relationship between the experimental values and the theoretical ones obtained at the MP2/6-31+G(d,p)//6-31G level after including the corresponding ZPE corrections (see Figure 21). Also significant is the fact that this correlation presents a slope very close to unity and that it covers a wide range (about 50 kcalmol-1) of the basicity scale. Figure 22 illustrates the reasonably good linear relationship between the aforementioned ab initio MP2 values and those obtained at the AMI semiempirical level. 

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