## Fragment Additivity Method

The jr-system was used for some 15 years, but was destined to give way to a much more general fragmentation method of calculating log P. The substituent scheme was only applicable, in general, to substituted benzene derivatives. For other compounds, the problem immediately arose, what does one take as "parent" and what as substituent? Moreover, rather serious errors occurred in the application and interpretation of lipophilicity calculations using the substituent approach. Hansch and Anderson [23] in 1967 suggested that the difference in calculated logP and in measured logP (which was lower) in compounds of the type C6H5CH2CH2CH2X indicated a folding of the alkyl chain, so that substituent X interacted with the aromatic ring through "intramolecular hydrophobic bonding". In 1973 Nys and Rekker [24] suggested that the difference did not arise from any intramolecular folding, but in fact arose because of the implicit neglect of the lipophilicity of hydrogen. The application of Eq. (7) to calculate logP for the compounds above requires the addition:

logP(C6H5 - CH2 - CH2 - CH2 - X) = logP(C6H6) + 3jt(CH3) + MX)

and makes no distinction between the lipophilicity of CH3 or CH2.

Nys and Rekker [24, 25] then suggested a totally different approach to logP calculation, which was to transform our understanding. This approach was based on the assignment of "fragmental constants", /, to a selection of structural fragments, the calculated logP then being simply the sum of fragment values appropriate to the molecule plus a number of interaction factors, F, that were necessary to correct for intramolecular electronic or steric interactions between fragments. The fragment system is expressed by Eq. (9):

Rekker used a large database of published logP values to derive both fragment values and correction factors statistically. His first book on the method was published in 1977 [26] and refinements were later made by Rekker and de Kort in 1979 [27] using a database of over one thousand logP measurements. A second book in 1992 by Rekker and Mannhold [28] includes further refinements and example calculations.

A feature of Rekker-type calculations as currently implemented is that many of the correction factors, F, are considered to be multiples of a so-called "magic constant", CM, the latest value for which is 0.219 [28]. The calculation of lipophilicity therefore follows Eq. (10) with, for example, a proximity correction of kn (key number) equal to 2 for a two-carbon separation of polar groups:

There has been much speculation as to whether the "magic constant" has any fundamental significance, Rekker having proposed that it might be related to a quantum displacement of water in the first solvation shell around the solute.

Not long after Rekker had published his hydrophobic fragmental system (based on a "reductionist" principle - the statistical analysis of a large database), Leo et al. [29] devised a fragmental system based on a "constructionist" principle, that is, based on the selection of just a small set of well-validated measurements on relatively simple molecules. In 1979, Hansch and Leo [30] went on to publish a book on their version of fragment additivity, outlining the method and giving sample calculations. By this time, though, the method (particularly the application of correction factors) had become extremely complex, and a computer program was clearly required. The program, CLOGP, was duly written to take a structural formula input, and output a logP value, along with some indication of confidence in the value, and a breakdown of fragments used and correction factors applied. The current version of this program is widely recognized as the "industry standard" for calculation of logP. An account of the history of logP calculations was given in 1985 by Dearden [31] and in 1993 Leo [32] reviewed the status of logP calculations based on fragment additivity and empirical correction terms. By this time, the MASTERFILE database maintained by the Hansch group at Pomona College in Claremont, California, contained over 40000 logP values measured in over 300 solvent systems, including over 18000 in octanol/water. Details of the fragment additivity method, including the all important methods of assigning the various correction factors, have been published by Leo [32, 33].

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