several different atom types depending on the environment of the atom within the molecule. While this method is generally the least accurate, the advantage is that it is the most general, being able to provide at least a rough estimate for a wide variety of molecules. Fragment-based The most common of these uses a group contribution method and is termed cLogP. It has been shown that the log P of a compound can be determined by the sum of its non-overlapping molecular fragments (defined as one or more atoms covalently bound to each other within the molecule). Fragmentary log P values have been determined in a statistical method analogous to the atomic methods (least-squares fitting to a training set). In addition, Hammett-type corrections are included to account of electronic and steric effects. This method in general gives better results than atomic-based methods, but cannot be used to predict partition coefficients for molecules containing unusual functional groups for which the method has not yet been parameterized (most likely because of the lack of experimental data for molecules containing such functional groups). Knowledge-based A typical data-mining-based prediction uses support-vector machines, decision trees, or neural networks. This method is usually very successful for calculating log P values when used with compounds that have similar chemical structures and known log P values. Molecule mining approaches apply a similarity-matrix-based prediction or an automatic fragmentation scheme into molecular substructures. Furthermore, there exist also approaches using maximum common subgraph searches or molecule kernels. Log D from log P and pKa For cases where the molecule is un-ionized: For other cases, estimation of log D at a given pH, from log P and the known mole fraction of the un-ionized form, , in the case where partition of ionized forms into non-polar phase can be neglected, can be formulated as The following approximate expressions are valid only for monoprotic acids and bases: Further approximations for when the compound is largely ionized: for acids with , , for bases with , . For prediction of pKa, which in turn can be used to estimate log D, Hammett type equations have frequently been applied. Log P from log S If the solubility, S, of an organic compound is known or predicted in both water and 1-octanol, then log P can be estimated as There are a variety of approaches to predict solubilities, and so log S. Octanol-water partition coefficient The