Calculation of Abraham descriptors from solvent–water partition coefficients in four different systems; evaluation of different methods of calculation

摘要

The use of properties that are easy to measure in order to calculatenor estimate properties that are difficult to measure is a wellknownnmethod in most fields of chemistry and biochemistry.nWith the advance of modern techniques such as combinatorialnchemistry, high throughput screening has become very importantnand therefore estimates of physical properties fromnstructure by calculations that can be performed rapidly arenof primary importance. A large number of transport-relatednprocesses involve either the equilibrium transfer (K or P) or thenrate of transfer (k) of a solute from one phase to another. Sincenlog K (or log P) and log k are free-energy related, Abrahamnand co-workers formulated a number of solute properties orndescriptors that are also free-energy related and could be usednfor the correlation of log K and log k values.nThe original work of Kamlet and Taft and co-workers 1,2nshowed that it was indeed possible to define a rather smallnnumber of descriptors that could be combined in a linear waynfor the correlation of solute properties. After considerablenpreliminary work,3,4 Abraham and co-workers, succeeded innconstructing a new and more rigorous set of five solutendescriptors,5–10 specified as follows. E is an excess molar refractionnthat is obtained from refractive index for solutes that arenliquid at 20 u0002C. For solids, the refractive index of the hypotheticalnliquid at 20 u0002C can be calculated, or E can be obtainednby the summation of fragments or substructures. S is thendipolarity/polarizability that can be obtained from gas liquidnchromatographic measurements on polar stationary phases, ornmore generally from water–solvent partition coefficients. A andnB are the overall or effective hydrogen bond acidity and basicitynthat are most easily obtained from water–solvent partitions,n† Present address: AstraZeneca Pharmaceuticals, Mereside, AlderleynPark, Macclesfield, Cheshire, UK SK10 4TG.nand V is the McGowan characteristic volume11 that can easilynbe calculated from bond and atom contributions.8 The range ofnsolutes for which descriptors are currently available is now quitenlarge, and encompasses compounds as far as helium, hydrogen,nnitrogen, etc. on one hand and drugs, environmental pollutantsnand pesticides on the other.nThese solute descriptors can be combined in a linear freenenergy relationship [eqn. (1)]. The dependent variable, log SP, isna solute property in a given system. For example, it might be lognP, for a set of solutes in a given water–solvent partition system.nThe coefficients in the equations are found by the method ofnmultiple linear regression.nDescriptors for a large number of solutes have been obtainednfrom experimental data; the maximum and minimum rangesnof these descriptors in our database are shown in Table 1. Thensolute descriptors represent the solute influence on variousnsolute–solvent phase interactions. Hence, the regression coefficientsnc, e, s, a, b and v correspond to the complementaryneffect of the phases on these interactions. The coefficients cannthen be regarded as system constants which characterize thenphase andAn example to illustrate the chemical information containednin the system constants is partition of solutes between twonphases; the system constants will reflect differences in propertiesnof the two phases, and hence can take positive or negativenvalues. The important water–octanol 12 system is characterizednby eqn. (2).n(n = 613, r = 0.9974, SD = 0.116, F = 23161.6)nThus, octanol (actually, wet octanol) is revealed to be ablento interact with π- and n-electron pairs more than is watern(positive e-coefficient), but is less dipolar/polarizable than watern(hence the negative s-coefficient). Octanol is as strong anhydrogen-bond base as is water (almost zero a-coefficient),nbut is a weaker hydrogen-bond acid (negative b-coefficient). Thenlarge v-coefficient means that octanol is able to interact withnsolutes by dispersion forces and/or that the energy required toncreate a given sized cavity in octanol is relatively low.nAny application of the general solvation equation [eqn. (1)]ndepends on the availability of the solute descriptors, and thenneed to calculate descriptors for new compounds will always benof primary importance. As explained earlier, the descriptor Vncan be calculated quite simply for any structure from thenmolecular formula and the number of rings in the molecule,nusing the algorithm of Abraham for the number of bonds innthe molecule.8 The E descriptor can be calculated from thenrefractive index at 20 u0002C, using either the observed refractivenindex for a liquid, or a calculated refractive index for the liquid.nThis descriptor can also be estimated by the addition ofnfragment values (substructures). The remaining three descriptorsnS, A and B have to be obtained by analogy to other compoundsn(within a homologous series for example), by fragmentnaddition 13,14 and by experimental measurements of physicochemicalnproperties such as log P values in a number of water–nsolvent systems.nIn order to obtain reliable descriptors from log P valuesnit is necessary to have at least three systems as different asnpossible. The difference in the physical properties of solventnsystems is reflected in the coefficients obtained for eachnsolvation equation as described earlier. Practical considerationsnare also of great importance. Such considerations includentoxicity, availability, viscosity and volatility of each solventnsystem. Apart from the physical considerations however, anmethod for categorising the equations is needed. Ishihamanet al.15 proposed a vector (v) methodology that is defined forna particular solvation equation, [eqn. (1)], as follows. Let vi =n(ei, si, ai, bi, vi). Then the analogy between any two or more givennsolvation equations SPi and SPj is expressed as cos θij betweennvi and vj as follows:nAs the linear correlation between SPi and SPj becomes better,nthe value of cos θ becomes closer to 1. An Excel macro programnwas written to automatically calculate cos θ and θ andndisplay the results in a matrix. The larger the θ value, the lessncorrelation there is between SPi and SPj. Identical equationsnwould give a cos θ value of 1 (Table 2). The four systems chosennfor use in the measurement of partition coefficients werenoctanol, chloroform, cyclohexane and toluene, which fulfil thencriteria set at the beginning of this work, and which have largenθ values between pairs of solvents.