Determination of Abraham model solute descriptors for the monomeric and dimeric forms of trans-cinnamic acid using measured solubilities from the Open Notebook Science Challenge

The Abraham solvation parameter model describes solute transfer between two condensed
phases, or between a condensed phase and a gas phase. Specific chemical and biological
processes that have been described by the basic model include water-to-organic solvent
and gas-to-organic solvent partition coefficients 1], blood-to-body tissue/fluid and gas-to-body tissue/fluid partition coefficients 2], skin permeability coefficients 3], median lethal concentrations of organic compounds for toxicity towards specific
aquatic organisms 3], nasal pungency thresholds 3], Draize eye irritation scores 3], and the minimum alveolar concentration for inhalation anthesia towards rats 3]. Expressed in terms of partition coefficients the Abraham general solvation equations
can be formulated as:

logPs=c+eE+sS+aA+bB+vV,(1)

logKs=c+eE+sS+aA+bB+lL,(2)

where P_s is a water-solvent partition coefficient of a solute, K_s is a gas-solvent partition coefficient, E, S, A, B, V, and L are the solute descriptors
and c, e, s, a, b, v and l are coefficients that describe the particular water-solvent
or gas-solvent process. The solute descriptors each describe an important solute property:
E represents the excess molar refractivity in units of (cm³ per mol)/10, S represents the dipolarity/polarity of the solute, A and B represent
the hydrogen bond acidity and basicity respectively, V is the solute’s McGowan characteristic
volume in units of (cm³ per mol)/100 and L is the logarithm of the gas-hexadecane partition coefficient at
298 K. 4],5]

The solute descriptor V is the easiest to obtain as it can be calculated directly
from structure. It is equal to the McGowan characteristic volume (cm³ per mol)/100 6]. V encodes sized-related solvent-solute dispersion interactions, including a measure
of the solvent cavity term that will accommodate the dissolved solute.

The solute descriptor E, the excess molar refractivity, can be calculated from a refractive
index at 293 K for a compound that is liquid at 293 K 4]. For other solutes E can be predicted, either directly using Absolv, part of ACD
Labs proprietary ACD/ADME Suite 7], or through the predicted molar refractivity, freely available for individual compounds
through ChemSpider 8], or some other source, such as the Open Source Chemistry Development Kit 9]. Another useful method for estimating E is through summation of structural fragments
from compounds with known values of E.

Equation (1) can be applied to saturated molar concentrations, C_s, of a compound in various organic solvents through Equation (3),

Ps=Cs/Cw(3)

where C_w is the aqueous solubility of the compound. If the aqueous solubility is unavailable
it can either be left unknown and determined by regression or predicted using ACD
Labs ACD/ADME Suite or through the freely available VCC Labs ALOGPS webservice 10].

The solute descriptors S, A, and B can also be predicted 7],11]-13] or in limited cases determined experimentally 14],15]. However, accurate results, in general much more accurate than predicted values,
are easily obtained by using regression with measured solubilities and/or partition
coefficient values 1].

Finally, we note that the applicability of the Abraham model to the solubility of
crystalline organic solutes assumes three conditions. Firstly, the solute has the
same form when dissolved in any solvent, including water. That is, we assume no solvate,
hydrate, or complex formation. Secondly, the secondary medium coefficient must be
at or near unity. This condition generally restricts the model to solutes that are
not too soluble. Thirdly, if the solute ionizes in water, the aqueous solubility,
C_w, is taken to be that of the neutral form. The second restriction may not be as important
as initially believed. The Abraham solvation parameter model has shown remarkable
success in correlating the solubility of several very soluble crystalline solutes.
For example, Equations (1) and (2) described the molar solubility of 1,4-dichloro-2-nitrobenzene in 24 organic solvents
to within overall standard deviations of 0.128 and 0.119 log units, respectively 16]. Standard deviations for aspirin dissolved in 13 alcohols, 4 ethers, and ethyl ethanoate
were 0.123 and 0.138 log units 17]. 1,4-Dichloro-2-nitrobenzene and aspirin exhibited solubilities exceeding 1 molar
in several of the organic solvents studied.

The Open Notebook Science Challenge 18] contains a valuable collection of Open Data (CC0 1.0 License: See the creative commons
website for more information about this license) solubility data that could be used
to determine Abraham descriptors for a large number of compounds. We illustrate the
utility of the Open Notebook Science Challenge data by determining the Abraham descriptors
for both the monomeric and dimeric forms of trans-cinnamic acid. The current study
represents the first time that we have calculated the solute descriptors for carboxylic
acid dimers. Solute descriptors are required input parameters in order to predict
solute solubilities, partition coefficients, and other chemical/biological properties
for which Abraham model correlations have been developed.