Editing Solubility (section)

==Solubility prediction==
Solubility is a property of interest in many aspects of science, including but not limited to: environmental predictions, biochemistry, pharmacy, drug-design, agrochemical design, and protein ligand binding. Aqueous solubility is of fundamental interest owing to the vital biological and transportation functions played by water.<ref name = "Skyner et al">{{cite journal |last1=Skyner |first1=R. |last2=McDonagh |first2=J. L. |last3=Groom |first3=C. R. |last4=van Mourik |first4=T. |last5=Mitchell |first5=J. B. O. | title = A Review of Methods for the Calculation of Solution Free Energies and the Modelling of Systems in Solution | year = 2015 | doi = 10.1039/C5CP00288E | pmid=25660403 | volume=17 | issue = 9 | journal=Phys Chem Chem Phys | pages=6174–91|bibcode=2015PCCP...17.6174S |url=https://research-repository.st-andrews.ac.uk/bitstream/10023/6096/1/c5cp00288e.pdf |doi-access=free}}</ref><ref name = "Tomasi et al">{{cite journal | last = Tomasi | first = J. |author2=Mennucci, B. |author3=Cammi, R. | title = Quantum Mechanical Continuum Solvation Models | year = 2005 | pages = 2999–3093 | doi = 10.1021/cr9904009 | pmid = 16092826 | volume=105 | issue = 8 | journal=Chemical Reviews}}</ref><ref name="Cramer et al">{{cite journal|last1=Cramer|first1=C. J.|last2=Truhlar|first2=D. G.|title=Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics| year = 1999 |journal=Chemical Reviews|pages=2161–2200|doi=10.1021/cr960149m|pmid=11849023|volume=99|issue=8}}</ref> In addition, to this clear scientific interest in water solubility and solvent effects; accurate predictions of solubility are important industrially. The ability to accurately predict a molecule's solubility represents potentially large financial savings in many chemical product development processes, such as pharmaceuticals.<ref name = "Abramov et al">{{cite journal | last = Abramov | first = Y. A. | title = Major Source of Error in QSPR Prediction of Intrinsic Thermodynamic Solubility of Drugs: Solid vs Nonsolid State Contributions? | year = 2015 | doi = 10.1021/acs.molpharmaceut.5b00119 | pmid = 25880026 | journal=Molecular Pharmaceutics | volume = 12 | issue = 6 | pages=2126–2141}}</ref> In the pharmaceutical industry, solubility predictions form part of the early stage lead optimisation process of drug candidates. Solubility remains a concern all the way to formulation.<ref name="Abramov et al" /> A number of methods have been applied to such predictions including [[quantitative structure–activity relationship]]s (QSAR), quantitative structure–property relationships (QSPR) and [[data mining]]. These models provide efficient predictions of solubility and represent the current standard. The draw back such models is that they can lack physical insight. A method founded in physical theory, capable of achieving similar levels of accuracy at an sensible cost, would be a powerful tool scientifically and industrially.<ref name="McDonagh et al book">{{cite thesis|last1=McDonagh|first1=J. L.|title=Computing the Aqueous solubility of Organic Drug-Like Molecules and Understanding Hydrophobicity|publisher=University of St Andrews | year = 2015|hdl=10023/6534|type=Thesis}}</ref><ref name="Palmer et al">{{cite journal|last1=Palmer|first1=D. S. |author2=McDonagh, J. L. |author3=Mitchell, J. B. O. |author4=van Mourik, T. |author5=Fedorov, M. V. |title=First-Principles Calculation of the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules| journal = Journal of Chemical Theory and Computation| year = 2012 | pages = 3322–3337 | doi = 10.1021/ct300345m|pmid=26605739 | volume=8|issue=9 |hdl=10023/25470 |s2cid=26334468 |hdl-access=free}}</ref><ref name="McDonagh_et_al">{{cite journal|last1=McDonagh|first1=J. L. |author2=Nath, N. |author3=De Ferrari, L. |author4=van Mourik, T. |author5=Mitchell, J. B. O. |title=Uniting Cheminformatics and Chemical Theory To Predict the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules|journal=Journal of Chemical Information and Modeling|year=2014|pages=844–856|doi=10.1021/ci4005805|pmid=24564264 |pmc=3965570 |volume=54|issue=3}}</ref><ref name="Lusci et al">{{cite journal|last1=Lusci|first1=A.|last2=Pollastri|first2=G.|last3=Baldi|first3=P.|title=Deep Architectures and Deep Learning in Chemoinformatics: The Prediction of Aqueous Solubility for Drug-Like Molecules| year = 2013 |journal=Journal of Chemical Information and Modeling|pages=1563–1575|doi=10.1021/ci400187y|pmid=23795551|volume=53|issue=7|pmc=3739985}}</ref>

Methods founded in physical theory tend to use thermodynamic cycles, a concept from classical [[thermodynamics]]. The two common thermodynamic cycles used involve either the calculation of the free energy of [[Sublimation (phase transition)|sublimation]] (solid to gas without going through a liquid state) and the free energy of solvating a gaseous molecule (gas to solution), or the [[enthalpy of fusion|free energy of fusion]] (solid to a molten phase) and the free energy of mixing (molten to solution). These two process are represented in the following diagrams.

[[File:Sublimation sol cycle3.png|thumb|left|Thermodynamic cycle for calculating solvation via sublimation]]
[[File:Fusion sol cycle3.png|thumb|Thermodynamic cycle for calculating solvation via fusion]]

These cycles have been used for attempts at first principles predictions (solving using the fundamental physical equations) using physically motivated [[solvent models]],<ref name="Palmer et al" /> to create parametric equations and QSPR models<ref name="Ran">{{cite journal |last1=Ran | first1 = Y. |author2=N. Jain |author3=S.H. Yalkowsky| title = Prediction of Aqueous Solubility of Organic Compounds by the General Solubility Equation (GSE)| year = 2001| doi = 10.1021/ci010287z | volume=41 | issue = 5 | journal=Journal of Chemical Information and Modeling | pages=1208–1217| pmid = 11604020}}</ref><ref name = "McDonagh_et_al" /> and combinations of the two.<ref name = "McDonagh_et_al" /> The use of these cycles enables the calculation of the solvation free energy indirectly via either gas (in the sublimation cycle) or a melt (fusion cycle). This is helpful as calculating the free energy of solvation directly is extremely difficult. The free energy of solvation can be converted to a solubility value using various formulae, the most general case being shown below, where the numerator is the free energy of solvation, ''R'' is the [[gas constant]] and ''T'' is the temperature in [[kelvin]]s.<ref name="Palmer et al" />

:<math>\log S(V_{m}) = \frac{\Delta G_\text{solvation}}{-2.303RT}</math>

Well known fitted equations for solubility prediction are the general solubility equations. These equations stem from the work of Yalkowsky ''et al''.<ref>{{cite journal|last1=Yalkowsky|first1=S.H.|last2=Valvani|first2=S.C.|title=Solubility and partitioning I: solubility of nonelectrolytes in water|journal=Journal of Pharmaceutical Sciences|date=1980|volume=69|issue=8|pages=912–922|doi=10.1002/jps.2600690814|pmid=7400936}}</ref><ref name = "JY GSE">{{cite journal|last1=Jain|first1=N.|last2=Yalkowsky|first2=S.H.|title=Estimation of the aqueous solubility I: application to organic nonelectrolytes|journal=Journal of Pharmaceutical Sciences|date=2001|volume=90|issue=2|pages=234–252|doi=10.1002/1520-6017(200102)90:2<234::aid-jps14>3.0.co;2-v|pmid=11169540 |doi-access=free}}</ref> The original formula is given first, followed by a revised formula which takes a different assumption of complete miscibility in octanol.<ref name = "JY GSE" />

:<math>
 \log_{10} (S) = 0.8 - \log_{10} (P) - 0.01(\text{melting point} -25)
 </math>

:<math>
 \log_{10} (S) = 0.5 - \log_{10} (P) - 0.01(\text{melting point} -25)
 </math>
These equations are founded on the principles of the fusion cycle.