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How to input Molecular Structure in DIY


For many of the modellers within HSPiP properties are calculated automatically by inputting SMILES data. Please refer to Power tool, Draw2Smiles, GUI HTML5 softoware to get Smiles.

Many users aren’t too familiar with SMILES so this form of input might appear useless. But we can say two things. First, SMILES are far easier than you might think and very quickly you get used to them. Second, it is usually very easy to find the SMILES for a chemical of interest to you with a simple web search such as MyChemical Smiles. Wikipedia, for example, includes SMILES for most of its chemicals. You can also find them in ChemSpider where you enter the chemical name or the CAS#. Even better for the long term is to find the molecule using InChIKeys – see the Y-MB section for more details.

We use them because the Y-MB technique can automatically take the SMILES and create the molecular fragments from which the relevant properties are calculated.

 That’s the background. Here’s a very simple explanation.

 SMILES - Simplified Molecular Input Line Entry Specification


Excellent guides to SMILES can be found at




and you can test out SMILES at



See http://www.pirika.com/NewHP/PirikaE/Smiles.html for a typical example of generating a Smiles in a freeware molecular drawing package and bringing it into HSPiP.

 This is a brief summary in case you want to make some small changes to a SMILES input.

 The standard atoms B, C, N, O, P, S, F, Cl, Br, and I are entered just like that, everything else needs a bracket around it – gold =[Au]. Hydrogens are implied

 Single bonds are implied, double bonds are “=” and triple bonds are “#”.


Simple linear molecules using these rules are


CCO                Ethanol

CC=O             Acetaldehyde

C=CC              Propene

CC#N              Acetonitrile


Branching is shown with brackets, with the branch being to the atom to the left of the bracket:


CC(C)C(=O)O            Isobutyric Acid

Where the first (C) is the side methyl group and the (=O) is the double-bond oxygen of the carboxylic acid.


Cyclic structures are shown by numbers that indicate where a ring starts and ends. So

C1CCCCC1    Cyclohexane

has a “1” after the first carbon to say “the ring starts here” and a “1” on the 6th carbon to say “and this is joined to the other C1”.


Aromatics can be shown in two ways:

C1=CC=CC=C1         Benzene


c1ccccc1                      Benzene

n1ccccc1                     Pyridine

o1cccc1                       Furan


It gets more complex with –NH members of aromatic systems and an [NH] symbol is used

n1c[nH]cc1                 Imidazole


Finally (for this simplified guide), cis-trans isomers across double bonds are shown as / and \


Cl/C=C/Cl                   Trans di-chloroethene

Cl/C=C\Cl                  Cis di-chloroethene



Because we believe that the relatively new InChI (International Chemical Identifier) standard for describing molecules is going to be of great future importance, we output the “standard” InChI and InChIKey.


These are created with the “No Stereochemistry” option so they are the simplest possible outputs. Importantly, if you use the first 14 digits of the InChIKey as the search string on places such as ChemSpider (probably the best one-stop-shop for information on a chemical) then you are guaranteed to get the correct matches. InChIKeys are unique identifiers created from the InChI so unlike CAS# they are directly traceable to specific molecules and there is only one InChIKey (well, the first 14 digits) to a molecule. The reason we emphasise the first 14 digits is that they will find all variants of a given molecule, independent of stereochemistry, isotope substitution etc. Once you start using InChIKeys for searches you’ll wonder how you ever survived without them.


For a useful quick guide to InChI, visit http://en.wikipedia.org/wiki/International_Chemical_Identifier


If you input an InChI then we output the Smiles for your reference.


DIY utilities.

There is no one, universal, simple, accurate way to calculate HSP from the molecular formula. This is frustrating for all of us who use HSP. Until such a method appears, the only alternative to measuring them directly yourself is to make do with a range of techniques which you can mix and match to reach your own best judgement on the HSP values. This really is a DIY (Do It Yourself) approach to HSP.



However, because of the power of Y-MB we recommend this as your basic HSP calculator.

 Six complementary methods are provided:


1 Numbers & Surfactants

You need to enter the Enthalpy of Vaporization (ΔHvap) in kJ/mol and the Molar Volume in cc/mole. The Cohesive Energy, E is then calculated as:

E= ΔHvap - RT

 These calculations all assume ΔHvap and E calculated at 25ºC, so the RT correction factor is 2.477 kJ/mol.

 You can choose your units of input. If you use kJ/kg or kcal/kg you must also specify the Molecular Weight.

 If you can only find the value of ΔHvap quoted at Tb its boiling point (a value lower than the value at 25ºC) then you can calculate the value at 25ºC by using the Fishtine approximation:


ΔHvap at 25 = ΔHvap at Tb *[(1-298.15/Tcr)/(1-Tb/Tcr)]0.38

 where both Tb and Tcr are in ºK.


If you don’t know Tcr then a reasonable guess is Tcr=Tb+225

 The Fishtine calculation is provided for you, with input temperatures in ºC for convenience.


From these δTot (the sum of the three components, i.e. Sqrt(δD² + δP² + δH²) can be calculated directly and accurately.

 δTot = (E /Molar Volume) ½ and like all δ values has units MPa½ or, equivalently, (Joules/cm³)½

 If you don’t know the Molar Volume you can either estimate it from the Y-MB method or you can find on-line tools that perform the calculations for you – or you can use your favourite molecular mechanics program – or even measuring the density and calculating Molar Volume (we provide the option to do this) as

 Molar Volume = Molecular Weight / Density

  From the Dipole Moment and the Molar Volume, the simple Beerbower formula can be used to calculate δP.

 δP=37.4 * Dipole Moment/MVol ½



There are arguments in favour of using the more complex Böttcher equation (see Equation 10.25 in the second edition of the Hansen handbook, for example), but as it is unlikely that you will have the accurate numbers for the dielectric constant, refractive index and dipole moment required for that equation, the Beerbower equation seems adequate.

 If you don’t know the dipole moment directly then in principle you can calculate it from within your favourite molecular mechanics program – but there are obvious problems with this approach which may give you idealised values for a single configuration in vacuuo rather than an averaged value representative of the solution environment.

 We now have to determine δH. The only way to do this is to provide an estimate for δD so that δH is calculated by subtraction. The Panayiotou method seems to provide very reasonable data (especially as it incorporates sophisticated 2nd-order corrections) for δD. If you don’t have a value for the Enthalpy of Vaporization, you can try various values till the calculated δTot matches the Panyiotou method.

  Alternatively you can use a correlation between δD and Refractive Index that we’ve obtained by a best fit to the current HSP database:

 δD=(RI - 0.803) / 0.0375


 Although there is some reasonable science behind the idea of a correlation, and although we’ve shown that incorporating extra terms such as Molar Volume makes the correlation worse, like all correlations the results have to be treated with caution.

 Clearly there is a chain of assumptions here, but it’s currently the state of the art for a purely numerical approach.


2 Y-MB

Dr Hiroshi Yamamoto is an expert on fitting large datasets using Neural Network techniques. He has taken the full HSPiP Solvent Data.hsd set plus thousands of other compounds and provided an optimal Neural Network and Multiple Regression fit and has then tested it extensively on a wide variety of compounds – this is made easy because he has provided the means to go straight from molecular descriptor (Smiles, (standard) InChI or 3D file such a .mol) to HSP.


In addition to the HSP δD, δP, δH, δTot (and also a Check δTot which is from the sum of the 3 HSP), Y-MB gives you molecular weight, molecular formula and estimated RI, MPt and BPt, each calculated via a Neural Network algorithm using literature data for each of the parameters. Values for  Antoine Coefficients and critical parameters are also estimated for your convenience and added to the output text box. Ovality and MCI (Molecular Connectivity Index) are added for convenience as they are now used in some of the property estimation schemes. The MCI, for example, significantly improves estimation of BPts. Even more parameters are available from the Y-Predict Power Tool.


The Expansion coefficient terms ExpA and Expansion coefficients are used in the expression:


 Where Te is the Thermal Expansion Coefficient at temperature TºK and Tc is the Critical Temperature (also provided in the output)


ExpA and ExpM are important for accurate calculations of HSP values at temperatures other than 25ºC because the HSP values depend in a complex way on the change of density caused by thermal expansion.


 As an aid to those concerned with Environmental issues, some extra parameters are estimated for you.


The Viscosity at 25ºC is estimated. This is a very difficult parameter to estimate and the values should be seen only as a guide. This output was requested by a number of customers who said that they were happy with an indicative value.  Vapour Pressure @ 25ºC is a useful guide to the relative volatility of a compound though you can also enter a ºC parameter and get the vapour pressure at that temperature too. From the vapour pressure, the RER (Relative Evaporation Rate, nBuAc=100) is estimated via the empirical formula RER=0.046*MVol*VapourPressure. The Flash Point estimate is handy to know if your chemical will fall in the wrong domain for your application. The Carter MIR value is an objective measure of the ability of the Volatile Organic Compound to react with ozone, and the Log[OH] value is an estimate of the rate of reaction with the .OH radical. When you combine the chemical knowledge from the HSP with the relative volatility and reactivity estimates you gain a powerful insight into possible substitutions for your current (high VOC) chemistry.


The default is for just the HSP and MVol to be placed onto the Clipboard for pasting (Ctrl-P) into other HSP fields or for going into Excel etc.


If you would like the full set of data on the Clipboard, select Full data to Clipboard.


After the calculation the data (with headings) is easily pasted into, say, Excel.


So it’s very easy to use – provided you have your molecule in one of the formats that Y-MB can read (Smiles, .mol, .mol2, .xyz, .pdb, .gpr). It’s generally easy to find Smiles or .mol for a molecule. You can also enter your molecule into any of the common (and often free) molecular drawing packages which will give you output in one of these formats). You can also use Open Babel (which is free) to convert from one format (such as InChI) to another. It would be nice to have InChI format as an input, but it is rather complex so it is easier for us to ask you to use Open Babel. For those who (for various reasons) don’t have molecular drawing packages and don’t like to risk revealing structures to on-line drawing tools, the Draw2SMILES Power Tool is simple but powerful.


As a bonus, when you load one of the 3D file formats (Load 3D), you can check that the molecule is what you think it is with a simple 3D viewer.


The bonds can be shown as Bonds, Semi, or Filling depending on your choice.


You can of course 3D rotate the molecule and Zoom (Shift-Click) or Pan (Ctrl-Click). The 3D technique is identical to that used in viewing the Sphere.


There are two options when using Load 3D. The first is No SMILES. This bypasses the built-in SMILES generator and for complex molecules can produce a considerable increase in speed in generating the HSP values. The second is an Auto Valence option. Some 3D files omit hydrogens and omit information as to whether a bond is single, double or triple. If you select the Auto Valence option, the program does its best to estimate the degree of the bond, without which Y-MB cannot function properly. This is particularly important for aromatic molecules where an alternating single-double pattern has to be created. It’s impossible for Auto Valence to be right all the time. It’s far better if you provide the 3D information with all hydrogens and bond-orders specified. But sometimes Auto Valence is better than nothing and just occasionally it makes matters worse. Use your discretion!


If you have a large set of compounds in Smiles format, you can use Y-MB to File Convert them into a standard .hsd file and a .sof (Optimizer) file. The file format (.txt or .bat) is very easy. For each chemical you need a Name, a Smiles and, optionally, a CAS No in that order. Each column is separated by a Tab (so you can, if you wish, create this from within Excel as “Tab separated format”). The file can, optionally, include a first line saying Name, Smiles, CAS – though this line will then be ignored.



If all goes well, the converted file will have the same name as the original but with .hsd (and, separately, .sof) instead of .txt or .dat. You can then load it straight into HSPiP. If Y-MB fails to convert a molecule it will be shown in the .hsd file but all the values will be empty. The line will be missing from the .sof file.


If you select the S-P Output option then the Y-MB routine also calculates the Stefanis-Panayiotou UNIFAC first-order groups for you and places them in the S-P tab.


There are, unfortunately, some limitations to this so please don’t accept the S-P output as being 100% true. In our experience it is usually more reliable than a normal chemist who doesn’t handle UNIFAC groups every day, but it can still make some mistakes.


The Y-MB method is a powerful source of other information.


If it thinks that it recognises the functionality in your Smiles input it will list the molecules in HSPiP Solvent Data that have identical functionality – along with the actual HSP. If you find that the Y-MB estimate is very wrong, you can click on the Y-MB Report button, enter the values you think are the correct ones, click the Put report on Clipboard button and past your report into your email program and send it to steve@hansen-solubility.com.


As you might be interested in other molecules with similar functionality, the Y-MB Analogs button creates a list of molecules (+HSP) which contain the functionality of your molecule.


This can be quite a long list. If you want just the functionality in your target molecule then click Exact Analogs for a more exclusive list. We find this functionality amazingly helpful as a source of ideas for alternative formulations and for problem solving. The list you create is automatically placed on the Clipboard in a format that is easy to paste into Excel. If you want the list as a .hsd file that’s then automatically imported into HSPiP, check the HSD Output option.


You can choose to search in the standard HSP list or by checking the 10K (short for 10,000) option, the entire database.


Although Y-MB provides a long list of parameters, even more are available in the Y-Predict Power Tool. Whilst there is no plan to increase the range of predictions for HSPiP, Y-Predict will continue to expand, depending on user needs and Hiroshi’s own research interests.

  Please Refer to e-Book, DIY HSP (Methods to Calculate/Estimate Your Own HSP)

3 Stefanis-Panayiotou

Stefanis and Panayiotou have produced a sophisticated group-contribution method for calculating δD, δP, δH, δTot and Molar Volume. All you have to do is break down your molecule into its component groups and enter how many of each group are in your molecule. For example, 1-Butanol possesses 1 CH3- group, 3 –CH2- groups and 1 –OH group.



If you enter the numbers for 1-Butanol and press the Calculate button you get the calculated values of 21.9 for δTot. The other values are compared to Hansen’s table.

δD       δP       δH       MVol

Calculated       15.9     6.1       13.2     94.3

Hansen                        16.0     5.7       15.8     91.5


There is also another Check δTot value calculated from the individual δD, δP and δH values which you can compare to the estimated δTot.


For a molecule such as 1-Butanol it’s easy to know how to break it down. For more complex molecules you need help. The first strength of the Stefanis-Panayiotou method is that the break-down uses the standard UNIFAC method and you will find numerous other examples in the literature of molecules being broken down in this manner. The second strength is that they have helpfully provided examples in their table that make it easy to work out the appropriate substructures.


Stefanis and Panayiotou recognised the fundamental flaw in the simple group contribution method – that, for example, 3 –CH2- groups behave very differently depending on whether they are part of 1-Butanol or cyclobutanol.


So they have added a further refinement. In addition to the 1st-order table, there is a 2nd-order table with important sub-structures. With a bit of practice you can quickly determine which 2nd-order contributions to include. By selecting them, the results for more complex molecules are more accurate.


It’s worth noting that δP and δH contribution methods must be less accurate than δD. The reason is simple. δD mostly depends heavily on how much “stuff” you have in the molecules. But δP and δH depend crucially on configuration which cannot simply be captured in a table of group contributions. As a further aid for this issue, if you suspect that the true δP and/or δH values of your molecule should be low, clicking the LowP and/or LowH option gives you values correlated especially for this scenario and therefore likely to be more accurate.


The authors of the technique stress that the technique is designed to be used with molecules with more than 3 carbon atoms or 3 functional groups. So although the program allows you to calculate the value for, say, methanol or ethanol, the results are not accurate. In practice this is not a limitation as HSP for such simple molecules are likely to be known already.


You might like to save your group assignments for reference, or for changing your mind later on. Click the Save button and the group assignments are saved as a .spg (Stefanis-Panayiotou Group) file. The Open button retrieves the group assignments from your chosen file.


To learn more of the S-P methodology, consult their paper on δTot and δD:

E. Stefanis, L. Constantinou, C. Panayiotou; A Group-Contribution Method for Predicting Pure Component Properties of Biochemical and Safety Interest; Ind. Eng. Chem. Res. 2004, 43, 6253-6261


Their work on δP and δH is included in:

Physical and Chemical Parameters of Paper Conservation, PhD thesis by

Emmanuel Stefanis (In Greek), Department of Chemical Engineering,

Aristotle University of Thessaloniki, Greece, 2007 and the full paper in International Journal of Thermophysics is found in:


Emmanuel Stefanis, Costas Panayiotou, Prediction of Hansen Solubility Parameters with a New Group-Contribution Method, International Journal of Thermophysics, 2008 , 29 (2), 568-585.


The parameters and equations used in this version differ slightly from those in the published work. Dr Stefanis kindly re-ran the correlations using the most up-to-date version of the HSP table. This, happily, removed many/most of the outliers shown in the Internationl Journal of Thermophysics paper and improved the correlation coefficients.


The Y-MB method allows you the option automatically to create (or at least produce a good estimate of) the S-P UNIFAC (first-order) groups. There are some known imperfections (e.g. a lack of pyridine groups) so use the results with caution.


4 Van Krevelen

Van Krevelen also admits that group contribution techniques cannot be expected to be accurate. But they are certainly better than nothing. Once again, you simply identify which groups make up your molecule and enter the number of each group. No 2nd-order effects are included.


You need to input a Molar Volume – see item (1) for how you might obtain this.


You also need to specify if you have multiple planes of symmetry. The more symmetry, the less polar effect there is (0.5 for 1 plane, 0.25 for 2 planes) and if you have 3 planes then both the polar and hydrogen bonding values are set to 0.


5 Hoy

Hoy’s approach is more complex and it attempts to take into account many more factors.


For example, there is a Polymer mode which takes into account the fact that values calculated for your simple repeat unit are unlikely to apply to the polymer itself. Hoy also assigns a partial molar volume to each group so you end up with an estimate of the molar volume as part of the calculation.


Remember to never mix Hoy values with other values – his scheme, whilst excellent, is based on a different partition of δTot. So it is self-consistent but not consistent with other methods.


6 Polymers

As an adjunct to the Y-MB method we have introduced Polymer Y-MB. In earlier editions this took (with his kind permission) the vast data table generously provided by Dr W. Michael Brown at Sandia National Laboratories.


For the 3rd Edition we increased the number of polymers to >600 and used an –X notation instead of the original “cyclic 0” nomenclature of Dr Brown. This has allowed us more versatility and also allowed us to correct a number of errors in the Smiles nomenclature in the original database. Double click (or Alt-click) on any of those polymers and the Smiles is put into the box, click on Calculate and the Polymer Smiles estimate is produced.


If you Ctrl-Click on a polymer then the tab changes to Y-MB where the 3D viewer shows you the monomer unit, with the dangling bonds clearly visible.



You can also calculate the Polymer Y-MB from this tab. If you set the N-Repeats to more than 1 then an n-mer Smiles is created and the Y-MB values calculated.


The calculated HSP change for different n-mers. This is because the science of predicting polymer-HSP is not yet robust, though it is greatly improved thanks to the new techniques in the 3rd Edition. At this stage (as with any HSP predictions) you have to use your judgement. You can enter Polymer Smiles by hand. You can also create AB, AABB or AAABBB polymers by selecting two monomer rows, clicking the appropriate selection then clicking the CP (Co-Polymer) button.


If your own polymer isn’t in the table you can create your own Smiles string. For complicated molecules, such as a cellulose derivative, it’s difficult to create the Smiles string accurately yourself. One way to do this to create the molecule in a standard molecular drawing package, using something like Br to show where the polymer chain goes:


The package can then automatically provide you with the Smiles string for this pseudo-molecule: OC1C(OC)C(OC(COCCC)C1Br)OBr

Now all you need to do is replace the two Br atoms with the X for polymer Smiles


This can go straight into Y-MB or the Polymer tab and you get your predicted HSP values.


The Draw2Smiles Power Tool allows you to enter a polymer structure in a simple chemical drawing program, add the Polymer “atoms” at the appropriate places and calculate a Polymer SMILES that can be pasted (Ctrl-C) into the text box. This can also be used as a quick way to find a polymer within the table. If the Polymer SMILES results in a match to one of the polymers in the table, this is shown in the output box.


For those who make more complex polymer blends there is a simple Blend option. Select 2 or more monomers from the table, click the Blend option and enter the % of each monomer, then click the Calculate button to obtain your estimate.


Clearly this is very limited. It assumes a random blend of your components (i.e. a reactivity ratio of 1 for each monomer) and determines the statistical blend of AA, AB, AC, BB, BC, CC (for a 3-component blend) diads and from their calculated HSP values and their volume-weighted (not mass weighted!) values obtains the final result. Such predictions need to be treated with due caution.


δD from tables

The δD parameter can also be found with the charts given in the second edition of the Handbook. This requires knowledge or estimate of the critical temperature. At the same time it could be noted that this procedure is a corresponding states calculation, CST, (in agreement with the Prigogine CST approach), and that this could be the basic reason for some differences in the group contribution methods.


Why no Beerbower table?

The Hansen handbook is honest about the limitations of the group contribution approach. The Beerbower values included in the handbook show wide error bars and it would not do justice to the table to simply include some fixed value. In addition, the table does not cover as wide a range of groups as the other methods. However, in the hands of an expert, the table can be valuable and users might find it instructive to derive their own estimates manually.


Which method is the best?

Only you can tell. The calculator is called DIY because you really do have to do it yourself. You are a scientist, so use your judgement. If the values of one approach don’t make sense when you compare them to a similar molecule for which you already know the value, then see if a different approach gives you a value which seems more reasonable. The Stefanis-Panayiotou method (2007) is based on a large data set using modern statistical techniques, is a method published in the literature and uses the much-used UNIFAC sub-structures so is a good choice. The Y-MB method is highly convenient because it takes you automatically from structure to HSP and the neural network and multiple-regression parameters have been trained on the entire HSP dataset provided with HSPiP so many users will find that it gives helpful results. In addition it also provides lots more parameter estimates. So it is our favourite. But in the end, use your own judgement.



Other predictions

Using the Y-MB method it is possible to obtain many predicted values. These can be used in many ways, described in this section.



On the Numbers & Surfactants tab, you have the ability to create HSP for your surfactant of choice. This is done by providing a set of hydrophils and a set of hydrophobes.


The idea is that you “mix and match” with whatever is the closest approximation to your desired surfactant. This is a relatively crude method, but the calculated values are a useful starting point that you can refine for your own purposes. The calculated value is the weighted average of the two components, based on their relative molar volumes. If you don’t like the pre-assigned values, you can enter your own HSP parameters and molar volumes into the respective boxes and the weighted average calculation is carried out for you.


SC Johnson have generously allowed us to use their table of surfactant HSP (calculated for them by Dr Hansen) which might give you an alternative way of estimating the values for your own specific surfactants. You can sort the table by HLB (Hydrophilic-Lipophilic Balance) or by type (Anionic, Cationic etc.) for your convenience.


As an alternative, the Y-MB button automatically generates a SMILES input to the Y-MB calculator and returns the HSP values.



This only works when Y-MB has relevant data. A number of the hydrophilic headgroups are undefined in SMILES terms so for these the Y-MB calculation is automatically disabled and a message appears to explain why.


You can also customize either the head or tail via your own SMILES string. This allows you greater versatility. Enter a SMILES then press the calculate button next to it and it will be added to the simple head + tail calculator. You can also click the Y-MB button to calculate the full molecule, though for large molecules this is very slow and not too satisfactory.


For those familiar with HLD-NAC surfactant theory (see AbbottApps for an app-based explanation) it is important to know the Effective Alkane Carbon Number (EACN) of the oil.



This can be estimated from the SMILES of your chosen oil.

  Please refer to e-Book, Cleaning by numbers (HSP for Surfactants)





HSE (Health, Safety and Environment)

Decisions on which solvents/chemicals to use are seldom simple. Trade-offs have to be made with cost, VOCs, toxicity, environmental impact and so forth. To make rational decisions, it’s good to have side-by-side comparisons of key, relevant properties. That’s what the HSE tab does. Enter two chemicals (as SMILES) and click the Calculate button.


In addition to standard properties such as molecular weight, molar volume, density, melting point, boiling point, properties provided include:

•   Vapour Pressure (at 25º, at specified temperature and in terms of Antoine Constants)

•   Flash point

•   RER – Relative Evaporation Rate (n-Bu Acetate=100)

•   Log(OHR) – the OH radical reactivity

•   MIR – the Carter MIR measure of VOC activity

•   Log(Ksoil) – the soil/water partition coefficient

•   Log(Kow) – the octanol/water partition coefficient

•   Log(S) – the water solubility


Furthermore there are two numerical estimates of similarity. In both cases values closer to zero mean greater similarity.


•   HSP Distance – the Distance in HSP space

•  Functional Distance – a measure of the difference in functional groups between the two molecules.

These two numbers are very helpful in “read across” estimation in, for example, REACH.

  Please refer to e-Book, Predictions (Many Physical Properties are Correlated with HSP)

Azeotropes and Vapour Pressures

If you can estimate the activity coefficients of two chemicals and if you know (or can estimate) their vapour pressures as pure liquids, then it is possible to calculate the vapour pressures of the two chemicals above the liquid. You can do this in two ways

•   Calculating the vapour pressures of the two components at various mole fractions at a temperature of interest

•  Calculating the vapour pressures at the boiling point of the mixture across the mole fraction range.


The first calculation is the classic vapour-pressure equilibrium curve. The second enable the classic calculation of Azeotropes.


To perform these calculations, simply enter the SMILES of the two chemicals and click Calculate.


This gives estimated values for boiling points, vapour pressures, Antoine Coefficients and also gives two numbers, the so-called Margules parameters, which allow the activity coefficients for the two chemicals to be calculated across the whole mole fraction range.


If you don’t like the estimates, you can always manually enter values for the key parameters and click the local Calculate button to update the graph.


The plots offer a lot of choice. The first choice is between Vapour Pressures and Azeotropes. If the latter is chosen then the full Azeotrope data are provided as outputs: Mole fraction, Weight % and Volume % and boiling point of the Azeotrope (if it exists), and the HSP of the Azeotrope.


The graphs include options to

Show the ideal curves so you can visually check the deviation from ideality

Show the 0-1 lines which simply show what would happen if the liquids were ideal and had the same vapour pressure – again, just as a visual reference

Show the Azeotrope boiling point, in ºC (disabled for the Vapour Pressures plot)

Plot X1, X2 means that the graphs for both liquids start with 0 at the left-hand origin. Conventionally, X1 is plotted in this manner, with X2 plotted with 0 in the right-hand origin. Use whichever you find more comfortable and informative

Plot Wt% - use a Wt% scale rather than (the conventional) mole fraction scale.

Show Gamma – plots the activity coefficients of the two liquids over the range. You cannot plot Temperature and Gamma on the same graph.


Feel free to use as many or as few of these options as give you the information you want.


When you move your mouse over the graph, you get a readout of the relevant properties at that point.



It seems odd to say that you cannot directly predict solubility from HSP! But HSP have always been about relative solubility and have never attempted to issue exact solubility predictions.


However, with some simple equations and some good estimations of key properties, it is possible to predict solubilities directly.


The equation is simple:


Ln(Solubility) =  – C + E – A – H


C is the “Crystalline” term. It is the Van ‘t Hoff (or Prausnitz) formula that depends on the difference between the current temperature, T, and the melting point Tm, the Gas Constant R and also on the Enthalpy of Fusion DeltaF.


C = DeltaF/R*(1/Tm – 1/T)


In other words, the higher the melting point and the higher the enthalpy of fusion, the more difficult it is to transform the solid into the dissolved (liquid) state.


This formula is a simplification which follows convention and ignores some other terms like heat capacities.


For calculations where Tm<T, C is set to zero. The calculations start to become meaningless in this liquid/liquid scenario, but it seems instructive to carry out the calculation. A warning is provided to alert you to the problem.


The E term is (combinatorial) Entropy. This is calculated from volume fractions (Phi) and molar volumes.


E = 0.5*PhiSolvent*(VSolute/VSolvent -1) + 0.5*ln(PhiSolute + PhiSolvent*VSolute/VSolvent)


It’s worth making an important reminder that molar volumes for solids are not based on their molecular weight and solid density. In the words of Ruelle: “(For a solid) the molar volume to consider is not that of the pure crystalline substance but the volume of the substance in its hypothetical subcooled liquid state.”


A comes from the activity coefficient. The larger the activity coefficient, the more negative A becomes. A simple estimate of activity coefficient comes from the HSP distance – not surprisingly, the larger the distance, the higher the activity coefficient and the lower the solubility. Because the simple HSP distance has been shown to be only an approximate guide to activity coefficients, the Margules coefficient predictor from the Azeotropes and Vapour Pressures calculator is used. Molar volumes play a significant role in activity coefficients, so a large molecule with similar HSP values is significantly less soluble than a smaller one.


H is a Hydrophobic Effect term that is very important for solublities in water, and somewhat important for solubilities in low alcohols. The calculation follows the method of Ruelle and depends on PhiSolvent*VSolute/VSolvent with extra terms depending on how many hydrogen-bond donors (alcohols, phenols, amines, amides, thiols) are on the solute and whether the solvent is water, a mono-alcohol or a poly-ol. If the solvent is water and the solute contains alcohol groups, there are special parameters depending on whether the alcohols are primary, secondary or tertiary. There is a further refinement (not included in this version) which discounts some of the solute’s hydrogen bond donors if they are likely to be internally bonded.


The complication is that the E, A and H terms all depend on the volume or molar fraction which is the precisely what you are trying to calculate, so there is an iterative process involved till the equation balances.


The output is the Ideal solubility (as mole fraction), the real solubility (as mole fraction, volume fraction and weight %) plus the following (which come from taking the exponential of their terms in the log-solubility equation):


•   The ideal solubility is divided by the Activity coefficient. For ideal solutes this is 1. For moderately soluble chemicals it is in the range 1 to 10, for highly incompatible solutes it can rise to more than 100.

•   The ideal solubility is multiplied by the Entropy term. This is usually larger than 1, except for small solutes in large solvents.

•   The ideal solubility is multiplied by the Hydrophobic term. This is usually less than 1 for large molecules in water or typical alcohols. It is 1 for non-water/alcohol solvents.


From these four terms you get a very good idea of where the solubility or insolubility is coming from.


Because water is such a special solvent, click the Use Water as the solvent option for the solvent rather than enter [H]O[H] into the solvent SMILES box. Because both the entropic and hydrophobic effects in water are so large, don’t expect the calculation to be amazingly accurate for solubilities below 0.05 mole fraction. At this stage there aren’t good Margules parameter estimates so they are both set to 0 (ideal!) and you’ll need to make your own judgement of what they should be. A warning label appears to remind you of this fact.


Because the predictions of HSP, MPt and Margules are all subject to error, feel free to override any/all of them and re-calculate solubility using the Manual Calculation button.


For those interested in the theory, the Solubility Theory button opens a form where the effects of MPt, Enthalpy of Fusion, Delta Heat Capacity, Heat of Mixing and Entropy of Mixing can all be explored, as well as the simple Yalkowsky assumption. The graph (which can be read with the mouse) plots the mole fraction solubility v temperature, with 0°C being the lowest temperature and the MPt being the highest temperature. Alternatively the data can be shown as a van’t Hoff plot of ln(x) v 1/T where the ideal case is a straight line shown in black as a reference.


Solubility is increased (i.e. you get a higher mole fraction at a lower temperature) with a lower MPt, a lower Enthalpy of Fusion, a higher Delta Heat Capacity and a negative Heat of Mixing. The theory is explained in the eBook. Note that at some positive values of Heat of Mixing the curve takes on an odd shape. For reasons explained in the eBook these curves are unrealistic (they violate the Gibbs phase rules) and instead represent “oiling out” phenomena.