Predicting solubility from σ-profiles: what works and what doesn't

Solubility is one of the most-requested predictions in early-stage chemistry, and one of the most misunderstood. σ-profiles plus COSMO-RS give you a rigorous handle on part of the problem — but only part. Knowing which part is the difference between a useful screen and a misleading number.

The two-term decomposition

For a solid dissolving in a liquid, the solubility splits into two physically distinct contributions:

• A mixing term — how happy the dissolved molecule is surrounded by solvent. This is the activity coefficient, and COSMO-RS predicts it well from σ-profiles.
• A fusion term — how much energy it costs to break the crystal lattice and melt the solid. This depends on the crystal, not on the solvent, and is outside the σ-profile picture.

Liquids skip the fusion term entirely, which is why miscibility and liquid–liquid partitioning are the natural home turf of COSMO-RS: there is no crystal to account for.

What σ-profiles nail

• Relative solubility across solvents for the same solute — because the fusion term cancels when you compare solvents, the σ-profile-driven activity coefficient does the work.
• Solvent and anti-solvent selection for crystallization.
• Co-solvency and the shape of solubility-vs-composition curves.
• logP / logD, which are pure partitioning and need no fusion term.

What needs the fusion term

Absolute aqueous solubility of a crystalline drug is the hard case: it needs the melting/fusion contribution. Practical options, in order of rigor:

1. Measure the melting point and enthalpy of fusion (DSC) and plug them in.
2. Use an estimate such as the general solubility equation, which approximates the crystal term from melting point.
3. Predict relative solubility only, and treat absolute numbers as indicative.

Being explicit about which of these you used is what keeps a solubility prediction honest. A single 'predicted solubility' number with no statement of how the crystal term was handled should be treated with suspicion.

A defensible workflow

1. Compute σ-profiles for solute and solvents with one fixed recipe.
2. Use COSMO-RS for activity coefficients and relative solubility ranking.
3. Add a clearly-labeled fusion term only when you need absolute numbers.
4. Validate the top candidates experimentally and feed results back.

mfsig.com gives you the rigorous half — reproducible σ-profiles with provenance — so the activity-coefficient side of your solubility model rests on solid ground.