Descriptors with meaning, and descriptors without.

3.1 Descriptors and model forms

A QSPR writes a property y as a function of descriptors d₁…d_p. Descriptor families include constitutional counts (atoms, groups), topological indices, geometric descriptors (volume, area, sphericity), quantum-chemical descriptors (charges, orbital energies, dielectric energy, σ-moments from COSMO) and, increasingly, learned representations. Group contribution (Chapter 2) is the simplest QSPR: a linear model whose descriptors are group counts.

3.2 Validation: what a QSPR has to prove

Fit statistics on training data say little about prediction. A defensible model reports external and cross-validated performance and passes a randomization test:

ŷ_(−i): prediction for point i from a model fitted without it. In y-randomization, the responses are shuffled and the model refitted many times; a sound model should fail on shuffled data.

For regulatory use, the OECD (2004) principles state that a (Q)SAR should be associated with a defined endpoint, an unambiguous algorithm, a defined domain of applicability, appropriate measures of goodness-of-fit, robustness and predictivity, and a mechanistic interpretation, if possible.

3.3 Applicability domain

A model is only trustworthy near the data it was trained on. For linear models the leverage of a new point measures its distance from the training descriptors:

A Williams plot shows standardized residuals against leverage. Points beyond h* are extrapolations, however good the fit looks. LILM is designed to attach such a domain score to every prediction and to refuse silent ranking outside it. Planned

3.4 The founder’s 2016 quantum-descriptor correlations

An ad hoc radius. Ionic radii from an equal-volume sphere (van der Waals radii, R_calc) overestimate real ionic radii. The paper fitted a linear correction against the few ions with measured (X-ray) radii and used the corrected value as a descriptor:

Sphericity of each ion, Ψ = π^1/3(6V_p)^2/3/A_p, entered through a symmetry value σ combining cation and anion sphericity. The resulting correlations:

a = 11.38, b = 0.05413, c = 196.6, d = 434.3, e = 0.649, f = 1661 (T_m in K; ρ in kg m⁻³).

a = 16.513, b = 2.2179, c = 0.00892, d = 15.0073, e = 0.02686, f = 0.02975, g = 15.8297, h = 48.1367 (η in cP).

The paper reports that 6.45% compares with about 18% for a model then in COSMOtherm; the reference it cites for that model (Preiss et al., 2010) is a melting-point study, so this is not a like-for-like benchmark. Three cautions apply, as with any QSPR: the data sets are small (37 melting points and 131 viscosity points, of which 20 and 48 were used for fitting); the viscosity split was by data point, and the paper does not say whether the same liquid appears in both sets at different temperatures; and the descriptors require a quantum-chemical calculation for each new ion. The founder’s 2015 dissertation reports the same coefficients with a different viscosity data set (78 points, 23 held out).

3.5 Latent descriptors: parameters with no physical meaning

The 2016 radius correction was an engineered descriptor: a fitted quantity standing in for something physical. Latent descriptors go one step further. Each cation and each anion gets a short vector of numbers, learned only because it predicts. The vectors have no assigned physical meaning. Jirasek and co-workers (2020) applied this matrix-completion approach to a solute × solvent table of activity coefficients at infinite dilution and reported that it “outperforms the state-of-the-art method that has been refined over three decades” (the comparison was with modified UNIFAC (Dortmund), on the mixtures it can predict).

For a cation j and anion i, a hybrid model keeps an additive, group-contribution-like part and adds an interaction term from the latent vectors:

Fixing all v makes the problem a ridge regression in each u_i, and vice versa, so alternating least squares fits it, to a local optimum. The penalty λ and the rank k control overfitting.

What latent parameters cannot do on their own. A new ion has no latent vector until it has data (the cold-start problem). To design new ions, the latent space has to be tied to structure, for example by predicting u from quantum descriptors or a molecular graph. LILM is designed to do this, with uncertainty and an applicability domain, so an optimizer can search latent space and decode back to synthesizable ions. Planned

3.6 QSAR for toxicity

QSAR applies the same machinery to biological endpoints: an EC₅₀, a mutagenicity call, a biodegradation rate. Structural alerts flag known toxicophores; read-across borrows data from close analogues; statistical QSARs regress endpoints on descriptors. For imidazolium ionic liquids, Ranke and co-workers (2004) quantified the influence of alkyl chain length on toxicity in Vibrio fischeri and WST-1 cell-viability assays by linear regression. A QSAR result is a screening estimate. It ranks what to test; it does not establish safety (Chapter 6).