1.1 Why thermodynamics decides solvent performance

An extraction solvent is judged by how strongly it takes up one component and rejects another, how much of it dissolves into the product stream, and how much energy it takes to regenerate. Each of these follows from activity coefficients and phase equilibrium. In the 2013 design study the founder co-authored (Karunanithi & Mehrkesh, part of his doctoral work), selectivity, solvent power and solvent loss were all computed from infinite-dilution activity coefficients:

A: aromatic solute (toluene); B: aliphatic (n-heptane); S: solvent. γ^∞_i,j: activity coefficient of i infinitely diluted in j.

1.2 Fugacity and the equilibrium criterion

Fugacity turns the chemical potential into a pressure-like quantity that behaves well in mixtures. Two phases α and β are in equilibrium when, for every component, the fugacities are equal:

Vapor fugacities are written with a fugacity coefficient φ_i = f_i/(y_iP), and liquid fugacities with an activity coefficient γ_i = f_i/(x_i f_i^∘). Equating them gives the γ–φ form of vapor–liquid equilibrium:

The exponential is the Poynting correction. For a sparingly soluble gas, the liquid-side reference is Henry’s constant, f_i = x_i H_i. The CO₂ screen the founder co-authored (Farahipour, Mehrkesh & Karunanithi, Chem. Eng. Sci. 2016) estimated it as H = P^satγ^∞, with γ^∞ from COSMO-RS and P^sat from the Peng–Robinson equation (Methods 02). Above the critical temperature, as for CO₂ at 45 °C, no true vapor pressure exists, and the pure-liquid reference state becomes hypothetical; P^sat must then be extrapolated.

1.3 Excess Gibbs energy and phase stability

Activity coefficients are partial molar derivatives of one function, the excess Gibbs energy. Any model for G^E therefore yields self-consistent activity coefficients for every component:

Equation 1.6, the Gibbs–Duhem equation, is a consistency test for measured data. Phase splitting follows from the Gibbs energy of mixing:

A binary mixture is unstable wherever this curve is concave in composition. The equilibrium phases are the two points that share a common tangent, which is the lower convex hull of the curve. The NRTL lab below finds them that way.

1.4 Local-composition models: Wilson, NRTL, UNIQUAC

Local-composition models assume the composition around a molecule differs from the bulk because interaction energies differ. Wilson’s equation (1964) handles strongly non-ideal miscible mixtures. It cannot represent liquid–liquid immiscibility, which is why NRTL and UNIQUAC are used for extraction systems.

NRTL (Renon and Prausnitz, 1968), binary form:

τ_ij: dimensionless interaction parameters (often written Δg_ij/RT); α: non-randomness parameter. ln γ₂ follows by exchanging indices 1 and 2.

UNIQUAC (Abrams and Prausnitz, 1975) splits ln γ into a combinatorial term, from molecular size and shape, and a residual term, from interaction energies:

Φ_i = r_ix_i/Σ r_jx_j (volume fraction); θ_i = q_ix_i/Σ q_jx_j (area fraction); l_i = (z/2)(r_i − q_i) − (r_i − 1); z = 10; τ_ij = exp(−Δu_ij/RT).

1.5 Group contribution: UNIFAC

UNIFAC (Fredenslund, Jones and Prausnitz, 1975) keeps the UNIQUAC structure but builds each molecule from functional groups, so it can predict mixtures never measured. Molecular parameters are sums over groups, r_i = Σ_k ν_k⁽ⁱ⁾R_k and q_i = Σ_k ν_k⁽ⁱ⁾Q_k, and the residual term becomes a sum of group activity coefficients:

Γ_k: group activity coefficient in the mixture; Γ_k⁽ⁱ⁾: in pure i; Θ_m: group area fraction; a_mn: group-interaction parameter fitted to data.

Ionic liquids strain this framework because the groups carry charge. The 2013 formulation followed the approach of Roughton and co-workers (2012): cation core, anion and alkyl groups are treated as separate groups, with interactions between the ionic groups assumed zero because the ions stay strongly paired. The a_mn values are empirical parameters fitted to equilibrium data. Learned latent descriptors (Chapter 3) take that idea further.

1.6 COSMO-RS: thermodynamics from surface charge

COSMO-RS (Klamt, 1995) starts from a quantum-chemical calculation of each molecule in a virtual conductor. The screening charge density σ on the molecular surface is summarized as a histogram, the σ-profile p(σ). Surface segments interact pairwise through an electrostatic misfit energy and a hydrogen-bond term, and the chemical potential of a segment in solvent S satisfies a self-consistent equation:

The chemical potential of a solute then follows by integrating μ_S(σ) over the solute’s own σ-profile, plus a combinatorial term. No group-interaction parameters are needed (a small set of global and element-specific parameters, periodically re-fitted by the developer), so COSMO-RS can screen ions that group-contribution tables do not cover. The electrostatic-potential surfaces in Methods 01 show the kind of charge distribution this starts from, though COSMO-RS uses conductor-screened charges, not gas-phase potentials.

1.7 Cubic equations of state: Peng–Robinson

Equations of state give fugacity coefficients for gases and, for cubic forms, for both phases at once. The Peng–Robinson equation (1976) is a standard choice for CO₂ and hydrocarbons:

In terms of the compressibility factor Z, with A = aP/(RT)² and B = bP/(RT), the equation is a cubic whose largest root is the vapor and smallest the liquid:

The saturation pressure is the pressure at which ln φ^L = ln φ^V, found by successive substitution P ← P·φ^L/φ^V. The lab does exactly this for CO₂ and compares the result with NIST reference data.

2.1 The inverse problem

Computer-aided molecular design (CAMD), and its ionic-liquid form, computer-aided ionic liquid design (CAILD), is defined in the 2013 paper (Karunanithi & Mehrkesh) as: “given a set of IL functional groups … and a specified set of target properties … find an IL structure that matches these properties.” The forward problem predicts properties of a known structure; the reverse problem searches structures for given properties. Four ingredients are needed: a way to fragment ions into groups, rules that enforce valence-feasible combinations, structure-based property models, and an optimization method to search the space.

2.2 Representation: cores, chains and anions

An ionic liquid is written as one cation core (imidazolium, pyridinium and so on), alkyl or functionalized side chains attached at the core’s free valences, and one anion. In the MINLP of Methods 04, binary vectors c and a select the core and the anion, a binary vector y marks which side chains exist, and integers ng_kl count how many groups of type k sit in chain l.

2.3 Structural feasibility as algebra

Chemical feasibility becomes linear constraints on those variables. From the 2013 paper (its Eqs. 12–18):

v_ci: number of free valences of cation core i; v_Gk: valency of group k (CH₃: 1; CH₂: 2). Eq. 2.1: exactly one core and one anion. Eq. 2.2: one chain per free valence. Eq. 2.3: the modified octet rule for the cation. Eq. 2.4: the octet rule for each chain (with only CH₃ and CH₂ available, exactly one CH₃ per chain). Eq. 2.5: size limits (12 groups per cation and 6 per chain in the paper’s case studies).

Further constraints in the paper (its Eqs. 19–24) cap or require occurrences of particular groups, for example at most one aldehyde per chain. The point is that whether a structure satisfies the valence rules becomes something an optimizer can check directly. Valence feasibility is necessary, not sufficient: it says nothing about stability or whether the ion can be synthesized.

2.4 Group-contribution property models

Each property is estimated by summing contributions of the groups present. The 2013 paper used, after Gardas and Coutinho (2009), a Vogel–Tammann–Fulcher form for electrical conductivity and an Orrick–Erbar form for viscosity:

The lab evaluates Eq. 2.7 with η in cP, ρ in g cm⁻³ and M in g mol⁻¹, which agrees with the paper’s tabulated viscosities to within 2% and reproduces its conductivity exactly (check table in the lab). V in ų; a = 0.8005, b = 6.652 × 10⁻⁴ K⁻¹, c = −5.919 × 10⁻⁴ MPa⁻¹ (coefficients of Gardas and Coutinho, 2008, as used in the 2013 paper). The melting-point model (the paper’s Eqs. 35–36, after Aguirre and co-workers, 2012) adds cation symmetry and flexibility terms.

2.5 Solving the design problem

The paper solved its case studies two ways: by decomposition, applying structural, pure-component and mixture constraints in sequence, and by a genetic algorithm. For maximum conductivity with η < 65 cP and T_m < 298.15 K, decomposition enumerated 138 structures, kept 26, and selected 1-methylimidazolium [Tf₂N]; the genetic algorithm picked the same structure. For toluene/heptane separation the sequence was 185 → 27 → 1. Chapter 4 reimplements the genetic algorithm on this lab’s design space.

2.6 Limits, and what comes next

Group contribution works only for groups with fitted parameters, assumes contributions add, and cannot see isomers or long-range effects. The founder’s next step (dissertation, 2015; Fluid Phase Equilib. 2016) built melting-point and viscosity correlations on quantum-chemical descriptors that can be computed for any ion with a COSMO calculation; Chapter 3 covers that work and the step after it, descriptors learned from data. LILM is designed to combine all three, each with an applicability domain and an interval. Planned

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).

4.1 Problem classes

With only continuous variables and linear functions, Eq. 4.1 is an LP; with nonlinear functions, an NLP; with integers and linear functions, an MILP; with both integers and nonlinear functions, an MINLP. Convexity matters: in a convex problem every local optimum is global. Activity-coefficient models make molecular design nonconvex, so local solvers can stop at poor designs, and certifying a global optimum requires bounding techniques.

4.2 Branch-and-bound

Branch-and-bound relaxes the integrality of y, solves the relaxation for a lower bound (for minimization), and branches on a fractional variable. A node is pruned when its bound is worse than the best feasible solution found. For nonconvex problems, spatial branch-and-bound also branches on continuous variables and builds convex underestimators; branch-and-reduce adds range reduction, the approach behind the BARON solver (Tawarmalani & Sahinidis, 2005); range reduction is used by most deterministic global solvers. The gap between the best bound and the best solution certifies how far from optimal the answer can be.

4.3 Decomposition: outer approximation and generalized Benders

Outer approximation (Duran & Grossmann, 1986) alternates two problems. Fixing y^k gives an NLP whose solution x^k is feasible and yields an upper bound. Linearizing at that point gives a mixed-integer master problem whose solution is a lower bound for convex MINLPs:

Generalized Benders decomposition (Geoffrion, 1972) projects onto the integer space and builds the master from Lagrangian cuts instead of full linearizations: fewer constraints, usually weaker bounds. The decomposition used in the 2013 study is a different, problem-specific kind: constraints are applied in stages, structural first, then pure-component, then mixture, so most candidates are eliminated before the expensive models run.

4.4 Genetic algorithms

A genetic algorithm evolves a population of encoded candidates: selection favors fitter parents, crossover recombines them, mutation adds random change, and elitism carries the best forward unchanged. It needs no derivatives and tolerates discontinuous or noisy objectives, but it certifies nothing about optimality. The 2013 study’s implementation (MATLAB, most parameters at default values) used a population of 20, a crossover fraction of 0.8, a mutation probability of 0.2 and two elite candidates per generation, with fitness equal to the objective.

4.5 Multiple objectives and the Pareto front

Design objectives conflict: capacity against viscosity, performance against toxicity, cost against life-cycle impact. A design x dominates x′ if it is no worse in every objective and strictly better in at least one; the non-dominated set is the Pareto front.

Weighted sums can miss parts of a nonconvex front; the ε-constraint method (optimize one objective, bound the others) traces it fully. NSGA-II (Deb et al., 2002) ranks a population by non-domination and preserves spread with a crowding distance. The Pareto chart on the Science page is a multi-objective replot of the founder’s 2016 thermal-storage results.

4.6 Bayesian optimization

When each evaluation is expensive, such as a synthesis and measurement, the number of evaluations matters more than computing time. Bayesian optimization fits a Gaussian-process surrogate (Chapter 8) and chooses the next point by an acquisition function. Expected improvement (Mockus, Tiešis & Žilinskas, 1978; used in the EGO algorithm of Jones, Schonlau & Welch, 1998), for minimization:

μ, σ: surrogate mean and standard deviation; Φ, φ: standard normal CDF and density; f_min: best value so far. The first term rewards predicted improvement; the second rewards uncertainty. With constraints, EI is multiplied by the predicted probability that each constraint holds.

4.7 Optimization under uncertainty

Every property in a design problem is a prediction with error. Three standard formulations carry that error into the decision:

In molecular design, a chance constraint reads naturally: the predicted chronic EC₅₀ must exceed a threshold with 95% probability, not merely on average. That requires calibrated predictive distributions, which is why uncertainty quantification (Chapter 8) is part of the optimization layer, not an add-on. Chapter 5 writes the full design problem this way. Planned

5.1 Why sequential design fails

The usual sequence finds a molecule, characterizes it, finds an application, engineers a process, and only then discovers toxicity, recovery or cost problems that send it back to the start. Each late failure discards the work of every earlier stage. A simultaneous formulation states every constraint up front, so a liquid with excellent selectivity but a carcinogenic precursor, or unrecoverable solvent loss, can be rejected by a cheap model before anyone makes it.

5.2 Seven levels

Specifications flow down from the market; constraints and costs flow up from chemistry and engineering. Each level has its own models and its own uncertainty.

5.3 The formulation

Let s be the ion pair, r the synthesis route, x the process and plant variables, z(s) the latent descriptors of s, and ξ the uncertain quantities (model errors, prices, yields). The planned problem:

The objective can be replaced by cost per functional unit or turned into several objectives for a Pareto analysis. Integer choices (s, r), nonconvex physics and expectations over ξ make this a stochastic MINLP; Section 5.5 describes how it is meant to be solved. Planned

5.4 Fourteen criteria

Each criterion in a commercial decision, with how it would be measured or predicted, a reference threshold where one exists, and its status today.

No chemical is non-toxic in an absolute sense; the design target is hazard below a stated threshold, with stated confidence, at the expected exposure. Ionic liquids are not automatically non-flammable: Smiglak and co-workers (2006) reported that many are not flammable themselves but a large group, including commercial ones, are combustible.

5.5 Solution strategy

Multi-fidelity filtering. Cheap models screen first, expensive ones confirm: structural rules and group contribution (microseconds per candidate), COSMO-RS (seconds per ion pair once ion σ-profiles exist; each new ion first needs a DFT/COSMO calculation of hours), higher-level quantum chemistry (hours to days), then synthesis and measurement (weeks). Each stage passes forward only candidates whose interval still overlaps the targets.

Bilevel decomposition. The outer problem chooses s and r; for each, an inner problem optimizes the process and returns its best value:

Constrained Bayesian optimization would choose which candidates get expensive evaluation, by expected improvement times the probability of satisfying every constraint (Gardner et al., 2014; Chapter 4). The product form assumes independent constraint models:

Decision. The planned output is a short list rather than a single score: make, do not make, or run the experiment expected to teach the most, each with expected performance, intervals and the evidence behind it.

5.6 Latent parameters as design variables

The founder’s 2016 work replaced van der Waals radii with radii from an empirical correlation calibrated to the few ions of known X-ray radius (Chapter 3, Eq. 3.4). Latent descriptors go further: each ion gets a vector z of fitted numbers with no assigned physical meaning, and the property model becomes p = f_phys(s) + g_θ(z). Lab 3.1 shows such vectors cutting the relative error on held-out cells of a published, COSMO-RS-computed table from about 5.8% to about 2.4–2.8% (k = 1–3). The cells are model outputs, not measurements, so this shows that ion-pair interaction structure can be learned; it does not show experimental accuracy.

Used as design variables, latent descriptors let an optimizer search a continuous space instead of a combinatorial one:

U: utility from the criteria above; σ(z): predictive uncertainty, penalized with weight κ so the search stays near data; dec: mapping from latent space back to a structure that passes the feasibility rules of Chapter 2. This requires a learned generative model of ion structures; the per-ion vectors of Lab 3.1 exist only for ions already in the table and cannot be decoded into new ions.

What latent parameters add: interaction effects that additive physics misses, and a smooth space to search. What they do not add: physical meaning, guaranteed extrapolation, or defensibility by themselves. Their value comes from the data they are fitted to, which is why Avestiq’s planned moat is proprietary measurement data, including failures, rather than the parameters. Planned

5.7 What exists today

6.1 Hazard and risk

Hazard is a substance’s intrinsic capacity to cause harm; risk combines hazard with exposure. Design can lower both: choose ions with lower intrinsic toxicity, and design processes that recover the solvent so little reaches people or water. The founder’s 2016 study found that, for five common ionic liquids and under its release assumptions, modeled freshwater ecotoxicity from making the liquid was nearly an order of magnitude larger than from its release during use. Precursor and route choices can therefore matter as much as the ion itself.

6.2 Dose–response

Concentration–effect data are commonly described by a log-logistic (Hill) curve. The effect at concentration c rises from 0 to E_max:

h: slope (Hill coefficient); EC_x: concentration giving x% effect. A steep curve means EC₁₀ is close to EC₅₀; a shallow one means effects start far below it.

6.3 From acute tests to chronic values

Many endpoints are short-term (acute) EC₅₀ or LC₅₀ values, while life-cycle characterization needs chronic values. In the founder’s 2016 USEtox study, acute data were converted to chronic with an acute-to-chronic ratio of 2 (following USEtox guidance), and no-observed-effect concentrations were extrapolated to EC₅₀ by a factor of 9. Such factors are conventions; they carry uncertainty that should travel with the result.

6.4 Species sensitivity distributions

Species differ in sensitivity. A species sensitivity distribution (SSD) treats the chronic EC₅₀ values of tested species as a sample from a log-normal distribution:

μ, s: mean and standard deviation of log₁₀ EC₅₀ across species; z_p: standard normal quantile (z_0.05 = −1.645). HC₅₀ is the geometric mean; HC₅ is the concentration at which 5% of species are exposed above their chronic EC₅₀.

USEtox builds its freshwater effect factor from the HC₅₀, and the characterization factor from fate, exposure and effect (USEtox 1.01 manual):

6.5 Persistence and bioaccumulation: a PBT screen

Under REACH Annex XIII, a substance is PBT if it meets all three criteria. Persistent: degradation half-life above 60 days in marine water, 40 days in fresh or estuarine water, 180 days in marine sediment, or 120 days in fresh or estuarine water sediment or in soil. Bioaccumulative: bioconcentration factor (BCF) above 2,000. Toxic: long-term NOEC or EC₁₀ below 0.01 mg L⁻¹ for aquatic organisms, or classification as carcinogenic, mutagenic or toxic for reproduction (categories 1A/1B; reproductive category 2 also counts), or specific target organ toxicity after repeated exposure (STOT RE 1 or 2). Very persistent (vP) and very bioaccumulative (vB) use stricter values (half-life above 60 days in water and 180 days in sediment or soil; BCF above 5,000).

Since 2023 the EU CLP Regulation also has hazard classes for persistent, mobile and toxic (PMT) and very persistent, very mobile (vPvM) substances, which matter for water-soluble ions. Mobility is judged from the organic carbon–water partition coefficient: M if log K_oc < 3, vM if log K_oc < 2. The 2016 paper’s K_oc values (log K_oc 2.15–2.60) meet M but not vM for all five liquids; a PMT conclusion would also need the P and T criteria.

Half-life t_½ = ln 2 / k from the paper’s first-order biodegradation rates in water; the paper assigned 1 × 10⁻²⁰ s⁻¹ (effectively no degradation) to liquids it classed as nonbiodegradable. The persistence entries marked “potentially P” are liquids with less than 1% degradation in 28 days, a failed screening test rather than a measured half-life. The bioaccumulation column uses the paper’s fish bioaccumulation factors, estimated from K_ow, as a stand-in for BCF; K_ow-based regressions were developed for neutral organics and are not validated for ions. The toxicity column compares the lowest chronic EC₅₀ with 0.01 mg L⁻¹, which is indicative only, because the criterion is defined on NOEC or EC₁₀. A screen on model inputs is not a regulatory assessment.

6.6 Flammability

Under the OSHA Hazard Communication Standard (Appendix B.6), a flammable liquid has a flash point at or below 93 °C, in four categories:

Negligible vapor pressure makes most ionic liquids hard to ignite as liquids, but it does not make them non-combustible. Smiglak and co-workers (2006) reported that while many ionic liquids are not flammable themselves, a large group, including commercial ones, are combustible, owing to positive heats of formation, oxygen content and decomposition products. Flammability is therefore a criterion to test, not to assume (Chapter 5, Eq. 5.6).

6.7 Human health: from cells to dose

Human-health assessment runs from computational alerts, through in vitro assays (including human cell lines), to in vivo studies where regulation requires them; the OECD test guidelines for each tier are listed in Methods 06. In vitro potency becomes a human dose through in vitro–in vivo extrapolation (IVIVE) and physiologically based pharmacokinetic (PBPK) models, whose equations are given there. Carcinogenicity classifications (IARC groups) apply to precursors and by-products as well as to the product.

7.1 The framework

ISO 14040 and 14044 define four phases: goal and scope (including the functional unit and the system boundary), inventory analysis, impact assessment and interpretation. The functional unit makes comparisons fair. The founder’s 2013 study compared an energetic ionic salt with TNT per megajoule of energy content, not per kilogram, because the two deliver different energy per mass (Methods 07).

7.2 The matrix form of LCA

Heijungs and Suh (2002) wrote inventory analysis as linear algebra. The technology matrix A holds each process’s inputs and outputs; scaling factors s make the system deliver the final demand f; the intervention matrix B converts scaled processes into emissions and resource use g; characterization factors Q turn those into impacts h:

Written this way, sensitivity and uncertainty analysis become matrix calculus, and a design optimizer can evaluate the life-cycle consequence of changing one process step.

7.3 Characterization: from emission to impact

For freshwater ecotoxicity, USEtox multiplies a fate factor (FF, days of persistence in the compartment), an exposure factor (XF, the dissolved fraction) and an effect factor (EF, from the HC₅₀ of Chapter 6): CF = FF × XF × EF, with EF = 0.5/HC₅₀ (USEtox 1.x; the 2023 global recommendations by Owsianiak and co-workers revised the effect basis). The impact of a release is its mass times the CF, in comparative toxic units (CTUe).

7.4 Uncertainty in LCA

Inventory data, characterization factors and use-phase assumptions are all uncertain. The 2016 study propagated part of this by Monte Carlo: metal characterization factors were varied by ±1 order of magnitude; each property input in its Table 2 and each HC₅₀ was given a uniform distribution spanning one order of magnitude either way; the use-phase release fraction was varied from 0.4% to 2%; and 1,000 samples gave 95% intervals. The 2013 study used a sensitivity analysis instead, varying the theoretical-to-actual energy conversion factor by ±30%. A design system should carry such intervals into the ranking, not report them after it (Chapter 5).

7.5 Green-chemistry metrics

Atom economy (Trost, 1991) uses the balanced equation and molar masses. The E factor (Sheldon) counts everything but the desired product as waste, per kilogram of product. Process mass intensity counts total materials used per kilogram of product. When both count the same inputs, E = PMI − 1.

Atom economy is a theoretical ceiling. At 100% yield with stoichiometric reagents and no solvent, the minimum E factor is 1/AE − 1 (with AE as a fraction); real E factors include solvents, excess reagents, work-up and yield losses.

7.6 First-pass cost

Early-stage capital estimates often scale a known plant by capacity with the six-tenths rule (Williams, 1947), C₂ = C₁(S₂/S₁)^0.6. It is an order-of-magnitude tool: the exponent differs by equipment type, and bottom-up techno-economic models replace it once a flowsheet exists. In the design problem of Chapter 5 it supplies a cost estimate early enough to rule candidates out.

8.1 Bayesian inference and MCMC

The posterior combines what the data say with what was known before. Metropolis–Hastings samples it without computing p(D): propose θ′, accept with probability α. With a symmetric proposal the q terms cancel. Methods 03 runs this live on 18 published Henry’s-constant points and shows that the published correction lies far outside the test-set posterior.

8.2 Gaussian processes

A Gaussian process (Rasmussen and Williams, 2006) puts a prior directly on functions. With a squared-exponential kernel and noisy observations y at inputs X, the prediction at x_* is Gaussian with:

ℓ: length scale; σ_f: signal amplitude; σ_n: noise. The variance grows away from the data, which is exactly the “know when it does not know” behavior a design system needs. Hyperparameters are usually set by maximizing the log marginal likelihood −½y^T(K + σ_n²I)⁻¹y − ½ ln|K + σ_n²I| − (n/2) ln 2π.

8.3 Calibration and conformal prediction

An interval is calibrated if a stated 95% interval contains the truth about 95% of the time on new data. Model-based intervals, from a GP, an ensemble or a Bayesian neural network, are only as good as the model’s assumptions. Split conformal prediction (Vovk, Gammerman and Shafer, 2005) adds a distribution-free guarantee: compute absolute residuals on a held-out calibration set of size n, take

If calibration and test points are exchangeable, the interval covers the truth with probability at least 1 − α. Exchangeability is the catch: a new ion family is not exchangeable with the training families, which is why validation splits matter.

8.4 Validation splits that do not leak

Random splits put near-duplicates of test liquids in the training set and overstate accuracy. Harder splits estimate what a design campaign will actually face: hold out whole cation or anion families, split by time of publication, or, the only test that cannot leak, predict before measuring. The founder’s 2016 correlations held out 17 of 37 melting points and 83 of 131 viscosity points, chosen at random; LILM’s planned benchmark uses ion-family holdouts and frozen prospective tests (Platform). Planned

8.5 Graph neural networks

Message-passing neural networks (Gilmer et al., 2017) learn representations directly from molecular graphs. At each step, every atom gathers messages from its neighbors and updates its state; a readout pools atom states into a molecular prediction:

For ionic liquids, cation and anion are separate graphs whose representations must be combined with their interaction; the latent vectors of Chapter 3 are one way to do it. Graph models are data-hungry, and for many ionic-liquid endpoints (toxicity, decomposition, process performance) data cover only tens to hundreds of liquids, which is why LILM is designed around physics-first hybrids. Planned

8.6 Hybrid physics–machine-learning models

Two hybrid patterns recur. In residual learning, a physical model makes the prediction and a learned term corrects it. In parameter learning, the learned model supplies parameters to a physical equation, which keeps the equation’s thermodynamic consistency:

The Henry’s-constant correction of the CO₂ screen (2016), H_mod = 0.7403 H_pred + 7.9697, is the simplest hybrid: a linear recalibration of the COSMO-RS output, fitted on 50 measurements. Predicting NRTL τ parameters from descriptors is a parameter-learning example. The design rule behind LILM: use physics for what physics already knows, and learn only what physics and sparse data cannot supply.

8.7 Active learning

Active learning chooses the next experiment for the information it is expected to provide, not only for its predicted performance. Expected improvement (Chapter 4) balances the two; pure exploration picks the point of largest predictive variance. In a closed loop, every result, including failures, updates the model before the next choice. That loop, run on proprietary measurements, is where Avestiq’s planned defensibility comes from. Planned