Electrospray ionization (ESI) converts dissolved molecules to gas-phase ions with efficiencies that vary by orders of magnitude between compounds, so mass-spectrometric sensitivity cannot be inferred from concentration alone. Oss, Kruve, Herodes and Leito (Analytical Chemistry 2010) established the first broad, self-consistent experimental scale of relative ionization efficiencies (logIE) for 62 diverse organic compounds, spanning six orders of magnitude, and a two-parameter regression on aqueous pKa and molecular volume — but with per-compound prediction errors exceeding 1 logIE unit for poorly ionizing compounds, possible need for chemical-class-specific models, unexplained outliers in the pairwise measurements, untested transferability across solvents and instruments, and no reproducible route to absolute ionization efficiencies. The 2010–2026 follow-up literature resolved parts of this program (a negative-ion model, quantified solvent and pH effects, scale transferability via anchoring measurements, and machine-learning predictors), yet on diverse chemical space the best held-out test errors remain near 0.7–0.8 logIE units, quantification without standards carries multi-fold errors, inter-laboratory variability persists, and absolute IE remains unmeasurable reproducibly. The open problem is a validated framework that predicts ESI ionization efficiency quantitatively from structure and conditions across chemical space, anchored to reproducible scale values.

Background

Electrospray ionization (ESI) is the standard interface for liquid chromatography–mass spectrometry (LC-MS): the eluent is dispersed into charged droplets from which gas-phase analyte ions emerge. The ionization efficiency (IE) of a compound — the fraction of sprayed neutral molecules converted to detected gas-phase ions — varies over more than six orders of magnitude across organic compounds, so two compounds at identical concentrations can give vastly different signals. Because the sprayed concentration CC and measured response RR are related by IE =R/C= R/C, unpredictable IE precludes quantification without authentic calibration standards, which is a central obstacle in non-targeted screening of environmental, food, and biological samples.

To make IE measurable, the Tartu group introduced a relative protocol: two compounds are infused together at known concentrations, and the relative ionization efficiency is RIE⁡(B1/B2)=R1C2/(R2C1)\operatorname{RIE}(B_1/B_2) = R_1 C_2 / (R_2 C_1); averaging over several target-mass settings controls mass-dependent transmission, and each pairwise value is cross-checked against a third compound. Anchoring all pairwise logRIE values by least squares to a reference (methyl benzoate, logIE =0= 0) yields a self-consistent scale of logIE values (logarithm of IE relative to the anchor). Oss, Kruve, Herodes and Leito (2010) built such a scale for 62 chemically diverse compounds under one fixed positive-mode condition (ionization by monoprotonation, i.e. formation of [B+H]+[B+\mathrm{H}]^+; acetonitrile/0.1% aqueous formic acid 80:20; Agilent XCT ion trap), from 407 pairwise measurements, and regressed logIE against computed molecular descriptors: aqueous acidity/basicity pKa\mathrm{p}K_{\mathrm{a}}, gas-phase basicity GB (the negative protonation free energy, from density-functional theory), molecular volume, and COSMO-RS distribution coefficients between the spray solvent and hexane (COSMO-RS is a quantum-chemistry-based solvation model predicting partitioning from screening-charge surfaces). A two-parameter model on scaled pKa\mathrm{p}K_{\mathrm{a}} and log molecular volume explained R2=0.675R^2 = 0.675 with residual standard error 0.81 logIE units; for the 21 amines a distinct three-descriptor model on molecular volume, GB, and the solvent/hexane distribution coefficient cut the residual error to 0.46 logIE units, indicating class-specific ionization behavior. Held-out predictions for 20 compounds erred by up to 1.57 logIE units, and 143 of the 407 pairwise measurements deviated by at least 0.2 logRIE units from the fitted scale for reasons only partly traced to examined experimental factors.

The paper itself framed what remained open: quantitative prediction fails worst for compounds that ionize poorly; other chemical classes may need their own models but the data are too sparse; the outlier sources are unidentified; the scale and its coefficients were established under a single solvent composition and instrument; and absolute IE values (IE =R/C= R/C under fully controlled conditions) could not be measured reproducibly, leaving the community with laboratory-specific relative scales. Subsequent work — negative-ion scales, mobile-phase and pH studies, instrument-transfer experiments, and machine-learning predictors built on molecular fingerprints and large aggregated IE datasets — has advanced each strand, and quantification without analytical standards is now the field's stated motivation, but the assembled evidence (a 2021 tutorial review still cataloguing contradictions, a 37-laboratory comparison with mean errors around 15-fold for the best IE-based approach, and 2023–2025 models with test errors near 0.8 logIE units) shows the general predictive problem is not solved.

Problem Statement

Establish quantitative, transferable prediction of electrospray ionization efficiency from molecular structure together with measurement conditions, completing the program opened by the 2010 ionization-efficiency scale. Concretely: (1) a validated predictive model assigning logIE (or relative response) to organic compounds — including compounds that ionize poorly in ESI — with a root-mean-square error below about 0.7 logIE units on held-out, chemically diverse test sets (improving on the best documented accuracies on diverse chemical space, prediction RMSE around 0.7–0.8 logIE units), together with determining whether chemically class-specific models are required and deriving statistically robust ones where they are; (2) identification of the residual sources of the discrepancies in pairwise logRIE measurements (the source scale was fitted from its pairwise logRIE measurements with consistency standard deviation s = 0.30 logRIE units, and the source analysis ruled out several experimental factors as causes of the remaining deviations without fully identifying them) and of the reproducibility limits of IE measurements across instruments and laboratories; (3) determination of how an established scale and its regression coefficients transfer across solvent compositions, additive identities, and instrument geometries — i.e. prediction either conditioned on, or demonstrated to be invariant under, these conditions; and (4) a measurement approach yielding reproducibly transferable absolute ionization efficiencies (IE = R/C under controlled conditions), removing complete dependence on laboratory-specific relative scales. The four strands are independent components of one objective — converting a laboratory-specific relative scale into a generally valid, quantitative predictor of ESI-MS response — and resolving a proper subset resolves only the strands it covers.

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