Competition-Derived Relative Reactivity and 3D Electronic-State Analysis of Site- and Facial Selectivity in NaBH₄/MeOH Ketone Reductions

Abstract

Yield-based measures of reactivity can be distorted by side reactions and reaction conditions and therefore may not accurately reflect intrinsic reaction rates. In this study, competition experiments, in which two substrates react simultaneously with the same reagent, were used to build a unified kinetic scale for the reduction of ketones by sodium borohydride (NaBH₄) in methanol, expressed as activation free energy differences (ΔΔG ^‡). Kinetic data for 89 structurally diverse ketone reaction faces tracked substituent electronic effects and steric congestion, and transition-state calculations identified methanolysis as the step that determines the identity of the active reductant. A Lasso model trained on 83 of these reaction faces with three-dimensional electron-density, electrostatic-potential, and carbonyl-centered projected CO π* descriptors achieved R ² = 0.804 under strict nested outer leave-one-out cross-validation. The monoketone-derived model recovers the dominant site and face for every diketone examined, with 85.5% of the cross-validation models reproducing all assignments; however, the predicted product distributions are indicative rather than quantitative. The workflow integrates a yield-independent kinetic scale with experimental measurements, theoretical calculations, and data-driven analyses within the evaluated NaBH₄/MeOH domain and provides a basis for testing broader applicability through reaction-specific data, retraining, and validation.

1. Introduction

The ability to precisely control reaction rates and selectivity is of fundamental importance in organic chemistry. The relationship between reaction rates or selectivity and factors such as substituent effects, − geometric features, − and grid-based information − has been studied extensively within the frameworks of quantitative structure–property relationships (QSPR) and quantitative structure–selectivity relationships (QSSR). These approaches have played a key role in understanding organic reactions and controlling both their reactivity and selectivity. , Although stereoselectivity and reaction rates have been examined under specific conditions, systematic analyses of reaction rates across structurally diverse substrates remain limited. Despite the critical importance of reaction-rate information for efficient molecular transformations, side-reaction control, and rational reaction design, kinetic analyses have mostly focused on substituent effects within specific scaffolds, limiting their extension to broader molecular diversity. , This is partly due to the inherent complexity of organic reactions, which often proceed through multistep pathways. In many cases, reactivity is approximated based on product yields , however, yields are influenced not only by intrinsic reactivity but also by competing side reactions and purification processes, rendering them an indirect and potentially misleading proxy for kinetic behavior. Moreover, yield-based evaluations often require optimized conditions, − and the numerous parameters that influence reaction yields are frequently difficult to identify and quantify. Consequently, there is a pressing requirement to establish methods for measuring reaction rates in complex, multistep reaction systems, and for analyzing their correlations with molecular structure.

Competitive reactions, in which two substrates react simultaneously with a common reagent, provide a valuable strategy for comparing relative reaction rates. − When the underlying reaction follows a simple second-order kinetic model, analytical treatment is possible, even in systems where the behavior of the reagent is unclear (eq ).

$$\begin{array}{l}\{\frac{d{A}_1}{dt}=-k_1{A}_{1}f(B)\\ \frac{d{A}_2}{dt}=-k_2{A}_{2}f(B)\Rightarrow \\ \frac{d{A}_2}{d{A}_1}=\frac{k_2{A}_{2}f(B)}{k_1{A}_{1}f(B)}\iff \ln \frac{{[A_2]}_f}{{[A_2]}_0}=\frac{k_2}{k_1}\ln \frac{{[A_1]}_f}{{[A_1]}_0}\end{array}$$ 1

Here, A ₁ and A ₂ represent the concentrations of ketones 1 and 2, respectively; [A ₁]₀ and [A ₂]₀ are their initial concentrations; [A ₁] _f and [A ₂]f are their final concentrations; k ₁ and k ₂ are the respective rate constants; and f(B) is an unknown function of reactant concentration.

Because rate information can be obtained solely from the initial and final substrate concentrations, continuous reaction monitoring is unnecessary. This renders the method particularly advantageous for rapid reactions or systems that are difficult to monitor using spectroscopic or titrimetric techniques. Moreover, when the rate constants k ₁ and k ₂ are expressed using the Eyring equation, their ratio can be represented as follows (eq ):

$$\begin{array}{l}\{k_1=A\exp (-\frac{\mathrm{\Delta }{G}_1^{‡}}{RT})\\ k_2=A\exp (-\frac{\mathrm{\Delta }{G}_2^{‡}}{RT})\\ \Rightarrow \frac{k_2}{k_1}=\exp (-\frac{\mathrm{\Delta }{G}_2^{‡}-\mathrm{\Delta }{G}_1^{‡}}{RT})\end{array}$$ 2

where A is the pre-exponential factor (assumed to be common to both reactions), $\mathrm{\Delta }{G}_1^{‡}$ and $\mathrm{\Delta }{G}_2^{‡}$ are the activation free energies for the two reactions, R is the gas constant [1.99 cal/(mol K)], and T is the reaction temperature (K).

By appropriately selecting substrate pairs with similar reactivities, the difference in activation free energies can be rendered significantly smaller than the absolute activation barriers, i.e.,

$$\mathrm{\Delta }{G}_1^{‡},\mathrm{\Delta }{G}_2^{‡}\gg |\mathrm{\Delta }{G}_2^{‡}-\mathrm{\Delta }{G}_1^{‡}|$$ 3

Under this condition, the exponential dependence of the rate ratio on temperature is markedly reduced, rendering competitive reactions inherently less sensitive to temperature fluctuations than direct kinetic measurements. Consequently, competitive reactions offer a robust and practical approach for quantifying relative reaction rates in organic synthesis and have been successfully employed in several studies. , However, when applied to multistep reactions, such analyses become difficult, as the overall kinetics cannot generally be solved analytically. Moreover, when the rate difference between substrates is large, accurate quantification becomes challenging, limiting the applicability of the method to a small number of closely related substrate pairs. As a result, compiling reliable and comprehensive data sets across a broader range of reactions remains difficult. Evaluating the kinetics of the individual elementary steps, however, extends the method to multistep systems involving structurally diverse substrate pairs.

In the context of ketone reductions, previous studies by our group have demonstrated that exchange repulsion, electrostatic interactions, and orbital effects can collectively account for the observed selectivity trends, − and this framework is therefore used again in the present study. , Lu, Paci, and Leitch previously combined competition-derived relative reactivities with regression analysis for nucleophilic aromatic substitution (SNAr) reactions using ground-state molecular descriptors. The present study applies the classical competition approach to the compositionally evolving NaBH₄/MeOH reduction system and couples the resulting kinetic scale with carbonyl-aligned 3D electron-density, electrostatic-potential, and projected CO π* fields, allowing site and facial selectivity to be treated within the same local reaction-face representation. Although site-selectivity for multifunctionalized ketones is of synthetic importance, , such substrates are often commercially unavailable, and their reactions are inherently complex. As a result, compared to stereoselectivity, data-driven analysis of site-selectivity has remained largely inaccessible. Here, we use competition experiments to convert experimentally measured relative reduction rates of simple ketones into a local-reactivity scale within the NaBH₄/MeOH domain, analyze the mechanistic origin of that scale, and evaluate a 3D electronic-state model for site- and face-selectivity in the examined diketones (Figure ).

1.

Concept of the current study. (A) Mechanistic analysis of NaBH₄ reduction and methanolysis pathways. (B) Acquisition and validation of the applicability of competitive reactions for quantifying NaBH₄ reduction reactivity in methanol. (C) Computation of 3D electronic states and analysis of their influence on competitive reactions. (D) Prediction of NaBH₄ reduction site- and facial selectivity. Together, (A–D) integrate competition-derived relative reactivity, mechanistic analysis, and 3D electronic-state modeling to evaluate site- and facial selectivity in the NaBH₄/MeOH system.

2. Experimental Section

2.1. Competition Experiments

Each commercially available monoketone was evaluated through competition experiments with reference ketones under standardized conditions (Scheme ). Equimolar mixtures of two ketones were prepared in methanol, and NaBH₄ was added as a methanolic solution while maintaining the temperature at 0 °C (ice bath). The relative amounts of unreacted ketones and their corresponding alcohol products were determined from integrated proton nuclear magnetic resonance (¹H NMR) spectra. Rate ratios were obtained from logarithmic plots of substrate consumption, and the corresponding ΔΔG ^‡ values were calculated. Each target ketone was paired competitively with one of three reference ketonesfluorenone (B7), benzophenone (A24), or dibenzosuberone (B9)selected for their distinct reactivity ranges and the reliability of their NMR quantification. This experimental design allows consistent and reproducible measurement of rate ratios across structurally diverse ketones, providing the foundation for subsequent mechanistic analysis and structure–reactivity modeling. For substrates exhibiting facial selectivity, separate ΔΔG ^‡ values were extracted for the two diastereomeric reaction pathways. All experiments were performed in parallel using 96-well plates and multichannel pipettes, enabling efficient data collection; detailed experimental procedures are provided in the Supporting Information.

1. Competitive Reaction Conditions and List of Substrates .

^a Ketone stock solutions were prepared in methanol, and NaBH₄ was dissolved in precooled methanol (−20 °C) immediately before addition. All reactions were conducted at low temperature (0 °C, ice bath) to suppress side reactions. Each target ketone was subjected to competitive reduction against one of three reference ketones: fluorenone (B7), benzophenone (A24), or dibenzosuberone (B9). *Diastereoselectivities were also measured.

In the 96-well format, different wells corresponded to independent substrate-pair/NaBH₄-amount conditions. After the reaction, each well was quenched, worked up, and analyzed individually by ¹H NMR. The accompanying XLSX records 309 occupied-well reactions, all of which yielded complete paired residual-substrate fractions used in rate-ratio regression. These measurements produced 89 quantified monoketone reaction-face entries for subsequent analysis.

2.2. Analysis of the Reaction Mechanism

Density functional theory (DFT) calculations were carried out using the ωB97X-D functional , in combination with the def2-TZVP basis set, as implemented in Gaussian 16. Solvent effects were included using the SMD model, with methanol as the solvent. Geometry optimizations and subsequent frequency calculations were performed to characterize stationary points. Ground states were confirmed by the absence of imaginary frequencies, and transition states were validated by the presence of a single imaginary frequency followed by intrinsic reaction coordinate (IRC) calculations to verify connectivity to the corresponding reactants and products. Free energy corrections were applied to adjust for standard-state changes of methanol, NaBH₄, and the ketone substrates. , The solvation free energy of methoxide (−104.5 kcal mol^–1) was taken from the literature and added to the gas-phase free energy. To model the coordination of sodium cations, explicit methanol molecules were included to reflect a coordination number of five. For cyclohexanone reduction, three representative mechanistic pathways were examined, namely the stepwise methanolysis of NaBH₄, ketone reduction mediated by Na⁺/BH₄ ^– ion pairs, and reduction via neutral borane intermediates. Natural bond orbital (NBO) analysis was conducted to evaluate the charge distribution on the hydride and carbonyl carbons in key transition states. Considering the most energetically favorable pathway, additional calculations were performed for benzophenone, p-nitroacetophenone, acetophenone, and p-methoxyacetophenone to extend the analysis to representative aromatic ketones with varying electronic substituents. Independent Gradient Model based on Hirshfeld partitioning (IGMH) and energy decomposition analysis combined with natural orbitals for chemical valence (EDA-NOCV) were also applied to selected transition states to examine real-space contacts and interaction-energy components, respectively; full computational protocols are provided in the Supporting Information.

2.3. Analysis of Reduction Site-Selectivity in 5α-Pregnane-3,20-dione

Site-selectivity in the reduction of 5α-pregnane-3,20-dione was examined by varying the number of NaBH₄ equivalents and monitoring the conversion of each alcohol product; detailed procedures are provided in the Supporting Information. Because this compound is sparingly soluble in pure methanol, it was dissolved in a MeOH/CH₂Cl₂ solvent mixture, and a methanolic solution of NaBH₄ was introduced under cooling (0 °C, ice bath). The reaction rate associated with each carbonyl site was quantified from the integrated ¹H NMR spectra. Reaction profiles were constructed by plotting the conversion at each carbonyl site against the overall reaction extent.

2.4. 3D Electronic-State-Based Reactivity Modeling and Site-Selectivity Prediction

The initial structures of the monoketone and diketone molecules were generated using the ETKDG method, and each structure was preoptimized using the MMFF94 force field with RDKit software. Subsequent refinements were performed at the B3LYP-D3­(BJ)/def2-SVP level of theory; vibrational frequency calculations using Gaussian 16 confirmed the absence of imaginary frequencies for all optimized conformers. Conformers were aligned in a right-handed coordinate system: the ketone carbon was placed at the origin, the oxygen atom at (x ₀, 0, 0) (x ₀ > 0), and the two α-carbon atoms at (x ₁, y, z ₁) and (x ₂, y, z ₂), with z ₁ > z ₂. For substrates possessing two diastereotopic faces, alignments were carried out separately for each face. For the diketones, alignment was performed for each carbonyl group. Single-point energy and wave function calculations were performed at the ωB97X-D/def2-TZVP level using Gaussian 16 with the SMD model for methanol. , Gaussian cube files were generated for the total electron density ρ­(r), electrostatic potential E(r), and a carbonyl-centered, HOMO-gap-damped projected CO π* orbital. The orbital descriptor was constructed by projecting a local carbonyl π* seed onto the canonical virtual-orbital space, scaling each projected component by the inverse of its energy gap from the HOMO, and normalizing the resulting field. The electronic density and electrostatic-potential fields were transformed with a density-dependent kernel centered at ρ = 10^–2 e Bohr^–3, whereas the projected-orbital values were squared. After 2-Bohr binning, folding about y = 0, Boltzmann averaging over conformers, and restriction to the compact carbonyl-centered region, each block contained 105 grid values plus maximum and minimum summary features, giving 321 features in total. PLS, Ridge, Lasso, Elastic Net, and orthogonal matching pursuit were compared using scikit-learn. The final model used Lasso with 83 of the 89 quantified monoketone reaction-face observations. The remaining six observations were displayed only as excluded comparisons and were not treated as an independent validation set; the substrates concerned and the domain criterion applied to each are listed in Table S4 of the Supporting Information. In strict nested outer leave-one-out cross-validation (LOOCV), descriptor scaling, α selection by inner LOOCV, and model fitting were repeated without the outer held-out entry; diketone entries were excluded from scaling and model selection. The finalized model was trained on monoketone ΔΔG ^‡ values (Figure A) and then applied to site- and face-specific diketone pathways (Figure B). Reduction outcomes for 5α-pregnane-3,20-dione were measured in this study, whereas outcomes for the other diketones were taken from the literature. Using the predicted values, product-ratio evolution was simulated over the reduction course. Predicted distributions at maximum total monoalcohol accumulation were compared with monoreduction outcomes, and complete-conversion distributions were used for fully reduced products. Detailed procedures and data set information are provided in the Supporting Information. The two levels differ because the mechanistic calculations involve a limited number of explicitly solvated transition states, whereas the descriptor workflow requires optimized geometries for every conformer of all 161 molecular entries; B3LYP-D3­(BJ)/def2-SVP geometries followed by ωB97X-D/def2-TZVP single-point wave function calculations were used to maintain computational tractability while preserving a consistent level of theory.

2.

3D electronic-state-based analysis of ketone reactivity and extension to diketone site-selectivity. (A) Relationship between competition-derived ΔΔG ^‡ and 3D electronic descriptors. The 3D electronic-state features computed for each ketone reaction face were correlated with the experimental ΔΔG ^‡ values to construct an interpretable structure–reactivity model. (B) Electronic-state-based analysis of unsymmetrical diketone reductions. The model derived from monoketone reaction faces was applied to the individual reaction faces of diketone carbonyl groups to predict site- and stereoselectivity.

3. Results and Discussion

3.1. Competition Experiments

Competitive experiments were performed for a series of ketones using fluorenone (B7), benzophenone (A24), and dibenzosuberone (B9) as reference substrates, as described in the Experimental section. The relative consumption of the competing ketones was quantified by ¹H NMR spectroscopy, and logarithmic plots of the substrate ratios yielded ΔΔG ^‡ according to eqs and . Data obtained using dibenzosuberone or fluorenone as the reference substrate were converted to an equivalent benzophenone-based scale, and the consolidated ΔΔG ^‡ values are summarized in Figure . These experiments yielded reproducible results, with uncertainties within ± 0.10 kcal mol^–1 or 10% in ΔΔG ^‡. The corresponding confidence intervals for the measured ΔΔG ^‡ values are included in Figure . Accordingly, Figure A can be read as a reactivity map: more negative ΔΔG ^‡ values indicate faster reduction relative to benzophenone, whereas more positive values indicate slower reduction. Thus, for a ketone or a diketone containing multiple carbonyl sites or faces, the site or face with the lowest ΔΔG ^‡ is expected to react preferentially. Within each structural class, electron-withdrawing substituents accelerate acetophenone analogues, steric congestion slows aryl and chain ketones, α-electron-withdrawing groups enhance aliphatic ketones, and facial accessibility affects cyclic and polycyclic ketones. For the chain-ketone series shown in Figure C, $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ increases from −1.81 kcal mol^–1 for C3 to +1.33 kcal mol^–1 for C14, with C5 and C13 intermediate reactivity, consistent with progressively greater steric congestion around the carbonyl group and slower hydride approach.

3.

Competitive reduction experiments and unified analysis of ΔΔG ^‡ values. (A) Summary of competition experiment results grouped by ketone scaffold. Relative reactivities expressed as $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ (along with the corresponding rate ratios) are shown for structurally diverse ketones, including aromatic, aliphatic, cyclic, and polycyclic systems. Bars indicate the confidence intervals of the experimentally determined $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ values. (B) Hammett relationship for m- and p-substituted acetophenones. The experimental activation free-energy differences $\left(\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}\right)$ obtained from competition experiments are plotted against the Hammett σ constants, revealing a linear free-energy relationship consistent with the electronic effects governing reactivity. (C) Steric comparison within the chain-ketone series. The $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ values for C3, C5, C13, and C14 are −1.81, −0.80, −0.28, and +1.33 kcal mol^–1, respectively, and increase with steric congestion around the carbonyl group. All $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ values are reported relative to benzophenone. For substrates with high or low reactivity, fluorenone or dibenzosuberone was used as the competing substrate, and the corresponding correction factors ( $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ = −1.75 kcal mol^–1 for fluorenone and +1.02 kcal mol^–1 for dibenzosuberone, relative to benzophenone) were applied.

To evaluate the internal consistency of the method, “cycle closure” was verified by comparing direct and indirect ΔΔG ^‡ values obtained through different reference ketones. Agreement among the three reference systems confirmed the additivity of ΔΔG ^‡ values and enabled construction of a unified kinetic scale, as shown in detail in the Supporting Information. This normalization procedure enabled quantitative comparison of structurally diverse ketones, including aromatic, aliphatic, cyclic, and acyclic systems, on a common energetic basis. Across all 89 quantified reaction-face entries, the ΔΔG ^‡ values spanned approximately −2.60 kcal mol^–1 (k ₂/k ₁ = 120) for 1-chloropinacolin to +3.70 kcal mol^–1 (k ₂/k ₁ = 0.00110) for the exo pathway of fenchone. Among the nonface-resolved substrate entries, the highest value was +2.83 kcal mol^–1 (k ₂/k ₁ = 0.00546) for 2,2,2-triphenylacetophenone. Linear free-energy relationships were also evident: for p- and m-substituted acetophenones, the ΔΔG ^‡ values correlated negatively with the Hammett σ constants, consistent with a nucleophilic reduction mechanism. Collectively, these results show that the competitive reaction method provides precise and internally consistent relative kinetic information across the evaluated substrate set. The extracted ΔΔG ^‡ values rationalize substituent and strain effects, while also establishing a robust basis for the mechanistic analysis and reactivity modeling described in the following sections.

3.2. Analysis of the Reaction Mechanism

Scheme summarizes the mechanism of NaBH₄ methanolysis in methanol and the subsequent reduction of a representative ketone substrate, cyclohexanone. Although previous computational studies have proposed several possible pathways for the methanolysis of NaBH₄, these mechanisms did not satisfactorily account for the trends observed in our competitive reduction experiments. , In contrast, the mechanism shown in Scheme provides a coherent explanation of the experimental results by explicitly considering both the methanolysis of NaBH₄ and the reduction of cyclohexanone as a model ketone substrate.

2. Mechanistic Analysis of NaBH₄ Reduction in Methanol and Comparison with Experimental Results .

^a (A–D) Computed Gibbs free energy ΔG _DFT profiles for the examined reaction pathways. The NBO charges of the hydride and the carbonyl carbon atoms in the transition states of each reduction step are also shown. (E) Comparison of $\mathrm{\Delta }{G}_{\mathrm{D}\mathrm{F}\mathrm{T}}^{‡}$ for methanolysis and ketone reduction across four borohydride species. Experimental activation free-energy differences Δ $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ obtained from competition experiments are reported relative to benzophenone. For facial selectivity analysis, the results obtained for 4-tert-butylcyclohexanone were used in place of cyclohexanone. All calculations were conducted at the ωB97X-D/def2-TZVP level using the SMD model with methanol as the solvent. Frequency analyses confirmed that each optimized ground-state structure corresponds to a local minimum, while each transition state exhibited a single imaginary frequency. IRC calculations verified that each transition state connects the corresponding reactant and product.

In this work, the methanolysis of NaBH₄ to afford Na­(MeO) _n BH_4–n (n = 0–3) was analyzed based on a protonation pathway, followed by the formation of ion pairs between the resulting boron species and NaOMe. The reduction pathways involving Na­(MeO) _n BH_4–n and the ketone substrates were then examined with explicit consideration of countercation effects. For NaBH₄ itself (n = 0), the calculated activation free energy for ketone reduction (26.5 kcal mol^–1) is higher than that for methanolysis (21.8 kcal mol^–1), indicating that methanolysis is favored and proceeds to generate Na­(MeO)­BH₃ as a more reactive intermediate (Scheme A). The experimentally observed hydrogen evolution during the reduction of 3,3,5-trimethylcyclohexanone with NaBH₄ in methanol is consistent with this methanolysis pathway.

In contrast, for Na­(MeO) _n BH_4–n (n = 1–3), the activation free energies for ketone reduction (13.8, 15.4, and 16.2 kcal mol^–1 for n = 1, 2, and 3, respectively) are lower than those for further methanolysis (23.0, 26.3, and 28.4 kcal mol^–1 for n = 1, 2, and 3, respectively, Scheme B–D). These results indicate that the methoxy-substituted borohydrides preferentially function as reducing agents, generating Na­(MeO) _n+1BH_3–n species as downstream intermediates. NBO charge analysis revealed that the hydride becomes more negatively charged upon methoxylation: BH₃–H (−0.094), MeOBH₂–H (−0.195), (MeO)₂BH–H (−0.218), and (MeO)₃B–H (−0.214), with similar values for n = 2 and 3. This enhanced hydride basicity/nucleophilicity suggests that these species can more effectively attack electrophilic carbonyl carbon atoms, whose partial positive charges lie in the range of +0.225 to +0.374. EDA-NOCV analysis further showed that the transition state leading to the equatorial alcohol has a more favorable ORCA EDA bond energy than that leading to the axial alcohol (−39.12 vs −34.92 kcal mol^–1), despite greater Pauli repulsion (200.49 vs 193.44 kcal mol^–1); the more favorable electrostatic, orbital, exchange–correlation preparation, and dispersion energy terms collectively compensate for this penalty (Figure S4 and Table S2 in Supporting Information).

A similar trend has been reported for isopropanol-mediated ketone reductions, wherein the second and subsequent reduction steps proceed more readily than the first, indicating that alkoxylation of the boron center enhances hydride nucleophilicity and overall reactivity. Likewise, the enhanced reactivity observed upon introduction of nucleophilic additives supports a positive correlation between hydride nucleophilicity and reduction efficiency. The high reactivity of boron hydrides in methanol or aqueous media can therefore be rationalized by the introduction of alkoxy or hydroxy groups, which increase the nucleophilic character of the B–H bond.

The barrier comparisons indicate that NaBH₄ preferentially undergoes methanolysis before direct ketone reduction, whereas Na­(MeO) _n BH_4–n (n = 1–3) preferentially transfers hydride to the ketone rather than undergoing further methanolysis (see Supporting Information). Thus, methanolysis determines the identity of the active reductant, whereas substrate and facial selectivity are expressed at the subsequent hydride-transfer transition states. For Na­(MeO)­BH₃, the pathway to equatorial cyclohexanol is 2.1 kcal mol^–1 lower than that to axial cyclohexanol (13.8 vs 15.9 kcal mol^–1); EDA-NOCV shows that this preference reflects the net balance of stabilizing and repulsive interactions rather than lower Pauli repulsion alone (Figure S4 and Table S2 in Supporting Information). The faster reduction of electron-poor acetophenones is likewise consistent with increased carbonyl electrophilicity indicated by the Hammett and NBO charge analyses.

Overall, the combined experimental and computational results support a mechanistic picture in which NaBH₄ is first converted by methanolysis to methoxy-substituted borohydrides, and the ensuing lower-barrier hydride-transfer steps from these more nucleophilic species determine substrate and facial selectivity. The high internal consistency of the competitive reaction data imposes strong constraints that significantly reduce the ambiguity typically associated with purely computational mechanistic studies.

3.3. Site-Selectivity of Diketone Reduction Reactions and Competition Experiments

To evaluate the applicability of the monoketone-derived kinetic scale, the reduction of 5α-pregnane-3,20-dione was examined while varying the amount of NaBH₄ (Figure A). The corresponding monoketone competition data predicted preferential reduction at C3 via pathway 2 (Figure B). Experimentally, the C3 monoalcohol was isolated in 88% yield with 87% dr. Thus, the monoketone-derived kinetic scale correctly identified both the dominant site and facial preference in an unsymmetrical diketone evaluated experimentally in this study under the stated MeOH/CH₂Cl₂ (3:2, v/v) conditions.

4.

Site-selectivity analysis of 5α-pregnane-3,20-dione and competition experiments using various monoketones. (A) Reaction progress showing the evolution of site-selectivity as a function of reducing equivalents, along with the isolated yields of the corresponding products. The plots illustrate the relative consumption of each carbonyl site during reduction. (B) Rate constant ratios k ₂/k ₁ and activation free-energy differences $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ obtained from the competitive reduction experiments. All $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ values and rate ratios are reported relative to benzophenone.

3.4. Machine Learning Modeling

Five regression methods were compared using identical outer leave-one-out cross-validation (LOOCV); Lasso showed the best predictive performance and was adopted for the final model (Figure A). Trained on the 83 monoketone reaction faces with 321 three-dimensional descriptors, it reproduced the training data with R ² = 0.986 (RMSE = 0.158 kcal mol^–1) using only 53 nonzero features. Under strict nested outer LOOCV, in which all scaling steps and the Lasso penalty α were redetermined after removing each held-out reaction face, it predicted the held-out ΔΔG ^‡ values with R ² = 0.804, RMSE = 0.581 kcal mol^–1, and MAE = 0.435 kcal mol^–1 (Figure B), with residuals distributed evenly over the five structural classes (class-wise RMSE 0.501–0.657 kcal mol^–1). The lower outer-LOOCV performance reflects prediction on held-out observations rather than in-sample fitting. Under the more stringent leave-one-structural-class-out validation, the pooled test-set predictions retained a degree of predictive ability (R ² = 0.498 and RMSE = 0.929 kcal mol^–1; Figure S13B and Table S13). The diketones discussed below were excluded from both descriptor scaling and model selection at every stage; their analysis therefore represents an application of a monoketone-only model rather than a fit. Feature selection was also stable to omission of individual training observations: all 53 features retained by the full-training model were selected in at least 63.9% of the 83 outer models (median selection frequency, 97.6%), and the coefficient sign of each feature was unchanged whenever it was selected (Figure S12 and Table S12).

5.

Machine-learning analysis of competition-derived ΔΔG ^‡ values. (A) Outer LOOCV R ² and RMSE values for PLS, Ridge, Elastic Net, Lasso, and orthogonal matching pursuit; Lasso was used for the final model. (B) Experimental versus predicted ΔΔG ^‡ values for the full-training Lasso fit and strict nested outer LOOCV predictions (N = 83 for each); six excluded monoketone observations are shown for comparison but were not used for model fitting. (C) Distributions of centered electronic, electrostatic, and projected-orbital block contributions over the 83 training observations. (D) Experimental ΔΔG ^‡ values for A1–A13 relative to A24 versus the electrostatic descriptor contribution (r ² = 0.95, N = 13). (E) Experimental ΔΔG ^‡ values for the C series relative to A24 versus the electronic descriptor contribution (r ² = 0.80, N = 15); C11 and C16 were omitted from the illustrative linear fit. The lower-center examples show that α-cyano substitution outside the ring-substituent Hammett series (A1 → A13) changes $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ by −1.86 kcal mol^–1 together with a −1.60 kcal mol^–1 change in the electrostatic model contribution, whereas chain branching (C13 → C14) changes $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t.}}^{‡}$ by +1.61 kcal mol^–1 together with a +0.92 kcal mol^–1 change in the electronic model contribution.

Descriptor contribution analysis identifies the features that most strongly influence model predictions. Here, the electron-density field locates the molecular density envelope around the aligned carbonyl, the electrostatic-potential field samples the signed potential over the same region, and the projected CO π* field represents local virtual acceptor character. Their regression-derived contributions are statistical terms in the predicted ΔΔG ^‡ values and do not represent independently calculated steric, electrostatic, or orbital interaction energies. The electron-density and electrostatic-potential blocks vary far more strongly across the training set than the projected CO π* block, and 50 of the 53 retained features belong to these two blocks (Figure C). Thus, within the present chemically diverse data set, the aligned 3D representation draws most of its fitted signal from spatial occupancy and electrostatic differences around the carbonyl. Consistently, the acetophenone series tracks the electrostatic contribution (r ² = 0.95, N = 13), whereas the chain aliphatic ketones track the electron-density contribution (r ² = 0.80, N = 15; Figure D, E). A single carbonyl-centered representation therefore recovers two chemically distinct structure–reactivity trends without requiring scaffold-specific descriptors to be encoded by hand. Because these relationships are derived from the fitted regression model, they should be interpreted as model-level consistency with established physical-organic trends, not as independent evidence for a unique physical decomposition.

Applied to 5α-pregnane-3,20-dione, this monoketone-trained model reproduced both the site- and the face-selectivity observed experimentally (Figure A and Scheme A). Among the four first-reduction pathways, the pathway leading to the equatorial C3 alcohol had the lowest predicted barrier, 1.49 kcal mol^–1 below the best C20 pathway, accounting for exclusive reduction at C3; the equatorial-over-axial preference at C3 was much smaller, 0.47 kcal mol^–1, and originated from the electron-density block. Propagating these barriers through the sequential network also reproduced the evolution of the product distribution with added NaBH₄: the C3 monoalcohol accumulated to a predicted 83.5%, with 69.7% dr, compared with an experimental isolated yield of 88% and 87% dr, before further reduction to the 3,20-diol, for which the model selects the observed diastereomer.

3. Predicted and Experimentally Observed Reduction Behaviors of Unsymmetrical Diketones .

^a Unless otherwise noted, reductions were carried out using NaBH₄ in methanol as the solvent. (A) Reduction performed at 0 °C in a mixed solvent system of MeOH/CH₂Cl₂ (3:2, v/v); isolated yields and stereoselectivities were determined after purification. The selectivity profiles were quantified by ¹H NMR analysis based on independently conducted experiments, with spectral assignments and structural references taken from the following reports. , (B) Reduction conducted in MeOH/THF (1:1, v/v) at 0–5 °C for 1 h, affording the product in 76.3% isolated yield. (C) Reduction carried out in MeOH/THF (4:1, v/v) at room temperature (298 K), yielding the corresponding product with >99% dr; isolated yield is shown. (D) Reduction performed in MeOH/CH₂Cl₂ (1:1, v/v) at 0 °C for 2 h, affording the product with >19:1 dr; isolated yield is shown. (E) Site-selective reduction to the monoketone carried out in MeOH/CH₂Cl₂ (1:1, v/v) at 0 °C using NaBH₄, and stereoselective reduction to the diol using LiAlH₄ in toluene/THF (1:1, v/v) at 0 °C; isolated yields are shown. (F) Selective reduction performed in methanol at 0 °C, affording the product with high selectivity; isolated yield is shown. Here, the original report described the reaction as stereoselective but did not quantify the other stereoisomer. First-step percentages are evaluated at maximum total monoalcohol accumulation; fully reduced-product ratios are evaluated at the final simulation point.

Five further unsymmetrical diketones whose NaBH₄ reductions in methanol-containing solvents have been reported were treated in the same way (Scheme B–F). Each presents 12 distinct reaction faces, and their selectivity changes with the amount of reductant because methanolysis of NaBH₄ generates a succession of solvated Na­(MeO)_nBH_4–n species in situ. Consequently, such networks are difficult to treat kinetically. The model identified the observed major monoalcohol in all five cases and, in one of them, the diastereomeric outcome of a second reduction carried out with LiAlH₄ (Scheme E); the barriers, descriptor-block contributions and simulated populations behind every assignment are collected in SI Tables S6–S11. Across the 83 observation-level LOOCV models, 85.5% reproduced all eight primary diketone assignments. Under the more demanding structural-class holdout, complete initial site-and-face assignments were correct in 66.7% of the first-reduction model–diketone cases; initial sites were correct in 90.0%, and facial assignments across the first and evaluated second reductions were correct in 72.5% (Table S15). Thus, site selectivity remained relatively well reproduced even after omission of an entire structural class, whereas facial assignment was more sensitive to the smaller energy differences between competing faces. These are qualitative to semiquantitative literature comparisons rather than an independent quantitative validation: the conditions differ from ours, and because synthetic reports preferentially document selective transformations, the set is biased toward well-differentiated cases. Hence, the agreement is best read as an upper bound on assignment accuracy.

Two natural extensions of the approachnew reagent systems and an absolute kinetic scalerequire additional data. The kinetic scale is calibrated for NaBH₄ in methanol, but the descriptors are defined uniformly and only the regression coefficients are reagent-specific. Therefore, another hydride donor or solvent needs a fresh competition series, retraining, and validation rather than a new methodologyand the 96-well workflow makes such a series inexpensive to acquire. Reactivity is likewise expressed as ΔΔG ^‡ relative to a reference ketone, so a single in situ kinetic measurement using that reference would place the whole data set on an absolute scale at once. Only 5α-pregnane-3,20-dione was measured under our own conditions, and the diketones with the smallest predicted pathway separations are at once the least tested and the most informative next targets for a parallel workflow.

Chemoselectivity is the wider opening. Carbonyl ΔΔG ^‡ values can already be quantified in the presence of ethers, epoxides, nitriles, conjugated and nonconjugated alkenes, nitro groups, halides and ketals, but the model ranks carbonyl sites and does not predict whether a highly conjugated diaryl enone will prefer undergoing borohydride-promoted alkene hydrogenation over carbonyl reduction under particular countercation and solvent conditions. A route forward lies in competition data involving a noncarbonyl group as the competing site, together with a descriptor that explicitly carries interaction information: the projected CO π* field used here is a model input rather than an interaction energy (Table S2 and Figure S4 in Supporting Information), and combining it with the energy-decomposition analysis of the transition states offers one route toward such a descriptor.

4. Conclusions

In this work, competition experiments were used to quantify relative reactivity in NaBH₄-mediated ketone reductions in methanol under synthetically relevant conditions. By exploiting the logarithmic relationships inherent in competitive reactions, the relative rate constants and ΔΔG ^‡ values were determined and organized on a unified kinetic scale for a broad set of structurally diverse ketones. Correlations with Hammett parameters and steric congestion revealed that electronic, electrostatic, and steric effects cooperatively govern reactivity across aromatic, aliphatic, cyclic, and polycyclic substrates. Transition-state calculations further identified methanolysis as the step that fixes the identity of the active reductant, whereas the subsequent hydride transfer step determines substrate and facial selectivity. Building on these data, an interpretable three-dimensional (3D) electronic-state model using electron-density, electrostatic-potential, and carbonyl-centered projected CO π* descriptors achieved R ² = 0.804 under strict nested outer LOOCV and correctly predicted the experimentally observed major site and face for every diketone examined, with 85.5% of the cross-validation models reproducing all eight assignments. The competition-derived kinetic scale and 3D electronic-state workflow may be adapted beyond NaBH₄ and methanol to other hydride reagents, solvents, and nucleophilic additions to carbonyl compounds, but each new reaction class will require reaction-specific competition data, retraining, and validation. Moreover, the curated kinetic database and descriptor workflow reported here provide a foundation on which researchers can perform further substrate–descriptor analyses, construct new predictive models, and test mechanistic hypotheses for complex reduction manifolds.

Processed competition/model data sets, fitted parameters, and prediction code are available in the GitHub repository: https://github.com/poclab-web/3D_electronic_analysis_for_site-selectivity. The complete model inputs, validation audits, and prediction results underlying the analyses reported here are provided in the accompanying Supporting Information ZIP.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.6c01269.

• Model inputs, specifications, validation audits, spatial and comparator analyses, and prediction evaluations and results (ZIP)

• Experimental data sets for monoketone and diketone reductions (XLSX)

• Optimized transition-state coordinates, corresponding energies, and energy decomposition analysis (XLSX)

• Experimental procedures, NMR quantification, cycle-closure validation, scope and mechanistic studies, diketone reductions, and data-driven modeling details (PDF)

Conceptualization, H.G. and D.S.; Methodology, D.S.; Formal analysis, D.S., T.K., M.I., and C.T.; Investigation, D.S., T.K., M.I., and C.T.; Resources, H.G.; Writingoriginal draft preparation, D.S.; Writingreview and editing, H.G. and D.S.; Supervision, H.G.; Project administration, H.G.; Funding acquisition, D.S. and H.G. All authors have read and approved the final version of the manuscript.

This research was partially supported by the Tokyo Ohka Foundation for the Promotion of Science and Technology. D.S. received support from the Next Generation AI Human Resource Development Project (YNU-BOOST), funded by JST under Grant Number JPMJBS2427, and from the JSPS KAKENHI Grant Number JP26KJ1212.

The authors declare no competing financial interest.