Efficient Black-Box Prediction of Hydrogen-Bond-Donor and Acceptor Strength

Corin C. Wagen

Jul 1, 2025

Hydrogen-bond strength is a critical determinant of physicochemical properties and binding affinity in drug discovery, but computationally predicting the strength of different hydrogen-bond donors acceptors remains challenging and inaccessible to non-experts. Here, we report a robust black-box workflow for predicting site-specific hydrogen-bond basicity and acidity in organic molecules with minimal computational cost. Our approach begins with rapid conformer generation and optimization with neural network potentials, followed by a single density-functional-theory calculation of the electrostatic potential. We then calibrate these results against an extensive reference set of experimentally determined pK_BHX and pK_α, achieving high accuracy in both cases. We illustrate the power of this tool in multiple published drug discovery programs, highlighting how per-site pK_BHX tuning can improve bioavailability, minimize efflux, and enhance selectivity.

This preprint can also be viewed on ChemRxiv.

Introduction

Hydrogen bonding is one of the most important non-covalent interactions, and hydrogen bonds frequently comprise key structural elements in biological systems or pharmaceuticals.^1–31. Doyle, A. G.; Jacobsen, E. N. Small-Molecule H-Bond Donors in Asymmetric Catalysis. Chem. Rev. 2007, 107, 5713–5743.
2. Bissantz, C.; Kuhn, B.; Stahl, M. A Medicinal Chemist's Guide to Molecular Interactions. J. Med. Chem. 2010, 53, 5061–5084.
3. Kenny, P. W. Hydrogen-Bond Donors in Drug Design. J. Med. Chem. 2022, 65, 14261–14275.
In medicinal chemistry, tuning the strength of hydrogen-bond donors and acceptors can modulate P-glycoprotein transport, efflux ratio, lipophilicity, and blood–brain barrier permeability.^4–74. Toulmin, A.; Wood, J. M.; Kenny, P. W. Toward Prediction of Alkane/Water Partition Coefficients. J. Med. Chem. 2008, 51, 3720–3730.
5. Desai, P. V.; Raub, T. J.; Blanco, M.-J. How hydrogen bonds impact P-glycoprotein transport and permeability. Bioorg. Med. Chem. Lett. 2012, 22, 6540–6548.
6. Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Sartori, G. R. Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design. J. Med. Chem. 2016, 59, 4278–4288.
7. Borges, N. M.; Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Rocha, J. R.; Sartori, G. R. The influence of hydrogen bonding on partition coefficients. J. Comput. Aided Mol. Des. 2017, 31, 163–181.
For this reason, quantifying the strength of individual hydrogen bonds and understanding how changes to molecular structure affect the strength of individual hydrogen bonds is important in rational molecular design.

Despite the ubiquity of hydrogen bonding in biological systems and medicinal chemistry, the relative strength of different hydrogen-bond donors and acceptors is much less appreciated than other key structural quantities like pK_a, bond-dissociation energy, or torsional preferences. Most frequently, the Brønsted acidity or basicity of a given functional group is used as a proxy for its hydrogen-bonding strength. Although this relationship can be valid along a narrow structural series, in general there is "little to no relationship"⁸8. Laurence, C.; Berthelot, M. Observations on the strength of hydrogen bonding. Perspect. Drug Discovery Des. 2000, 18, 39–60
between a molecule's Brønsted acidity and its hydrogen-bond-donor or acceptor characteristics.^8–108. Laurence, C.; Berthelot, M. Observations on the strength of hydrogen bonding. Perspect. Drug Discovery Des. 2000, 18, 39–60
9. Gurka, D.; Taft, R. W. Studies of hydrogen-bonded complex formation with p-fluorophenol. IV. Fluorine nuclear magnetic resonance method. J. Am. Chem. Soc. 1969,91, 4794–4801.
10. Taft, R. W.; Gurka, D.; Joris, L.; Schleyer, P. v. R.; Rakshys, J. W. Studies of hydrogen-bonded complex formation with p-fluorophenol. V. Linear free energy relationships with OH reference acids. J. Am. Chem. Soc. 1969, 91, 4801–4808.

The strength of different hydrogen-bond acceptors can be measured experimentally by measuring the association constant with a model hydrogen-bond donor in a given solvent.^8–118. Laurence, C.; Berthelot, M. Observations on the strength of hydrogen bonding. Perspect. Drug Discovery Des. 2000, 18, 39–60
9. Gurka, D.; Taft, R. W. Studies of hydrogen-bonded complex formation with p-fluorophenol. IV. Fluorine nuclear magnetic resonance method. J. Am. Chem. Soc. 1969,91, 4794–4801.
10. Taft, R. W.; Gurka, D.; Joris, L.; Schleyer, P. v. R.; Rakshys, J. W. Studies of hydrogen-bonded complex formation with p-fluorophenol. V. Linear free energy relationships with OH reference acids. J. Am. Chem. Soc. 1969, 91, 4801–4808.
11. Laurence, C.; Brameld, K. A.; Graton, J.; Le Questel, J.-Y.; Renault, E. The pKBHX Database: Toward a Better Understanding of Hydrogen-Bond Basicity for Medicinal Chemists. J. Med. Chem. 2009, 52, 4073–4086.
Taking the base-10 logarithm of this association constant gives pK_BHX, the strength of the hydrogen-bond acceptor. While pK_BHX values can be measured for any combination of hydrogen-bond donor, hydrogen-bond acceptor, and solvent, for "a mixture of historical and technical reasons" (Laurence et al.¹¹11. Laurence, C.; Brameld, K. A.; Graton, J.; Le Questel, J.-Y.; Renault, E. The pKBHX Database: Toward a Better Understanding of Hydrogen-Bond Basicity for Medicinal Chemists. J. Med. Chem. 2009, 52, 4073–4086.
) 4-fluorophenol is typically used as the hydrogen-bond donor and carbon tetrachloride is typically used as the solvent. Hydrogen-bond-acceptor strengths measured under these conditions correlate with pK_BHX values measured with other hydrogen-bond donors or in different solvents, although exceptions exist: for instance, pK_BHX values measured with 4-fluorophenol are poorly predictive for C–H hydrogen-bond donors.¹¹11. Laurence, C.; Brameld, K. A.; Graton, J.; Le Questel, J.-Y.; Renault, E. The pKBHX Database: Toward a Better Understanding of Hydrogen-Bond Basicity for Medicinal Chemists. J. Med. Chem. 2009, 52, 4073–4086.

Here, we follow precedent & existing datasets and consider only pK_BHX values measured with 4-fluorophenol in carbon tetrachloride. These pK_BHX values typically vary between about −1 and 5—weak hydrogen-bond acceptors like alkenes have a pK_BHX value between −1 and 0, while strong hydrogen-bond acceptors like amides have pK_BHX values between 2 and 2.5, and only very strong hydrogen-bond acceptors like N-oxides have pK_BHX values greater than 3 (Figure 1).

Figure 1: Archetypal pK_BHX values for various functional groups; this figure depicts only general trends, and exceptions exist in all cases. pK_BHX values were measured using 4-fluorophenol as the hydrogen-bond donor and carbon tetrachloride as the solvent.

While hundreds of pK_BHX values have been experimentally measured under these conditions over the past three decades,^11,1211. Laurence, C.; Brameld, K. A.; Graton, J.; Le Questel, J.-Y.; Renault, E. The pKBHX Database: Toward a Better Understanding of Hydrogen-Bond Basicity for Medicinal Chemists. J. Med. Chem. 2009, 52, 4073–4086.
12. Kenny, P. W. Hydrogen bond basicity data: text file with measured pKBHX val- ues, isomeric SMILES strings and literature references. https://figshare.com/articles/dataset/Hydrogen_bond_basicity_data_text_file_with_measured_pKBHX_values_isomeric_SMILES_strings_and_literature_references/12084183, 2020; [Accessed 17-01-2025].
there is still a need to compute hydrogen-bond-acceptor strength for new organic compounds. Experimental pK_BHX measurements produce a single measure of hydrogen-bond-acceptor strength for the entire molecule, while rational design of functional molecules typically requires atom-level quantification of hydrogen-bond basicity. The strength of different hydrogen-bond acceptors is quite sensitive to the electronic properties of the acceptor, making it crucial to correctly account for the specific substitution of the molecule in question. For this reason, the efficient and accurate prediction of hydrogen-bond basicity has been a topic of active research in computational chemistry for decades.^6,13–216. Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Sartori, G. R. Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design. J. Med. Chem. 2016, 59, 4278–4288.
13. Kenny, P. W. Prediction of hydrogen bond basicity from computed molecular electrostatic properties. J. Chem. Soc., Perkin Trans. 2 1994, 199–202.
14. Le Questel, J.-Y.; Berthelot, M.; Laurence, C. Can semi-empirical calculations yield reasonable estimates of hydrogen-bonding basicity? The case of nitriles. J. Chem. Soc., Perkin Trans. 2 1997, 2711–2718.
15. Platts, J. A. Theoretical prediction of hydrogen bond basicity. Phys. Chem. Chem. Phys. 2000, 2, 3115–3120.
16. Gancia, E.; Montana, J. G.; Manallack, D. T. Theoretical hydrogen bonding parameters for drug design. J. Mol. Graph. Model. 2001, 19, 349–362.
17. Lamarche, O.; Platts, J. A. Theoretical Prediction of the Hydrogen-Bond Basicity pK_HB. Chem. Eur. J. 2002, 8, 457–466.
18. Besseau, F.; Graton, J.; Berthelot, M. A Theoretical Evaluation of the pKHB and ΔH°_HB Hydrogen-Bond Scales of Nitrogen Bases. Chem. Eur. J. 2008, 14, 10656–10669.
19. Devereux, M.; Popelier, P. L. A.; McLay, I. M. A refined model for prediction of hydrogen bond acidity and basicity parameters from quantum chemical molecular descriptors. Phys. Chem. Chem. Phys. 2009, 11, 1595–1603.
20. Green, A. J.; Popelier, P. L. A. Theoretical Prediction of Hydrogen-Bond Basicity pKBHX Using Quantum Chemical Topology Descriptors. J. Chem. Inf. Model. 2014, 54, 553–561.
21. Bauer, C. A.; Schneider, G.; Göller, A. H. Machine learning models for hydrogen bond donor and acceptor strengths using large and diverse training data generated by first-principles interaction free energies. J. Cheminform. 2019,11, 59.

Since the 1990s, researchers have found that the minimum electrostatic potential $V_\text{min}$ in the region of lone pairs (Figure 2) can be used to predict the strength of various hydrogen-bond acceptors, with different scaling parameters employed for each functional group.^6,13,22,236. Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Sartori, G. R. Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design. J. Med. Chem. 2016, 59, 4278–4288.
13. Kenny, P. W. Prediction of hydrogen bond basicity from computed molecular electrostatic properties. J. Chem. Soc., Perkin Trans. 2 1994, 199–202.
22. Hagelin, H.; Murray, J. S.; Politzer, P.; Brinck, T.; Berthelot, M. Family-independent relationships between computed molecular surface quantities and solute hydrogen bond acidity/basicity. Can. J. Chem. 1995, 73, 483–488.
23. Kenny, P. W. Hydrogen Bonding, Electrostatic Potential, and Molecular Design. J. Chem. Inf. Model. 2009, 49, 1234–1244.
Nevertheless, the computational cost and complexity of these workflows has limited their broader adoption in rational molecular optimization. Here, we report an efficient workflow for the $V_\text{min}$ -based automated prediction of hydrogen-bond basicity for unseen organic molecules. Rowan's pK_BHX prediction workflow uses neural network potentials to accelerate geometry optimization, requires only a single low-cost DFT calculation per molecule, and gives high-accuracy results across a wide set of structurally varied molecules and medicinally relevant scaffolds. We illustrate the utility of these predictions with a variety of case studies drawn from the medicinal chemistry literature, and show that this same strategy can be applied to the prediction of hydrogen-bond-donor strength.

Figure 2: Visualization of the −0.04 $E_\text{H}/e$ electrostatic potential isosurface at the r²SCAN-3c level of theory²⁴24. Grimme, S.; Hansen, A.; Ehlert, S.; Mewes, J.-M. r²SCAN-3c: A "Swiss army knife" composite electronic-structure method. J. Chem. Phys. 2021, 154, 064103.
for a multifunctional druglike molecule in Rowan.²⁵25. Wagen, C. C.; Wagen, A. M.; Mann, E. L.; Vandezande, J. E.; Schneider, S. C. Rowan. https://www.rowansci.com, 2023–2025.
Values of $V_\text{min}$ are obtained by numerical minimization within the regions illustrated.

Results and Discussion

Rowan's hydrogen-bond-basicity workflow begins by running a conformer search on the input molecule using the ETKDG algorithm as implemented in RDKit.^26–2826. Riniker, S.; Landrum, G. A. Better Informed Distance Geometry: Using What We Know To Improve Conformation Generation. J. Chem. Inf. Model. 2015, 55, 2562–2574.
27. Wang, S.; Witek, J.; Landrum, G. A.; Riniker, S. Improving Conformer Generation for Small Rings and Macrocycles Based on Distance Geometry and Experimental Torsional- Angle Preferences. J. Chem. Inf. Model. 2020, 60, 2044–2058.
28. RDKit: Open-source cheminformatics. https://www.rdkit.org. https://www.rdkit.org, 2013–2025.
Following initial conformer generation and MMFF94 optimization,²⁹29. Halgren, T. A. Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94. J. Comp. Chem. 1996, 17, 490–519.
we filter the resulting conformational ensemble using the CREST screening protocol and GFN2-xTB energies to de-duplicate structures and remove high-energy conformers.^30,3130. Pracht, P.; Bohle, F.; Grimme, S. Automated exploration of the low-energy chemical space with fast quantum chemical methods. Phys. Chem. Chem. Phys. 2020, 22, 7169–7192.
31. Pracht, P.; Grimme, S.; Bannwarth, C.; Bohle, F.; Ehlert, S.; Feldmann, G.; Gorges, J.; Müller, M.; Neudecker, T.; Plett, C.; Spicher, S.; Steinbach, P.; Weso lowski, P. A.; Zeller, F. CREST—A program for the exploration of low-energy molecular chemical space. J. Chem. Phys. 2024, 160, 114110.
A 2% rotational constant threshold, a 0.25 Å RMSD similarity threshold, and a 50 kcal/mol energy cutoff window are employed for CREST screening.

We score & optimize the output conformers with the AIMNet2 neural network potential³²32. Anstine, D.; Zubatyuk, R.; Isayev, O. AIMNet2: A Neural Network Potential to Meet your Neutral, Charged, Organic, and Elemental-Organic Needs. ChemRxiv 2024.
and use the lowest energy conformer for subsequent calculations. Following Peter Kenny, we predict the basicity of each hydrogen-bond acceptor by computing $V_\text{min}$ around the hydrogen-bond-accepting atom (using the low-cost "Swiss-army knife" r²SCAN-3c method)²⁴24. Grimme, S.; Hansen, A.; Ehlert, S.; Mewes, J.-M. r²SCAN-3c: A "Swiss army knife" composite electronic-structure method. J. Chem. Phys. 2021, 154, 064103.
and linearly scaling these potentials to match experimental pK_BHX values.⁶6. Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Sartori, G. R. Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design. J. Med. Chem. 2016, 59, 4278–4288.
Electrostatic potential minima were located by numerical minimization of the electrostatic potential (computed via the ESPPropCalc object in Psi4)³³33. Turney, J. M. et al. Psi4: an open-source ab initio electronic structure program. Wiley Interdiscip. Rev.:Comput. Mol. Sci.2012, 2, 556–565.
with the BFGS algorithm in Scipy.³⁴34. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 2020, 17, 261–272.

All density-functional-theory computations were conducted with Psi4 1.9.1.³³33. Turney, J. M. et al. Psi4: an open-source ab initio electronic structure program. Wiley Interdiscip. Rev.:Comput. Mol. Sci.2012, 2, 556–565.
(The default settings in Psi4 were modified somewhat: a (99,590) integration grid with "robust" pruning, the Stratmann–Scuseria–Frisch quadrature scheme was employed,³⁵35. Stratmann, R.; Scuseria, G. E.; Frisch, M. J. Achieving linear scaling in exchange-correlation density functional quadratures. Chemical Physics Letter 1996, 257, 213–223.
and an integral tolerance of 10⁻¹⁴ was used throughout.³⁶36. Gray, M.; Bowling, P. E.; Herbert, J. M. Comment on "Benchmarking Basis Sets for Density Functional Theory Thermochemistry Calculations: Why Unpolarized Basis Sets and the Polarized 6-311G Family Should Be Avoided". J. Phys. Chem. A 2024, 128, 7739–7745.
) Density fitting was employed for all calculations and a level shift of 0.10 Hartree was applied to accelerate SCF convergence.³⁷37. Saunders, V. R.; Hillier, I. H. A "Level-Shifting" method for converging closed shell Hartree–Fock wave functions. Int. J. Quantum Chem., 1973, 7, 699–705.
AIMNet2 geometry optimizations were run using geomeTRIC 1.0.2.³⁸38. Wang, L.-P.; Song, C. Geometry optimization made simple with translation and rotation coordinates. J. Chem. Phys. 2016, 144, 214108.

To find values for the scaling constants, we employed Kenny's 2020 database of experimentally measured pK_BHX values,¹²12. Kenny, P. W. Hydrogen bond basicity data: text file with measured pKBHX val- ues, isomeric SMILES strings and literature references. https://figshare.com/articles/dataset/Hydrogen_bond_basicity_data_text_file_with_measured_pKBHX_values_isomeric_SMILES_strings_and_literature_references/12084183, 2020; [Accessed 17-01-2025].
and predicted the measured per-molecule pK_BHX values by combining the predicted pK_BHX values from each distinct electrostatic potential minimum (up to three per hydrogen-bond acceptor, following Equation 3 from Kenny et al.⁶6. Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Sartori, G. R. Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design. J. Med. Chem. 2016, 59, 4278–4288.
). A total of 434 molecules were employed after excluding those for which 3D conformations could not be generated using ETKDG. We used Levenberg–Marquardt least-squares fitting^39,4039. Levenberg, K. A method for the solution fo certain non-liner problems in least squares. Q. Appl. Math. 1944, 2, 164–168.
40. Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431–441.
as implemented in LMFIT⁴¹41. Newville, M. et al. lmfit/lmfit.py 1.3.2. 2024; https://doi.org/10.5281/zenodo.12785036.
to solve the resulting non-linear optimization problem.

Functional Group	Number	Slope ( $e/E_\text{H}$ )	Intercept	MAE	RMSE
Amine	171	-34.4386	-1.4884	0.212	0.324
Aromatic N	71	-52.8126	-3.1376	0.113	0.150
Imine	28	-48.4007	-2.3309	0.180	0.236
Nitrile	28	-50.1167	-3.2273	0.144	0.198
N-oxide	16	-74.3261	-4.4159	0.455	0.589
Chalcogen oxide	17	-47.7009	-2.2794	0.186	0.224
Pnictogen oxide	16	-61.1141	-3.3839	0.437	0.549
Carbonyl	128	-57.2911	-3.5271	0.160	0.208
Ether/hydroxyl	99	-35.9245	-2.0338	0.188	0.239
Thiocarbonyl	10	-51.8837	-2.2649	0.330	0.384
Divalent S	17	-39.1666	-2.1243	0.086	0.127
Aromatic O	11	-35.9245	-2.0338	0.125	0.158
Fluorine	23	-16.4441	-1.2540	0.202	0.276
Total	434			0.188	0.270

Table 1: Summary of number of data points, scaling slope, scaling intercept, mean absolute error (MAE), and root mean squared error (RMSE) for each functional group.

Our final workflow gives a mean error of approximately 0.19 pK_BHX units (Table 1), comparable to previously reported methods.^6,426. Kenny, P. W.; Montanari, C. A.; Prokopczyk, I. M.; Ribeiro, J. F. R.; Sartori, G. R. Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design. J. Med. Chem. 2016, 59, 4278–4288.
42. Graton, J.; Le Questel, J.-Y.; Maxwell, P.; Popelier, P. Hydrogen-Bond Accepting Properties of New Heteroaromatic Ring Chemical Motifs: A Theoretical Study. J. Chem. Inf. Model. 2016, 56, 322–334.
Most of the outliers are bulky amines (Figure 3): electrostatic potential–based predictions seem to overestimate the basicity of these sites, since bulky groups will block the approach of hydrogen-bond donors like 4-fluorophenol while minimally perturbing the electrostatic potential of the lone pair. For instance, triisopropylamine has a predicted pK_BHX value of 1.39 units, but an experimental pK_BHX value of 0.30 units, likely due to the bulky substituents preventing access to the central nitrogen.

Figure 3: Plot of predicted vs. experimental pK_BHX values for compounds in Kenny's 2020 pK_BHX database.¹²12. Kenny, P. W. Hydrogen bond basicity data: text file with measured pKBHX val- ues, isomeric SMILES strings and literature references. https://figshare.com/articles/dataset/Hydrogen_bond_basicity_data_text_file_with_measured_pKBHX_values_isomeric_SMILES_strings_and_literature_references/12084183, 2020; [Accessed 17-01-2025].
Dotted lines indicate errors of ±0.5 pK_BHX units.

This sequence of steps avoids time-consuming geometry optimizations at the DFT level of theory, instead using the AIMNet2 neural network potential to optimize structures and running a single low-cost r²SCAN-3c calculation on the final minimum. Predictions can be run for the entire dataset above in a few hours on a conventional laptop, and even 50-atom systems run in fewer than 10 minutes. The above hydrogen-bond-acceptor-strength-prediction workflow has been implemented in the Rowan cloud computational-chemistry platform,²⁵25. Wagen, C. C.; Wagen, A. M.; Mann, E. L.; Vandezande, J. E.; Schneider, S. C. Rowan. https://www.rowansci.com, 2023–2025.
making it simple to submit calculations and quickly visualize the relative strength and position of different hydrogen-bond acceptors (Figure 4).

Figure 4: Visualization of predicted pK_BHX sites and values for an example small molecule through the Rowan platform.²⁵25. Wagen, C. C.; Wagen, A. M.; Mann, E. L.; Vandezande, J. E.; Schneider, S. C. Rowan. https://www.rowansci.com, 2023–2025.

Hydrogen-Bond Acidity

We next investigated whether the above workflow could be modified to simultaneously predict hydrogen-bond acidity (pK_α). Hydrogen-bond-donor sites have no such associated extrema on the electrostatic-potential surface, making naïve extension of the above $V_\text{min}$ -based strategy to hydrogen-bond donors impossible. However, previous work by Peter Kenny showed that the electrostatic potential at a fixed distance from the donor hydrogen atom could be linearly scaled to match experimental hydrogen-bond-donor-strength values, prompting us to investigate including this approach within our existing workflow.²³23. Kenny, P. W. Hydrogen Bonding, Electrostatic Potential, and Molecular Design. J. Chem. Inf. Model. 2009, 49, 1234–1244.

Following Kenny, we compute the characteristic electrostatic potential V_α for a given hydrogen-bond-donor motif X–H at a point 0.55 Å past the hydrogen along the bond axis, following precedent from Kenny.²³23. Kenny, P. W. Hydrogen Bonding, Electrostatic Potential, and Molecular Design. J. Chem. Inf. Model. 2009, 49, 1234–1244.
This electrostatic potential is converted to a per-donor hydrogen-bond-acidity value through linear scaling, and per-donor hydrogen-bond acidities are combined into a single per-molecule hydrogen-bond-acidity value that can be compared to experimental pK_α values.

The above protocol has only two tunable parameters: the slope m and intercept b used to scale V_α. To obtain values for these parameters, we employed Kenny's dataset of 41 association constants between hydrogen-bond donors and N-methylpyrrolidone in 1,1,1-trichloroethane. Levenberg–Marquardt least-squares fitting^39,4039. Levenberg, K. A method for the solution fo certain non-liner problems in least squares. Q. Appl. Math. 1944, 2, 164–168.
40. Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431–441.
yielded values of 42.18 $E_H/e$ for m and -12.46 for b, in rough agreement with constants obtained by Kenny,²³23. Kenny, P. W. Hydrogen Bonding, Electrostatic Potential, and Molecular Design. J. Chem. Inf. Model. 2009, 49, 1234–1244.
and a good fit to experimental data (Figure 5).

Figure 5: Plot of predicted vs. experimental pK_α values for compounds in Kenny’s 2009 pK_α database.²³23. Kenny, P. W. Hydrogen Bonding, Electrostatic Potential, and Molecular Design. J. Chem. Inf. Model. 2009, 49, 1234–1244.
Dotted lines indicate errors of ±0.5 pK_α units.

Case Studies

Here, we demonstrate how hydrogen-bond-basicity and acidity prediction can be used to gain chemical insight and motivate the design of molecules with better potency or biophysical properties. The original compound numbers from each paper have been kept for easy reference back to the original publication, with a prefix added for disambiguation.

The below discussion assumes some familiarity with terminology from medicinal chemistry. Briefly: medicinal chemists commonly rely on parameters such as IC₅₀, EC₅₀, logD_7.4, permeability, and efflux ratio to guide the optimization of pharmacokinetic and pharmacodynamic properties.⁴³43. Di, L.; Kerns, E. H. Drug-Like Properties: Concepts, Structure Design and Methods, 2nd ed.; Academic Press: Boston, 2016.
The IC₅₀ value quantifies the concentration of a compound needed for half-maximal inhibition of a specific enzyme or pathway, while the EC₅₀ is the concentration at which half the maximal effect (e.g., in a cellular or functional assay) is observed—lower values of either indicate higher potency or efficacy. LogD is the distribution coefficient (often measured at a specific pH, such as 7.4) between n-octanol and water: higher values indicate that a compound is more lipophilic, while lower values indicate that a compound is more hydrophilic.⁴³43. Di, L.; Kerns, E. H. Drug-Like Properties: Concepts, Structure Design and Methods, 2nd ed.; Academic Press: Boston, 2016.

The efflux ratio, often measured in polarized cell monolayer assays such as the human Caco-2 cell line, captures how readily a compound is transported out of cells. In such assays, the apparent permeability from the apical to basolateral side ( $P_\textrm{app}(A \to B)$ ) is compared to the permeability in the reverse direction ( $P_\textrm{app}(B \to A)$ ).⁴³43. Di, L.; Kerns, E. H. Drug-Like Properties: Concepts, Structure Design and Methods, 2nd ed.; Academic Press: Boston, 2016.
A high efflux ratio suggests active pumping by transporters like P-glycoprotein (P-gp), an ATP-dependent efflux transporter. Mean residence time refers to the average time a drug molecule remains in the body—from the moment it enters circulation until it is completely eliminated—providing a useful measure of how long the compound stays available for therapeutic effect. In most drug discovery campaigns, scientists aim to increase permeability and decrease efflux while maintaining high on-target potency.⁴³43. Di, L.; Kerns, E. H. Drug-Like Properties: Concepts, Structure Design and Methods, 2nd ed.; Academic Press: Boston, 2016.

A: Lowering Efflux Ratio In IRAK4 Inhibitors

In 2018, Sébastien Degorce and co-workers embarked on a campaign to optimize the biophysical properties of IRAK4 inhibitors, with the goal of identifying potent and orally bioavailable inhibitors as potential treatments for diffuse large B-cell lymphoma.⁴⁴44. Degorce, S. L.; Anjum, R.; Dillman, K. S.; Drew, L.; Groombridge, S. D.; Halsall, C. T.; Lenz, E. M.; Lindsay, N. A.; Mayo, M. F.; Pink, J. H.; Robb, G. R.; Scott, J. S.; Stokes, S.; Xue, Y. Optimization of permeability in a series of pyrrolotriazine inhibitors of IRAK4. Bioorg. Med. Chem. 2018, 26, 913–924.
As a part of this effort, scaffold hopping between different pyrrolopyrimidine and pyrrolotriazine cores was investigated, with the goal of increasing lipophilicity and lowering the hydrogen-bond basicity of the scaffold. The authors found that moving from the original pyrrolopyrimidine scaffold (exemplified by A.14) to an isomeric pyrrolopyrimidine (A.17) decreased permeability and lipophilicity, despite removing one hydrogen-bond donor (Figure 6).

We investigated these systems with the $V_\text{min}$ -based pK_BHX workflow described above, and found that the pyrimidine ring in A.17 was predicted to show significantly increased hydrogen-bond basicity. The basicity of the pyrimidine increased by $0.6$ pK_BHX units, thus offsetting any potential gains in lipophilicity. In contrast, pyrrolotriazine A.20 showed dramatic improvements in permeability and efflux ratio, which can be attributed to the computed 0.7 pK_BHX-unit decrease in the hydrogen-bond basicity of the aromatic nitrogen. The order-of-magnitude increase or decrease in hydrogen-bond-acceptor-strength induced by single-atom changes underscores the utility of prospective pK_BHX prediction in silico.

Figure 6: Pyrrolopyrimidine and pyrrolotriazole cores investigated by Degorce and co-workers. Basic nitrogens are labeled in green, with the corresponding pK_BHX values computed by Rowan next to them. For experimental assay details, refer to Degorce et al.⁴⁴44. Degorce, S. L.; Anjum, R.; Dillman, K. S.; Drew, L.; Groombridge, S. D.; Halsall, C. T.; Lenz, E. M.; Lindsay, N. A.; Mayo, M. F.; Pink, J. H.; Robb, G. R.; Scott, J. S.; Stokes, S.; Xue, Y. Optimization of permeability in a series of pyrrolotriazine inhibitors of IRAK4. Bioorg. Med. Chem. 2018, 26, 913–924.

B: Designing PI3Kα-Selective Kinase Inhibitors

Bernard Barlaam and co-workers modified a kinase inhibitor (B.1) to achieve high selectivity for the PI3Kα kinase.⁴⁵45. Barlaam, B.; Cosulich, S.; Fitzek, M.; Green, S.; Harris, C. S.; Hudson, K.; Lambert- van der Brempt, C.; Ouvry, G.; Page, K.; Ruston, L.; Ward, L.; Delouvrié, B. Design of selective PI3Kα inhibitors starting from a promiscuous pan kinase scaffold. Bioorg. Med. Chem. Lett. 2015, 25, 2679–2685.
Based on structural data, the authors hypothesized that introducing a nitrogen at "N₁" (Figure 7) on the five-membered ring might induce lone-pair repulsion with several carbonyl groups found in other kinase binding pockets and thus lower the compound's affinity for these "anti-targets." A variety of azaarene linkers were tested against PI3Kα and the kinase anti-target KDR, and the addition of a nitrogen did indeed increase the selectivity for PI3Kα (Figure 7). Nitrogens that were better hydrogen-bond acceptors were found to be more selective: strong hydrogen-bond acceptors B.4 and B.6 bound to KDR with low potency, while weaker hydrogen-bond acceptors like B.2, B.3, and B.5 bound to KDR with high potency. Ultimately, triazole B.4 best balanced potency against PI3Kα with inter-kinase selectivity and was selected for further optimization.

Computed hydrogen-bond-acceptor strengths correlate well with the observed KDR activity: azaarenes with N₁ pK_BHX values greater than 1 have KDR IC₅₀ values above 1 μM, while azaarenes with N₁ pK_BHX below 1 have have KDR IC₅₀ values in the high nanomolar regime. If further scaffold exploration was necessary, computed pK_BHX values could be used to rapidly screen out compounds that were likely to competitively inhibit KDR.

Figure 7: Kinase inhibitors investigated by Barlaam and co-workers.⁴⁵45. Barlaam, B.; Cosulich, S.; Fitzek, M.; Green, S.; Harris, C. S.; Hudson, K.; Lambert- van der Brempt, C.; Ouvry, G.; Page, K.; Ruston, L.; Ward, L.; Delouvrié, B. Design of selective PI3Kα inhibitors starting from a promiscuous pan kinase scaffold. Bioorg. Med. Chem. Lett. 2015, 25, 2679–2685.
Basic nitrogens are labeled in green, with the corresponding pK_BHX values computed by Rowan next to them. Hydrogen-bond-acceptor-strength calculations were run on the abbreviated structure shown in the box. For experimental assay details, refer to Barlaam et al.⁴⁵45. Barlaam, B.; Cosulich, S.; Fitzek, M.; Green, S.; Harris, C. S.; Hudson, K.; Lambert- van der Brempt, C.; Ouvry, G.; Page, K.; Ruston, L.; Ward, L.; Delouvrié, B. Design of selective PI3Kα inhibitors starting from a promiscuous pan kinase scaffold. Bioorg. Med. Chem. Lett. 2015, 25, 2679–2685.

C: P-gp Transport In Glycosylceramide Synthase Inhibitors

Andreas Roecker and co-workers investigated a series of pyrazole-based compounds as glucosylceramide synthase inhibitors, with the goal of identifying a CNS-penetrant compound capable of reducing glycosphingolipid accumulation often seen in Parkinson's disease.⁴⁶46. Roecker, A. J. et al. Pyrazole Ureas as Low Dose, CNS Penetrant Glucosylceramide Synthase Inhibitors for the Treatment of Parkinson's Disease. ACS Med. Chem. Lett. 2023, 14, 146–155.
High-throughput screening and direct-to-biology screening of c. 1300 compounds resulted in a highly potent lead compound that suffered from high P-gp transport. Performing a scaffold modification to replace a pyrazolyl amide (C.10) with a pyrazolyl urea (C.11) dramatically decreased efflux and extended the residence time in rat studies. Further optimization efforts around the pyrazolyl urea scaffold resulted in the development of several candidates suitable for in vivo testing.

Hydrogen-bond-basicity calculations can be used to rationalize these effects (Figure 8). Switching from amide to urea reduces the hydrogen-bond basicity of the key carbonyl group by approximately an order of magnitude, consistent with the decreased efflux and increased lipophilicity observed. Strong correlations between P-gp efflux and hydrogen-bond basicity have been reported previously in the literature.^5,475. Desai, P. V.; Raub, T. J.; Blanco, M.-J. How hydrogen bonds impact P-glycoprotein transport and permeability. Bioorg. Med. Chem. Lett. 2012, 22, 6540–6548.
47. Schnider, P. et al. Discovery of Balovaptan, a Vasopressin 1a Receptor Antagonist for the Treatment of Autism Spectrum Disorder. J. Med. Chem. 2020,63, 1511–1525.

Figure 8: Glycocosylceramide synthase inhibitors investigated by Roecker and co-workers.⁴⁶46. Roecker, A. J. et al. Pyrazole Ureas as Low Dose, CNS Penetrant Glucosylceramide Synthase Inhibitors for the Treatment of Parkinson's Disease. ACS Med. Chem. Lett. 2023, 14, 146–155.
The basic oxygen is labeled in green, with the corresponding pK_BHX values computed by Rowan nearby. For experimental assay details, refer to Roecker et al.⁴⁶46. Roecker, A. J. et al. Pyrazole Ureas as Low Dose, CNS Penetrant Glucosylceramide Synthase Inhibitors for the Treatment of Parkinson's Disease. ACS Med. Chem. Lett. 2023, 14, 146–155.

D: Managing Efflux In Oral PARP Inhibitors

In the process of developing poly-ADP ribose polymerase (PARP) inhibitors as potential anti-cancer agents,⁴⁸48. Johannes, J. W. et al. Discovery of AZ0108, an orally bioavailable phthalazinone PARP inhibitor that blocks centrosome clustering. Bioorg. Med. Chem. Lett. 2015, 25, 5743–5747.
Chungang Gu and co-workers studied how modulating the strength of hydrogen-bond acceptors could be used to optimize the bioavailability of PARP inhibitors.⁴⁹49. Gu, C. et al. Modulating the strength of hydrogen bond acceptors to achieve low Caco2 efflux for oral bioavailability of PARP inhibitors blocking centrosome clustering. Bioorg. Med. Chem. Lett. 2016, 26, 4775–4780.
They found that tuning the electronic properties of a key triazole ring was able to simultaneously modulate binding affinity, permeability, and efflux ratio (Figure 9). Compound D.15 maintained potency while dramatically increasing permeability and decreasing efflux (Table 2), and was selected for further in vivo studies.⁴⁸48. Johannes, J. W. et al. Discovery of AZ0108, an orally bioavailable phthalazinone PARP inhibitor that blocks centrosome clustering. Bioorg. Med. Chem. Lett. 2015, 25, 5743–5747.

pK_BHX predictions can be used to interpret these experimental results. Compound D.1, the strongest hydrogen-bond acceptor, has pK_BHX values of $2.28$ and $2.37$ on the two triazole nitrogens (Table 2). Adding additional fluorines to the compound reduces the basicity of the triazole nitrogens, which makes the compound more permeable and less susceptible to efflux—compound D.15, which has a difluoroethyl group, preserves the activity of the parent compound while dramatically improving its biophysical properties. Surprisingly, moving from difluoroethyl to trifluoromethyl causes a fourfold decrease in EC₅₀, a decrease in permeability, and an increase in efflux ratio (Table 2), contrary in all three cases to what simple trends based on pK_BHX would predict. Activity cliffs like this are not uncommon in chemical structure–activity relationships, illustrating the limitations in using any single descriptor to predict compound performance.

Figure 9: General scaffold of the PARP inhibitors investigated by Gu and co-workers.⁴⁹49. Gu, C. et al. Modulating the strength of hydrogen bond acceptors to achieve low Caco2 efflux for oral bioavailability of PARP inhibitors blocking centrosome clustering. Bioorg. Med. Chem. Lett. 2016, 26, 4775–4780.
Key basic nitrogens are labeled in green. Hydrogen-bond-acceptor-strength calculations were run on the abbreviated structure shown in the box.

Compound	R	EC₅₀ (µM)	P_app(A→B) (10^-6 cm/s)	Efflux Ratio	pK_BHX N1	pK_BHX N2
D.1	C(H)Me₂	0.052	2.0(1.5)	44(37)	2.38	2.47
D.14	C(F)Me₂	0.043	5.9(2.4)	7(3.0)	1.90	2.07
D.15	C(Me)F₂	0.053	15.6(2.7)	2(0.8)	1.48	1.71
D.12	CF₃	0.216	6.7(2.4)	6(2.3)	1.40	1.55

Table 2: Summary of R-groups, ( $\mathrm{EC_{50}}$ ), permeability ( $P_{\mathrm{app}}$ ), efflux ratio, and pK_BHX values. For experimental assay details, refer to Gu et al.⁴⁹49. Gu, C. et al. Modulating the strength of hydrogen bond acceptors to achieve low Caco2 efflux for oral bioavailability of PARP inhibitors blocking centrosome clustering. Bioorg. Med. Chem. Lett. 2016, 26, 4775–4780.

E: Predicting Hydrogen-Bond-Donor Strength in Organocatalysts

In 2014, Walvoord and co-workers used a colorimetric molecular sensor to assay the strength of various hydrogen-bond-donor catalysts. They were able to measure binding free energy values for a variety of catalysts and demonstrated that these hydrogen-bond-donor-strength measurements correlated with observed rate acceleration in Diels–Alder reactions.⁵⁰50. Walvoord, R. R.; Huynh, P. N.; Kozlowski, M. C. Quantification of electrophilic activation by hydrogen-bonding organocatalysts. Journal of the American Chemical Society 2014,136, 16055–16065

We used the Walvoord dataset to test the ability of our computational hydrogen-bond-acidity workflow to reproduce hydrogen-bond-donor-strength values recorded under different experimental conditions. To simplify comparisons and eliminate the need to consider cooperative binding, we restricted the set of compounds studied to those containing only a single active hydrogen-bond donor. The predicted hydrogen-bond-acidity values showed excellent correlation with experimental binding free energies across a set of 16 compounds (Pearson correlation of 0.93) suggesting that the electrostatic-potential-based method employed here can be used as a generalizable probe of hydrogen-bond-donor strength (Figure 10).

Figure 10: Plot of predicted pK_α values and experimental binding free energies for neutral single hydrogen-bond-donor compounds from Walvoord’s 2014 database.⁵⁰50. Walvoord, R. R.; Huynh, P. N.; Kozlowski, M. C. Quantification of electrophilic activation by hydrogen-bonding organocatalysts. Journal of the American Chemical Society 2014,136, 16055–16065
The dotted line indicates the line of best fit.

Conclusion

Improved scientific tools are a key driver of scientific progress.⁵¹51. Dyson, F. J. Is Science Mostly Driven by Ideas or by Tools? Science 2012, 338, 1426–1427.
While computational methods for prediction of hydrogen-bond-acceptor strength were first reported over three decades ago,¹³13. Kenny, P. W. Prediction of hydrogen bond basicity from computed molecular electrostatic properties. J. Chem. Soc., Perkin Trans. 2 1994, 199–202.
the broader utilization of these tools has been impeded by the lack of a workflow usable by non-computational scientists. Here, we address this lacuna through the development of a robust and efficient algorithm for pK_BHX prediction. Our hydrogen-bond-basicity-prediction workflow predicts per-site pK_BHX values directly from 2D- or 3D-representations of molecules, with no additional input required, and provides insight into otherwise opaque structural features of lead molecules, as illustrated by examples from the medicinal chemistry literature. We anticipate that this approach will be a valuable addition to the armamentarium of tools available to the modern drug hunter, and hope that this software can be more closely integrated into lead optimization programs in the future.

To run this hydrogen-bond-basicity prediction workflow on your own molecules, subscribe to Rowan today.

Acknowledgement

C.C.W. thanks Gilles Ouvry for initial discussions on this topic & for suggesting the papers discussed in case studies B and D, Ari Wagen for designing and implementing the visuals shown in Figures 2 & 4, and Ari Wagen, Jonathon Vandezande, Eugene Kwan, Hayden Sharma, Marcus Sak, Jonathan Wong, Lewis Martin, Gilles Ouvry, Harry Stern, Michael Nielsen, & an anonymous industry scientist for feedback on drafts of this manuscript.

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