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Proton affinity
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The proton affinity (PA, Epa) of an anion or of a neutral atom or molecule is the negative of the enthalpy change in the reaction between the chemical species concerned and a proton in the gas phase:[1]
These reactions are always exothermic in the gas phase, i.e. energy is released (enthalpy is negative) when the reaction advances in the direction shown above, while the proton affinity is positive. This is the same sign convention used for electron affinity. The property related to the proton affinity is the gas-phase basicity, which is the negative of the Gibbs energy for above reactions,[2] i.e. the gas-phase basicity includes entropic terms in contrast to the proton affinity.
Acid/base chemistry
[edit]The higher the proton affinity, the stronger the base and the weaker the conjugate acid in the gas phase. The (reportedly) strongest known base is the ortho-diethynylbenzene dianion (Epa = 1843 kJ/mol),[3] followed by the methanide anion (Epa = 1743 kJ/mol) and the hydride ion (Epa = 1675 kJ/mol),[4] making methane the weakest proton acid[5] in the gas phase, followed by dihydrogen. The weakest known base is the helium atom (Epa = 177.8 kJ/mol),[6] making the hydrohelium(1+) ion the strongest known proton acid.
Hydration
[edit]Proton affinities illustrate the role of hydration in aqueous-phase Brønsted acidity. Hydrofluoric acid is a weak acid in aqueous solution (pKa = 3.15)[7] but a very weak acid in the gas phase (Epa (F−) = 1554 kJ/mol):[4] the fluoride ion is as strong a base as SiH3− in the gas phase, but its basicity is reduced in aqueous solution because it is strongly hydrated, and therefore stabilized. The contrast is even more marked for the hydroxide ion (Epa = 1635 kJ/mol),[4] one of the strongest known proton acceptors in the gas phase. Suspensions of potassium hydroxide in dimethyl sulfoxide (which does not solvate the hydroxide ion as strongly as water) are markedly more basic than aqueous solutions, and are capable of deprotonating such weak acids as triphenylmethane (pKa = ca. 30).[8][9]
 | An editor has expressed concern that this table does not seem to have correct values and some of them seem to be heat of formation instead of enthalpy. may have a number of irrelevant and questionable citations. (May 2022) |
To a first approximation, the proton affinity of a base in the gas phase can be seen as offsetting (usually only partially) the extremely favorable hydration energy of the gaseous proton (ΔE = −1530 kJ/mol), as can be seen in the following estimates of aqueous acidity:
| Proton affinity | HHe+(g) | → | H+(g) | + He(g) | +178 kJ/mol | [6] | HF(g) | → | H+(g) | + F−(g) | +1554 kJ/mol | [4] | H2(g) | → | H+(g) | + H−(g) | +1675 kJ/mol | [4] | ||
| Hydration of acid | HHe+(aq) | → | HHe+(g) | +973 kJ/mol | [10] | HF(aq) | → | HF(g) | +23 kJ/mol | [7] | H2(aq) | → | H2(g) | −18 kJ/mol | [11] | |||||
| Hydration of proton | H+(g) | → | H+(aq) | −1530 kJ/mol | [7] | H+(g) | → | H+(aq) | −1530 kJ/mol | [7] | H+(g) | → | H+(aq) | −1530 kJ/mol | [7] | |||||
| Hydration of base | He(g) | → | He(aq) | +19 kJ/mol | [11] | F−(g) | → | F−(aq) | −13 kJ/mol | [7] | H−(g) | → | H−(aq) | +79 kJ/mol | [7] | |||||
| Dissociation equilibrium | HHe+(aq) | → | H+(aq) | + He(aq) | −360 kJ/mol | HF(aq) | → | H+(aq) | + F−(aq) | +34 kJ/mol | H2(aq) | → | H+(aq) | + H−(aq) | +206 kJ/mol | |||||
| Estimated pKa | −63 | +6 | +36 | |||||||||||||||||
These estimates suffer from the fact the free energy change of dissociation is in effect the small difference of two large numbers. However, hydrofluoric acid is correctly predicted to be a weak acid in aqueous solution and the estimated value for the pKa of dihydrogen is in agreement with the behaviour of saline hydrides (e.g., sodium hydride) when used in organic synthesis.
Difference from pKa
[edit]Both proton affinity and pKa are measures of the acidity of a molecule, and so both reflect the thermodynamic gradient between a molecule and the anionic form of that molecule upon removal of a proton from it. Implicit in the definition of pKa however is that the acceptor of this proton is water, and an equilibrium is being established between the molecule and bulk solution. More broadly, pKa can be defined with reference to any solvent, and many weak organic acids have measured pKa values in DMSO. Large discrepancies between pKa values in water versus DMSO (i.e., the pKa of water in water is 14,[12][13] but water in DMSO is 32) demonstrate that the solvent is an active partner in the proton equilibrium process, and so pKa does not represent an intrinsic property of the molecule in isolation. In contrast, proton affinity is an intrinsic property of the molecule, without explicit reference to the solvent.
A second difference arises in noting that pKa reflects a thermal free energy for the proton transfer process, in which both enthalpic and entropic terms are considered together. Therefore, pKa is influenced both by the stability of the molecular anion, as well as the entropy associated of forming and mixing new species. Proton affinity, on the other hand, is not a measure of free energy.
List of compound affinities
[edit]Proton affinities are quoted in kJ/mol, in increasing order of gas-phase basicity of the base.
References
[edit]- ^ "Proton affinity." Compendium of Chemical Terminology.
- ^ "Gas-phase basicity." Compendium of Chemical Terminology.
- ^ Poad, Berwyck L. J.; Reed, Nicholas D.; Hansen, Christopher S.; Trevitt, Adam J.; Blanksby, Stephen J.; MacKay, Emily G.; Sherburn, Michael S.; Chan, Bun; Radom, Leo (2016). "Preparation of an ion with the highest calculated proton affinity: ortho-diethynylbenzene dianion". Chem. Sci. 7 (9): 6245–6250. doi:10.1039/C6SC01726F. PMC 6024202. PMID 30034765.
- ^ a b c d e Bartmess, J. E.; Scott, J. A.; McIver, R. T. (1979). "Scale of acidities in the gas phase from methanol to phenol". J. Am. Chem. Soc. 101 (20): 6046. Bibcode:1979JAChS.101.6046B. doi:10.1021/ja00514a030.
- ^ The term "proton acid" is used to distinguish these acids from Lewis acids. It is the gas-phase equivalent of the term Brønsted acid.
- ^ a b Lias, S. G.; Liebman, J. F.; Levin, R. D. (1984). Title J. Phys. Chem. Ref. Data. 13':695.
- ^ a b c d e f g Jolly, William L. (1991). Modern Inorganic Chemistry (2nd Edn.). New York: McGraw-Hill. ISBN 0-07-112651-1.
- ^ Jolly, William L (1967). "The intrinsic basicity of the hydroxide ion". J. Chem. Educ. 44 (5): 304. Bibcode:1967JChEd..44..304J. doi:10.1021/ed044p304.
- ^ Jolly, William L (1968). "σ-Methyl-π-Cyclopentadienylmolybdenum Tricarbonyl". Inorganic Syntheses. Vol. 11. p. 113. doi:10.1002/9780470132425.ch22. ISBN 9780470132425.
- ^ Estimated to be the same as for Li+(aq) → Li+(g).
- ^ a b Estimated from solubility data.
- ^ Meister, Erich C.; Willeke, Martin; Angst, Werner; Togni, Antonio; Walde, Peter (2014). "Confusing Quantitative Descriptions of Brønsted-Lowry Acid-Base Equilibria in Chemistry Textbooks – A Critical Review and Clarifications for Chemical Educators". Helvetica Chimica Acta. 97 (1): 1–31. doi:10.1002/hlca.201300321. ISSN 1522-2675.
- ^ Silverstein, Todd P.; Heller, Stephen T. (2017-06-13). "pKa Values in the Undergraduate Curriculum: What Is the Real pKa of Water?". Journal of Chemical Education. 94 (6): 690–695. Bibcode:2017JChEd..94..690S. doi:10.1021/acs.jchemed.6b00623. ISSN 0021-9584.
- ^ Jolly, William L. (1991). Modern Inorganic Chemistry (2nd Edn.). New York: McGraw-Hill. ISBN 0-07-112651-1
- ^ Pommerening, Cynthia Ann; Bachrach, Steven M.; Sunderlin, Lee S. (1999). "Proton affinity of SO3". Journal of the American Society for Mass Spectrometry. 10 (9): 856–861. doi:10.1016/S1044-0305(99)00055-0.
Proton affinity
View on Grokipediafrom Grokipedia
Proton affinity (PA) is a thermodynamic quantity in gas-phase chemistry that measures the energy released when a base accepts a proton, defined as the negative of the standard enthalpy change (ΔH°) for the reaction B + H⁺ → BH⁺, where B is a neutral atom, molecule, or anion, and BH⁺ is its conjugate acid.[1] This value, typically expressed in kJ/mol or kcal/mol, quantifies the intrinsic basicity of a species in the absence of solvent effects, providing a direct probe of molecular interactions with protons under isolated conditions.[1]
Unlike pKa values, which are influenced by solvation in solution, proton affinity offers a solvent-free metric for comparing the relative strengths of bases across diverse chemical systems, revealing trends that may differ markedly from those in aqueous environments—for instance, gas-phase basicity orders can invert due to the lack of stabilizing solvation shells around ions.[2] Typical proton affinities range from approximately 600 to 1750 kJ/mol (143 to 418 kcal/mol), with values for common molecules like ammonia around 854 kJ/mol and for stronger gas-phase bases like certain superbases exceeding 1000 kJ/mol.[2] These measurements are crucial for understanding ion-molecule reactions, as higher proton affinities indicate greater stability of the protonated species and enhanced reactivity in proton transfer processes.[3]
Proton affinity plays a pivotal role in fields such as mass spectrometry, where it informs fragmentation patterns and ionization efficiencies, and in astrochemistry, aiding the modeling of interstellar ion chemistry.[3] In biological contexts, it is essential for predicting protonation states in enzymes and nucleic acids, influencing biocatalytic mechanisms and pKa estimations in protein active sites—for example, the proton affinity of guanine at the N7 site is approximately 950 kJ/mol (227.6 kcal/mol), guiding simulations of DNA base pairing and reactivity.[4] Computational methods like CBS-QB3 and G3B3 are widely employed to calculate accurate proton affinities, often benchmarking against experimental data with errors below 5 kJ/mol, enabling precise studies of substituent effects and molecular design in catalysis and materials science.[4]
Anionic species exhibit significantly higher proton affinities due to the stabilizing effect of the negative charge, with carbanions representing superbases. For instance, halide and hydroxide anions show moderate values, while alkyl carbanions approach the upper limits observed for organic bases.
Rare gases and exotic species further highlight the range of proton affinities. Helium, as a noble gas, has one of the lowest values due to its closed-shell configuration, while designed dianions like ortho-diethynylbenzene dianion achieve record-high affinities through cumulative negative charge and conjugation effects.
Recent measurements, such as those for aldehydes using selected-ion flow-drift tube techniques with pentanal as reference, demonstrate incremental increases in proton affinity with chain length due to inductive effects from alkyl groups. For example, pentanal has a proton affinity of 796.6 ± 4 kJ/mol, while hexanal is 809.6 ± 4 kJ/mol. These values, updated in 2025, align with broader trends where electron-donating substituents enhance basicity.[46]
Overall, proton affinities increase with electron-donating groups in neutrals and are markedly elevated by negative charges in anions, providing a scale for comparing intrinsic gas-phase basicities across diverse chemical classes.[5]
Fundamentals
Definition
Proton affinity (PA) is a thermodynamic quantity that measures the strength of a base in the gas phase, defined as the negative of the standard enthalpy change (ΔH°) for the reaction B(g) + H⁺(g) → BH⁺(g), where B represents a neutral molecule, atom, or anion. This definition, established by the International Union of Pure and Applied Chemistry (IUPAC), emphasizes a hypothetical or real gas-phase process without subsequent proton loss from the conjugate acid BH⁺. Positive PA values indicate an exothermic protonation reaction, reflecting the energetic favorability of proton attachment to B. The term "proton affinity" derives from its analogy to electron affinity, denoting the binding energy of a proton to a chemical species, and was formalized in the context of gas-phase ion chemistry. Values are conventionally reported in kJ/mol (SI units) or kcal/mol (1 kcal/mol ≈ 4.184 kJ/mol), allowing comparison across diverse species.[5] The first quantitative measurements of proton affinities occurred in the 1960s through ion cyclotron resonance (ICR) spectroscopy, which enabled determination of proton transfer equilibria in low-pressure gas phases. For illustration, the ortho-diethynylbenzene dianion exhibits the highest recorded PA of 1843 kJ/mol, underscoring its exceptional gas-phase basicity, while helium has the lowest at 177.8 kJ/mol, highlighting weak proton binding in noble gases.[6][7]Thermodynamic Relations
The proton affinity (PA) of a base B is defined as the negative of the standard enthalpy change for the gas-phase protonation reaction B(g) + H⁺(g) → BH⁺(g), measured at 298 K.[8] This thermodynamic quantity captures the enthalpy contribution to the strength of the B–H bond in the protonated species BH⁺. Through Hess's law and thermochemical cycles, PA can be expressed in terms of standard enthalpies of formation: where the standard enthalpy of formation of the gaseous proton, , is 1530 kJ/mol at 298 K.[8] This relation allows PA values to be derived or verified using independent thermochemical data for the neutral base, its protonated form, and the proton itself. Protonation energy is often used interchangeably with PA, emphasizing the enthalpic stabilization upon proton addition, though it may sometimes refer more broadly to energy changes at 0 K.[8] Proton affinity is distinct from gas-phase basicity (GB), which is the negative of the standard Gibbs free energy change for the same protonation reaction: GB(B) = −ΔG°(B + H⁺ → BH⁺) at 298 K.[8] The two are related through the Gibbs free energy equation: yielding GB(B) = PA(B) − TΔS°, where T is 298 K and ΔS° is the standard entropy change for protonation, typically negative due to the loss of translational freedom of the proton.[8] The entropy term TΔS° generally ranges from 20 to 40 kJ/mol (approximately 5 to 10 kcal/mol), making GB values 20–40 kJ/mol smaller than corresponding PA values for most molecules.[8] This difference arises primarily from the restriction of the proton's three-dimensional translational motion upon binding, with minor contributions from rotational and vibrational entropy changes in BH⁺.[8] The deprotonation enthalpy, or gas-phase acidity (Δ_acid H°), for a conjugate acid BH⁺ is the enthalpy change for the reverse reaction BH⁺(g) → B(g) + H⁺(g), such that Δ_acid H°(BH⁺) = PA(B). Thus, proton affinity provides a direct measure of gas-phase acidity for the conjugate base, linking basicity and acidity scales through thermodynamic cycles. Ionization energies can connect to PA via appearance energy measurements in mass spectrometry, where the energy to form BH⁺ from a precursor ion relates the protonation enthalpy to electron removal processes, though such relations are indirect and depend on specific fragmentation pathways.[8] All standard PA and GB values are referenced to the 298 K state to ensure consistency across thermochemical data.[8]Relation to Acidity and Basicity
The proton affinity of a base B is equivalent to the gas-phase acidity enthalpy of its conjugate acid BH⁺.Gas-Phase Basicity
Gas-phase basicity refers to the intrinsic tendency of a species to accept a proton in the absence of solvent effects, quantified as the negative standard Gibbs free energy change (GB = -ΔG°) for the protonation reaction B + H⁺ → BH⁺.[9] This measure complements proton affinity (PA = -ΔH°), which focuses on the enthalpic contribution to the same reaction; a higher PA generally correlates with stronger gas-phase basicity, as the entropic term (TΔS°) is often small and similar across related compounds, making PA a reliable indicator of intrinsic basic strength.[9] For instance, aliphatic amines exhibit PAs around 900–1000 kJ/mol, reflecting their strong electron-donating ability via the nitrogen lone pair, which enhances basicity without solvation stabilization. Proton transfer equilibria in the gas phase provide a direct method to compare basicities, governed by the equilibrium B + B'H⁺ ⇌ BH⁺ + B', with the equilibrium constant defined as The free energy difference relates to the basicities via ΔGB = GB(B') - GB(B) = -RT ln K, allowing relative GB values to be determined experimentally; if K > 1, B is the stronger base.[9] This approach has established scales spanning a wide range of basicities, from simple molecules like ammonia (GB ≈ 808 kJ/mol) to more complex systems, highlighting how structural features influence proton acceptance without environmental interference.[10] In polyfunctional molecules such as amino alcohols, site-specific protonation preferences arise from differences in local proton affinities, with the nitrogen atom typically favored over oxygen due to its higher PA (e.g., ~930 kJ/mol for nitrogen versus ~775 kJ/mol for the hydroxyl oxygen in ethanolamine).[11] This selectivity stems from the greater electron density and lower ionization energy at nitrogen, directing protonation to the amine site and influencing subsequent gas-phase reactivity, such as intramolecular hydrogen bonding in the protonated species.[12] Superbases, defined as compounds with PA exceeding 1000 kJ/mol (or ~239 kcal/mol), exemplify extreme gas-phase basicity, enabling proton transfers and reactions infeasible in solution due to the lack of solvation leveling. Phosphazenes, such as P4(t-Bu)6 and related derivatives, achieve these values through cumulative electron donation from multiple nitrogen lone pairs to a central phosphorus, with measured GBs up to ~1250 kJ/mol; these properties facilitate applications in gas-phase ion chemistry and synthesis of unstable species.Comparison to pKa
The pKa value is defined as the negative logarithm of the acid dissociation constant for the equilibrium in solution, where this measure incorporates solvation energies of the ions that are absent in the gas-phase proton affinity.[9] Proton affinity quantifies the intrinsic basicity of a species in isolation, free from counterion or solvent stabilization, while pKa captures the overall free energy change influenced by solvation of both the protonated species and the free proton.[9] For instance, the gas-phase basicity order aniline > ammonia reverses in aqueous solution (ammonia > aniline) due to differential hydration energies; the delocalized lone pair in aniline reduces its basicity more in solution than in the gas phase.[9] In protic solvents like water, a leveling effect occurs for strong bases, making them appear weaker than their intrinsic gas-phase strength; for example, is leveled to an effective pKa of 15.7 for , as the proton affinity of water (691 kJ/mol) sets an upper limit on proton acceptance in the medium.[13][14] This contrasts with gas-phase measurements, where no such solvent-imposed ceiling exists, allowing differentiation of bases stronger than water.[9] Additionally, solution-phase pKa values include solvation entropy contributions from ion reorganization and solvent structuring around charged species, which differ markedly from the gas-phase entropy change primarily arising from vibrational and rotational modes in the isolated protonated complex.[15] These entropy effects can amplify or dampen apparent basicity trends observed in proton affinity data, particularly for polar solvents where hydrophobic contributions further modulate the free energy.[9]Solvation Effects
Hydration and Solvent Influence
The hydration of the proton in water releases a large amount of energy, with the standard enthalpy of hydration ΔH_hyd(H⁺) ≈ -1090 kJ/mol, primarily due to strong electrostatic interactions between the proton and the dipole moments of surrounding water molecules. This stabilization of H⁺ dramatically enhances the acidity of compounds in aqueous media compared to the gas phase, where no such solvation occurs. For example, hydrogen fluoride (HF) has a gas-phase proton affinity (PA) for its conjugate base F⁻ of 1554 kJ/mol, indicating weak acidity in isolation, but in water, HF dissociates appreciably with a pK_a of 3.17, as the hydrated proton and solvated fluoride ion lower the overall free energy of dissociation.[16][17] Solvation shells play a crucial role in modulating proton affinity, particularly for anions. Small, charge-dense anions like F⁻ form robust hydrogen-bonded networks in their first hydration shell, with up to four water molecules coordinating directly to the anion, which preferentially stabilizes the deprotonated form over the protonated neutral. This differential solvation between conjugate acid-base pairs—where the anion receives stronger solvation than the less polar neutral acid—effectively reduces the proton affinity in water, shifting equilibria toward greater acidity. In contrast, larger or less electronegative anions exhibit weaker interactions, leading to smaller shifts, but the overall effect underscores how protic solvents like water amplify intrinsic gas-phase basicities through selective anion stabilization.[18] In non-aqueous solvents, such as dimethyl sulfoxide (DMSO), solvation influences proton affinity differently due to reduced hydrogen-bonding capacity and lower dielectric constant (ε ≈ 47 versus 78 for water). The Born solvation model provides a continuum approximation for the electrostatic contribution to the solvation free energy, given by ΔG_solv ∝ (1 - 1/ε)/r, where r is the ion radius; this predicts weaker ion solvation in DMSO, resulting in diminished stabilization of conjugate bases and thus higher pK_a values compared to water. For instance, gas-to-liquid transfer free energies in DMSO show reduced anion solvation, making acids appear weaker; this is evident in the leveling of strong bases, where the amide ion (NH₂⁻, gas-phase PA = 1689 kJ/mol, the strongest known gas-phase base) has a conjugate acid (NH₃) with pK_a ≈ 38 in water but even higher effective basicity in DMSO due to poorer anion solvation.[19][20][21]Intrinsic vs. Extrinsic Properties
Proton affinity (PA) and gas-phase basicity (GB) represent intrinsic properties of molecules, quantifying their inherent tendency to accept a proton in the absence of solvent interactions. These measures reflect the electronic structure and bonding characteristics of the base B in the isolated gas-phase reaction B + H⁺ → BH⁺, where PA is defined as the negative of the enthalpy change (-ΔH) and GB as the negative of the Gibbs free energy change (-ΔG) at 298 K.[22][23] By excluding solvation effects, gas-phase studies provide a direct probe of molecular intrinsic basicity, unaffected by environmental stabilization of ions.[24] In contrast, extrinsic properties such as pKₐ values and solution-phase basicity incorporate solvation contributions, making them composite measures that deviate from intrinsic gas-phase behavior. The relationship between gas-phase and solution protonation thermodynamics is captured by the transfer free energy, ΔG_transfer = ΔG_solution - ΔG_gas, which accounts for the differential solvation of the protonated species BH⁺ relative to the neutral base B and the solvated proton. This term arises primarily from stronger solvation of the charged BH⁺ ion compared to neutral B, often reversing basicity trends observed in the gas phase—for instance, alkylamine basicity follows the order tertiary > secondary > primary > ammonia intrinsically, but inverts in aqueous solution due to solvation stabilization of smaller ions.[25][18] Gas-phase PA measurements are particularly valuable for elucidating structure-activity relationships, as they reveal the "true" preferred protonation sites on multifunctional molecules, helping to interpret anomalies in solution-phase reactivity where solvation masks intrinsic preferences. For example, in biomolecules like peptides, intrinsic PA data highlight electronic factors in protonation without solvent interference, aiding the design of catalysts or ligands.[26][24] Cluster ions of the form [B·(H₂O)ₙ]⁺ serve as models bridging gas-phase intrinsic properties and bulk solution behavior, demonstrating how stepwise solvation progressively attenuates the effective PA of B. Early equilibrium studies on protonated water clusters H⁺(H₂O)ₙ showed decreasing solvation energies with increasing n, from about 37 kcal/mol for the first water molecule to 13 kcal/mol for n > 4, reflecting a transition toward bulk-like hydration shells that stabilize the protonated species and modulate basicity. Similar stepwise attenuation occurs for organic bases B, where initial water molecules solvate the BH⁺ ion externally, gradually mimicking solution-phase extrinsic effects.[27][18]Determination Methods
Experimental Techniques
Proton affinities are experimentally determined through gas-phase techniques that probe proton transfer equilibria or ionization processes, allowing the construction of relative scales anchored to known standards. These methods rely on mass spectrometry variants to measure equilibrium constants or rate constants, from which thermodynamic quantities such as proton affinity (PA) and gas-phase basicity (GB) can be derived using van't Hoff analyses.[28] Ion cyclotron resonance (ICR) mass spectrometry, pioneered in the 1960s by V. L. Talrose and further developed by J. L. Beauchamp, measures proton transfer equilibria by trapping ions in a magnetic field and observing reaction rates and equilibrium constants (K) for protonation reactions. By establishing ladders of relative PAs through sequential proton transfers between reference compounds, absolute values are obtained with uncertainties typically around 4-8 kJ/mol, enabling comprehensive scales for hundreds of molecules. High-pressure mass spectrometry (HPMS) determines rate constants for protonation reactions at elevated pressures (1-10 Torr) and variable temperatures, facilitating the extraction of enthalpy (ΔH) and entropy (ΔS) changes for proton transfer equilibria via Arrhenius plots. This technique, advanced by P. Kebarle in the 1970s, achieves accuracies of ±4-6 kJ/mol for PA by stabilizing collisionally relaxed ions and measuring forward and reverse rate constants.[29] Pulsed electron beam methods, often integrated with high-pressure mass spectrometry, provide time-resolved measurements of ion formation and proton transfer kinetics following short electron pulses, yielding equilibrium constants and kinetic estimates of PAs. These approaches, refined in the 1980s, allow temperature-dependent studies (200-500 K) with precisions of ±5 kJ/mol, particularly useful for volatile organics like alkenes.[30][31] Threshold photoelectron spectroscopy (TPES) infers protonation energies by measuring the ionization thresholds of neutral molecules and protonated species, combining these with known dissociation energies to derive PAs with typical accuracies of ±4 kJ/mol for many small molecules. This vacuum-ultraviolet technique, enhanced by coincidence detection in the 1990s, provides direct energetic insights without relying on transfer equilibria.[32] Recent advances as of 2025 highlight ongoing challenges in site-specific protonation for heteronuclear species, where experimental methods like mass spectrometry struggle to distinguish multiple protonation sites, leading to averaged PA values that obscure regioselectivity in complex molecules such as peptides or heterocycles. Studies emphasize the need for hybrid techniques to resolve these ambiguities, with quantum chemical benchmarks guiding interpretations.[33]Computational Methods
Ab initio methods provide a foundational approach for computing proton affinities (PA) through direct evaluation of the protonation energy difference, ΔE_protonation, defined as the energy change for the reaction B + H⁺ → BH⁺. At the Hartree-Fock level, calculations offer a starting point but often overestimate PA due to neglect of electron correlation, while post-Hartree-Fock methods like second-order Møller-Plesset perturbation theory (MP2) improve accuracy by incorporating dynamic correlation effects. For high precision, coupled-cluster methods with single, double, and perturbative triple excitations, CCSD(T), combined with correlation-consistent basis sets such as aug-cc-pVTZ, yield reliable ΔE_protonation values, particularly for anions where diffuse functions are essential to capture the extended electron density.[34][35] Density functional theory (DFT) offers a computationally efficient alternative for PA calculations, balancing accuracy and scalability for larger systems. Functionals like B3LYP provide PA estimates with typical errors of 5-10 kJ/mol relative to experimental benchmarks, making it suitable for screening protonation sites in organic molecules. More advanced range-separated hybrids, such as ωB97X-D, enhance performance by better handling long-range interactions and dispersion, reducing errors in systems with weak bonds. To account for environmental effects, polarizable continuum models (PCM) are integrated with these DFT calculations, enabling hybrid gas-phase and solution-phase predictions that bridge intrinsic and solvated PAs without explicit solvent molecules.[36][37] Recent advancements in nuclear electronic orbital (NEO)-DFT address limitations in traditional methods by explicitly incorporating nuclear quantum effects, such as delocalization and zero-point energies, into the electronic structure calculation. Benchmarks from 2025 demonstrate that NEO-DFT significantly reduces prediction errors for PAs, achieving a mean absolute deviation of 6.2 kJ/mol compared to 31.6 kJ/mol for conventional DFT, representing an improvement of approximately 80%, particularly benefiting predictions involving proton transfer in hydrogen-bond networks. This approach treats protons as quantum particles within a multicomponent framework, improving fidelity for light nuclei dynamics without relying on post-Hartree-Fock corrections.[38] Composite methods combine multiple levels of theory to achieve near-chemical accuracy for PA on large molecules, where single-level ab initio or DFT calculations become prohibitive. The Gaussian-4 (G4) method, which extrapolates high-level correlation energies from MP2 and CCSD(T) components with systematic basis set improvements, delivers PA values within ±4 kJ/mol of experiment for systems up to dozens of atoms. Similarly, complete basis set (CBS)-QB3 employs a quadratic configuration interaction model with empirical corrections, offering comparable accuracy but with faster scaling; however, its performance degrades slightly for very large molecules due to basis set incompleteness. These methods are particularly valuable for benchmarking against experimental data.[39] A 2025 IUPAC project is redefining PA for molecules with asymmetric protonation sites, proposing site-specific values to resolve ambiguities in multi-site protonation, informed by composite method calculations that highlight energetic differences between isomers. Validation of these computational approaches relies on benchmark sets, such as those developed in 2025 NEO-DFT studies encompassing aldehydes and superbases, where predicted PAs align closely with gas-phase measurements, confirming the methods' robustness across chemical classes.[40][41]Data and Applications
Selected Proton Affinities
Proton affinities provide a quantitative measure of the basicity of species in the gas phase, with values typically ranging from low for inert species like rare gases to high for anions and superbases. Representative examples illustrate key trends, such as higher proton affinities for species with lone pairs or negative charges compared to hydrocarbons. Data are primarily drawn from evaluated compilations, with uncertainties generally ±4–8 kJ/mol unless specified otherwise.[5][42] For neutral bases, proton affinities increase with the presence of electron-donating functional groups, following the order amines > ethers > alkanes. This trend reflects the availability of lone pairs for protonation: nitrogen lone pairs in amines yield higher values than oxygen in ethers or the weaker C-H bonds in alkanes.| Species | Proton Affinity (kJ/mol) | Functional Group Trend Example |
|---|---|---|
| CH₄ (methane) | 543.5 ± 4 | Alkanes (lowest) |
| H₂O (water) | 691 ± 5 | Ethers/oxygen bases |
| (CH₃)₂O (dimethyl ether) | 792 ± 4 | Ethers |
| NH₃ (ammonia) | 853.6 ± 2 | Amines (highest among neutrals) |
| Species | Proton Affinity (kJ/mol) | Notes |
|---|---|---|
| F⁻ | 1555 ± 8 | Halide anion |
| OH⁻ | 1634 ± 8 | Oxide-related anion |
| CH₃⁻ | 1743 ± 8 | Carbanion superbase |
| Species | Proton Affinity (kJ/mol) | Notes |
|---|---|---|
| He (helium) | 177.8 ± 2 | Rare gas (lowest overall) |
| ortho-C₆H₄(C≡CH)₂²⁻ (dianion) | 1843 | Strongest known superbase |