A high-level theoretical study into theatmospheric phase hydration, bonddissociation enthalpies, and acidity ofaldehydesSierra Raynea* and Kaya Forestb

CBS-Q//B3, G4(MP2), and G4 composite method calculations were used to estimate atmospheric phase standard state(298.15K, 1 atm) free energies of hydration (ΔhydrG°(g)), hydration equilibrium constants (log Khydr,(g)), bond dissociation en-thalpies (BDEs), and enthalpies (ΔdH°(g)) and free energies (ΔdG°(g)) of aldehydic proton acid dissociation for varioussubstituted aldehydes with electron withdrawing and electron releasing groups. Good quality log Khydr,(g) correlations withthe Swain–Lupton resonance effect parameters R and R+ were found, allowing extension of the model to predict log Khydr,(g)values for 487 substituted aldehydes having available R-values and 108 substituted aldehydes having available R+ values.Good correlations were also found between experimental aqueous phase hydration equilibrium constants (log Khydr,(aq))and summative R/R+ values for peripheral substituents on a range of carbonyl derivatives (aldehydes, ketones, esters, andamides), suggesting that the structure–reactivity modeling approach can be extended to include all possible combinationsof R1C(O)R2 carbonyl substitution in both gas and aqueous systems. Computationally derived BDEs and ΔdH°(g)/ΔdG°(g) werein good agreement with the limited experimental and theoretical datasets. BDEs did not generally correlate with any of theHammett substituent constants or Swain–Lupton parameters considered. Gas phase acidities exhibited high correlation coef-ficients with Hammett inductive substituent constants (σI) and field effect parameters (F), allowing these to be employed assurrogates for estimating the gas phase aldehydic proton acidities of a larger potential compound range. The resultingmodels will be of use in predicting the environmental behavior for a broad range of environmentally relevant compoundscontaining carbonyl functionalities. Copyright © 2016 John Wiley & Sons, Ltd.

Keywords: acidity; aldehydes; atmospheric chemistry; bond dissociation enthalpies; hydration

INTRODUCTION

The solution phase hydration of carbonyl compounds not onlyplays a fundamental role in organic chemistry and biochemistryowing to the mechanistic importance of tetrahedral intermedi-ates,[1,2] the reactions also have substantial thermodynamic and ki-netic relevance towards the environmental chemistry of naturaland anthropogenically derived materials.[3,4] Aqueous phase stud-ies have shown that hydration equilibria can be substantial forsome substituted aldehydes,[5–10] and corresponding structure–reactivity investigations have correlated equilibrium constantswith Hammett substituent parameters and applied other linearfree energy approaches.[10–16] Because carbonyl hydration is lessfavorable in the gas phase, theoretical studies have generally con-centrated on aqueous phase reactivity and mechanistic/kineticmodeling and are typically limited to smaller compounds such asformaldehyde, with fewer studies focusing on larger databases ofmolecules and/or gas phase equilibria.[17–31]

Among the various classes of carbonyl derivatives, aldehydesplay an important role in the chemistry of natural and polluted at-mospheres.[32–34] Recent findings suggest that some hydrated alde-hydes may have significant populations in air samples,[35–38]

warranting their consideration in environmental fate and toxicologymodeling efforts, gas-particle and air-water partitioning studies, andour understanding of formation pathways for secondary organicaerosols. Furthermore, given the complexity of atmospheric chem

istry, and the ever increasing diversity of anthropogenic com-pounds being emitted into the troposphere, there is also a needto investigate the potential gas phase hydration behavior for abroad range of substituted aldehydes. An additional goal is thedevelopment of reliable structure–reactivity relationships, as thesecan be included in environmental models and be applied tosystems that are difficult to measure experimentally or model theo-retically. In some cases, experimental measurements of gas phasealdehyde hydration may not be possible because of the low valueof an equilibrium constant or competitive side reactions for reac-tants and products.In the current work, we employ high-level theoretical methods

and established physical organic substituent constant/structure–property approaches to study equilibria for the gas phase hydra-tion of a wide range of substituted aldehydes. In addition, wehave examined the gas phase bond dissociation enthalpies

* Correspondence to: S. Rayne, Chemologica Research, Moose Jaw, Saskatchewan,Canada.E-mail: sierra.rayne@alumni.ubc.ca

a S. RayneChemologica Research, Moose Jaw, Saskatchewan, Canada

b K. ForestDepartment of Environmental Engineering Technology, Saskatchewan Poly-technic, Moose Jaw, Saskatchewan, Canada

Research article

Received: 23 October 2015, Revised: 12 December 2015, Accepted: 07 January 2016, Published online in Wiley Online Library: 12 February 2016

(wileyonlinelibrary.com) DOI: 10.1002/poc.3539

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(BDEs) and aldehydic hydrogen acidities for various aldehydeswith the intent of benchmarking the composite methods and ex-amining possible structure–activity relationships. Gas phaseBDEs are directly relevant for atmospheric chemistry, as theyare strongly related to rates of degradation by oxidants such asthe hydroxyl, nitrate, and chlorine radicals. In addition, gas phaseBDEs are often correlated with solution phase BDEs, and conse-quently offer insights into likely condensed phase reactivitytrends. Gas phase acidities of these compounds are both of fun-damental interest and often correlate with solution phase acidi-ties in various solvents.

MATERIALS AND METHODS

Calculations were conducted using Gaussian 09.[39] All calcula-tions used the same gas phase starting geometries obtainedwith the PM6[40] semiempirical method as implemented inMOPAC 2009 (http://www.openmopac.net/; v. 9.281). Completebasis set (CBS) calculations used the CBS-Q//B3 method.[41,42]

Gaussian-n calculations used the G4[43] and G4(MP2)[44]

methods. All molecular enthalpies and free energies include zeropoint and thermal corrections. For hydrated aldehydes, no apriori assumptions were made regarding molecular conforma-tions. All hydrated compounds were subjected to a molecularmechanics (MM) molecular dynamics (MD) conformationalsearch with an unconstrained MD trajectory via the Verlet veloc-ity algorithm and quasi-Newton gradient (maximum number ofiterations = 10 000; ε= 10�4) using the following default parame-ters in Gabedit v.2.2.12 (http://gabedit.sourceforge.net/)[45]: Am-ber MM model with inclusion of bond stretch, angle bend,torsion, non-bonded, and electrostatic charge–charge terms;post-processing identical structure removal with an energy toler-ance of 0.01 kcal/mol and distance tolerance of 0.01 Å; and max-imum 10 final lowest energy structures. Additional MMconformational studies were conducted using the MMFF94 forcefield and a systematic rotor search within Avogadro v.1.0.1(http://avogadro.openmolecules.net/).Depending on the number of conformers generated by each

approach, between two and nine lowest energy MM conforma-tions for each hydrated compound were subjected to calcula-tions at each of the CBS-Q//B3, G4(MP2), and G4 levels oftheory. For the aldehydes, acyl radicals, and acyl anions, multiplestarting conformations were also considered where relevant.Only the lowest energy conformation for each compound fromeach composite method calculation was used for further analy-sis. Optimized structures were confirmed as true minima byvibrational analysis at the same level. Unless otherwise noted,all Hammett substituent constants and resonance and fieldparameters are from the compendium of Hansch et al.[46] Statis-tical analyses were conducted using KyPlot v.2.0.b.15 (http://www.kyenslab.com/en/).As described by Hansch et al.,[46] Hammett constants are

widely employed in all branches of chemistry to describe a linearrelationship between differing substituent identities and theequilibrium constant or rate of a reaction. For example, in theequation log (K/Ko) = σ× ρ, K is the equilibrium constant withsubstituent R, Ko is the reference equilibrium constant where Ris a hydrogen atom, σ is the substituent constant that dependsonly on the specific substituent R, and ρ is the reaction constantthat depends only on the type of reaction but not on the substit-uent used. Depending on the effect of interest (e.g., inductive, σI;

resonance, σR; and field, σF), the positional relationship to thereaction center (e.g., meta, σm and para, σp), and/or thecharge/developing charge at the reaction center (e.g., σp

+, σp�,

σR+, and σR

�), a range of substituent constants are availableand have been determined experimentally and calculated theo-retically. In the Swain–Lupton approach, field (F) and resonance(R) effects for a substituent are related to σp as follows: σp= fF+ rR. A linear free energy relationship can be subsequentlyprobed for equilibrium constants (or reaction rates) of thegeneral form log (K/Ko) = fF+ rR+ C (or log (k/ko) = fF+ rR+C),where f, r, and C (a constant) are obtained via multiple linearregression of the dependent variables F and R against the inde-pendent variable log (K/Ko) (or log (k/ko)) for a series of differingsubstituents and their corresponding equilibrium constants (orreaction rates). Analogous to the Hammett constants, theSwain–Lupton constants can reflect the charge/developingcharge at the reaction center (e.g., R+ and R�).

RESULTS AND DISCUSSION

Aldehyde substituents were chosen to span a broad range ofelectron withdrawing group (EWG) and electron releasing group(ERG) abilities. The resulting gas phase standard state (298.15 K,1 atm) Gibbs free energies of hydration (ΔhydrG°(g); Fig. 1) calcu-lated at the CBS-Q//B3, G4(MP2), and G4 levels of theory span28.0 kcal/mol from �6.8 (H(O)CPF4) to 21.2 (H(O)CN(CH3)2)kcal/mol (Table 1). The corresponding equilibrium constants(log Khydr,(g)) range over 20.5 orders of magnitude from +5.0 to�15.5. Good agreement was found among the three theoreticalmethods, with mean unsigned maximum variations in ΔhydrG°(g)and log Khydr,(g) of 1.3 kcal/mol and 1.0 units, respectively.

Our ΔhydrG°(g) for formaldehyde (1.2 to 2.3 kcal/mol) are ingood agreement with the HF/6-31G(d,p) and HF/6-31+G(d,p) re-sults of Ventura et al. (0.5 and 2.3 kcal/mol, respectively),[19,22]

but these authors found substantially more favorable ΔhydrG°(g)at the other levels of theory they considered (all values inkcal/mol): HF/4-31G (�1.7), MP2/6-31G(d,p) (�0.2), and MP3/6-31G(d,p) (�1.4). In another study, Erion and Reddy[23] foundformaldehyde ΔhydrG°(g) using various levels of theory of �1.1(HF/6-31G**), �0.6 (MP4/6-31G**), �1.0 (QCISD(T)/6-31G**),�1.8 (MP2/6-31G**), and �3.0 (MP3/6-31G**) kcal/mol. Thisgroup also conducted calculations on CCl3C(O)H, obtaining thefollowing ΔhydrG°(g): �0.7 (HF/6-31G**), �1.1 (MP4/6-31G**),�1.9 (QCISD(T)/6-31G**), �2.6 (MP2/6-31G**), and �3.9 (MP3/6-31G**) kcal/mol. By comparison, we obtain ΔhydrG°(g) between0.5 to 2.1 kcal/mol at the CBS-Q//B3, G4(MP2), and G4 levels oftheory for CCl3C(O)H.

The calculated ΔΔhydrG°(g) of about zero between formalde-hyde and CCl3C(O)H is, however, equivalent between our workand that of Erion and Reddy[23] at all levels of theory in bothstudies. These authors also found ΔΔhydrG°(g) between formalde-hyde and acetaldehyde at 3 to 4 kcal/mol, in qualitative agree-ment with our value of 1.5 kcal/mol using each of the CBS-Q//

Figure 1. General scheme for the gas phase hydration of substitutedaldehydes

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B3, G4(MP2), and G4 methods. The comparison suggests a sys-tematic difference in the results between our two investigations,with qualitative agreement but modest quantitative disagree-ment. There is clearly substantial disagreement (on the order ofseveral kcal/mol) between various levels of theory regardingthe ΔhydrG°(g) for even simple aldehydes. It is of interest thatmany of the prior semiempirical, Hartree-Fock (HF), density func-tional theory, and Møller–Plesset perturbation theory calcula-tions predicted a ΔhydrG°(g)< 0 for formaldehyde. If such wasthe case, we would expect to see a dominant population of thehydrated form during gas phase studies of this compound,which is not observed experimentally.[9,47]

More recently, Kent et al.[48] have conducted a theoreticalstudy of the conversion of gas phase methandiol to formalde-hyde. Using the HF, MP2, MP4, CCSD, CCSD(T), and QCI(T)model chemistries with the cc-pVDZ and cc-pVTZ basis sets,these authors obtained ΔhydrG°(g) ranging from 1.0 to 3.3 kcal/mol, with the highest level CCSD(T)/cc-pVTZ and QCI(T)/cc-pVTZ methods yielding ΔhydrG°(g) of 1.0 and 1.1 kcal/mol,respectively. The values are in excellent agreement with ourcalculations, particularly our G4 ΔhydrG°(g) of 1.2 kcal/mol.Consequently, the similar positive ΔhydrG°(g) of 1 to 2 kcal/mol

reported herein and by Kent et al.[48] using high-level methodsare likely the most accurate thermodynamic data for the gasphase hydration of formaldehyde.Increasing EWG strength results in more favorable ΔhydrG°(g) at

the CBS-Q//B3, G4(MP2), and G4 levels of theory, as the electronwithdrawing substituents increase the electrophilicity of the car-bonyl carbon. To quantify this effect, we applied the Swain–Lupton approach[49–51] using field effect (F) and resonance effect(R) parameters[46] for each of the substituted aldehydes in thefollowing equation, where f and r are coefficients obtained frommultiple linear regression and C is a regression constant: logKhydr,(g) = fF+ rR+C. During our initial statistical investigations,we observed that C≡C-CH3 (R=�0.26) was clustering separatefrom the other α-sp carbons (C≡C-H, C≡C-CF3, and C≡N).R values are commonly derived from F values and Hammett

substituent constants by way of equations such as R= σp� αF(where α= 0.921).[52] Using this equation and the σp and F valuesgiven by Hansch et al.[46] consistently yields R values for C≡C–H(0.03 vs. 0.01), C≡N (0.19 vs. 0.15), C≡C–CH3 (�0.24 vs. �0.26),C≡C-CF3 (0.17 vs. 0.14), and C≡C-C6H5 (0.03 vs. 0.01) within±0.04 units of those provided in ref..[46] If one assumes the con-tribution of the α-C≡C moiety to the σp of C≡C–H, C≡C–CH3,

Table 1. Substituent constants and estimated gas phase standard state (298.15 K, 1 atm) free energies of hydration (ΔhydrG°(g))and corresponding hydration equilibrium constants (log Khydr,(g)) for various aldehydes with electron withdrawing and electron re-leasing substituents at the CBS-Q//B3, G4(MP2), and G4 levels of theory

Substituent Substituent constants ΔhydrG°(g) (kcal/mol) Log Khydr,(g)

F R R+ CBS-Q//B3 G4(MP2) G4 CBS-Q//B3 G4(MP2) G4

C(O)CH3 0.33 0.17 n/a 0.9 2.1 1.0 �0.6 �1.6 �0.7NH2 0.08 �0.74 �1.38 16.6 17.2 16.5 �12.1 �12.6 �12.1C(CH3)3 �0.02 �0.18 �0.17 4.3 5.4 4.4 �3.2 �4.0 �3.2C≡N 0.51 0.15 0.15 1.1 2.5 1.5 �0.8 �1.9 �1.1N(CH3)2 0.15 �0.98 �1.85 20.7 21.2 20.3 �15.1 �15.5 �14.8CH=CH2 0.13 �0.17 �0.29 7.1 8.0 7.1 �5.2 �5.9 �5.2C≡CH 0.22 0.01 �0.04 4.6 5.7 4.8 �3.4 �4.2 �3.5F 0.45 �0.39 �0.52 6.9 7.8 6.7 �5.0 �5.8 �4.9H 0.03 0.00 0.00 1.3 2.3 1.2 �0.9 �1.6 �0.9OH 0.33 �0.70 �1.25 14.4 15.3 14.3 �10.5 �11.2 �10.5CH3 0.01 �0.18 �0.32 2.8 3.8 2.7 �2.0 �2.7 �2.0NO2 0.65 0.13 0.14 �1.8 �0.1 �1.3 1.4 0.1 0.9C6H5 0.12 �0.13 �0.30 7.0 8.0 7.1 �5.1 �5.9 �5.2CF3 0.38 0.16 0.23 �2.4 �0.9 �2.0 1.8 0.6 1.5Si(CH3)3 0.01 �0.08 0.01 1.7 2.9 1.8 �1.3 -2.2 �1.3Br 0.45 �0.22 �0.30 7.7 9.5 8.2 �5.6 �6.9 �6.0Cl 0.42 �0.19 �0.31 8.0 9.4 8.3 �5.9 �6.9 �6.1SiCl3 0.44 0.12 0.13 �0.4 1.8 0.5 0.3 �1.3 �0.4SiF3 0.47 0.22 n/a 0.1 1.8 0.4 �0.1 �1.3 �0.3SiH3 0.06 0.04 0.08 3.2 4.4 3.2 �2.4 �3.2 �2.4CBr3 0.28 0.01 n/a 2.3 3.1 1.9 �1.7 �2.3 �1.4CCl3 0.38 0.09 n/a 0.5 2.1 0.9 �0.4 �1.5 �0.7C≡CCF3 0.37 0.14 n/a 2.4 3.6 2.6 �1.7 �2.6 �1.9C≡CCH3 0.29 �0.10 n/a 4.4 4.6 3.6 �3.2 �3.3 �2.7C(C≡N)3 0.92 0.04 n/a �3.2 �1.6 �2.8 2.3 1.2 2.0C6H4-4-Br 0.18 �0.06 �0.38 6.5 7.7 6.8 �4.8 �5.7 �5.0C6H4-4-Cl 0.18 �0.06 �0.37 6.7 7.8 6.8 �4.9 �5.7 �5.0C6H4-4-F 0.17 �0.11 n/a 7.0 8.1 7.1 �5.1 �5.9 �5.2C6H4-4-CH3 0.12 �0.15 n/a 7.7 8.8 7.9 �5.6 �6.4 �5.8PF4 0.54 0.26 n/a �6.8 �4.3 �5.8 5.0 3.1 4.3GeH3 0.03 �0.02 n/a 3.1 4.8 3.6 �2.3 �3.5 �2.6

S. RAYNE AND K. FOREST

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C≡C–CF3, and C≡C–C6H5 is constant, and that the σp are all accu-rate, linearly regressing the σp of H (0.00), CH3 (�0.17), CF3 (0.54),and C6H5 (-0.01) against the σp of C≡C–H (0.23), C≡C–CH3 (0.03),C≡C–CF3 (0.51), and C≡C–C6H5 (0.16) should give a high correlationcoefficient, which is the case (y=mx+b; r=0.981, p=0.02,m=0.64, b=0.17).Similarly, assuming that the contribution of the α-C≡C moiety

to the F value of C≡C-H, C≡C–CH3, C≡C–CF3, and C≡C–C6H5 isconstant, and that the F-values are all accurate, linearlyregressing the F of H (0.03), CH3 (0.01), CF3 (0.38), and C6H5

(0.12) against the F of C≡C–H (0.22), C≡C–CH3 (0.29), C≡C–CF3(0.37), and C≡C–C6H5 (0.15) should also yield a straight line. Thisis not observed, and the regression is non-significant (p= 0.40).Omitting C≡C–CH3 does not result in a significant regression(p= 0.36). F values can also be estimated from equations of theform F= aσm+ bσp+ ε, where constants of a= 1.369/b=�0.373/ε=�0.009[52] and a=1.297 ± 0.147/b=�0.385 ± 0.089/ε=0.033± 0.026[46] have been reported. Use of these constants and theσm and σp values from ref.[46] yields F values of 0.27 and 0.29,respectively, in agreement with the original F value of 0.29. Toexamine the potential inaccuracy of σm for C≡C–CH3, σm forH (0.00), CH3 (�0.07), CF3 (0.43), and C6H5 (0.06) were linearlyregressed against the σm of C≡C–H (0.21), C≡C–CH3 (0.21),C≡C–CF3 (0.41), and C≡C–C6H5 (0.14). Neither regressions usingall four paired compounds (p= 0.13) or C≡C–H, C≡C–CF3, andC≡C–C6H5 (p=0.24) yield significant relationships.However, the available substituent constant dataset for α-sp

carbons may be insufficient to evaluate the reliability of theC≡C–CH3 R value. Thus, we looked at the correlation betweenthe Σσm values (σm,R1 + σm,R2) for substituents on CH=C(R1R2)functionalities and the σm values for the entire CH=C(R1R2) moi-eties on the following groups: CH=CH2, CH=C(CN)2, CH=CH(NO2)-t, CH=CH(CF3)-c, CH=CH(CF3)-t, CH=CH(SO2CF3), CH=CH(CN), CH=CH(CHO), CH=CH(Me)-t, CH=CH(COMe), CH=CH(COOEt), CH=CH(C6H5), and CH=CH(COC6H5). In this largerdataset, we found a significant linear relationship (r=0.942,p< 10-5, m=0.46, b= 0.02), suggesting that an analogous trendshould exist for C≡C–R groups. Thus, approximating the trendbetween σm for H, CF3, and C6H5 against the σm of C≡C–H,C≡C–CF3, and C≡C–C6H5 (m=0.56, b=0.16), and intersectingthe σm of CH3 (�0.07), yields a revised C≡C–CH3 σm of 0.12. Witha σm= 0.12 for C≡C–CH3, F values of 0.14 and 0.18 are obtainedwith the equation F= aσm+ bσp+ ε and the correspondingregression constants from ref.[52] and,[46] respectively. Conse-quently, revised R values of �0.10 and �0.14 for C≡C–CH3 arisefrom the relationship R= σp� 0.921 F. The use of R=�0.10 forC≡C–CH3 places this substituent substantially closer to otherα-sp carbons in plots of ΔhydrG°(g) against R at each level of the-ory we examined, and we use this revised R value in subsequentanalyses and discussions. However, future experimental clarifica-tion on this issue is required.Using both the field and resonance effect substituent con-

stants, we obtain reasonable training set correlation coefficients(n= 31) using multiple linear regression of the form log Khydr,(g)= fF+ rR+ C with corresponding values for f, r, and C at the threelevels of theory (error bars are standard errors throughout themanuscript): CBS-Q//B3, r=0.926, SE=1.61, CV=�0.51, f=2.79±1.44(p=0.06), r=13.1± 1.1 (p< 10�11), C=�2.68± 0.54 (p< 10�4); G4(MP2), r= 0.918, SE = 1.61, CV =�0.40, f =2.24 ± 1.44 (p= 0.13),r= 12.5 ± 1.1 (p< 10�10), C =�3.51 ± 0.54 (p< 10�6); and G4,r=0.918, SE=1.64, CV=�0.50, f=2.40±1.47 (p=0.11), r=12.7±1.2(p< 10�10), C=�2.74 ± 0.55 (p< 10�4). All three levels of theory

yield statistically non-significant (p> 0.05) regression coefficientsfor the field effect constant F, suggesting a significant probabilitythat f≈ 0 (and thus, negligible field effects) within the multiple re-gression equation. However, there is a highly significant (p=0.01)individual relationship between F and log Khydr,(g). AlthoughHammett substituent constants (σm, σp, σp

+, σp-, σF, σI, σR, σR

+, σ*/Es, and σR

�) and R� values are not available for all substituentsunder consideration, the available subsets we examined did notprovide as good correlations as the F/R values and were notconsidered further.

Consequently, we omitted the field effect term from furtheranalysis and investigated the theoretical gas phase hydrationthermodynamics using only the resonance effect parameters R(Fig. 2) and R+ (Fig. 3). Linearly regressing the CBS-Q//B3, G4(MP2), and G4 log Khydr,(g) against the corresponding R valuesgave the regression statistics in Table 2. Although strong

Figure 2. Correlations between the Swain–Lupton resonance effect pa-rameter (R) and estimated gas phase standard state (298.15 K, 1 atm) hy-dration equilibrium constants (log Khydr,(g)) for various substitutedaldehydes at the (a) CBS-Q//B3, (b) G4(MP2), and (c) G4 levels of theory.A best fit regression for all datapoints (n = 31) is shown as a solid line.Identities of the substituents are given in Table 1, and summaries ofthe statistical analyses are provided in Table 2

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correlations for log Khydr,(g) were observed at each level of theory,the use of the R+ resonance effect parameter for positivelycharged reaction centers substantially improved the quality offit for all compounds (r> 0.958) on the subset of 20 substituentshaving available R+ values. By comparison, correlation coeffi-cients of 0.941 (CBS-Q//B3), 0.938 (G4(MP2)), and 0.937 (G4) werefound between the estimated log Khydr,(g) and corresponding Rvalues for this 20 substituent subset.

We note our use of a revised R+ value of �0.38 for para-bromophenyl (C6H4-4-Br), corrected from the value of +0.38given in Table V of Hansch et al.[46] The positive R+ for C6H4-4-Brin ref.[46] is likely a typographic error, as analogous σ-EWG andπ-electron donating substituents on benzene have negative R+

values (C6H4-4-Cl, �0.37; C6H4-3-Cl, �0.34), the unambiguously

EWG C6H4-4-NO2 substituent has a negative R+ value of �0.22,as do the parent halogen substituents (e.g., F =�0.52,Cl =�0.31, and Br =�0.30). The use of either R or R+-basedresonance parameters for log Khydr,(g) correlation analysis is theo-retically defensible, because both the neutral and charge sepa-rated carbonyl resonance forms (C=O and C+–O�) are expectedto contribute to the hydration reaction. Multiple linear regres-sions of the general form log K= rR+ r+R+ + C (where r and r+ po-tentially represent the relative contributions of the neutral andpositively charged resonance forms) are precluded given themulticollinearity between R and R+ (r=0.977 for the 20 substitu-ents we considered).Application of the R value-based regression equations towards

487 substituted aldehydes (including the 31 compounds in thetraining set) with available R values for uncharged substituentsyields the estimated log Khydr,(g) ranging between �16.0 (N(C3H7)2)and +9.2 (N=NPO(OEt)2) shown in Table S1. Analogous applicationof the R+ value-based regression equations towards 108 substitutedaldehydes (including the 20 compounds in the training set) withavailable R+ values for uncharged substituents yields the estimatedlog Khydr,(g) ranging between �17.7 (N(C2H5)2) and +2.8 (P(C6H5)2)shown in Table S2. Charged substituents (e.g., O�, CO2

�, andN+(CH3)3) were not considered in these gas phase log Khydr estimatesusing either the R or R+ based approaches because these chargedside groups are generally considered non-volatile and are notexpected to have significant gas phase populations amenableto hydration reactions. Similarly, a number of substituentsincluded in our analysis would also be expected to undergohydrolysis in the presence of atmospheric water (e.g., acyl halidesand transition metal complexes) at rates competitive with, orexceeding, that of corresponding aldehyde hydration reactions,but they are retained in the database for completeness.Regression-derived standard errors in the log Khydr,(g) estimatesare about 1.0 to 1.5 units for most compounds. For the 108 sub-stituents with both R and R+ values, good agreement was ob-served between log Khydr,(g) obtained using both correlationapproaches at each level of theory (r values ranging from +0.85to +0.86, p< 10�31). The value of such correlations and resultinglog Khydr,(g) estimates resides in the conformational complexityand large size of many substituents for which R/R+ values areavailable. In many cases, high-level calculations on these moietiesare either impossible (beyond the basis set limits) or impractical(large numbers of low-energy conformers requiring investigationand/or many heavy atoms present).As a sample application of these results, experimental[35] and

theoretical[36] evidence suggests perfluoroalkyl aldehydes(PFAlds) are likely present in the atmosphere in significant quan-tities as the hydrated form. These compounds are both deriva-tives and precursors of other well-known perfluorinatedcompounds and are thought to play an important role towardsour understandings into the global cycling of these contami-nants.[53–55] As part of our initial suite of calculations provided inTable 1, we found that the C1 PFAld (CF3C(O)H) is expected to havea log Khydr,(g) ranging from 0.6 (G4(MP2)) to 1.8 (CBS-Q//B3), consis-tent with the experimental data.[35] Additional calculations at theCBS-Q//B3 and G4(MP2) levels on the C2 (CF3CF2C(O)H), C3 (CF3(CF2)2C(O)H), and C4 (CF3(CF2)3C(O)H) PFAlds gave the followinglog Khydr,(g): C2, 0.9 (CBS-Q//B3) and �0.3 (G4(MP2)); C3, 0.7 (CBS-Q//B3) and �0.4 (G4(MP2)); and C4, 1.1 (CBS-Q//B3) and �0.1 (G4(MP2)). Corresponding G4 calculations on the C2 through C4 PFAldderivatives were impractical because of the high computationalexpense. By comparison, the Swain–Lupton regression-derived

Figure 3. Correlations between the Swain–Lupton positively chargedreaction center resonance effect parameter (R+) and estimated gas phasestandard state (298.15 K, 1 atm) hydration equilibrium constants (logKhydr,(g)) for various substituted aldehydes (n = 20) at the (a) CBS-Q//B3,(b) G4(MP2), and (c) G4 levels of theory. A best fit regression for alldatapoints is shown as a solid line. Summaries of the statistical analysesare provided in Table 2. Aldehyde substituents in the analysis include thefollowing: NH2; C(CH3)3; C≡N; N(CH3)2; CH=CH2; C≡CH; F; H; OH; CH3; NO2;C6H5; CF3; Si(CH3)3; Br; Cl; SiCl3; SiH3; C6H4-4Br; and C6H4-4Cl

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log Khydr,(g) for these compounds using correlations with R valuesare 0.1CBS-Q//B3/�1.0G4(MP2) (C2), �0.2CBS-Q//B3/�1.3G4(MP2) (C3), and0.1CBS-Q//B3/�1.0G4(MP2) (C4). R

+ substituent constants are not avail-able for CF3CF2, CF3(CF2)2, and CF3(CF2)3.The results show that the longer chain (i.e., >C4) PFAlds –

which are of primary interest to the environmental chemistrycommunity – may be present substantially as the hydrated formin the atmosphere. Similarly, other aldehydes with α-EWGs suchas nitro and variously substituted carbonyl moieties are also ex-pected to have significant hydrated populations in gas phase at-mospheric samples. Consequently, ambient atmosphericmodeling efforts and associated risk assessments, as well asstudies in engineered systems, will need to account for the gasphase hydration of such compounds. However, it is also impor-tant to note that various loss mechanisms (e.g., uptake on sur-faces), the possible failure to achieve atmospheric equilibrium,and the relatively low equilibrium vapor pressure of water inthe atmosphere will act collectively to reduce actual populationsof the hydrates below their theoretical maxima. In anotherexperimental study, Axson et al.[37] have recently provided anexperimental log Khydr,(g) of 2.2 ± 0.1 for methylglyoxal (H3CC(O)C(O)H). Our calculations at the CBS-Q//B3, G4(MP2), and G4 levelsobtain log Khydr,(g) of �0.6, �1.6, and �0.7, respectively. In theirwork, Axson et al.[37] noted that their reported log Khydr,(g) is “sig-nificantly more favorable than theoretical predictions, even onesmade in aqueous solution.” Our results are, however, consistentwith those of Barsanti and Pankow, who estimated that gasphase hydration of methylglyoxal would not be thermodynami-cally favorable.[56] Further clarification is required to better de-fine whether the two theoretical estimates, or the experimentaldatapoint, accurately reflect the gas phase hydration thermody-namics of this model secondary organic aerosol precursor.Our calculations were limited to gas phase asymmetric car-

bonyl substitutions of the general form R1C(O)R2 where R2 =H(i.e., aldehydes). We sought to examine whether the findingscould be extended into the aqueous phase and also towardssymmetric and asymmetric carbonyl substitutions where R2≠Hand R1 = R2 or R1≠ R2 (i.e., ketones and carboxylic acid deriva-tives). Gomez-Bombarelli et al.[28] have published a compilationof experimental log Khydr,(aq) and conducted correspondingB3LYP/6-31++G(d,p), MP2/6-31++G(d,p), and CBS-Q log Khydr,(aq)calculations directly using the integral equation formalism ofthe polarizable continuummodel implicit solvation model. Whenthe sum of the R values (ΣR= RR1 + RR2) on either side of the

carbonyl moiety from this compilation is plotted against the ex-perimental log Khydr,(aq) values, a strong correlation exists (n= 35,r= 0.947, p< 10�17, SE = 1.56, CV =�0.44, m= 14.43 ± 0.85,b= 1.70 ± 0.41) among all datapoints, although the threethioesters (H(O)CSC2H5, H3CC(O)SC2H5, and F3CC(O)SC2H5) areoutliers (Fig. 4(a)). The use of R+ (ΣR+ = R+R1 + R

+R2) does not

substantially change the summary statistics for the correlation(n=28, r=0.972, p< 10�17, SE= 1.20, CV=�0.28, m=8.08±0.38,b=2.31±0.38), but removes the outlying nature of various substit-uent groups (notably the thioesters), thereby allowing greater con-fidence in applying the regression towards substituent functionalgroup classes not included in the training set. SC2H5 does not havea R+ value in Hansch et al.[46]; thus, a value of�0.81 was estimatedbased on the R+ =�0.83 for SCH3 and the ΔR+ = 0.02 between CH3

(R+ =�0.32) and C2H5 (R+ =�0.30).

The strong agreement for ΣR and ΣR+-based approachestowards log Khydr,(aq) estimation across multiple functional groupclasses and over a log Khydr,(aq) range of about 20 units suggeststhat not only can the gas phase R/R+ value log Khydr modelingapproaches extend into aqueous systems but also that a simplesummative approach to R/R+ values about the carbonyl moietycan likely be used to extend our log Khydr,(g) regression equationspresented previously towards all possible functional group com-binations of R1C(O)R2. A sample application of the ΣR+-basedapproaches towards log Khydr,(aq) estimation for various alde-hydes is provided in Table S3. Using the regression equationshown in Fig. 4(b), log Khydr,(aq) were estimated for 115 aldehydeshaving available R+ substituent constants from ref.[46] Predictedlog Khydr,(aq) range from�18.4 (S�) for strongly electron releasingsubstituents to +7.2 (P(C6H5)2) for strongly EWG groups. Theestimated log Khydr,(aq) end members are the symmetric ketonesC(O)S2

2� (log Khydr,(aq) =�39.0) and C(O)(P(C6H5)2)2 (log Khydr,(aq)= +12.0), well outside the current experimental range of �14.2 to+3.4. We note that many of the substituents are susceptible torapid aqueous phase hydrolysis (e.g., various carboxylic acidderivatives) and would therefore hydrolyze having kineticparameters competitive with – or exceeding – that of hydrationreactions, but we retain these functional groups in the databasefor completeness.

Gas phase standard state (298.15K, 1 atm) BDEs for the acyl C-Hbond were also calculated at the CBS-Q//B3, G4(MP2), and G4 levelsof theory on various substituted aldehydes (Table 3). Good agree-ment (i.e., generally within 1kcal/mol) was found between thetheoretical values and the limited available experimental dataset.

Table 2. Linear regression statistics for CBS-Q//B3, G4(MP2), and G4 estimated gas phase log Khydr,(g) against Swain–Lupton res-onance effect (R) and positive charged resonance effect (R+) parameters for the substituted aldehydes in Figs. 2 and 3, respectively

Level of theory Resonance effect (R) parameters

r p SE CV m b

CBS-Q//B3 0.923 <10�12 1.62 �0.51 13.6 ± 1.1 �1.89 ± 0.31G4(MP2) 0.921 <10�12 1.55 �0.38 12.8 ± 1.0 �2.87 ± 0.29G4 0.920 <10�12 1.60 �0.49 13.1 ± 1.0 �2.06 ± 0.30

Level of theory Positive charged resonance effect (R+) parameters

r p SE CV m b

CBS-Q//B3 0.960 <10�10 1.24 �0.29 7.55 ± 0.52 �1.69 ± 0.32G4(MP2) 0.958 <10�10 1.23 �0.24 7.20 ± 0.51 �2.70 ± 0.32G4 0.959 <10�10 1.23 –0.28 7.31 ± 0.51 -1.90 ± 0.32

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The radical species of several α- and β-unsaturated members (R=C(O)CH3, CH=CH2, C≡C–H, NO2, C≡C–CH3, C≡C–CF3, and C(CN)3), aswell as R=PF4, did not readily converge at all three levels of theory,and thus were omitted from further analysis. We found no highquality general correlations between BDEs at any of the levels oftheory and F, R, R+, R�, σm, σp, σp

+, σp-, σF, σI, σR, σ

*/Es, σR+, and

σR� substituent constants, in contrast to expectations that electron

donating substituentsmay favor a lower BDE for these compoundsin a quantitatively predictive fashion using the Hammett andSwain-Lupton modeling approaches.Analogous calculations were conducted to estimate the gas

phase standard state (298.15 K, 1 atm) enthalpies (ΔdH°(g)) andfree energies (ΔdG°(g)) of aldehyde proton acid dissociation forthese compounds (Table 4). As with the BDE calculations, goodagreement was found between the theoretical values and theavailable experimental dataset. The deprotonated anionic formsdid not converge at all levels of theory for the following alde-hyde substituents: NH2, C≡N, C≡C–H, C≡C–CH3, C≡C–CF3, NO2,CF3, Cl, Br, SiH3, Si(CH3)3, SiH3, SiF3, SiCl3, CCl3, CBr3, C(C≡N)3,PF4, and GeH3.Multiple linear regression of the σm/σp, σI/σR, and F/R pairs did

not yield high quality correlations with statistical significance forboth independent variables. Among the univariate correlations,σI displayed an excellent quality of fit (n=9, r=�0.966, SE = 3.1,CV=0.008, m=�60.3± 6.1, b=387.1± 1.4) against the G4 ΔdG°(g)data, in addition to the CBS-Q//B3 (n= 9, r=�0.965, SE = 3.1,CV = 0.008, m=�59.7 ± 6.1, b=387.2 ± 1.4) and G4(MP2) (n= 9,r=�0.967, SE = 3.0, CV = 0.008, m=�59.0 ± 5.9, b= 386.7 ± 1.4)datasets. Multiple regression of the general form ασI +βσR =ΔdG°(g)gave insignificant (p> 0.05) β-coefficients for σR, suggesting in-ductive influences dominate gas phase acidity variations forsubstituted aldehydes. Similar qualities of fit were obtained betweenσI and the theoretical ΔdH°(g) (all n=9): CBS-Q//B3, r=�0.967,SE = 3.1, CV = 0.008, m=�60.6 ± 6.0, b=395.4 ± 1.4; G4(MP2),r=�0.969, SE=2.9, CV=0.008, m=�59.8±5.7, b=394.8±1.3; andG4, r=�0.969, SE= 3.0, CV=0.008,m=�61.3 ± 5.9, b=395.3± 1.4.Using these correlations and σI values for a range of substitu-

ents reported by Charton[57] yields the estimated ΔdH°(g) andΔdG°(g) given in Table S4. The predicted ΔdH°(g) range withinthese substituents is from 351.8 to 396.0 kcal/mol, and a ΔdG°(g)range from 344.3 to 387.8 kcal/mol. These boundaries corre-spond to the currently known experimental data end membersfor fluorine and dimethylamino substituents, respectively. Wealso note that the Swain–Lupton F parameter yields a modestlylower quality of fit as compared with the σI substituent constant(e.g., r of �0.924 against the G4 ΔdG°(g) data, compared with acorresponding r of �0.966 for σI), but a larger parameter data-base is available for F, thereby substantially extending the range

Figure 4. Correlation between the sum of Swain–Lupton resonance effect parameters (a) R and (b) R+ on carbonyl substituents with experimentalaqueous phase hydration equilibrium constants (log Khydr,(aq)) for various aldehydes, ketones, esters, thioesters, and amides. Experimental data takenfrom the compilation in ref..[28] Best fit linear regressions for each plot that include all datapoints are shown as solid lines

Table 3. Estimated gas phase standard state (298.15 K,1 atm) bond dissociation enthalpies (BDEs) of the aldehydeC–H bond for various aldehydes with electron withdrawingand electron releasing substituents at the CBS-Q//B3, G4(MP2), and G4 levels of theory

Substituent Expt. CBS-Q//B3 G4(MP2) G4

NH2 n/aa 94.5 93.2 93.5C(CH3)3 89.7 89.7 86.7 87.7C≡N n/a 91.1 91.1 91.4N(CH3)2 n/a 95.0 92.5 93.2F 101.1 101.9 100.3 100.8H 88.0 ± 0.2 89.1 87.9 88.2OH 96.6 100.9 99.1 99.6CH3 89.4 ± 0.3 89.0 87.7 88.0C6H5 88.7 ± 2.6 91.5 88.2 89.3CF3 93.3 93.5 90.0 91.1Si(CH3)3 n/a 79.5 76.7 77.6Br n/a 86.0 84.7 85.2Cl n/a 91.7 90.4 90.9SiCl3 n/a 81.6 78.6 79.7SiF3 n/a 81.9 78.7 79.8SiH3 n/a 79.8 78.5 78.9CBr3 n/a 99.1 90.4 91.5CCl3 n/a 93.9 90.7 91.7C6H4-4-Br n/a 91.7 87.8 89.1C6H4-4-Cl n/a 91.7 87.8 89.1C6H4-4-F n/a 91.6 87.7 89.0C6H4-4-CH3 n/a 91.5 87.5 88.9GeH3 n/a 79.3 78.0 78.4

Available experimental BDEs[58,59] are shown for comparison.Values are in kcal/mol.aNot available.

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of possible substituents that can be modeled. In addition, σI canbe estimated from F values using equations such as F= 0.888σI+ 0.017,[46] further extending the scope of our ΔdH°(g)/ΔdG°(g)models.

CONCLUSIONS

Gas phase standard state (298.15 K, 1 atm) free energies of hydra-tion (ΔhydrG°(g)) and corresponding equilibrium constants (logKhydr,(g)), BDEs, and enthalpies (ΔdH°(g)) and free energies (ΔdG°(g))of aldehydic proton acid dissociation were calculated using thecomposite method CBS-Q//B3, G4(MP2), and G4 levels of theoryon a range of substituted aldehydes with various EWG and ERGs.More EWG substituents increasingly favor higher log Khydr,(g), the-oretical values display excellent correlation with the Swain-Lupton resonance effect parameters R and R+, and no significantcorrelation with the corresponding field effect parameter (F).Using these correlations, log Khydr,(g) was predicted for 487substituted aldehydes having available R values and 108substituted aldehydes having available R+ values. The sum of Rand R+ on substituents attached to members of various carbonylderivative classes also displays strong correlations with aqueousphase hydration equilibrium constants (log Khydr,(aq)), reliablyextending the modeling efforts into the condensed phase andsuggesting the gas phase modeling approach can be used topredict log Khydr,(g) for all possible symmetric and asymmetriccarbonyl derivatives.

Both the computationally derived BDEs and ΔdH°(g)/ΔdG°(g)exhibited good agreement with the limited experimental andtheoretical datasets. No predictive univariate or multivariatecorrelations were found between the theoretical gas phase BDEsand the major Hammett substituent constants or Swain–Luptonparameters, suggesting that general structure–activity relation-ships across different types of functional groups may be absentfor this combination of physical property and general compoundclass. High correlation coefficients were observed between gasphase acidities and the Hammett inductive substituent constant(σI), facilitating estimation of ΔdH°(g)/ΔdG°(g) for other com-pounds with known σI values. Good correlations were also foundbetween ΔdH°(g)/ΔdG°(g) and the corresponding F values,allowing this substituent parameter (which is available for a largenumber of compounds, and can also be used to estimate σIvalues) to also be employed for the estimation of gas phasealdehydic proton acidities.

Acknowledgements

This work was made possible by the facilities of the WesternCanada Research Grid (WestGrid:www.westgrid.ca; project100185), the Shared Hierarchical Academic Research ComputingNetwork (www.sharcnet.ca; project aqn-965), and Compute/Calcul Canada. We thank the anonymous reviewers whosecomments greatly improved the quality of the manuscript.

Table 4. Estimated gas phase standard state (298.15 K, 1 atm) enthalpies (ΔdH°(g)) and free energies (ΔdG°(g)) of aldehyde protonacid dissociation for various aldehydes with electron withdrawing and electron releasing substituents at the CBS-Q//B3, G4(MP2),and G4 levels of theory

Substituent ΔdH°(g) ΔdG°(g)

Expt. CBS-Q//B3 G4(MP2) G4 Expt. CBS-Q//B3 G4(MP2) G4

C(O)CH3 n/aa 376.0 376.2 376.0 n/a 368.9 369.0 368.9C(CH3)3 387.4 ± 4.1[61] 392.1 391.9 392.6 381.0 ± 4.0[61] 383.7 383.7 384.4N(CH3)2 399.1 ± 4.1[62] 392.4 392.1 392.5 392.0 ± 4.0[62] 383.8 384.1 384.5CH=CH2 n/a 392.2 391.8 392.3 n/a 384.1 383.4 383.9F 349.7 ± 3.3[63] 362.1 361.6 361.2 n/a 353.8 353.5 353.1

352.6 ± 4.6[64]

H 394.5 ± 0.1[65] 397.2 395.2 395.2 386.6 ± 0.3[65] 389.3 387.6 387.6394.0 ± 4.5[66]

OH n/ab 379.2 378.8 378.9 n/ab 371.4 370.9 371.1CH3 393.1 ± 0.9[67] 393.3 393.3 393.4 385.4 ± 1.1[67] 384.4 384.3 384.4

391.0 ± 2.1[68] — — — 383.3 ± 2.0[68] — — —387.0 ± 8.0[69] — — — <374.30 ± 0.6[69] — — —<382.0[70] — — — — — — —

C6H5 n/a 388.1 387.6 388.3 n/a 380.6 380.1 380.7C6H4-4-Br n/a 382.3 382.0 382.6 n/a 374.7 374.3 374.9C6H4-4-Cl n/a 383.0 382.8 383.4 n/a 375.4 375.1 375.7C6H4-4-F n/a 384.9 384.5 385.0 n/a 377.4 376.9 377.4C6H4-4-CH3 n/ac 389.2 388.8 389.4 n/ac 382.1 381.6 382.2

Available experimental values[60] are shown for comparison. Values are in kcal/mol.aNot available.bExperimental ΔdH°(g) and ΔdG°(g) are available for formic acid, but the values are for the more acidic carboxylic acid moiety (ΔdH°(g)≈340to 346kcal/mol[71–74]; ΔdG°(g)≈338 to 339kcal/mol[71–75]).cExperimental ΔdH°(g) and ΔdG°(g) are available for 4-methylbenzaldehyde, but the values are for the more acidic methyl group(ΔdH°(g) = 359.8 ± 2.4 kcal/mol[76]; ΔdG°(g) = 352.6 ± 2.3 kcal/mol[76]).

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