Effect of Protonation State and Interposed Connector Groups on Bond

Article pubs.acs.org/JPCA

Effect of Protonation State and Interposed Connector Groups on Bond Dissociation Enthalpies of Alcohols and Related Systems Michael Morris, Bun Chan,* and Leo Radom* School of Chemistry and ARC Centre of Excellence for Free Radical Chemistry and Biotechnology, University of Sydney, Sydney, New South Wales 2006, Australia S Supporting Information *

ABSTRACT: High-level quantum chemical procedures have been used to study how the C−H bond dissociation enthalpies (BDEs) of alcohols and related systems are affected by changes to their protonation state. The high-level procedures used have been determined from a benchmark of 25 neutral, protonated, and deprotonated substituted methanes. The benchmark calculations suggest that the experimental C−H BDEs for CH3NH2 and CH3SH should be reassessed. We confirm previous findings that protonation increases the BDEs of alcohols, while deprotonation decreases the BDEs. For the prototypical alcohol, methanol, reducing the strength of the proton donor or acceptor leads to a smaller change in the BDE, and a smooth variation of C−H bond strength with the extent of protonation or deprotonation is observed. Changes in the BDE with protonation state are reduced for alcohols with a connector group separating the oxygen center and the site of C−H bond scission. These changes are rationalized through introduction of three new quantities, termed the effect of protonation state on dissociation energies, the alcohol radical connector energy, and the alcohol molecule connector energy. Gas-phase acidities and proton affinities for all relevant alcohols have been computed and compared with experiment. The agreement between theory and experiment is generally reasonable, with just one notable outlier (the proton affinity of CH3CH2CH2OH). In this case, we suggest that the experimental value should be reevaluated.

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INTRODUCTION The effect of protonation and deprotonation on the strength of chemical bonds is a topic of considerable interest. This is in part because of the fundamental importance of the strength of bonds, because of the ubiquitous nature of proton-transfer reactions, and because the addition or removal of a proton can lead to substantial changes in bond strength. Several studies have looked at how bond dissociation enthalpies (BDEs) change as a result of protonation and deprotonation of an adjacent group.1−6 For example, it has been found that protonation of methanol to form CH3OH2+ leads to an increase in the C−H BDE, while deprotonation to form CH3O− leads to a decrease in the BDE. This has been rationalized in terms of stabilization or destabilization of the resultant radical. In more recent work, the effect on BDEs of deprotonation of a remote group has also been examined.7,8 The effect was found to be quite significant, leading to a change in the ordering of the orbitals (referred to as orbital conversion9,10), and also to an unexpectedly large increase in the gas-phase stabilities of the radicals that are formed. It was suggested that this behavior could be exploited in creating devices such as molecular switches.7,8 In this paper, we report the use of high-level quantum chemical calculations to investigate the effect on C−H BDEs of alcohols of both adjacent and remote protonation and deprotonation. We © 2014 American Chemical Society

focus our attention on alcohols as these species are simple, are amphoteric, and often undergo complete or partial protonation and deprotonation in various important chemical environments, such as in aqueous solution. Using a sample of substituted methanes (CH3X) as a test set, we first assess the performance of a range of different theoretical procedures (G3X(MP2)-RAD,11 G4(MP2)-6X,12 W1X-1,13 W1X-2,13 W1w,14 W2w,14 W3X,15 and W3.216) for calculating accurate BDEs for neutral, protonated, and deprotonated species. Some general features of the changes in BDEs of substituted methanes with protonation state are also briefly discussed. We then use the optimal highlevel methods to evaluate the BDEs of alcohols and their partially and fully protonated and deprotonated variants. Trends in the associated gas-phase acidities and proton affinities are explored, as is the effect of interposing connector groups on the alcohol BDEs.17 This work on the effect of adjacent and remote protonation and deprotonation on the C−H BDEs of alcohols augments our previous investigations on the effect of protonation and deprotonation on the C−H BDEs associated with carboncentered radicals,4−6 and on the effect of connector groups.17 It Received: February 4, 2014 Revised: March 17, 2014 Published: April 7, 2014 2810

dx.doi.org/10.1021/jp501256f | J. Phys. Chem. A 2014, 118, 2810−2819

The Journal of Physical Chemistry A

Article

Table 1. Comparison of G3X(MP2)-RAD, G4(MP2)-6X, W1X-1, W1w, W1X-2, W2w, W3X, and W3.2 C−H Bond Dissociation Enthalpies (298 K, kJ mol−1) for CH3X with Experimental Values X

G3X(MP2)-RAD

G4(MP2)-6X

W1X-1

W1X-2

W1w

W2w

W3X

W3.2

expta

H BH2 BH− CH3 CH2− NH3+ NH2 NH− OH2+ OH O− FH+ F AlH2 AlH− SiH3 SiH2− PH3+ PH2 PH− SH2+ SH S− ClH+ Cl MADc MDc LDc

440.6 399.5 196.5 426.9 312.4 459.4 395.1 306.1 465.4 407.7 324.9 490.2 427.2 412.7 344.5 428.6 380.5 446.2 416.7 333.1 452.6 403.5 353.3 467.3 419.6 5.4 +5.1 +18.1

444.9 400.3 200.9 429.2 296.2 460.9 394.8 291.3 466.0 408.3 320.9 491.3 428.4 412.9 353.9 427.6 375.0 447.8 416.8 334.1 453.7 403.6 352.5 469.6 421.1 5.0 +4.8 +7.5

438.7 396.9 196.6 423.5 304.6 456.4 388.7 292.0 461.4 402.4 313.8 487.1 423.3 410.3 347.9 423.2 368.7 443.3 411.5 329.9 449.0 397.9 347.9 463.2 415.6 0.9 +0.4 +10.3

439.0 397.1 196.7 423.8 308.4 456.6 388.9 295.1 461.5 402.6 314.5 487.1 423.5 410.5 348.2 423.5 369.1 443.6 412.0 330.0 449.4 398.3 348.3 463.6 416.2 1.1 +1.0 +14.1

439.0 397.2 196.5 423.9 303.2 456.9 389.1 296.1 461.9 403.0 314.3 487.7 423.9 410.7 347.5 423.3 369.5 443.5 412.0 330.1 449.4 398.5 349.1 463.8 416.6 1.1 +1.0 +8.9

439.1 397.1 197.5 424.0 294.2 456.9 389.0 294.4 461.8 402.8 315.0 487.5 423.8 410.4 347.7 423.2 369.4 443.3 411.8 329.7 448.9 398.0 348.5 463.2 415.9 0.4 +0.4 +1.3

438.5 396.6 197.2 423.3 304.8 456.2 388.4 292.3 461.2 402.1 314.0 487.0 423.0 409.9 347.2 422.8 367.8 443.0 411.0 329.7 448.7 397.5 347.5 463.0 415.2 0.8 +0.2 +10.5

438.9 396.7 197.7 423.6 294.3 456.6 388.7 294.4 461.5 402.4 314.9 487.4 423.5 410.0 346.4 422.7 368.5 442.8 410.9 329.3 448.4 397.3 347.8 462.7 415.3

439.3 ± 0.4

423.0 ± 1.7b

392.9 ± 8.4

401.9 ± 0.6

423.8 ± 4.2

392.9 ± 8.4

419.0 ± 2.3

a Experimental values from ref 23 unless stated otherwise. bExperimental value from ref 24. cMean absolute deviation (MAD), mean deviation (MD), and largest deviation (LD) from W3.2 values.

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RESULTS AND DISCUSSION Assessment of Theoretical Procedures. The C−H BDEs for a range of substituted methanes, CH3X, computed using the G3X(MP2)-RAD, G4(MP2)-6X, W1X-1, W1X-2, W1w, W2w, W3X, and W3.2 procedures, are compared with experimental values23,24 in Table 1. It can be seen that the agreement between theoretical and experimental values is, in general, quite good: the mean absolute deviation (MAD) between the two sets of data is just 2.0 kJ mol−1 for the high-level W3.2 procedure, and less than 6.0 kJ mol−1 for all the other methods. It is notable that, although the differences between W3.2 and experiment are in most cases small (less than 1.0 kJ mol−1), there are two cases (X = NH2, SH) for which the discrepancies are significantly larger (more than 4.0 kJ mol−1). In these instances, we have carried out higher-level W4-lite calculations16 to try to ascertain the origin of the disagreement. The W4-lite values (388.5 and 397.3 kJ mol−1) for BDE(H−CH2NH2) and BDE(H−CH2SH) are quite close to their respective W3.2 values (388.7 and 397.3 kJ mol−1). This finding, in conjunction with the large experimental uncertainties (±8.4 kJ mol−1), suggests that the source of the disagreement might lie with the reported experimental values. We therefore suggest that the experimental C−H BDEs for CH3NH2 and CH3SH should be reassessed. As expected, both G3X(MP2)-RAD and G4(MP2)-6X give somewhat less accurate BDEs than the Wn-type procedures, with MADs of 5.4 and 5.0 kJ mol−1, respectively, from the W3.2 data. Of the two methods, G4(MP2)-6X has the smaller overall MAD, performing much better than G3X(MP2)-RAD for substituents

also serves as a basis for our current studies on the effect of solvent on BDEs.

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COMPUTATIONAL DETAILS

Standard ab initio quantum chemistry calculations were carried out using the Gaussian 09,18 MOLPRO 2010,19 and MRCC20 programs. Geometries for the G3X(MP2)-RAD11 calculations were optimized at the B3-LYP/6-31G(2df,p) level. The resulting single-point energies were corrected with zero-point vibrational energies (ZPVEs) and thermal corrections (ΔH298), derived from scaled (0.9854) B3-LYP/6-31G(2df,p) harmonic vibrational frequencies,11 to provide enthalpies at 298 K. For the G4(MP2)-6X12 procedure, geometries were optimized at the BMK/6-31+G(2df,p) level,21 and the energies were corrected to enthalpies at 298 K using ZPVE and ΔH298 corrections, derived from scaled (ZPVE = 0.9770, ΔH298 = 0.9627) BMK/631+G(2df,p) harmonic vibrational frequencies.12 The W1X1,13 W1X-2,13 W1w,14 W2w,14 W3X,15 and W3.216 energies were calculated for geometries obtained using the B3-LYP method with the aug-cc-pV(T+d)Z basis set. These energies incorporate scaled B3-LYP/aug-cc-pV(T+d)Z harmonic vibrational frequencies for ZPVEs (0.9884) and ΔH298 (0.9987),22 giving the desired enthalpies at 298 K. Unless stated otherwise, all enthalpies correspond to gas-phase species at 298 K and are reported in kJ mol−1. 2811



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Table 2. Statistical Performance of Various Gn- and Wn-Type Procedures for Calculating Bond Dissociation Enthalpies and Radical Stabilization Energies (298 K, kJ mol−1) for the CH3X Molecules of Table 1a MADb G3X(MP2)-RAD G4(MP2)-6X W1X-1 W1X-2 W1w W2w W3X

MDb

LDb

BDE

RSE

BDE

RSE

BDE

RSE

5.4 (4.1) 5.0 (5.2) 0.9 (0.3) 1.1 (0.5) 1.1 (0.7) 0.4 (0.4) 0.8 (0.2)

4.1 (2.6) 1.6 (1.1) 1.0 (0.4) 1.1 (0.5) 1.1 (0.6) 0.3 (0.3) 0.8 (0.3)

+5.1 (+4.1) +4.8 (+5.2) +0.4 (+0.2) +1.0 (+0.5) +1.0 (+0.7) +0.4 (+0.4) +0.2 (−0.1)

−3.6 (−2.6) +1.3 (+0.9) −0.7 (−0.4) −0.9 (−0.4) −0.9 (−0.6) −0.2 (−0.3) −0.6 (−0.3)

+18.1 (+6.4) +7.5 (+6.9) +10.3 (+0.6) +14.1 (+1.1) +8.9 (+1.3) +1.3 (+0.8) +10.5 (−0.4)

−16.4 (−4.7) +9.1 (+3.1) −10.5 (−0.8) −14.0 (−1.0) −8.9 (−1.2) −1.1 (−0.6) −10.8 (−0.7)

a

MADs, MDs, and LDs calculated using the entire set of C−H BDEs in Table 1. Values given in parentheses calculated using the C−H BDEs in Table 1 for the neutral and cationic species only. bMADs, MDs, and LDs from W3.2 values.

RSE(•CH 2X) = BDE(H−CH3) − BDE(H−CH 2X)

with a negative charge. However, for the neutral and positively charged substituents, G3X(MP2)-RAD has a slight edge, with an MAD of 4.1 kJ mol−1 (see Table 2). A comparison between the various theoretical procedures shows that BDEs are systematically overestimated and generally become smaller as the procedure is improved, as reflected in the generally decreasing mean deviations (MDs). The average magnitude of this decrease is quite small, being less than 1.0 kJ mol−1 for Wn-type BDEs, although for first-row anionic substituents the average decrease is much larger than this. For example, deprotonated ethane exhibits a decrease in BDE of 14.1 kJ mol−1 going from W1X-2 to W3.2. Changes in the basis-set size for the extrapolation to the complete-basis-set (CBS) limit appear to account for most of this variation. For instance, switching from W1w to W2w, which corresponds to a direct increase in the size of the basis sets used for the CBS extrapolations, leads to reductions in the MAD, MD, and largest deviation (LD) from the benchmark W3.2 data from 1.1, +1.0, and +8.9 to 0.4, +0.4, and +1.3 kJ mol−1, respectively. The influence of basis-set size on the BDEs is most prominent for anionic substituents because the electron distribution is more diffuse; as the diffuse nature increases, the basis-set size must also increase in order to provide an accurate description of the electronic wave function. Post-CCSD(T) effects also contribute to the decrease in the overestimation of the BDEs with increasing sophistication of the computational procedure, as indicated in the difference between W1X-1 and W3X BDEs. However, as with basis-set size, the overall effect of including post-CCSD(T) terms is small, never exceeding 1.0 kJ mol−1 in magnitude. Unlike the effect of basisset size, there does not appear to be a significant difference in the magnitude of the post-CCSD(T) effect with respect to the nature of the substituent, i.e., whether the substituent is anionic, cationic, or neutral. In addition to examining the performance of various theoretical procedures with respect to absolute BDEs, it is also useful to look at how these procedures perform for relative BDEs. Relative BDEs are important from the point of view of investigating substituent effects, and have the benefit of enabling the partial cancellation of errors, a factor that can be significant for lower-level procedures. In the present case, we consider BDEs computed relative to methane, conventionally referred to as radical stabilization energies (RSEs). The RSE of a radical •CH2X is defined as the enthalpic change in the formal reaction: •

CH 2X + CH4 → CH3X + •CH3

(2)

Table 2 compares the overall statistical performance of the various theoretical procedures for calculating BDEs and RSEs of substituted methanes. The MADs, MDs, and LDs correspond to values for the entire set of substituted methanes shown in Table 1 and have been computed with respect to the benchmark W3.2 values. MADs, MDs, and LDs for the smaller set of neutral and cationic substituted methanes, i.e., excluding the anionic systems, have also been calculated, and are given in parentheses. It can be seen from Table 2 that the MADs and MDs for RSEs are generally slightly smaller than those for BDEs. This can be attributed to the partial cancellation of errors, made possible by the isodesmic nature of reaction 1. For G4(MP2)-6X, the cancellation of errors is such that the MADs, MDs, and LDs for the RSEs are only slightly larger than those for the Wn-type methods. It is also clear from Table 2 that, once the anionic systems have been removed from the analysis, the BDEs and RSEs predicted using the various Wn-type procedures are similar to one another. Relative to both experiment and the benchmark W3.2 data, the next most accurate method appears to be W2w, with its larger component basis sets better accommodating the anionic substituents. Since W2w is much more expensive than the other Wn-type procedures, being more than an order of magnitude more expensive than W1X-1 and W1X-2,13 we use the cheaper W1X-1 and W1X-2 procedures as cost-effective and reliable alternatives to W2w and W3.2 for the remainder of this study. In cases where W1X-1 and W1X-2 have proven too expensive, the G4(MP2)-6X procedure has been used. Effect of Protonation and Deprotonation on C−H BDEs of CH3X. It is useful at this stage to summarize in qualitative terms how protonation state affects the C−H BDEs of substituted methanes. Much of this discussion is based upon previous studies,1−6,25,26 which outline in detail how the C−H BDEs of substituted methanes change with substituent and protonation state, although in this particular instance we use the benchmark W3.2 BDEs given in Table 1 as the basis for our analysis. Variations in the C−H BDEs of substituted methanes are to a large extent dictated by the relative stabilities of the •CH2X radicals. For substituted methanes with a neutral substituent, the factors influencing radical stability can be summarized as follows: • CH2X radicals with lone-pair-donor substituents (X = NH2, OH, F, PH2, SH, and Cl) are stabilized by the n(X) → p(C•) interaction, the radicals with π-acceptor substituents (X = BH2 and AlH2) are stabilized by delocalization of the unpaired electron to X, and the interaction between p(C•) and a pseudo-π orbital on X confers stability to radicals with hyperconjugative

(1)

This corresponds to defining the RSE as 2812



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The same qualitative changes to the C−H BDE of methanol are observed for intermediate protonation states. That is, the C− H BDE increases with partial protonation and decreases with partial deprotonation. The magnitude of the change is related to the strength of the proton donor or acceptor, and a relatively smooth variation of BDE with protonation state can be seen. For example, the C−H BDE of fully protonated methanol is almost 60 kJ mol−1 larger than that for neutral methanol. Partial protonation by H3O+ leads to a smaller increase in BDE of 40 kJ mol−1, while interaction between methanol and the weakest proton donor, HOH, increases the BDE by only 5−6 kJ mol−1. Similarly, the C−H BDE of fully deprotonated methanol is almost 90 kJ mol−1 smaller than that for neutral methanol. Partial deprotonation by OH− leads to a smaller decrease in the BDE of 64 kJ mol−1, while interaction between methanol and the weakest proton acceptor, OH2, decreases the BDE by only 5−6 kJ mol−1. Although not unexpected, these results suggest that full protonation and deprotonation can be used as probes to predict, qualitatively, how weaker proton interactions might affect bond strength, as well as providing estimates of upper bounds for the magnitude of their effect. This has important implications for a wide range of chemical contexts, for example understanding how biological reaction processes operate.27 Effect of Remote Protonation and Deprotonation on C−H BDEs. In this section, we explore how the C−H BDEs of alcohols change with protonation state when the oxygen and radical centers are not adjacent to one another, i.e., when there is a connector group separating the two centers. This follows our earlier study of the effect of interposing a connector group on radical stabilities.17 The alcohols and radicals we consider are of the form CH3WOH and •CH2WOH, where W is one of the connector groups listed in Figure 1. Using the main result of the

donor substituents (X = CH3 and SiH3). In all cases, the presence of a neutral substituent leads to a smaller BDE compared with that of methane (i.e., a positive RSE). Protonation of the substituent in CH3X leads to a less stable radical and an increase in C−H BDEs. For lone-pair-donor substituents, the larger BDEs are a result of a weakened n(X) → p(C•) interaction; protonation lowers the energy of the lone-pair orbital n(X), which increases the energy gap between the n(X) and p(C•) orbitals, and reduces the strength of the n(X) → p(C•) interaction. The C−H BDEs for the deprotonated substituted methanes are all much smaller than those of their respective neutral and protonated analogues, reflecting stabilized radicals. The smaller BDEs can be attributed to the beneficial effect of a negative charge on the electron-deficient radical center, and the additional π-character present in the C−X bond of the radical anion. For the lone-pair-donor and hyperconjugative donor substituents, the C−X bond in the radical anion is a partial double bond, whereas for the π-acceptor substituents it is a full double bond. Effect of Adjacent Protonation and Deprotonation on C−H BDEs of Alcohols. The effect of adjacent protonation and deprotonation on the C−H BDEs of alcohols can be investigated by using methanol as a model system. In this section we look at how the C−H BDE of methanol changes as its protonation state is varied. Fully protonated or deprotonated states are modeled as in the previous section by considering the charged species, CH3OH2+ and CH3O−, while intermediate protonation states, where protonation or deprotonation is incomplete, are modeled by looking at the interaction of methanol with a number of weak proton donors and acceptors, H3O+, H2O, and OH−. The variation in the C−H BDE of methanol with protonation state is outlined in Table 3. We note first that, although the Table 3. Comparison of C−H Bond Dissociation Enthalpies (298 K, kJ mol−1) for Methanol and its Protonated and Deprotonated Variantsa species

G4(MP2)-6X

W1X-1

W1X-2

CH3OH2+ CH3OH···HOH2+ CH3OH···HOH CH3OH CH3OH···OH2 CH3OH···OH− CH3O−

466.0 (+57.8) 448.6 (+40.3) 412.8 (+4.6) 408.3 402.1 (−6.2) 344.3 (−64.0) 320.9 (−87.3)

461.4 (+59.0) 442.9 (+40.5) 408.1 (+5.7) 402.4 397.1 (−5.2) 338.3 (−64.1) 313.8 (−88.6)

461.5 (+59.0) 443.0 (+40.4) 408.3 (+5.8) 402.6 397.3 (−5.2) 338.5 (−64.1) 314.5 (−88.0)

Figure 1. CH3WOH alcohols used to investigate the effect of remote protonation and deprotonation at OH on C−H BDEs. The various W connector groups are highlighted in red. C−H bond dissociation occurs at the terminal CH3 group.

a

C−H BDEs relative to that of neutral methanol are given in parentheses.

previous section, namely, that full protonation and deprotonation can be used as probes for the effects of partial protonation and deprotonation, we focus our attention on full proton transfer and infer the effects of intermediate protonation states from these results. Before continuing, we first define some additional quantities to help us understand the change in BDEs with connector group and protonation state. We define the effect of protonation state on dissociation energies (EPDW) as the enthalpic change for the reaction:

absolute BDEs for the G4(MP2)-6X method differ from the W1X-1 and W1X-2 values, the BDEs computed relative to methanol are all quite similar; the largest difference between the three methods is just 1.2 kJ mol−1. This is a further example of the partial cancellation of errors in appropriately constructed comparisons, as discussed above. It is clear from Table 3 that protonation state has a significant effect on C−H bond strength when the oxygen and radical centers are adjacent to one another. The C−H BDE of methanol changes by almost 150 kJ mol−1 as the protonation state changes from full protonation to full deprotonation. The largest deviation from that of neutral methanol occurs for full deprotonation, with the C−H BDE decreasing by close to 90 kJ mol−1. In comparison, full protonation leads to an increase in the C−H BDE of almost 60 kJ mol−1.

•

CH 2WX + CH3WOH → CH3WX + •CH 2WOH

(3)

Here, W represents one of the connector groups listed in Figure 1, and X = OH2+, OH, or O−. Expressed in terms of C−H BDEs, the EPDW can be rewritten: 2813



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Table 4. G4(MP2)-6X C−H Bond Dissociation Enthalpies (BDEs), Effect of Protonation State on Dissociation Energies (EPDWs), Alcohol Radical Connector Energies (RCEas), and Alcohol Molecule Connector Energies (MCEas) (298 K, kJ mol−1) for Protonated, Neutral, and Deprotonated Alcohols (CH3WX, X = OH2+, OH, or O−) with a Connector Group (W), and Related Species (CH3WX, X = H) X

BDE(CH3WX)

EPDW(CH3WX)

NIL NIL NIL NIL −CH2− −CH2− −CH2− −CH2− −CH2CH2− −CH2CH2− −CH2CH2− −CH2CH2− −CH2CH2CH2− −CH2CH2CH2− −CH2CH2CH2− −CH2CH2CH2− −CHCH− −CHCH− −CHCH− −CHCH− −CC− −CC− −CC− −CC− −o-C6H4− −o-C6H4− −o-C6H4− −o-C6H4− −m-C6H4− −m-C6H4− −m-C6H4− −m-C6H4− −p-C6H4− −p-C6H4− −p-C6H4− −p-C6H4−

OH2+

466.0 408.3 320.9 444.9 433.3 435.0 423.8 428.5 432.0 428.9 412.5 430.9 434.7 428.8 418.7 429.1 389.2 366.3 324.7 373.2 384.0 384.6 326.8 386.7 398.7 391.2 358.0 389.6 396.5 390.4 377.0 389.6 396.3 390.1 344.2 389.6

−57.8 0.0 +87.3

0.0 0.0 0.0

0.0 0.0 0.0

+1.7 0.0 +11.2

+81.8 0.0 −63.6

+22.3 0.0 +12.6

−3.1 0.0 +16.3

+83.2 0.0 −54.7

+28.6 0.0 +16.3

−5.9 0.0 +10.1

+85.2 0.0 −59.5

+33.4 0.0 +17.7

−22.9 0.0 +41.6

+26.8 0.0 +52.6

−8.1 0.0 +98.3

+0.6 0.0 +57.8

−34.3 0.0 +149.7

−92.6 0.0 +179.3

−7.5 0.0 +33.2

+48.2 0.0 +82.5

−2.1 0.0 +136.6

−6.1 0.0 +13.4

+52.2 0.0 +59.7

+0.5 0.0 +133.7

−6.2 0.0 +45.9

+50.6 0.0 +85.8

−1.0 0.0 +127.2

OH O− H OH2+ OH O− H OH2+ OH O− H OH2+ OH O− H OH2+ OH O− H OH2+ OH O− H OH2+ OH O− H OH2+ OH O− H OH2+ OH O− H

− BDE(H−CH 2WX)

(4)

The EPDW measures how the protonation state of X affects the C−H BDE of a neutral alcohol, CH3WOH. A positive EPDW indicates that changing the protonation state of CH3WOH to CH3WX would lead to a smaller C−H BDE. If there is no connector group, the EPD (in this case termed EPD0) is given by EPD0(•CH 2X) = BDE(H−CH 2OH) − BDE(H−CH 2X)

CH3WX + CH3OH → CH3WOH + CH3X

(5)

and is equal to the enthalpic change for the reaction: •

CH 2X + CH3OH → CH3X + CH 2OH

CH 2WX + •CH 2OH → •CH 2WOH + •CH 2X

(8)

The MCEa measures how the connector group W affects the interaction between X and CH3, compared with that between OH and CH3. The effect of the connector group W on the EPD is given by the difference between EPDW and EPD0. It is straightforward to show that this is equal to the difference between the RCEa and the MCEa:

(6)

Following previous research on the effect of interposing connector groups on radical stabilities,17 we now introduce the alcohol radical connector energy (RCEa) of •CH2WX as the enthalpic change for the formal reaction: •

MCEa(CH3WX)

where again, W represents one of the connector groups listed in Figure 1, and X = OH2+, OH, or O−. The RCEa measures how the connector group W affects the interaction between X and •CH2, relative to that between OH and •CH2. A positive value of the RCEa indicates that W enhances the interaction between X and • CH2, relative to that between OH and •CH2. Likewise, we also introduce the alcohol molecule connector energy (MCEa) of CH3WX as the enthalpic change for the formal reaction:

EPD W (•CH 2WX) = BDE(H−CH 2WOH)

•

RCEa(•CH2WX)

W

EPD W − EPD0 = RCEa − MCEa

(7) 2814

(9)



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Table 4 lists the C−H BDEs, EPDWs, RCEas, and MCEas for the various protonated, neutral, and deprotonated alcohols (CH3WX, X = OH2+, OH, or O−), and related species (CH3WX, X = H), calculated at the G4(MP2)-6X level of theory. A number of interesting features can be identified in Table 4. The most prominent of these is that the C−H BDEs exhibit considerable variation with respect to the choice of connector group W. For example, the C−H BDE of CH3WOH with W = −CH2− is 435.0 kJ mol−1, whereas for W = −CHCH− it is 366.3 kJ mol−1. This compares with a C−H BDE of 408.3 kJ mol−1 recorded for CH3OH (i.e., W = NIL). The large variation in BDEs arises, in part, because of the inherent interaction that occurs between the connector group W and the radical center when W is introduced into CH3X. The strength of this interaction is of sufficient magnitude that we can rationalize the C−H BDEs of CH3WX in terms of the C−H BDEs of CH3WH, perturbed by the substituent X. This is demonstrated in Figure 2, which displays Figure 3. Variation with W of EPDW(•CH2WX) values (G4(MP2)-6X, 298 K, kJ mol−1) for various protonation states (X = OH2+ or O−).

This is in stark contrast to methanol (W = NIL), which exhibits significant variation in its C−H BDE with protonation state. The relatively small variation in BDEs reflects the fact that alkyl chains are generally poor transmitters of π-effects, and that σ-effects usually only operate over short distances. As a consequence, it is reasonable to expect that as the size of a saturated alcohol increases, the terminal C−H BDE will reach a limiting value, irrespective of the protonation state, i.e., EPDW approaches zero. The convergence of the C−H BDEs toward the limiting value is, however, less rapid for the charged species (X = OH2+ and particularly X = O−) than for the neutral alcohols (X = OH). As an aside, it is interesting to note that the C−H BDEs for alcohols with saturated connector groups are smaller than that for methanol in the protonated state, but that this relationship reverses in the neutral and deprotonated states, i.e.,

Figure 2. Variation with W of C−H BDEs (G4(MP2)-6X, 298 K, kJ mol−1) for CH3WX (X = OH2+, OH, or O−), computed relative to CH3WH (= BDE(H−CH2WX) − BDE(H−CH2WH)).

the BDEs of CH3WX computed relative to CH3WH. The effect of different choices of W on the C−H BDE of CH3WH has been discussed previously.17,25,26 In brief, •CH2WH radicals with a vinyl group (W = −CHCH−), a phenyl group (W = −C6H4−), or an ethynyl group (W = −CC−) are stabilized via conjugation, whereas those with saturated hydrocarbon groups (W = −CH2−, −CH2CH2−, and −CH2CH2CH2−) are stabilized (to a significantly smaller extent) through hyperconjugation. Another notable feature in Table 4 is that the change in BDEs with protonation state, i.e., the EPDW, illustrated in Figure 3 for • CH2WX, is generally in the same direction as that for methanol (W = NIL). That is, protonation generally leads to an increase in BDEs while deprotonation leads to a decrease in BDEs. The magnitude of the change is in all cases smaller than that for methanol, indicating that protonation state has the largest effect on the BDEs of alcohols when the oxygen and radical centers are adjacent to one another. Looking at the C−H BDEs for alcohols with a saturated connector group (W = −CH 2 −, −CH 2 CH 2 −, and −CH2CH2CH2−), we see that there is little change in C−H BDE with protonation state, in particular for full protonation.

BDE(H−CH 2OH 2+) > BDE(H−CH 2WOH 2+)

(10)

BDE(H−CH 2OH) < BDE(H−CH 2WOH)

(11)

−

−

BDE(H−CH 2O ) < BDE(H−CH 2WO )

(12)

where W = −CH2−, −CH2CH2−, or −CH2CH2CH2−. This observation suggests that the favored site of C−H bond dissociation can be tuned via a change in protonation state. To illustrate this possibility, Figure 4 shows the possible C−H BDEs for CH3CH2CH2CH2OH in its three protonation states. It can be seen that, in the neutral and deprotonated states, the smallest BDE occurs for the carbon closest to the alcoholic center, i.e., the

Figure 4. Variation in C−H BDEs (G4(MP2)-6X, 298 K, kJ mol−1) with carbon atom position for CH3CH2CH2CH2OH in its three protonation states. The smallest BDE for each protonation state is encircled. 2815



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α-carbon. Following protonation, however, the clear preference is for C−H bond dissociation at the γ-carbon. Such a result has significance for C−H bond scission in, for example, biological environments.28−30 From the previous section, we can expect that this mechanism would be operative with weaker proton donors and acceptors, though to a lesser degree. The C−H BDEs for alcohols with an unsaturated connector group (W = −CHCH− and −CC−) exhibit greater variation with protonation state than when the connector group is saturated. For example, the greatest difference in EPDW values for unsaturated alcohols is 64.5 kJ mol−1 (W = −CH CH−), whereas for saturated alcohols it is 19.4 kJ mol−1 (W = −CH2CH2−). The largest EPDW values, in terms of magnitude, arise for deprotonation, with protonation leading to EPDW values that are less than half as large. Most of this variation can be understood using resonance concepts. Figure 5 illustrates the

when deprotonated, this same interaction is favorable, resulting in smaller BDEs and a more positive EPDW. The effect of protonation state is greater for deprotonation because of the greater electron delocalization possible for the deprotonated radical anion. Although the changes in BDE following protonation are similar for each of the three different benzene derivatives, there are notable differences for deprotonation. In particular, the meta form has a much smaller EPDW than either the ortho or para forms. This can be attributed to the fact that the alcohol group and radical centers are not conjugated in the meta form, and hence there is no direct interaction between the surplus charge and the unpaired electron in contrast to the ortho and para situations. We also find that whereas, for the protonated forms, there is only a small difference between the BDEs in the ortho and para isomers, there is a larger difference in the deprotonated forms. It is interesting to note that the difference between the EPDW and EPD0 (i.e., W = NIL) values shown in Table 4 is quite large, being greater than 29.5 kJ mol−1 in all cases. That is, the effect of the protonation state on the C−H BDE of methanol is attenuated by more than 29.5 kJ mol−1 when one of the connector groups shown in Figure 1 is interposed between the oxygen and the center of bond dissociation. Using reaction 9, we can rationalize these changes in terms of the RCEas and MCEas. We illustrate this through a few examples. If X = OH2+ and W = −o-C4H6−, then EPDW is the enthalpic change for the reaction:

Figure 5. Main resonance contributors for the neutral, protonated, and deprotonated radicals of alcohols (X = OH2+, OH, or O−) with an unsaturated connector group. Note that the furthermost right structures are not relevant for the protonated state.

most important resonance structures for the alcohols with an unsaturated connector group. We can see from Figure 5 that, for alcohols containing either double- or triple-bonded connecting groups, there are contributing resonance structures in which the electron-deficient radical center is adjacent to the alcohol functional group. When the alcohol is deprotonated, these resonance contributors are favorable because the negative charge stabilizes the electron-deficient radical center, as in the directly connected parent systems. On the other hand, when the alcohol is protonated these same resonance structures are less favorable, again as in the directly connected parent systems. The change in BDE with protonation state is much larger for deprotonation than for protonation due to the possibility of delocalizing the negative charge on the oxygen atom in the deprotonated alcohol (see furthermost right resonance contributors in Figure 5). The alcohols with a phenylene connector group exhibit similar patterns in BDEs to those with the simpler unsaturated connectors. This is somewhat to be expected, given that the defining feature of both these connector groups is their πnetworks. The C−H BDEs are seen to increase with protonation and decrease with deprotonation, with the magnitude of the change being largest for deprotonation. This behavior can again be explained using resonance concepts. As Figure 6 shows, resonance allows the unpaired electron and alcohol group to interact. When protonated, this interaction is unfavorable, leading to larger BDEs and a more negative EPDW. Conversely,

•

CH 2−o‐C6H4−OH 2+ + CH3−o‐C6H4−OH → CH3−o‐C6H4−OH 2+ + •CH 2−o‐C6H4−OH

(13)

Here, EPDW = −7.5 kJ mol−1. This is much smaller than EPD0, the enthalpic change for the reaction in the absence of the orthophenylene connector group: •

CH 2−OH 2+ + CH3−OH → CH3−OH 2+ + •CH 2−OH (14) −1

whose large negative value (−57.8 kJ mol ) reflects the large destabilizing effect of a positively charged substituent at a carbon radical center. The relevant RCEa for this case corresponds to the enthalpic change for the reaction •

CH 2−o‐C6H4−OH 2+ + •CH 2−OH → •CH 2−o‐C6H4−OH + •CH 2−OH 2+

(15)

while the relevant MCEa corresponds to the enthalpic change for the reaction CH3−o‐C6H4−OH 2+ + CH3−OH → CH3−o‐C6H4−OH + CH3−OH 2+ −1

(16) −1

Here, RCEa = +48.2 kJ mol and MCEa = −2.1 kJ mol . By comparing the magnitudes of the RCEa and MCEa, we can see

Figure 6. Main resonance contributors for the radicals of neutral, protonated, and deprotonated alcohols (X = OH2+, OH, or O−) with a phenylene connector group. Note that several more resonance contributors can be formed via delocalization of the charge on the alcohol functional group. 2816



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Figure 7. Calculated alcohol radical connector energies (RCEas, blue) and alcohol molecule connector energies (MCEas, red) (G4(MP2)-6X. 298 K, kJ mol−1).

The full set of RCEas and MCEas for the interposed alcohols are displayed in Figure 7. We can see that, with just a few exceptions (most significantly, when W = −CC− and X = OH2+), both the RCEa and MCEa values are positive. This indicates that interposition of a connector group is more favorable for protonated or deprotonated alcohols than it is for neutral alcohols. As the difference between EPDW and EPD0 is given by the difference between the RCEa and MCEa, almost all values of EPDW − EPD0 are smaller than their matching RCEas or MCEas. Gas-Phase Acidities and Proton Affinities. The G4(MP2)-6X gas-phase acidities (ΔacidH°) and proton affinities (PAs) for CH3WOH alcohols and •CH2WOH radicals are compared with experimental values31−38 in Table 5. The agreement between the theoretical and experimental values is generally reasonable, with 13 of the 14 comparisons showing differences of less than 8.5 kJ mol−1. A much larger difference between theory and experiment is observed for the PA of • CH2CH2CH2OH, with the G4(MP2)-6X value being 27.0 kJ mol−1 larger than experiment. Given that G4(MP2)-6X agrees with experiment for the PAs for similar systems (•CH2OH and • CH2CH2OH), it is likely that the source of the discrepancy lies with the reported experimental value, in particular, the heat of formation for •CH2CH2CH2OH2+ used to derive the experimental PA; both theory and experiment agree on the heat of formation for •CH2CH2CH2OH to within 1.5 kJ mol−1. We therefore suggest that the experimental heat of formation for • CH2CH2CH2OH2+, and the resultant PA, should be reassessed. One notable feature of the data in Table 5 is that the ΔacidH° values and PAs for the CH3WOH molecules and •CH2WOH radicals exhibit similar variation with the nature of the connector group. For example, the largest values for both quantities arise for the molecules and radicals with a saturated connector group. Replacing W with a phenylene connector group yields smaller ΔacidH° values (corresponding to greater acidities) and PAs, while the analogous quantities for molecules and radicals with an unsaturated connector are even smaller. The respective values for CH3WOH are generally larger than those for •CH2WOH, the two exceptions being the PAs for W = −CH2− and −CC−.

that the difference between the EPDW and the EPD0 is largely a consequence of the favorable (positive) RCEa. The positive RCEa (reaction 15) indicates that interposition of the W = −oC4H6− connector group leads to a more favorable interaction between OH2+ and •CH2, relative to that between OH and •CH2. In particular, the W = −o-C4H6− connector attenuates the strongly unfavorable interaction between OH2+ and the radical center, leading to a favorable enthalpic change. On the other hand, the near-zero MCEa (reaction 16) tells us that interposing W = −o-C4H6− between the oxygen and the carbon atoms makes almost no difference to the strength of the interaction between OH2+ and CH3, relative to that between OH and CH3. As a further example, if X = O− and W = −CHCH−, then there is a large decrease from EPD0 (+87.3 kJ mol−1) to EPDW (+41.6 kJ mol−1) involved with interposition of the W = −CH CH− connector group in •CH2CHCHO−. This decrease can be primarily attributed to the large positive MCEa (+98.3 kJ mol−1), i.e., the enthalpic change for the reaction CH3−CH=CH−O− + CH3−OH → CH3−CH=CH−OH + CH3−O−

(17)

although the RCEa (+52.6 kJ mol−1), i.e., the enthalpic change for the reaction •

CH 2−CH=CH−O− + •CH 2−OH → •CH 2−CH=CH−OH + •CH 2−O−

(18)

is also quite large. The large magnitudes for both the MCEa and RCEa are a consequence of the extensive resonance delocalization of the negative charge in the interposed species. That is, CH3CHCHO− and •CH2CHCHO− can be represented by more resonance forms than either CH3O− or •CH2O−, respectively, and hence we can expect the two interposed species to be relatively stable. The main difference between the MCEa and RCEa values arises in the relative stabilities of methanol derivatives. In particular, •CH2O− is somewhat more stable than CH3O−, relative to •CH2OH and CH3OH, respectively, because of the partial double-bond that can be formed in •CH2O−. 2817



Article

variation of C−H bond strength with protonation state is observed. These results suggest that full protonation and deprotonation can be used as probes to predict qualitatively how weaker proton interactions might affect the bond strengths of alcohols. The effect of remote protonation and deprotonation on C−H BDEs was studied using the set of methanol derivatives, CH3WOH. A variety of different connector groups (W) were considered, representing a diverse range of common alcohols. Three new quantities were introduced  the effect of protonation state on dissociation energies (EPDW), the alcohol radical connector energy (RCEa), and the alcohol molecule connector energy (MCEa)  to better understand the changes in the C−H BDEs with protonation state. As with methanol, we find the C−H BDEs for CH3WOH to increase with protonation and decrease with deprotonation. The magnitude of the change is in all cases smaller than that for methanol. For saturated connector groups, the change in BDEs with protonation state is small, generally becoming smaller as the size of the connector group increases. Unsaturated and o- and p-phenylene connector groups lead to larger changes in BDEs with protonation state, due primarily to resonance delocalization. Gas-phase acidities and proton affinities were calculated for CH3WOH alcohols and •CH2WOH radicals, and compared with experiment. The agreement between the two sets of data was generally found to be reasonable, with the only significant deviation being recorded for the proton affinity of • CH2CH2CH2OH. In this case, we recommend that the experimental value should be reevaluated. In general, the CH3WOH alcohols were found to be less acidic than the related • CH2WOH radicals, as observed previously for the parent CH3OH and •CH2OH systems.

Table 5. Comparison of G4(MP2)-6X Gas-Phase Acidities and Proton Affinities (298 K, kJ mol−1) for Alcohols (CH3WOH) and Radicals (•CH2WOH) with Experimental Values W

ΔacidH°

NIL −CH2− −CH2CH2− −CH2CH2CH2− −CHCH− −CC− −o-C6H4− −m-C6H4− −p-C6H4−

1592.4 1579.9 1576.2 1574.7 1494.1 1413.2 1455.9 1458.8 1465.2

NIL −CH2− −CH2CH2− −CH2CH2CH2− −CHCH− −CC− −o-C6H4− −m-C6H4− −p-C6H4−

1505.1 1568.7 1559.8 1564.6 1452.6 1355.4 1422.6 1445.4 1419.3

expt CH3WOH 1599 ± 3a 1586 ± 5a 1574.9 ± 7.1c 1570.3 ± 8.4d

1448.5 ± 12.6e 1453.1 ± 12.6e 1456.7 ± 12.6e • CH2WOH

PA

expt

749.5 771.9 778.1 782.9 741.4 656.9 747.5 750.0 748.5

754.3b 776.4b 786.5b 789.2b

691.8 773.5 775.0 777.0 718.5 657.5 740.0 743.9 742.4

695b 771f 748g

a

Experimental values from ref 31. bExperimental values from ref 32. Experimental value from ref 33. dExperimental value from ref 34. e Experimental values from ref 35. fObtained using the heat of formation for •CH2CH2OH from ref 36 and •CH2CH2OH2+ from ref 37. gObtained using the heat of formation for •CH2CH2CH2OH from ref 36 and •CH2CH2CH2OH2+ from ref 38. c

■

This tells us that carbon-centered radicals derived from alcohols are relatively more acidic than their closed-shell counterparts, consistent with previous observations.4−6

ASSOCIATED CONTENT

S Supporting Information *

■

Optimized geometries of relevant species (Table S1), ZPVEs, thermal corrections to enthalpies, and G4(MP2)-6X single-point energies (Table S2), and full citations for refs 18 and 19 (Table S3). This material is available free of charge via the Internet at http://pubs.acs.org.

CONCLUDING REMARKS In the present study, we have used high-level quantum chemical procedures to investigate how the C−H bond dissociation enthalpies of alcohols and related systems vary with changes to their protonation state. A wide range of alcohols and protonation states have been considered, corresponding to different combinations of adjacent and remote, and full and partial protonation and deprotonation. An initial assessment of theoretical procedures, performed using a set of 25 neutral, protonated, and deprotonated substituted methanes, CH3X, led us to pick G4(MP2)-6X, W1X-1, and W1X-2 as appropriate methods for studying the C− H BDEs of alcohols with varying protonation state. We find that BDEs tend to be overestimated at lower levels of theory, and become smaller as the level of theory is improved. Basis-set size was found to be of particular significance when looking at the BDEs of first-row anionic systems. Based on a comparison with our highest-level W3.2 data, we believe the experimental C−H BDEs for CH3NH2 and CH3SH should be reevaluated. Methanol was used as a model to investigate how adjacent full and partial protonation and deprotonation affects the C−H BDEs of alcohols. We find that protonation increases the BDE relative to methanol, while deprotonation decreases the BDE, with the extent of the change being larger for deprotonation. Reducing the strength of the proton donor or acceptor leads to a concomitantly smaller change in the BDE, and a smooth

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (B.C.), radom@chem. usyd.edu.au (L.R.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge the receipt of an Australian Postgraduate Award (to M.M.), funding (to L.R.) from the Australian Research Council (ARC), and generous grants of computer time from the National Computational Infrastructure (NCI) National Facility and Intersect Australia Ltd.

■

REFERENCES

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Effect of Protonation State and Interposed Connector Groups on Bond

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