Article pubs.acs.org/JPCA
A Computational Study of RXHn X−H Bond Dissociation Enthalpies Kenneth B. Wiberg*,† and George A. Petersson‡,§ †
Department of Chemistry Yale University, New Haven Connecticut 06520, United States Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459, United States
‡
S Supporting Information *
ABSTRACT: Bond dissociation enthalpies can exhibit dramatic variations resulting from substituent effects. These variations result from changes in electronic structure that accompany bond dissociation. We have studied bond dissociation enthalpies (BDEs) at the W1BD level of theory for a series of RX−H compounds where X = CH2, NH, O, PH, and S. The substituents, R, included H, H3C, H2N, HO, F, H2P, HS, and Cl. The experimentally available BDEs were reproduced in a very satisfactory fashion. Most of the substituent effects could be related to a conjugative interaction in the two-center threeelectron systems in the radicals formed by H abstraction. Comparisons of isoelectronic species demonstrate the important roles that variations in electronegativity and hybridization can play in determining BDEs. The OH and SH BDEs were linearly related, and the same was found with N−H and P−H BDEs. The relative effects of H2P and HS as substituents, in contrast to H2N and HO, could be related to the need to promote a 3s electron to 3p before H2P can participate in π-bonding. We must also include electronegativity differences to account for the observed transfer of a sulfur lone pair to an oxygen but the absence of the reverse process.
1. INTRODUCTION Our previous study focused on substituent effects on RO−H bond dissociation enthalpies (BDE) where R is a first row substituent.1 Here, the BDE for H2O, CH3OH, and H2O2 decrease from 119 to 105 and 88 kcal/mol. An examination of the RO bond length changes on H abstraction as well as the changes in RO bond orders and the spin densities at oxygen in the product RO radicals indicated that the changes in BDE resulted from conjugative effects in the three-electron twocenter radicals. This was further confirmed by examining the HOMOs of the parents and the product radicals. The RO−H BDE calculations made use of the CBS-APNO model2,3 that gave very good agreement between calculations and observations. We now wish to examine other X−H bonds as well as the effect of second row substituents such as PH2 and SH. These data should provide information for comparison between first row−first row, first row−second row, and second row−second row conjugative interactions. Because the CBSAPNO model is restricted to first row elements, we must consider alternative compound models that are appropriate for both first and second row elements, G4,4 ROCBS-QB3,5 and W1BD.6,7 Here it should be noted that Chan and Radom8 have recently reported a comprehensive computational study of bond dissociation enthalpies at the W1w level that includes some of the compounds in the present report. Their study was largely concerned with comparisons with lower level methods. In the cases where there is overlap with our study, there was very good agreement. As an initial step, we have calculated the Y−H bond dissociation enthalpies for a number of compounds that have relatively accurate experimental determinations with estimated uncertainties of 0.7 kcal/mol9−13 or less. The BDEs were obtained from calculations of the enthalpies of the reactant, the radical and a hydrogen atom, and are summarized in Table 1. © XXXX American Chemical Society
The four procedures all reproduce the experimental values in a satisfactory fashion. The G4 model requires twice the CPU time needed for CBS-APNO calculations, but the deviation from experiment is 1/3 larger. The ROCBS-QB3 model is an order-of-magnitude faster, but the accuracy is only marginally better than the G4 model. The W1BD method is more reliable than the CBS-APNO model and although significantly more expensive, is still affordable for the relatively small species in this study. Because most of the compounds in this study have not been studied experimentally, the W1BD values will be given in the following discussion. The G4 BDEs have been obtained in all cases and are given in the Supporting Information. For each radical center, the W1BD and G4 BDEs have been compared in order to ensure that errors have not been made, and in each case they were linearly related with R = 0.99. In the following, we shall examine the formation of C, N, O, P, and S centered radicals via hydrogen abstraction. Substituents include H, CH3, NH2, OH, F, PH2, SH, Cl, NC, CHO, NO2, and CF3 that cover both electron donating and accepting groups, and both first and second row elements. The final four substituents were chosen because they might lead to interesting effects on the BDE’s
2. OXYGEN CENTERED RADICALS Because a detailed analysis of substituent effects has been presented for the RO−H BDEs where R is a first row element or group, we will begin by examining these compounds where now R includes the second row elements or groups. The data are summarized in Table 2 where the calculated W1BD BDEs Received: January 2, 2014 Revised: March 4, 2014
A
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
Article
Table 1. Calculated Bond Dissociation Enthalpies, D298 (kcal/mol)
a
compd
G4
ROCBS-QB3
CBS-APNO
W1BD
obsd9,10
dev
H−H HO−H O−H NH2−H HS−H S−H CH3−H CH2−H CH−H CH3CH2−H Me2CH−H Me3C−H CH2CH−H •CHCH−H HCC−H C6H5−Ha H2CCHCH2−H CH3O−H HOCH2−H CH3S−H HOO−H HC(O)−H NC−H F−H rms error rel CPU time
104.5 118.2 102.9 106.7 90.8 84.1 104.5 110.7 100.3 100.7 97.9 96.0 109.9 36.4 131.5 112.6 87.1 104.4 96.0 86.1 86.8 88.2 127.2 136.4 0.82 2.5
105.3 118.9 102.9 107.4 91.4 83.1 105.2 111.2 99.9 101.5 98.8 97.1 110.0 36.0 133.2 113.0 87.2 104.4 96.8 86.7 87.6 88.9 126.7 136.9 0.75 0.1
104.7 118.9 102.5 107.8
104.0 119.1 102.8 107.5 91.5 84.5 104.9 110.8 101.3 101.2 98.5 97.0 110.7 36.0 133.3 113.1 88.0 105.2 96.3 86.9 87.4 88.5 127.2 136.9 0.42 80.2
104.2 118.8 101.8 107.6 91.2 84.4 105.0 110.4 101.3 101.1 98.6 96.5 110.7 35.4 133.2 112.9 88.8 105.2 96.1 87.4 87.5 88.1 126.3 136.3
0.003 0.07 0.07 0.1 0.1 0.2 0.03 0.2 0.3 0.4 0.4 0.4 0.6 0.7 0.07 0.5 0.4 0.5 0.2 0.5 0.07 0.01 0.2 0.01 0.33
105.4 111.4 100.9 101.8 99.1 97.4 111.1 36.4 133.9 112.4 87.6 105.4 96.6 86.7 88.2 126.4 136.2 0.62 1.0
Phenyl radical.
Table 2. Calculations for RO−H Bond Dissociation Enthalpies (kcal/mol)a compd
calc BDE
obsd BDE9,10
HO−H MeO−H H2NO−H HOO−H FO−H H2PO−H HSO−H ClO−H NCO−H HC(O)O−H HC(S)O−H H2CCHO−H O2NO−H F3CO−H
119.2 105.8 78.0 87.6 100.3 83.9 74.9 95.8 86.9 114.4 86.8 85.3 103.9 120.2
118.8 ± 0.07 105.2 ± 0.5
Δr(RO) −0.012 0.043 0.162 0.115 0.074 0.165 0.160 0.110 0.128 0.093 0.126 0.094 0.161 −0.016
87.5 ± 0.07 101.0 ± 2
94.3 ± 0.3 112 ± 3
101.7 ± 0.4
(−1.2%) (3.1%) (11.2%) (8.0%) (5.2%) (9.9%) (9.5%) (6.5%) (9.8%) (6.8%) (9.5%) (6.6%) (11.6%) (1.2%)
Δbo(R−O)
spin density at O
−0.066 0.018 0.170 0.072 0.030 0.332 0.264 0.094 0.274 0.168 0.295 0.250 0.196 −0.070
0.961 0.817 0.569 0.708 0.834 0.358b 0.469c 0.681 0.305d 0.487e 0.062f 0.309g 0.330h 0.870
a
Bond dissociation enthalpies were calculated using W1BD. The change in bond length on going to the radical was calculated using CCSD/aug-ccpVTZ and the change in bond order and the spin density were obtained using B3LYP/aug-cc-pVTZ. b0.518 at P. c0.512 at S. d0.622 at N. e0.487 at both O. f0.907 at S. g0.592 at C(H2). h0.330 at each O.
are compared with the available experimental data. There is very good agreement between the values. In our earlier study, we found that an examination of the changes in structure on going from the parent compound to its radical was very useful. Because the structures of some of the compounds and most of the radicals are not known experimentally, we have obtained optimized geometries at the CCSD/aug-cc-pVTZ level that should give very reliable structures.14 This should provide good estimates of the change in R−O bond lengths that result from hydrogen abstraction. The shortening of this bond is one of the clear indicators of
conjugation between R and O in the radicals, and this can be confirmed by calculating the change in bond order. This is done by mapping the B3LYP/aug-cc-pVTZ electron density onto a minimal basis set15 followed by a Mulliken population analysis.16,17 Finally, conjugation should lead to a decreased spin density at the radical center, and this quantity was obtained using the Hirshfeld population method.18 All of these quantities are included in Table 2. It may first be noted that F3COH has a high BDE similar to that of H2O, and as seen below this is found in other cases in comparing H and F3C as the substituent. In these cases, the R− B
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
Article
and H2PO−H increase the bond order to oxygen and reduce the spin density at O to less than 0.5, but these changes are greater in H2PO•, whereas HSO• shows the larger stabilization of the radical. The formate radical is planar with the spin density equally distributed between the two oxygens. The NO3 radical had a 3fold symmetry axis, with most of the spin density equally distributed among the three oxygens. A still smaller spin density at oxygen was found in the NCO radical, and here most of the spin density appeared at the nitrogen. The spin density of the thioformate radical is almost completely transferred to the sulfur. These last two species will be examined in detail below when we consider the analogous R−S−H species.
Y bond lengthens rather than shortening as found with the other substituents. This appears to result from the lack of conjugative interactions with these substituents. Electron donating substituents such as NH2 would be expected to provide a good opportunity for a conjugative three-electron two-center system, and indeed it leads to a large decrease in R− O bond length and a corresponding increase in the R−O bond order. At the same time, the spin density at O is dramatically decreased. For the first row substituents there is a relationship between these quantities (Figure 1).
3. SULFUR CENTERED RADICALS There are some similarities between compounds with OH and SH bonds, and therefore we will next present the corresponding data for the sulfur containing compounds. The structures of some of the compounds and radicals are not known, but in all cases the calculations found them to be energy minima with no imaginary vibrational frequencies. The results of the calculations are summarized in Table 3. The similarity between S and O can be seen in Figure 2 that shows the correlation between the two sets of BDEs. The first row substituents give a good linear correlation and that for the second row substituents is only slightly displaced. There are three interesting things about Figure 2. First, although the first row substituents give a very good correlation of BDEs between RSH and ROH, the slope is only 0.47. This is consistent with the correlation between Δbo(R−S) from Table 3 and Δbo(R−O) from Table 2, for which the slope is 0.43. Both are presumably a result of the S−H bond being longer and weaker than O−H, leading to a smaller BDE for H2S. Here, the symmetrical HS stretching frequency in H2S was calculated to be 2681 cm−1, whereas that for H2O was 3817 cm−1. The second, as noted above, is that HS and H2P are reversed in their effect on BDE as compared to HO and H2N. Finally, the anomalous position of NC as a substituent might be noted. The other “extra” substituents shown in blue lie close to the line for the other substituents. A further examination showed that NCOH was the unstable enol derived from HNCO and has a higher enthalpy than the latter by 24.9 kcal/mol. The BDE of HNCO was calculated to be 111.8 kcal/mol, similar to that of NH3. On the other hand,
Figure 1. Relationship between spin densities and changes in bond lengths for ROH with first row substituents.
The effects of the first row substituents on the BDEs are straightforward. NH2 with the highest energy lone pair gives the lowest BDE along with the largest change in bond length, the largest increase in bond order, as well as the smallest spin density at O. The second row substituents behave differently. Here, HS gives a larger decrease in BDE than H2P, whereas the opposite is true in the first row counterparts. Both HSO−H
Table 3. Calculations for RS−H Bond Dissociation Enthalpies (kcal/mol)
a
compd
calcd BDE
obsd BDE9
HS−H MeS−H H2NS−H HOS−H FS−H H2PS−H HSS−H ClS−H NCS−H HC(O)S−H HC(S)S−H O2NS−H F3CS−H
91.7 87.0 72.2 78.4 84.1 78.9 73.8 82.2 83.6 90.1 79.3 86.5 91.0
91.2 ± 0.1 87.4 ± 0.5
Δr(R−S) −0.005 0.017 0.087 0.034 0.020 0.136 0.089 0.049 0.056 0.008 0.077 0.033 −0.003
(0.4%) (0.9%) (5.0%) (2.0%) (1.3%) (6.3%) (4.3%) (2.4%) (3.3%) (0.4%) (4.4%) (1.8%) (−0.2%)
Δbo(R−S)
spin density at S
−0.032 0.000 0.082 0.010 0.000 0.194 0.098 0.024 0.100 −0.004 0.100 0.034 −0.016
0.967 0.906 0.699a 0.806 0.885 0.596b 0.670c 0.811 0.691d 0.907 0.526e 0.833 0.927
0.273 at N. b0.404 at P. c0.319 at S. d0.317 at N. e0.491 at S. C
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
Article
H2PCHO. This confirms the reduced conjugative ability of H2P. The HSCHO ground state structure was planar, with an H− S−C angle of 94°. Although this angle requires the use of mostly 3p-orbitals at S, there is another p-orbital that can be involved with the carbonyl group. On the other hand, the phosphorus analogue has two C−P−H angles of 96° along with an H−P−H angle of 96°. This leaves very little p-character remaining for interaction with the carbonyl group, resulting in a small rotational barrier. Although these data indicate that H2P is much less effective in conjugation than SH and would explain the smaller effect of H2P on the BDEs, it must also be noted that H2P and HS lead to about as large a change in bond length and spin density as found with H2N as the substituent. The availability of 3p electrons for π-bonding without the need to excite the 3s electrons appears to be the key advantage of sulfur over phosphorus. The bond lengths and bond orders in Table 4 Table 4. Geometry and Population Data for H2POH and HSOH
Figure 2. Correlation of W1BD BDE for ROH and RSH (kcal/mol).
NCSH was found to have a smaller enthalpy than HNCS (7.2 kcal/mol), probably because the CS bond is weaker than CO. An examination of the spin density of the radicals (Tables 2 and 3) shows that NCO has it mainly on N, whereas with NCS it is mainly on S. In view of this, it is not surprising that CN falls off the correlation line in Figure 2. In this series, F3C as a substituent gives essentially no decrease in BDE with respect to H2S, as well as a negative change in bond length and a large spin density at S. Formic acid and HC(S)SH exhibit similar behavior with the symmetric radicals showing modest stabilization, which can be attributed to delocalization of a lone pair from the carbonyl (CS) as the spin density becomes distributed equally between the two oxygens (sulfurs). The corresponding mixed oxygen−sulfur species demonstrate the importance of electronegativity differences. The HC(S)OH BDE is reduced by more than 25 kcal/mol relative to HC(O)OH as a lone pair is transferred from sulfur to the more electronegative oxygen in the HCSO radical for which the unpaired electron resides almost entirely on the sulfur. In contrast, the HC(O)SH BDE is increased by 10 kcal/mol relative to HC(S)SH because a lone pair cannot transfer from oxygen to the less electronegative sulfur in the HCSO radical for which the unpaired electron remains on the sulfur. The BDE of HC( O)SH is almost the same as HSH as a consequence of the lack of delocalization stabilization in the radical. These BDEs, Δrs, Δbos, and spin densities are consistent with the general trends in Tables 2 and 3. In comparing H2P and HS as substituents, it is helpful to consider a case where conjugation is clear: the formamide analogues. The rotational barrier is usually taken as indicating the magnitude of the ground state stabilization. Calculations at the W1BD level gave the barriers as ΔH = 15.5 kcal/mol for H2NCHO,19 ΔH = 11.4 kcal/mol for HOCHO, ΔH = 8.5 kcal/mol for the HSCHO, and only ΔH = 2.1 kcal/mol for
P
PH2
H2P−OH
H2PO
PO
N(P3s) AHPH (deg) RPO BOPO
2.000
1.853 91.8
SH2
1.493 101.7 1.502 0.965 HSO
1.832
S
1.732 92.2 1.674 0.626 HS−OH
N(S3s) AHSO (deg) RSO BOSO
2.000
1.893 92.6
1.886 98.7 1.694 0.525
1.840 104.5 1.517 0.795
1.481 0.944 SO 1.892 1.498 0.784
clearly indicate that both H2PO• and HSO• have double bonds to the oxygens, but H2PO• must promote electron density from the 3s to the 3p orbital to develop this π-bond. Hybridization must be included in the factors that determine BDEs. The thermodynamic cycle for H2POH dissociation to H2P + O + H lends further support to the reduced PO bond energy in H2PO.
4. NITROGEN AND PHOSPHORUS CENTERED RADICALS The corresponding calculations for the formation of nitrogen centered radicals are summarized in Table 5. These compounds might best be examined by comparing them with their P counterparts. The data for the latter may be found in Table 6, and a comparison of their BDE is shown in Figure 3. Again, there is a smaller range of BDE for the phosphines as compared to the amines. Here, the substituent that falls far from the others is HCO with formamide, giving an NH BDE of 115.8 kcal/mol. This surely a result of the loss of much of the amide stabilization20 on going to the radical, and in fact the rotational barrier for the radical is calculated to be only 3.2 kcal/mol. D
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
Article
Table 5. Calculations for RNH−H Bond Dissociation Enthalpies (kcal/mol)
a
compd
calcd BDE
obsd BDE9
H2N−H MeNH−H H2NNH−H HONH−H FNH−H H2PNH−H HSNH−H ClNH−H NCNH−H HC(O)NH−H O2NNH−H F3CNH−H
107.6 100.0 80.5 85.4 91.2 96.1 86.4 92.3 96.6 115.8 107.2 110.3
107.6 ± 0.1
Δr(R−N) −0.013 0.019 0.122 0.162 0.054 0.071 0.080 0.063 0.066 −0.023 −0.026 −0.022
Δbo(R−N)
spin density at N
−0.066 −0.018 0.144 0.042 0.022 0.140 0.104 0.042 0.162 −0.102 −0.146 −0.088
0.899 0.805 0.632a 0.727b 0.813 0.558c 0.602d 0.741e 0.492f 0.817 0.778 0.828
(−1.2%) (0.1% (8.3%) (11.2%) (3.8%) (4.1%) (4.6%) (3.6%) (4.9%) (−1.7%) (−1.9%) (−1.6%)
0.283 at N. b0.225 at O. c0.321 at P. d0.353 at S. e0.223 at Cl. f0.483 at N.
Table 6. Calculations for RPH−H Bond Dissociation Enthalpies (kcal/mol) compd
calcd BDE
obsd BDE
PH2−H MePH−H H2NPH−H HOPH−H FPH−H H2PPH−H HSPH−H ClPH−H NCPH−H HC(O)-PH−H O2NPH−H F3CPH−H
82.9 81.5 76.2 77.3 79.0 78.6 75.6 77.6 79.4 81.6 82.4 83.9
82.5 ± 0.521−24
Δr(R−P) −0.004 0.005 0.015 0.008 0.006 0.042 0.033 0.022 0.024 0.009 0.001 0.004
Δbo(R−P)
spin density at P
−0.028 −0.012 −0.020 −0.020 −0.014 0.048 0.018 0.000 0.032 0.008 −0.024 −0.014
0.929 0.877 0.753 0.820 0.869 0.797 0.756 0.827 0.781 0.804 0.865 0.889
(−0.3%) (0.2%) (0.9%) (0.4%) (0.3%) (1.9%) (1.5%) (1.1%) (1.3%) (0.5%) (0.05%) (0.2%)
HOCHO + H 2S → HSCHO + H 2O ΔH = 7.6 kcal/mol H 2NCHO + PH3 → H 2PCHO + NH3 ΔH = 14.1 kcal/mol
The second reaction is much more endothermic than the former, again indicating that P is much less able to conjugate than S. The phosphines give the smallest effect on the bond length to P. In Figure 3, the slope for the first row substituents is 0.26 (much smaller than found in comparing ROH and RSH). The slope for the second row substituents is 0.31.
5. CARBON CENTERED RADICALS The C−H bond dissociation energies might be expected to respond differently to substituents than the other cases because of the low electronegativity of carbon. The calculated results are summarized in Table 7. It is more convenient to examine the BDE in the form of a plot, and the correlation between the ROH series and the RCH3 is shown in Figure 4. The slope is small (0.29 for first row substituents and 0.20 for the second row). The formyl and vinyl substituents fall far from the average for the other first row species, but the slope for the two isoelectronic YC− substituents is the same as the others. The range of CH BDEs is relatively small, but the changes in R−CH bond lengths are significantly larger than those for R−PH.
Figure 3. Correlation of W1BD BDE for RNH2 and RPH2 (kcal/mol).
It might be noted that whereas both formic acid and thioformic acid gave expected BDE as shown in Figure 2, suggesting that both have normal carboxylic acid type stabilization, PH2 does not give significant amide stabilization. A difference between S and P may be seen from the following equations (W1BD): E
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
Article
Table 7. Calculations for the C−H Bond Dissociation Enthalpies (kcal/mol)
a
compd
calcd BDE
obsd BDE9,10
Δr(R−C)
Δbo
spin density at C
H3C−H H3CCH2−H H2NCH2−H HOCH2−H FCH2−H H2PCH2−H HSCH2−H ClCH2−H NCCH2−H HC(O)CH2−H H2CCHCH2−H O2NCH2−H F3CCH2−H
104.9 101.3 93.1 96.4 101.4 98.5 95.2 99.4 96.9 95.9 88.0 102.2 106.5
105.0 ± 0.03 101.1 ± 0.4
0.010 (0.9%) 0.036 (2.3%) 0.068 (4.7%) 0.054 (3.8%) 0.045 (3.3%) 0..075 (4.0%) 0.094 (5.1%) 0.096 (5.3%) 0.071 (4.8%) 0.072 (4.8%) 0.117 (7.7%) 0.072 (4.1%) 0.015
0.010 0.054 0.076 0.044 0.032 0.146 0.150 0.109 0.182 0.036 0.251 0.126 0.048
0.826 0.744 0.631a 0.690b 0.753c 0.667d 0.634e 0.706f 0.592g 0.770 0.450h 0.670h 0.769
96.1 ± 0.2
88.8 ± 0.4
0.226 at N. b0.188 at O. c0.136 at F. d0.192 at P. e0.262 at S. f0.198 at Cl. g0.329 at N. h0.450 at both CH2s.
latter being less than half of that for the former. The changes in the X−O and X−S bond orders follow the same pattern, with the X−S Δbos less than half those of the X−O bonds. A similar observation was made for the NH−H and PH−H BDEs. Most of the substituent effect could again be related to a conjugative interaction in the two-center three-electron systems in the radicals formed by H abstraction. Comparisons of isoelectronic species demonstrate the important roles that variations in electronegativity and hybridization can play in determining BDEs. For example, an anomaly was found with the H2P substituent that gave a smaller effect than HS whereas H2N gives a much larger effect than HO corresponding to the relatively high lone pair energy at N. The difference between H2P and HS could be related to the p-character in the bonds at the heteroatoms. It is necessary to promote a 3s electron to 3p before H2P can participate in π-bonding. We must also include electronegativity differences to account for the observed transfer of a sulfur lone pair to an oxygen and the absence of the reverse process. In general, it is important to consider all changes in electronic structure that accompany bond dissociation. For example, the substituent effect of the cyanogroup on the O−H BDE can only be understood by recognizing that the structure of the resulting radical: NC−O−H → •NCO + H• → H‐NCO
represents significant changes in the NCO electronic structure.
7. CALCULATIONS All calculations were carried out using Gaussian-09.25
Figure 4. Correlation between The RCH2−H and RO−H bond dissociation energies.
■
ASSOCIATED CONTENT
S Supporting Information *
6. SUMMARY The X−H bond dissociation enthalpies have been calculated at the W1BD level for a series of RX−H compounds where X = CH2, NH, O, PH, and S. The substituents, R, included H, H3C, H2N, HO, F, H2P, HS, and Cl. The experimentally available BDEs were reproduced in a very satisfactory fashion. Our previous study1 found the effect of substituents on OH BDEs to be a consequence of conjugative interactions of the radical center with the substituent. The OH BDEs were found to be linearly related to the spin density at the O radical center and also to the change in X−O bond order and bond length in going from X−O−H to XO. The current study shows that the O−H and S−H BDEs are linearly related, with changes in the
Tables of W1BD and G4 relative calculated energies and tables of properties of parent molecules and the related radicals. Full ref 10 and 25 citations. This material is available free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. § For G.A.P.: E-mail,
[email protected]. F
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
■
Article
(18) Hirshfeld, F. L. Bonded Atom Fragments for Describing Molecular Charge Densities. Theor. Chim. Acta 1977, 44, 12−138. (19) The rotational barrier in formamide has been found to be ΔH = 18.5 kcal/mol in methyl propyl ketone: Drakenberg, T.; Forsen, S. The Barrier to Internal Rotation in Amides. I. Formamide. J. Phys. Chem. 1970, 74, 1−7. (20) Wiberg, K. B. In The Amide Linkage; Greenberg, A., Breneman, C. M., Liebman, J. F., Ed.; Wiley-Intersciece: Hoboken, NJ, 2003; pp 33−46. (21) Berkowitz, J.; Curtiss, L. A.; Gibson, S. T.; Green, J. P.; Hillhouse, G. L.; Pople, J. A. Photoionization Mass-Spectrometric Study and Ab Initio Calculations of Ionization and Bonding in P−H Compounds. Heats of Formation, Bond Energies and the 3B1−1A1 Separation in PH2. J. Chem. Phys. 1986, 84, 375. (22) Jordan, A. S.; Robertson, A. Thermodynamic Analysis of AsH3 and PH3 Decomposition Including Subhydrides. J. Vac. Sci. Technol., A 1994, 12, 204−214. (23) Ervin, K. M.; Lineberger, W. C. Photoelectron Spectroscopy of Phosphorus Hydride Anions. J. Chem. Phys. 2005, I12, 194303. (24) A CCSD(T) calculation for PH3 gave D298 = 81.2 kcal/mol: Ricca, A.; Bauschlicher, C. W., Jr. Accurate Heats of Formation for PHn, PHn+ and PHn•. Chem. Phys. Lett. 1998, 285, 455−458. (25) Frisch, M. J., et al. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2009.
ACKNOWLEDGMENTS We thank Prof. Robert Crabtree for helpful comments concerning the difference between trivalent phosphorus and divalent sulfur. Computational efforts were supported in part by the Yale University Faculty of Arts and Sciences High Performance Computing Cluster and by the National Science Foundation under grant CNS-0821132 which partially funded the acquisition of the requisite computer facilities. The authors also acknowledge support from Gaussian, Inc., and Wesleyan University through computational facilities supported by National Science Foundation grant CNS-0959856.
■
REFERENCES
(1) Wiberg, K. B.; Ellison, G. B.; McBride, J. M.; Petersson, G. A. Substituent Effects on O−H Bond Dissociation Enthalpies: A Computational Study. J. Phys. Chem. A 2013, 117, 213−218. (2) CBS-APNO: Montgomery, J. A, Jr.; Ochterski, J. W.; Petersson, G. S.. A Complete Basis Set Model Chemistry. An Improved Atomic Pair Natural Orbital Method. J. Chem. Phys. 1994, 101, 5900−5909. (3) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. The Use of the Minimum Population Allocation Method. J. Chem. Phys. 2000, 112, 6533−6542. (4) G4: Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory Using Reduced Order Perturbation Theory. J. Chem. Phys. 2007, 127, 124105. (5) CBS-QB3: Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry VI Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822−2827. (6) W1BD: Barnes, E. C.; Petersson, G. A.; Montgomery, J. A., Jr.; Frisch, M.. J.; Martin, J. M. L. The Unrestricted Coupled Cluster and Breuckner Doubles Variations of W1 Theory. J. Chem. Theory Comput. 2009, 5, 2687−2693. (7) W1BD is based on W1: Martin, J. M. L; De Oliveria, G. Towards Standard Methods for Benchmark Quality ab Initio ThermochemistryW1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843−1856. (8) Chan, B.; Radom, L. BDE261: A Comprehensive Set of High Level Theoretical Bond Dissociation Enthalpies. J. Phys. Chem. A 2012, 116, 4975−4986. (9) Most of the data were taken from Blanksby, S. J.; Ellison, G. B. Bond Dissociation Energies of Organic Molecules. Acc. Chem. Res. 2003, 36, 255−263. (10) CH3 and H2O2: Ruscic, B.; et al. IUPAC Critical Evaluation of Thermochemical Properties of Selected Radicals. Part 1. J. Phys. Chem. Ref. Data 2005, 34, 573−656. (11) FOH: Berkowitz, J.; Dehmer, P. M.; Chupka, W. A. Photoionization Mass Spectometry of F2O. J. Chem. Phys. 1973, 59, 925. (12) Berkowitz, J.; Appleman, E. H.; Chupka, W. A. Photoionization of HOF with Mass Analysis. J. Chem. Phys. 1973, 58, 1950−1954. (13) ClOH: Meyer, M. M.; Kass, S R. Experimental and Theoretical Gas-Phase Acidities, Bond Dissociation Energies and Heats of Formation for HClOx, x = 1−4. J. Phys. Chem. A 2010, 114, 4086− 4092 Also see ref 1.. (14) Shavitt, I.; Bartlett, R. J. Many Body Methods in Chemistry and Physics; Cambridge University Press: Oxford, U.K., 2009. (15) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. The Use of the Minimum Population Allocation Method. J. Chem. Phys. 2000, 112, 6532−6542. (16) Mulliken, R. S. Electron Population Analysis on LCAO-MO Molecular Wave Functions. 2. Overlap Populations, Bond Orders and Covalent Bond Energies. J. Chem. Phys. 1955, 23, 1841−1846. (17) Mulliken, R. S. Criteria for the Construction of Good SelfConsistent-Field Molecular Orbital Wave Functions and Significance of MO Population Analysis. J. Chem. Phys. 1962, 36, 3428−3433. G
dx.doi.org/10.1021/jp500035m | J. Phys. Chem. A XXXX, XXX, XXX−XXX
