Substituent Effects on OâH Bond Dissociation Enthalpies: A

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Substituent Effects on O-H Bond Dissociation Enthalpies. A Computational Study Kenneth B Wiberg, G. Barney Ellison, J. Michael McBride, and George A. Petersson J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp310510y • Publication Date (Web): 03 Dec 2012 Downloaded from http://pubs.acs.org on December 9, 2012

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The Journal of Physical Chemistry

Substituent Effects on O-H Bond Dissociation Enthalpies. A Computational Study Kenneth B. Wiberg,*† G. Barney Ellison,*‡ J. Michael McBride*† and George A. Petersson*§ Departments of Chemistry, Yale University, New Haven, CT 06520-8107, University of Colorado, Boulder, CO 80309, and Wesleyan University, Middletown, CT 06459 [email protected],[email protected],[email protected], [email protected]

Abstract: Bond dissociation enthalpies can exhibit dramatic variations resulting from substituent effects. The remarkable range of experimental OH bond dissociation enthalpies have been reproduced using CBS-APNO calculations with very good accuracy, so we have employed these calculations to extend the available BDE data. The effect on these BDEs of lone pairs on the atom adjacent to oxygen shows that conjugation in the product radicals is the most important interaction leading to the wide range of values. The BDE’s were found to be linearly related to both the spin density at the radical center and to the change in X-O bond order in going from X-O-H to X-O·.

Key words: RO-H BDE, CBS-APNO, spin densities, bond orders.

† Yale University ‡ University of Colorado § Wesleyan University

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1. Introduction, Calculated Bond Dissociation Enthalpies Bond dissociation enthalpies (BDE = DH298) have received wide use in studying reactions, and reviews of both the methods used to measure the BDE’s and tabulations of experimental values are available.1 Our present interest is in the changes in BDE with structural changes. For example, Table 1 below shows the O-H bond dissociation enthalpies of water, aliphatic alcohols, and hydroperoxides vary by over 30 kcal/mol; DH298(HO-H) = 118.8.81±0.07 kcal/mol, DH298(CH3O-H = 105.2±0.5 kcal/mol, DH298(HOO-H) = 87.49±0.07 kcal/mol. What is the origin of these large changes? In order to obtain information about this question, it is first necessary to demonstrate that it is possible to reproduce the available experimental data. Based on our previous experience, we have chosen to use the CBS-APNO model chemistry.2 This makes use of HF/6-311G and a scaling factor for the vibrational frequencies, QCISD/6311G(d,p) for the geometry optimization, and a QCISD/6-311++G(2df,p) calculation using this structure followed by a complete basis set extrapolation. We have carried out calculations for the parent compounds and the resulting radicals for a range of first row compound.3 The DH298 were obtained from the differences in calculated enthalpies corrected for that of a hydrogen atom and the results are shown in Table 1. It can be seen that most of the experimental X-H dissociation energies are reproduced quite well. In a few cases of interest, the BDE have not been measured, but in view of the generally good agreement, it seems reasonable to accept these calculated values.


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Table 1. CBS-APNO Calculated and observed X-H bond dissociation energies, 298K Compound

calc DH298 spin dens(X) ∆r(X-O)/Å ∆BOa kcal mol-1

expt’l DH298 kcal mol-1

ref

118.81 ±0.07

4

105.2 ± 0.5

4

101.76 ±0.07

4

-0.0008

106.3 ±0.7

5

0.0696

-0.0292

101 ± 2

0.7369

0.1118

-0.0804

91.1 ±3

8

86.7

0.7269

0.1081

-0.0729

87.49 ±0.07

4

CH3OO-H

85.1

0.7003

0.1158

-0.0863

88 ±1

9

(CH3)3COO-H

83.9

0.6904

0.1176

-0.0894

84 ±2

10

H2NO-H

77.4

0.6090

0.1541

-0.1717

H-OO–

63.7

0.5000

0.1803

-0.1227

H2C O-H

-

43.9

0.3054

0.2349

-0.3213

C6H5O-H

88.2

0.3321

0.1238

-0.1894

NH2-H

107.8

0.9087

CH3NH-H

100.2

0.8385

0.0426

100 ± 1

12

(CH3)2N-H

94.5

0.7860

0.0148

94±1

12

CH3-H

105.4

0.8344

CH3CH2-H

101.8

0.7696

(CH3)2CH-H

99.1

0.7170

CH3CH2CH2-H

102.5

HO-H

118.9

0.9767

0.0689

H3N+O-H

116.7

0.9283

0.0111

0.0307

CH3O-H

104.4

0.8601

0.0383

-0.0019

O-H

102.5

1.0000

(CH3)3CO-H

106.9

0.8494

0.0403

FO-H

98.8

0.8625

trans-CH3C(O)OO-H

90.4

HOO-H

0.0000

4

87.3 ± 0.5

11

104.99 ± 0.03

0.0330


,

63.8 ± 0.1

107.6 ±0.1

0.0336

67

5

4

101.1 ±0.4

13

98.6 ±0.4

13


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(CH3)3C-H

97.4

0.6783

0.030

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96.5 ±0.4

13

(a) Change in the bond order on going from X-OH to X-O , Section 5

2. Properties of Radicals: Conjugative Interactions Having shown that the calculations can reproduce the observed BDE, it is now possible to examine the reasons for the large changes. Some of the product radicals have received considerable attention. The methoxy radical formed in the O-H bond dissociation for methanol has been the subject of many investigations. The first theoretical study by Yarkony, Schaefer and Rothenberg14 noted that the C3v radical would undergo Jahn-Teller distortion. This has been the focus of most of the subsequent studies.15

This is, of course, important for spectroscopic studies, but is of less

significance for thermochemical studies. Geometry optimization for a slightly distorted structure led to a Cs structure for the ground state. This structure is compared in Table 2 with those found in recent J-T distortion studies.15,16


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Table 2. Structural parameters for methoxy radical parameter

MCSCF Ref 16

MRCI Ref 5

CBS-APNO

r(CO) Å

1.383

1.393

1.379

R(C-Ha)a

1.111

1.092

1.106

R(C-Hb)

1.086

1.088

1.099

∠H a CO

106.1

105.3

105.3

∠Hb CO

111.7

112.3

112.7

a. Ha is in the mirror plane The results are in agreement that the H in the mirror plane has a longer C-H than the other hydrogens, and it also has a smaller H-C-O bond angle. The C-O bond length found in this investigation is in very good agreement with that determined via microwave spectroscopy (1.376 Å).17 , and it is considerably smaller than that in methanol (1.414 Å) The shorter C-O bond along with Ha tilting toward the O and increasing in length suggest a hyperconjugative interaction between the C-H bond and oxygen radical center that may be described as: H

H C

C

O

O

H

H

H

H

The bond effect is further seen in the hydroperoxy radical where the O-O bond length is calculated to be 1.299Å as compared to 1.441Å in hydrogen peroxide. Other changes in bond lengths may be found in Table 1. An examination of the series FOH, HOOH, H2NOH and CH2-OH in which the BDE decreases by over 50 kcal/mol clearly indicates a conjugative interaction between 5 ACS Paragon Plus Environment


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the radical center and the adjacent lone pair whose energy increases through the series. This increase is evident from the calculated orbital energies of the lone pairs of the corresponding hydrides: CH3- = -0.0388, NH3 = -0.4257 ; H2O = -0.5004; HF = -0.637718 The role of the adjacent lone pair is further confirmed by the observation that protonation of the lone pair increases the BDE by 38 kcal/mol in hydroxylamine and by 50 kcal/mol in hydroxymethylcarbanion. The nature of the conjugative interaction may also be seen in Figure 1 that gives the OH bond (MO6) and N lone pair (MO9) orbitals of hydroxylamine and the “delocalized lone pair” of the H2NO radical formed in the OH bond dissociation (MO8).


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H2NOH MO6

H2NOH MO9

H2NO MO8

Figure 1. The OH bond (MO6) of hydroxylamine and the N lone pair (MO9) orbitals of hydroxylamine and of the H2NO radical (MO8).

3. Spin Densities The conjugative interaction between the lone pair and the adjacent radical center described above must lead to some redistribution of electron density. It is therefore useful to examine the electron density distribution in the radicals. The problem of how to assign



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charge densities to individual atoms has received much attention.19 This assignment invariably involves some assumptions, and often involves the calculated molecular orbitals. This does lead to some dependence on the basis set, although this is minimized using NPA.20 It is possible to make an appropriate assignment based only on the geometry and the charge density without any initial assumptions of which electrons should be associated with a given atom. Bader’s Atoms-in-Molecules (AIM)21 method makes use of volume elements for each of the atoms that are bounded by zero-flux surfaces. Although this is well defined in terms of theory, it has the disadvantage in the present context of having the zero-flux surfaces quite sensitive to electronegativity changes, thereby leading to changing volume elements for atoms. The Hirshfeld method22 makes use of a reference promolecule having uncharged spherically symmetrical proatoms placed at the coordinates of the atoms in the real molecule. A cubic grid is placed about the molecule and the charge density for the real molecule is calculated at each grid point from the wave function thus describing the 3-D charge distribution. A corresponding grid is placed about the promolecule and its charge density is derived from its wavefunction. Then, at each point of the grid the real density is apportioned to the real atoms in proportion to the contribution of the proatoms to the promolecule derived density. The result is integrated over all space to give the charges assigned to the individual atoms. In this way, the atoms in real molecules are referred to the same set of proatoms, facilitating comparisons. In the case of radicals, the wave functions may be obtained separately for the α and β electrons, and so the corresponding charges can be obtained for each atom. The sum of the calculated charges gives the total charge and the difference gives the spin


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density. The spin densities were calculated using the UQCISD/6-311G(d,p) geometries obtained in the course of the APNO calculations and UQCISD/6-311++G(2df,p) wave functions, and are included in Table 1. The calculated charges may be found in the Supporting Information. It would be expected that conjugation would lead to a reduction in spin density at the radical center, and this is what is found. Although one might expect some correlation between spin density at the O center and the bond dissociation enthalpies, it was interesting and unexpected to find a linear relationship (Figure 2a). A similar relationship was also found for the N and C centered radicals (Figure 2b). The correlation line for the N radicals was close to that for the O radicals, but the line for the C radicals was displaced from the others. The N and C centered radicals continue to be studied and this report will concentrate on the O centered radicals. In order to further explore the latter radicals, we have also examined the changes in bond orders on going from the parent compounds to the radicals.



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120 +

y = 8.5933 + 111.24x R= 0.99224

HO 2

H N OH 3

110 (CH ) COH 3 3

CH OH 3

100

FOH trans-CH CO-OH 3 HO

90 CH OOH 3

2

2

(CH ) COOH

80

3 3

H NOH 2

70 -

HOO 60

50 -

H C OH 2

40 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

spin density

Figure 2a Relationship between spin densities and OH bond dissociation enthalpies


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108

NH3

y = 59.858 + 53.935x R= 0.99877 106

y = 7.0594 + 110.7x R= 0.99988

CH

4

104

102

C2H6 CH NH

100

3

CH3CH2CH3

98

96

(CH ) CH 3 3

94

92 0.65

2

(CH ) NH 3 2

0.7

0.75

0.8

0.85

0.9

0.95

spin density

Figure 2b Relationship between spin densities and NH or CH bond dissociation enthalpies..

4. Bond Energies and Bond Orders Conjugative interactions between a lone pair and the adjacent radical center should also affect the bonds, and it is possible to use the results of the calculations to study the changes in bonding. The population analysis devised by Mulliken23 partitions the total electron density into intra-atomic charge, and inter-atomic bond contributions: N (e

−

Natoms

)= ∑

Natoms

qA +

A=1

∑ ∑ BO

AB

A =1 B ≠ A

where: Nbf ( A ) Nbf ( A )

qA =

∑ ∑ µ ν =1

=1

 Nocc   ∑ C j µ S µν C jν  ,  j =1 



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and Nbf ( A ) Nbf ( B ≠ A )

BO AB =

∑ ∑ µ ν =1

=1

 Nocc   ∑ C j µ S µν C jν  .  j =1 

The strength of covalent bonds has often been associated with the bond order term. It is widely known that the Mulliken population analysis does not have a well defined complete basis set limit and that the bond orders can take on very non-physical values with large basis sets, especially if diffuse functions are included in the basis set. However, it is somewhat less well known that these problems are easily avoided if we simply project the molecular orbitals onto a minimum basis set before performing the population analysis.24 Since the current study includes many species with significant HF spin contamination, we have employed B3LYP/6-311G(d,p) molecular orbitals in the present work. We note that the B3LYP spin densities closely mimic those obtained from far more costly Brueckner doubles calculations.25 One might expect OH bond dissociation enthalpies to correlate with the OH Mulliken bond orders, but Figure 3 demonstrates that this is not correct. The OH bond dissociation enthalpies of the sample set vary by almost a factor of 3 (almost 80 kcal/mol), but the OH bond orders vary by less than 20%. If the variations in OH bond dissociation enthalpies are not caused by changes in the OH bonds, then they must result from changes elsewhere in the molecules.


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120

+

HO

H N OH

2

3

(CH ) COH 3 3

CH OH 3

OH 100

FOH

HOOH

CH OOH 3

80

(CH ) COOH 3 3

H NOH 2

60

H COH

-

2

40 0.46

0.48

0.5

0.52

0.54

0.56

Bond Order (OH)

Figure 3 The variation of O-H bond dissociation enthalpies with the H-O Mulliken bond orders

The XO bond dissociation enthalpies in a sample of XOH species do correlate fairly well with the XO bond orders (Figure 4). Both the bond orders and the XO bond dissociation energies vary by a factor of 3. This figure includes examples where the X functional group represents H, O, F, CH3, CH2–, NH2, and OH. It is perhaps a little surprising that such a broad range of examples follow the same linear correlation as well as they do. Nevertheless, we note that related species show similar deviations from this linear behavior. For example, the pairs OH and H2O, OF and HOF, CH3OO and CH3COOH, and CH2O– and CH2OH–, all show similar deviations for the two members of the pair. This will play an obvious role in the success of the next section.



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160 y = -9.1508 + 200.8x R= 0.91632

-

H CO 2

140

HO

120

2

OH

100

CH OH 3

H COH

-

CH O

2

H NO 2

3

80 HOO 60

H NOH 2 CH OO

OF

3

HOOH

HOF

CH OOH 3

40 0.2

0.3

0.4

0.5

0.6

0.7

0.8

Bond Order (X-O)

Figure 4. The variation of X–O bond dissociation enthalpies with the X–O Mulliken bond order

5. BDE(XO–H) vs X-O Bond Order

We concluded above that if the variations in OH bond dissociation enthalpies are not caused by changes in the OH bonds themselves, then they must result from changes elsewhere in the molecules. The thermodynamic cycle in scheme 1 shows that the bond dissociation enthalpy for the O–H bond of any species X–O–H is equal to the bond dissociation enthalpy for the hydroxyl radical modified by the difference in bond dissociation enthalpies between the X–O bonds of X–O–H and X–O•:

DH298(XO–H) = DH298(O–H) + [ DH298(X–OH) – DH298(X–O) ]. 14 ACS Paragon Plus Environment

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Any energetic consequences of variations in the electronic structure of the O–H bonds is necessarily expressed in the change in the X–O bond dissociation enthalpies. This complementary behavior of the two bonds to oxygen would not apply to elements that are not bivalent (and thus would require a more detailed analysis).

DH298(XO–H) X–O–H

X–O• + H•

DH298(X–OH)

DH298(X–O)

DH298(O–H) X• + •O–H

X• + O• + H• Scheme 1

We observed earlier (Figure 4) that the bond dissociation enthalpies of X–O bonds are approximately proportional to the bond orders. Combining this result with scheme 1 suggests the approximation: DH298(XO–H) ≈ DH298(O–H) + EXO x [ BOXO(X–OH) – BOXO(X–O) ]. The results shown in Figure 5 indicate that this is indeed a very good approximation. It is not obvious that the parameter, EXO, should be independent of the identity of the group, X, but this is clearly the case, and is a consequence of the parallel displacement of the related pairs in Figure 4. One might have expected the O–H bond dissociation enthalpies to correlate with the O–H bond orders, but Scheme 1 15 ACS Paragon Plus Environment


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demonstrates that this is not correct. Variations in the O–H bond order must necessarily correlate with the change in the X–O bond order. Including both would double count this effect. The combination of Figure 3 with Figure 5 would seem to unambiguously show that the large variations in O–H bond dissociation enthalpies results from the highly variable effect that removing the hydrogen has on the remaining X–O bond, rather than the very limited variations in the O–H bonds themselves.

120 +

H N OH

HO 2

3

110 CH OH 3

100

(CH ) COH 3 3 OH FOH

90 HOOH (CH ) COOH

CH OH 3

3 3

80 H NOH 2

70

60

50 H COH 40 -0.4

-

2

-0.3

-0.2

-0.1

0

0.1

0.2

Bond Order (X-OH) - Bond Order (X-O)

Figure 5. The variation of O–H bond dissociation enthalpies with the change in the X–O Mulliken bond orders. Since the bond dissociation enthalpies have been found to be linearly dependent on both the spin densities at the O radical site and the change in bond order on going


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from XOH to XO, the latter two quantities must also be related. The relationship is quite good as may be seen from Figure 6

0.1 y = -0.49726 + 0.57302x R= 0.9933

0

-0.1

-0.2

-0.3

-0.4 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Spin density

.

Figure 6. The change in the XO bond order is proportional to the oxygen spin density in the XO radical

6. Summary The CBS-APNO bond dissociation energies are in very good agreement with the experimental data. The effect of substituents on the OH BDE is a consequence of conjugative interactions of the radical center with the substituent. Lone pairs on this group are particularly effective and the BDE decreases as the lone pair energy increases. 17 ACS Paragon Plus Environment


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The most effective substituent (C-) reduces the BDE of water (119 kcal/mol) to 50 kcal/mol. A hyperconjugative interaction with an adjacent CH bond is less effective, but serves to reduce the OH BDE by 14 kcal/mol on going from water to methanol. The BDE’s have been found to be linearly related to the spin density at the O radical center, and also to the change in X-O bond order in going from X-O-H to XO. The NH and CH BDE’s are also linearly correlated with the spin density at the radical center. The origin of the changes in BDE for these compounds is somewhat different than for the ROH series, and is the subject of a continuing investigation.

Calculations: All of the ab initio calculations, the Hirshfeld spin densities and Mulliken bond orders were carried out using Gaussian 09.26

Supporting Information Available: Tables of CBS-APNO calculated energies of parent compounds and the derived radicals. A summary of the Hirshfeld charges for the radicals. This material is available free of charge via the Internet at http://pubs.acs.org.


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101, 5900-5909. Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 2000, 112, 6532-6542. 3

4

The calculated energies are given in the Supporting Information. Ruscic, B.; Boggs, J. E.; Burcat, A.; Csaszar, A. G.; Demaison, J.; Janoschek, R.;

Martin, J. M. L.; Morton, M. L.; Rossi, M. J.; Stanton, J. F.; Szalay, P. G.; Westmoreland, P. R.; Zabel, F.; Berces, T. J. Phys. Chem. Ref. Data 2005, 34, 573-656. 5

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Berkowitz, J.; Dehmer, P. M.; Chupka, W. A. J. Chem. Phys. 1973, 59, 925.

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Karton, A.; Parthiban, S; Martin, J. M. L. J. Phys. Chem. A 2009, 113, 4802-4816

reported the W4 heats of formation for FOH and FO leading to BDE = 99.4. 8

Villano, S. M.; Eyet, N.; Wren, S. W.; Ellison, G. B.; Bierbaum, V. M.;

Lineberger, W. C. Eur. J. Mass Spectrom. 2010, 16, 255-269. 9

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10

Clifford, E. P.; Wenthold, P. G.; Gareyev, R.; Lineberger, W. C.; DePuy, C. H.;

Bierbaum, V. M.; Ellison, G. B. J. Chem. Phys. 1998, 109, 10293-10310. 11

Nix, M. G. D.; Devine, A. L.; Cronin, B.; Dixon, R. N.; Ashfold, M. N. R. J.

Chem. Phys. 2006, 125, 133318. 12

The bond energies of methylamine and dimethylamine can be deduced by the use

of the acidity/EA thermochemical1 cycle: DH298(R2NH) = ∆acidH298(R2N-H) +EA(R2N) – IE(H). The gas phase acidities of CH3NH2 and (CH3)2NH have been measured (Mackay, G. I.; Hemsworth, R. S.; Bohme, D. K. Can. J. Chem. 1976, 54, 1624-1642 ∆acidH298(CH3NH2 = 403.2±0.8 kcal/mol; ∆acidH298((CH3)2N-H = 396.4±0.9 kcal/mol) The electron affinities of the methylamino radicals have only recently been measured (Radisic, D.; Xu, S. J.; Bowen, K. H. Chem. Phys. Lett. 2002, 354, 9-13. EA(CH3NH) = 0.432±0.015 eV; EA((CH3)2N) = 0.504±0.030 eV) Application of the acidity/EA cycle to methylamine and dimethylamine leads to the bond energies listed in Table 1.. 13

Seakins, P. W.; Pilling, M. J.; Niiranen, J. T.; Gutman, D.; Krasnoperov, L. N. J.

Phys. Chem. 1992, 96, 9847-9855. 14

Yarkony, D. R.; Schaefer, H. F. III; Rothenberg, S J. Am. Chem. Soc. 1974, 96,

656-659. 15

Höper, U.; Botschwina, P.; Köppel, H. J. Chem. Phys. 2000, 112, 4132-4142 and

references therein. Nee, M. J.; Osterwalder, A.; Zhou, J.; Neumark, D. M J. Chem. Phys. 2006, 125, Article no. 014306 16

Page, M.; Lin, M. C.; He, Y.; Choudhury, T. K. J. Chem. Phys. 1989, 93, 4404-

4408.


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17

Endo, Y.; Saito, S.; Hirota, E. J. Chem. Phys. 1984, 81, 122-125.

18

The APNO calculated protonation enthalpies are: FOH, -114.6; H2O2, -156.5;

NH2OH, -192.5 kcal/mol. 19

Cf. Wiberg, K. B.; Rablen, P. R. J. Comput. Chem 1993, 14, 1504-1508 for a

comparison of “atomic charges” obtained using different methods 20

Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735-746.

21

Bader, R. F. W. “Atoms in Molecules, A Quantum Theory” Oxford University

Press, Oxford 1990. 22

Hirshfeld, F. L. Theor. Chim. Acta 1977, 44, 129-138. Nalewajski, R. F.; Parr, R.

G. Proc. Natl. Acad. Sci. 2000, 97, 8879-8882. Parr, R. G.; Ayers, P. W.; Nalewajski, R. F. J. Phys. Chem. A, 2005, 109, 3957-3959. 23

Mulliken, R. S J. Chem. Phys. 1955, 23, 1833-1840.

24

Montgomery, J. A.. Jr; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem.

Phys. 2000, 112, 6532-6542. 25

Barnes, E. C.; Petersson, G. A.; Frisch, M. J.; Montgomery, J. A. Jr.; Martin, J. J.

Chem. Theory and Comp. 2009, 5, 2687-2693. 26

Gaussian 09, Revision C.01 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.;

Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et. al. Gaussian, Inc. Wallingford, CT 2009



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TOC Graphic:

Delocalized lone pair of the H2NO radical


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