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Methoxymethane C-O Bond Stengths: Do Their Changes Result from Hyperconjugation or Polar Effects? Kenneth B Wiberg, and Paul R. Rablen J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03923 • Publication Date (Web): 21 Jun 2018 Downloaded from http://pubs.acs.org on June 23, 2018

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The Journal of Physical Chemistry

Methoxymethane C-O Bond Strengths: Do Their Changes Result from Hyperconjugation or Polar Effects?

Kenneth B. Wiberg and Paul R. Rablen Department of Chemistry, Yale University, New Haven, Connecticut 06520 Department of Chemistry, Swarthmore College, Swarthmore, PA 19081

Abstract. The methoxymethanes have been studied and compared with the fluoromethanes. The energies and atomic charges were calculated using MP2/aug-cc-pVTZ and the group separation energies and bond dissociation enthalpies were calculated using CBS-QB3. The group separation energies are endothermic and the BDE increases with additional substitution as a result of the increase in charge at the central carbon. The greater charge leads to a stronger bond to the new substituent as well as to the original substituents. With the methoxymethanes there is a linear relationship between the BDE and the atomic charge at C. The energies of the several methoxymethane conformers were calculated, and their energies usually increase with increasing values of the electronic spatial extent in accord with a proposal by Gillespie. The role of hyperconjugation in these cases is not settled. 1.

Introduction The methoxymethanes with 1-4 methoxy groups have received considerable study.1,2

3

Their relative energies and structures have been the subject of a series of papers by Venkatesan, et. al. making use of matrix isolation and infrared spectroscopy supplemented by relatively low level ab initio calculations.

This includes dimethoxymethanes,4,5 dimethoxyethanes6 and

trimethoxymethanes.7 Structural information has also been obtained using electron diffraction8,9. The relative energies of these compounds are usually attributed to the anomeric effect,10 although 1 ACS Paragon Plus Environment

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Gillespie, Robinson, and Pilme have proposed an entirely different approach using ligand close packing.11 Since hyperconjugation has been suggested to be of importance with these compounds it seems appropriate to first take note of related compounds, the halomethanes, which also have received considerable study.12,13,14 It is well known that the strength of C-F bonds increase with increasing fluorine substitution, whereas this not the case with the chloromethanes. 2.

Fluoromethanes. Isodesmic group separation reactions are useful in examining the effect

of multiple substitutions on methane. The CBS-QB315 energies of reactions for fluoromethanes, chloromethanes and cyanomethanes are summarized in Table 1. The full data are available in the Supporting Information. Table 1. CBS-QB3 Calculated Isodesmic Reactions for Substituted Methanes, kcal/mol. Reaction

X=F

X = Cl

X = CN

CX4 + CH4 = HCX3 + CH3X

17.6

-2.0

-18.2

HCX3 + CH4 = H2CX2 + CH3X

19.6

0.5

-13.6

H2CX2 + CH4 = 2 CH3X

12.7

1.2

-7.7

CX4 + 3 CH4 = 4 CH3X

49.8

-0.2

-39.5

The fluoromethanes reactions are all endothermic indicating that the reactants are more stable than the product, showing that multiple fluorine substitution leads to stronger C-F bonds. In the case of chlorine as the substituent, the C-Cl bonds are essentially unaffected by multiple substitution, and with the cyanomethanes, the reaction energies are exothermic showing that increasing CN substitution leads to weaker C-CN bonds.

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The change in C-F bond strengths was studied by Salzner and Schleyer 16 who made use of an NBO analysis17 and proposed that it was due to hyperconjugation in which there is an interaction between a fluorine lone pair and the C-F* bond orbital of another fluorine as shown below in Figure 1.. The calculated stabilization energies were quite large, and for CF4 it was 188 kcal/mol. They recognized additional hyperconjugative interactions and concluded that CF4 has a total delocalization energy of 338 kcal/mol. In view of the much smaller energy changes on F substitution in Table 1, the estimate of the delocalization energy of CF4 must be overstated.

Figure 1. Example of a hyperconjugative interaction in carbon tetrafluoride Examples such as these in which two identical atoms are both donors and acceptors may need a more detailed study of how hyperconjugation operates in such cases This is especially true with CF4 where each F will serve both as a donor and acceptor for 3 other fluorines. As far as we are aware, there has not been a theoretical examination of this type of interaction. Such a study would be very valuable. In cases such as these, there are often both hyperconjugative and polar terms. As we shall show below, there is a dramatic increase in the positive charge at the central carbon with increasing F substitution. This in turn leads to a large decrease in C-F bond lengths, as the polar contribution to the bond is increased. There is no way in which hyperconjugation can lead to a large selective change in charge at the carbon of an F-C-F triad. Thus there must be significant polar contributions to the change in energy with increasing F substitution.



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Another way to gain information on the strength of bonds is to obtain the bond dissociation enthalpies of the above compounds. Table 2 gives the calculated BDE obtained by calculating the energies of the compound in question and of the radicals formed in the bond dissociation. These quantities were obtained using CBS-QB3. The calculated enthalpies are in good agreement with the available experimental results.18 Table 2. CBS-QB3 Calculated Bond Dissociation Enthalpies for Substituted Methanes, kcal/mol. compound C-F CF4

131.5

HCF3

128.5

H2CF2 H3CF CH4

C-H

compound C-Cl CCl4

71.8

107.4

HCCl3

76.9

121.0

102.4

H2CCl2

111.9

101.8

H3CCl

C-H

compound C-CN

C-H

C(CN)4

78.8

93.8

HC(CN)3

92.2

78.8

81.2

96.4

H2C(CN)2

106.7

87.5

85.4

99.9

H3CCN

123.6

96.1

105.3

Here, the BDE’s increase with increasing fluorine substitution, change very little on increasing chlorine substitution, and decrease with increasing cyano substitution. This matches was what seen in the Table 1 with the isodesmic reactions.. There is an attractive explanation for the changes in bond energies that appeals to fundamental physics and that does not require invoking orbital interactions.19 In our earlier study we made use of Bader’s Atoms in Molecules (AIM)20 method to study the C-F bonds in the fluoromethanes. Here, the volume associated with an atom is defined by a set of zero-flux surfaces (i.e. surfaces across which the derivative of the election density is zero). Each of these atomic volumes in a molecule obeys the virial theorem. It was found that the volume for each of the fluorines was essentially unchanged as the number of fluorines was increased and integration 4 ACS Paragon Plus Environment

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of the charge led to a marked increase in positive charge at the central carbon giving the result shown in Table 3. As the positive charge at carbon increases substantially as each new fluorine was introduced, it leads to a more polar and stronger bond to both the new fluorine and those already present.

This was possible because of the considerable difference in electronegativity

between carbon and fluorine.21 It seemed interesting to see how other population analyses would treat these compounds (Table 3). Although the numerical values are quite different, the large change in carbon charge is found with all of them. It was found that despite the differences in values, the different population analyses gave results that were linearly dependent: with NPA vs AIM, R=0.980 with NPA and Hirshfeld, R = 0.990; and with Hirshfeld vs AIM, R = 0.991 (see Supporting Information) Table 3. Atomic charges and C-F bond lengths, MP2/6-311+G* compound

AIM20

Hirshfeld22

NPA23

r(C-F)

C

F

C

F

C

F

CH3F

0.682

-0.706

0.0234

-0.1594

-0.0707

-0.3808

1.391Å

CH2F2

1.2817

-0.705

0.0633

-0.1515

0.4856

-0.3596

1.361Å

CH3F

2.776

-0.714

0.2714

-0.1117

0.9131

-0.3375

1.338Å

CF4

2.776

-0.698

0.3276

-0.0930

1.2667

-0.3167

1.323Å

The electronegativity of chlorine is much less than that of fluorine, and as a result the charge on carbon is not so much changed with increasing chlorine substitution, and the increase in BDE with increasing substitution is not found. The decrease in BDE with increasing Cl substitution is probably due to steric interactions between the large chlorine atoms. The Cl-C-Cl bond angle in



chloroform is 111.2° whereas that in fluoroform it is 108.5°. The small angle in the latter is due to the increase in p-character in the bonds to F.24 The bond dissociation enthalpies, besides being increased by more polar character in the bonds, may also be affected by stabilization of the resulting radical by delocalizing the odd spin into the C-X bonds. With the radicals, a Hirshfeld population analysis also gives the spin density at each of the atoms. The central carbons are of main interest here, and their spin densities are obtained. The calculated values are: CF3, 0.712; HCF2, 0.735, H2CF, 0.785. The values would be 1.0 if all of the odd electron remained on the carbon. The smaller values indicate that some of the spin is spread out over the other atoms, but the values are close to each other suggesting that this may not be a major factor in examining the difference in BDE’s. Salzner and Schleyer16 also considered the case of the cyanomethanes that led to the surprising conclusion that the central carbon of tetracyanomethane has a negative charge. We have used several population analyses for C(CN)4 with the following results for the central carbon: Hirshfeld, +0.128; Mulliken, +2.160; NPA, -0.386, and Petersson’s MBS15 that maps the results of a large basis set calculation onto a minimal basis set followed by a Mulliken analysis, +0.129. All except NPA give a positive charge, and so it is reasonable to conclude that it is indeed positive. We were primarily interested in gaining further information about the methoxymethanes. Fluorine substitution on methane leads to an increase in bond dissociation energies. Will the same be true for the methoxymethanes? In this connection it should be noted that Mo has carefully studied dimethoxy methane and related compounds via a valence-bond type of approach and concluded that hyperconjugative effects are not important.25 In the following discussion, we shall assume that this is correct 6 ACS Paragon Plus Environment

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2.

Results and Discussion

In order to calculate the group separation energies and the

bond dissociation enthalpies (BDE) we must first determine which conformer has the lowest energy. Therefore we have carried out higher level calculations for these compounds making use of both MP2/aug-cc-pVTZ and the very successful compound method CBS-QB3.15 The results of these calculations are summarized in Table 4. Only the ∆∆H values are given because some of the ∆∆G values appear unreliable, probably as a result of the many methyl rotors that are treated as librations. The structures of the compounds are shown in Figure 2. The details of these calculations may be found in the supporting Information. Table 4. Calculated relative energies, kcal/mole and the electronic spatial extent, R**2 compound

(MeO)2CH2

(MeO)3CH

(MeO)4C

conformer

MP2/aug-cc-pVTZ

CBS-QB3

∆∆H(298)

∆∆H(298)

R**2

g,g C2

0.00

0.00

471.1

g,t

2.68

2.54

518.3

t,t C2v

6.71

5.55

576.3

t,g,g

0.00

0.00

834.1

t,g+,g-

0.11

0.45

828.6

g,g,g C3

1.02

0.84

869.1

S4

0.00

0.00

1173.8

D2d

0.64

0.68

1160.0

The relative energies calculated using the two theoretical levels are fairly similar, and the CBSQB3 values are probably the more accurate.



2a.

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Dimethoxymethane. There are two relatively low energy conformers along with one

with significantly higher energy. Lower level calculations also find a g+g- conformer, but optimization at the CBS-QB3 level leads one of the g arrangement to transform into t giving g,t. . What is the origin of the differences in energy between conformers? It may be noted that the electronic spatial extent, that is part of the Gaussian output, increases with increasing energy. The Gillespie proposal would predict such a relationship.11 Another possibility is that there is some polar factor. This was examined by calculating the Hirshfeld charges for the two lower energy conformations and the values are given in Table 5 Table 5. Hirshfeld charges in the methoxymethanes

conformer CH3CH2OCH3

O1

C

H4

O5

g,t

-0.1726

0.0921

0.0205

-0.1767

g,g

-0.1794

0.0918

0.0354

-0.1794

change

0.0068

0.0003

-0.0149

0.0027

It may be noted that the change in oxygen electron populations has the same sign for both oxygens, and it is H4 that has the largest change in charge. H3 is unchanged. Most of the loss at H4 is derived from the change at the oxygens. The origin of the charge shifts is not clear, but


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they are not due to hyperconjugation in the usual sense since there is not charge transfer between the oxygens. 2b.

Methyl orthoformate. There are three conformers having relatively low energies. The

energies increase in accord with R**2 2c.

Methyl orthocarbonate (tetamethoxymethane) Here, there are two low energy

conformers, both having high symmetry. Knowing the lowest energy structures, it is possible to examine group separation reactions as was done for the halomethanes. The results are shown in Table 6. Table 6. Group separation enthalpies calculated using CBS-QB3 Reaction

∆H(298)

(MeO)4C + CH4 = (MeO)3CH + MeOMe

21.4

(MeO)3CH + CH4 = (MeO)2CH2 + MeOMe

17.6

(MeO)2CH2 + CH4 = 2 MeOMe

14.0

(MeO)4C + 3 CH4 = 4 MeOMe

52.9




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Figure 2. Structures of the methoxymethanes in order of increasing energies The result is similar to that of the fluoromethanes, with each reaction being endothermic, but it is surprising that they are larger than those for the fluoromethanes. There must be an extra source of stabilization for these compounds. The difference is probably the result of the methoxy group hydrogens that have a significant positive charge. Consider S4 tetramethoxymethane: in the CBS-QB3 structure there are 4 attractive non-bonded CH…O interactions with a distance of 2.508Å and 4 with a distance of 2.588 Å. It would be interesting to know the energy of these 8 CH…O interactions, but one cannot simply use Coulomb’s law to obtain them in a molecule because of the unknown influence of the other groups. The O-C-O bond angles do show some attractive forces. For S4 tetramethoxymethane they are 107.8° (4x) and 113.6° (2x). In methoxymethane it is 113.9°. 3. Bond Dissociation Enthalpies

It was also of interest to compare the BDE’s of the

methoxymethanes with those of the fluoromethanes. They were calculated using CBS-QB3 that is known to reproduce experimental BDE’s very satisfactorily. We also calculated the charge at the central carbons using the Hirshfeld method. The results are compared with those for the fluoromethanes in Table 7. As with the fluoromethanes, there is a large increase in charge at the central carbon, leading to stronger bonds to both the old and the new substituents. The effect is a little smaller with OMe substitution than with F because of the smaller electronegativity of O vs F. The details of these calculations may be found in the Supporting Information.



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Table 7. Calculated bond dissociation enthalpies and central carbon charges compound

X = OMe

X=F

∆H(298)

qC

∆H(298)

qC

XCH3

85.1a

-0.0073

111.9

0.0937

X2CH2

90.6

0.1200

121.0

0.1677

X3CH

95.1

0.1799

128.5

0.2788

X4C

100.2

0.2663

131.5

0.3836

a. MeOMe experimental BDE = 83.2±0.926 With the methoxymethanes, there is a linear relationship between the BDE and the charge at the central carbon as can be seen in Figure 3. The same trend is seen with the fluoromethanes, although it is not quite so linear.

y = 84.979 + 55.613x R= 0.99367

100

95

90

85

-0.05

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0.05

0.1

0.15

0.2

charge on carbon

0.25

0.3

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Figure 3. Correlation between the BDE ‘s and the calculated Hirshfeld charges at the central carbons of the methoxymethanes.

3. Conclusions

Hyperconjugation requires a donor and an acceptor. In most cases, this is easily

observed, but when the compound has A-B-A groups in which there are two identical groups A and A, it is not so clear how to calculate the hyperconjugative interaction. If the A groups have greater electronegativity than B, the charge at B will be depleted, but hyperconjugation cannot lead to this change Thus, there also must be polar effects.. . A major factor controlling the group separation enthalpies and the bond dissociation enthalpies for the fluoromethanes is the large increase in positive charge at the central carbon as the number of substituents is increased. This leads to more polar, stronger and shorter C-F bonds. It is what one might call a cooperative electrostatic effect. The same is true, but to a smaller extent, with MeO substitution as a result of the smaller electronegativity of oxygen with respect to fluorine. As a final note related to hyperconjugation, we may consider methylamine. It has a lone pair on N that can act as a donor, and there is a C-H* bond that could be the accepter. The MP2/aug-cc-pVTZ rotational barrier of methylamine is only 2.1 kcal/mol, about 2/3 that of the ethane rotational barrier,27 corresponding to the number of hydrogens at nitrogen vs carbon. The rotational barrier for ethane involves the repulsion between the C-H bonds and leads to a slightly larger C-C bond length for the eclipsed form.28 The main structural change on rotation of methylamine is a small increase in C-N bond length, just as found with ethane. 13 ACS Paragon Plus Environment

Here, the


difference in energy between the nitrogen lone pair and the C-H* orbital is too great to allow a significant hyperconjugative stabilization. A comparison with fluoromethylamine provides a contrast. The C-F* bond orbital will be a good acceptor, and as a result a hyperconjugative interaction involving the N lone pair leads to a larger rotational barrier, 8.99 kcal/mol (see Supporting Information), and a shift of charge of 0.045e from nitrogen to fluorine in going from the TS to the GS. Hyperconjugation is an important concept, but its effects are most clearly important when there is both a good donor and a good acceptor, and when the two are different, so that a significant net redistribution of charge takes place. The importance of hyperconjugation in "symmetrical" cases, in which the same or very similar groups serve as both donor and acceptor, has often been overestimated in the literature, and the importance of simple electrostatic considerations has been underestimated.

Calculations. All calculations were carried out using Gaussian-1629 Supporting Information Tables of calculated atomic coordinates and energy changes, plots showing the relationship among the population analyses. This information is available free of charge at the ACS Publications website. Author Informaton Corresponding Authors *E-mail; [email protected] *E-mail: [email protected] Present Address 14 ACS Paragon Plus Environment

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(KBW) 865 Central Ave. Apt A404, Needham, MA 02492. Notes The authors declare no competing financial interest

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