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Relationship between Rotational Barriers and Charge Shifts Kenneth B Wiberg J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.9b01526 • Publication Date (Web): 29 Jul 2019 Downloaded from pubs.acs.org on July 30, 2019
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The Journal of Organic Chemistry
. 7/26/19 Relationship between Rotational Barriers and Charge Shifts Kenneth B. Wiberg Department of Chemistry, Yale University, New Haven, Connecticut, 06520
Me2N-CH=CH-X, MP2/aug-cc-pVTZ 12 y = 2.0079 + 62.572x R= 0.99706
NO2
11 CN
10 9 8 7 H 6 Cl Me
5 F 4 0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
charge shift
ABSTRACT Conjugation and hyperconjugation are closely related stereoelectronic effects that are usually discussed in a qualitative fashion. It is possible to make it more quantitative. The NBO method provides a means of estimating the energetic consequence. They may also be studied by a charge shift analysis. Rotational barriers are often appropriately discussed in terms of such effects where the rotational transition state has broken the interaction between donor and acceptor atoms or groups. A comparison of charge distribution between the ground state and the transition state will show how much charge transfer occurs, and if any other atoms are involved. This has been studied for substituted vinyl methyl ethers, substituted N,N-dimethylvinylamines, p-substituted anilines and some esters and amides. Linear relationships were found for the rotational barriers vs 1 ACS Paragon Plus Environment
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. the charge shifts. For some compounds the σ and π components of the charge were obtained and showed that competition for σ-charge can lead to changes in the π-charge. Cases where there cannot be charge transfer are also discussed. 1. INTRODUCTION
π-Electron conjugation such as found in amide “resonance” has been
studied for many years.1 Hyperconjugation was first proposed by Mulliken in a 1939 study of the effect of alkyl substitution on the electronic transitions of alkenes and dienes.2 He wrote: “This mild sort of conjugation apparently not recognized as such hitherto, between saturated groups and double or triple bond or even saturated groups.” Both conjugation and hyperconjugation have received wide application. It often involves a lone pair or a C-X bond as a donor and an excited state of a bond such as C=C or C=O as an acceptor. In many cases there is no clear distinction between conjugation and hyperconjugation. Although widely applied,3 these effects are usually discussed in a qualitative manner. They can be made more quantitative by using NBO to estimate the energetic consequences.4 Since they often involve a donor and an acceptor, there should be some charge transfer. This can be studied by calculating the atomic charges using the Hirshfeld method.5 These charges have been found to be the only one of the commonly available atomic charges that is in accord with a variety of experimental data.6 They are obtained from the calculated density matrix by a simple procedure and as a result they closely approximate the electron density distribution.5,7 As part of a recent study,8 we examined the charge transfer that occurred during bond rotation that would disrupt hyperconjugation, and the energy barrier to such rotation, making use of MP2/6-311+G* calculations and the shift in the Hirshfeld atomic charges. The examples were propene (2.0 kcal/mol barrier, 0.0013e charge shift), fluoromethylamine (8 kcal/mol. 0.040 e) and formamide (18.25 kcal/mol, 0.115 e). The first two would be described as hyperconjugation and 2 ACS Paragon Plus Environment
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The Journal of Organic Chemistry
. the latter would be considered conjugation. It is interesting to note that these quantities are found to be linearly related (Figure 1). Further examples have now been studied in order to see if this might be generally true.
20 y = 0.76754 + 154.45x R= 0.99335
15
10
5
0 0
0.02
0.04
0.06
0.08
0.1
0.12
charge shift Figure 1. Relation between charge transfer and rotational barriers, MP2/6-311+G*
2. N,N-DIMETHYLVINYLAMINE This amine should have a larger rotational barrier than found with propene because the N lone pair should be a better donor than a C-H bond. The barrier was calculated at the MP2/aug-cc-pVTZ level and was found to be 6.50 kcal/mol as compared to 2.0 kcal/mol for propene.
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. The conventional approach for these compounds is to recognize that the lone pair electrons on nitrogen can interact with the pi*(C=C) orbital of the alkene to transfer some π density to the carbons. With a negative charge at the carbons, one might expect that electronegative atoms or groups such as F, Cl and CN might stabilize the ground state, leading to a larger rotational barrier. The trans-substituted compounds were initially studied at the MP2/6-311+G* level, and the energies are summarized in the Supporting Information. In order to be sure that the results are adequate for the present purpose, they were reoptimized at the MP2/aug-cc-pVTZ level and the Hirshfeld populations were obtained. In the case of the transition states, the optimizations were started using the vibrational frequencies obtained using MP2/6-311+G*. These data are summarized in Table 1. The charge shift is the change in the charge of the atoms of the Me2N group on going from the transition state to the ground state and the charge transferred to the substituent is given in the last column. The full data may be found in the Supporting Information. The relationship between the rotational barriers and the charge shift is shown in Figure 2. It might be noted that the values in the last two columns of Table 1 are linearly related (R =0.963). Table 1 Calculated MP2/aug-cc-pBVTZ energies and Hirshfeld charge shifts for N-C bond rotation in trans Me2N-CH=CH-X. X
ΔEa
charge shift
charge to X
H
6.50
0.0798
-0.0133
Me
5.13
0.0523
-0.0153
F
4.56
0.0345
-0.0075
Cl
5.47
0.0575
-0.0173
CN
10.12
0.1288
-0.0532
NO2
11.96
0.1576
-0.0770
a. Energy relative to the ground state
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The Journal of Organic Chemistry
.
Me2N-CH=CH-X, MP2/aug-cc-pVTZ 12 y = 2.0079 + 62.572x R= 0.99706
NO2
11 CN
10 9 8 7 H 6 Cl Me
5 F 4 0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
charge shift
Figure 2 Correlation between rotational barrier and the charge shift. The Figure shows a remarkably good linear correlation and reinforces the idea that rotational barriers are directly related to charge shifts from the Me2N groups. This charge will be distributed between the C=C double bond and the substituent. The right hand column of Table 1 shows the charge that was transferred to the substituent. The order of the substituents in Figure 2, F
