Direct Evaluation of the Hyperconjugative Interactions in 1,1,1

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Direct Evaluation of the Hyperconjugative Interactions in 1,1,1-Trihaloethane (CHCX, X = F, Cl and Br) 3

3

Zhenhua Chen, Clémence Corminboeuf, and Yirong Mo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp403587s • Publication Date (Web): 16 Sep 2013 Downloaded from http://pubs.acs.org on September 23, 2013

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The Journal of Physical Chemistry

Direct Evaluation of the Hyperconjugative Interactions in 1,1,1-Trihaloethane (CH3CX3, X = F, Cl and Br) Zhenhua Chen1, Clemence Corminboeuf2,*, and Yirong Mo1,* 1

Department of Chemistry, Western Michigan University, Kalamazoo, Michigan 49008, USA

2

Laboratory for Computational Molecular Design, Institut des Sciences et Ingénierie Chimiques,

Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

* Corresponding authors: Yirong Mo Western Michigan University Phone: +1-269-387-2916 E-mail: [email protected]

Clemence Corminboeuf Ecole Polytechnique Fédérale de Lausanne Phone: +41 (0)21 693 93 57 E-mail: [email protected]

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ABSTRACT Following the computational strategy proposed by Mulliken in 1939 (J. Chem. Phys. 7 (5), 339-352 (1939)) when the concept of hyperconjugation was coined, we evaluated the hyperconjugative stabilization energy in 1,1,1-trihaloethane using the block-localized wavefunction (BLW) method. The BLW method is the simplest and most efficient variant of ab initio valence bond (VB) theory, and can derive the strictly electron-localized state wavefunction self-consistently. The latter serves as a reference for the quantification of the electron delocalization effect in terms of the resonance theory. Computations show that the overall hyperconjugative interactions in 1,1,1-trihaloethane, dominated by contribution from

with minor

, ranges from 9.59 to 7.25 kcal/mol in the staggered structures and

decreases in the order Br > Cl > F. This is in accord with the 1H NMR spectra of CH3CX3. Notably, the hyperconjugation effect accounts for 35-40% of the rotation barriers in these molecules, which are dominated by the conventional steric repulsion. This is consistent with the recent findings with 1,2-difluoroethane (Freitas, Bühl and O’Hagan, Chem. Comm. 48, 24332435 (2012)) that the variation of 1JCF with the FCCF torsional angle cannot be well explained by the hyperconjugation model.

Keywords Hyperconjugation; Steric repulsion; Trihaloethane; Valence bond (VB) theory; Block-localized wavefunction (BLW)


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INTRODUCTION The term hyperconjugation was coined in 1939 by Mulliken in the explanation of the spectra of conjugated molecules,1 and generally refers to the orbital interaction between an occupied σ bond (

) and an adjacent virtual π or σ anti-bond (

), which leads to a

delocalized molecular orbital (MO)2-3 (1) and the stabilization of the system, as generally shown in Fig. 1a. The hyperconjugation effect can be probed experimentally via infra-red spectra and nuclear magnetic resonance and plays an important role in conformational preferences.4-6 For instance, there is a general belief that the high electronegativity of fluorine results in a highly polarized C-F bond and a low energy antibond

.7 Subsequently, the

hyperconjugative interaction is strong and governs

the conformational preferences of molecules like 1,2-difluoroethane which prefers a gauche conformation over the anti conformation. However, we note that recent study of the 1JCF coupling constant in 1,2-difluoroethane showed that the variation of 1JCF with the FCCF torsional angle cannot be explained by the hyperconjugation model.8 To probe the exact role of hyperconjugation in conformational preferences and molecular reactivity, it is pivotal to develop computational approaches to derive the hyperconjugation energy, which is not an experimental observable and thus whose quantification is often controversial, as evidenced by the recent debate over the role of hyperconjugation effect in the ethane rotation barrier.9-14 This is due to the fact that on one hand, delocalized MOs such as

in Eq. 1 are linear combinations of atomic

orbitals (LCAO) and can be optimized self-consistently, but on the other hand, there are few methods which can generate optimal localized orbitals such as energy is dependent on both

and

. Since the hyperconjugation

, it is essential to get both of them optimized at the very

same theoretical level. The non-optimization of

would lead to the increasing of its orbital

energy and consequently the overestimation of the hyperconjugation energy. For certain molecules of high symmetries, fortunately, there are stringent solutions to the computation of hyperconjugation energy, which can be served as benchmarks. Significantly, in the introduction of the hyperconjugation concept, Mulliken particularly laid out a computational 3 ACS Paragon Plus Environment


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strategy for the hyperconjugative interactions in ethane.1 He perceived that “hyperconjugation in ethane involves interaction among eight electrons which in the absence of any conjugation may be assigned to two sets of “[πe]” C-H bonding MO’s, one set localized in each CH3 group”. In other words, the degenerate e-symmetric orbitals are responsible for the hyperconjugation contribution to the ethane rotation barrier, as the rest electrons occupy the fully symmetric orbitals and thus are unaffected by the rotation. In the absence of any hyperconjugation, each set of e orbitals with four electrons are localized on one methyl group. The key now lies in the optimization of these localized e orbitals together with the delocalized a orbitals, as shown in Fig. 2.

ϕ kl*

* σCH σCX

H

C

ϕ ij

* σCH σCX

H

C

C

X

C

X

ϕ ij'

(a)

(b)

(c)

Fig. 1. (a) General description of the hyperconjugative interaction; (b) Hyperconjugative interaction in the staggered structure of trihaloethanes; (c) Hyperconjugative interaction in the eclipsed structure of trihaloethanes.

H

H C

H

C

C H

H H

H

H

degenerate e orbitals

H a orbital

Fig. 2. Schematic diagram of a- and e-symmetric group orbitals of the methyl group. With the block-localized wavefunction (BLW),15-16 which is the simplest and most efficient ab initio valence bond (VB) method,17-21 we realized Mulliken’s proposal and computed the hyperconjugation energy in the staggered (7.3 kcal/mol) and eclipsed (6.6 kcal/mol) structures of ethane. In other words, the hyperconjugation effect contributes only about 0.7 kcal/mol to the


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ethane rotational barrier (3 kcal/mol) which is consequently dominated by the conventional steric effect.13 Since the magnitude of the hyperconjugation is closely related to the energy gap between the localized occupied and virtual orbitals as well as their overlap, it would be of significance to quantitatively examine the hyperconjugation between C-H and C-X bonds where X evolves from H to Br to Cl to F, with electronegativity increasing from 2.20, 2.96, 3.16 to 3.98 based on the Pauling scale.22 Here we studied the series of trihaloethanes CH3CX3 (X = F, Cl, Br and H) using the Mulliken strategy and compared the hyperconjugation effect therein, with the reference to the ethane molecule.

COMPUTATIONAL DETAILS With the C3v point group for both staggered and eclipsed structures (see Fig. 1b and 1c), irreducible bases are of either a or e symmetries (see Fig. 2). We first build the irreducible bases for the CH3 and CX3 functional groups separately. Afterwards, we get an electron-localized state by defining a BLW as 4 ΨL = Aˆ ( a m eCH en ) 3 CX 3

(2)

where am represents a direct product of a-symmetric delocalized orbitals occupied by m electrons, 4 refers to e-symmetric group-localized orbitals confined to the methyl group with 4 electrons, eCH 3

n is a product of e-symmetric group-localized orbitals confined to CX3 with n electrons (n and eXH 3

= 4, 20, 36 and 72 for H, F, Cl and Br, respectively, and can be derived from the CX3 fragmental orbital energies). Note that in the above function, there is no intramolecular electron transfer (delocalization) from occupied group-localized orbitals in one group to vicinal unoccupied * * group-localized orbitals in another group (i.e., σ CH → σ CX and σ CX → σ CH ), while steric effect,

which generally comprises the classical electrostatic term and the quantum mechanical Pauli exchange repulsion between the CH3 and CX3 groups, retains. If we allow the full electron delocalization between the CH3 and CX3 groups as in the conventional MO theory, we get the regular Hartree-Fock wavefunction as ΨD = Aˆ ( a m e 4+ n )

(3)

where e orbitals are canonical MOs expanded over the entire system or more specifically,



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combinations of eCH and eCX . It should be pointed out that in the BLW computation, ΦL is 3

3

optimized variationally like ΨD. The energy difference between the delocalized and localized states reflects the hyperconjugative stabilization

E hc = E ( ΨD ) − E ( ΨL )

(4)

We note that the BLW method (Eq. 2) is similar to previous practices by imposing constraints in order to derive the wavefunction for an electron-localized state.23-29 Here the strictly localized orbitals are non-orthogonal, as it is the physical law in quantum mechanics that bonding interaction originates from the overlap of interacting orbitals. The nonorthogonality also plays a central role in ab initio VB theory. In addition, the hyperconjugation energy is not computed with the two interacting orbitals as in perturbation theory with orthogonal MOs. Rather, the hyperconjugation energy arises from the difference between diabatic (ΨL) and adiabatic (ΨD) state wavefunctions. Since there is no intramolecular electron delocalization in the electron-localized Lewis state as defined by the BLW method, only the steric effect, which is a combination of Pauli repulsion and electrostatic interactions, dominates. Certainly any computational method must be critically examined by viable experimental evidences. The reliability of the BLW method is well documented by its computed structural parameters, vibrational frequencies, and NMR data which are consistent with experimental proofs.30-33

RESULTS AND DISCUSSION We first performed geometry optimizations at the MP2/6-311+G(d,p) theoretical level, followed by BLW computations. CH3CI3 was not considered in this work due to the unavailability of the 6-311+G(d,p) basis set for iodine and the relativistic effects. The major structural change along the rotation of the methyl group in CH3CX3 are the C-C and C-H bond distances, which are compiled in Table 1, together with the C-H symmetrical stretching frequencies. The frequencies have been scaled by a factor of 0.9513 as suggested by Merrick, Moran and Radom for this level of computations.34 In all species, the staggered structure exhibits a shorter C-C distance than the eclipsed structure, while the C-C bond lengthens in the order of X = F < Cl < Br < H. The very same order is observed for the C-H bond distances as well, though the magnitude of variations is much smaller. All these structural changes are in accord with the hyperconjugation explanation. An interesting finding is the variation of the C-H vibrational


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frequency. According to the hyperconjugation model, the

interaction increases with

the increasing electronegativity of X, accompanied by the lengthening of the C-H bond and the decreasing C-H stretching frequency, due to the polarization of the

anti-bond orbital. But

both computational and experimental data show that the C-H stretching vibrational frequency increases, rather than decreases, in the order of X = Br < Cl < F. Since 1,1,1-trihaloethanes exists as liquid while ethane is a gas at ambient condition, the experimental data for 1,1,1trihaloethanes and ethane seem not directly comparable. Based on our computations where all species are in gas phase, the C-H frequency order is X = H < Br < Cl < F. This highlights that the hyperconjugation is not dependent on the overlap between

and

alone. It is also related to

their energy gap (see Fig. 1a). The increasing electronegativity lowers the energy level of the CX bond orbital but oppositely pushes up the energy level of its anti-bond orbital

,

consequently diminishes the hyperconjugative interactions. Previous NBO computations also interaction decreases in the order X = Br > Cl > F > H.3 For the same

shows that the

species of CH3CX3, however, as expected the C-H frequency in staggered structure is always a few wavenumbers higher than in eclipsed structure. Table 1. Carbon-carbon distances (Å) and CH3 symmetrical stretching frequencies (cm-1) and hyperconjugation energies (Ehc, kcal/mol) in staggered (s) and eclipsed (e) ethane and 1,1,1trihaloethane in comparison to experimental values X

RCC(s) RCC(e)

RCH(s) RCH(e)

F

1.499

1.099

1.514

1.089

νCH(s)

νCH(e)

νCH(exptl)

2968

2963

297035

7.25

5.90

35

9.23

7.31

Εhc(s) Ehc(e)

Cl

1.514

1.539

1.091

1.090

2960

2945

2943

Br

1.519

1.543

1.092

1.090

2954

2935

293835

9.59

7.74

H

1.529

1.542

1.093

1.092

2937

2929

295436

7.37

6.62

The energetic impact of the hyperconjugation effect can be evaluated by Eq. 4. Table 1 listed the hyperconjugation stabilization energies in the staggered and eclipsed structures of CH3CX3. Computational results show that there is stronger hyperconjugative interaction in the staggered structure than in the eclipsed structure due to the better overlap between the orbitals and the

bond

anti-bond orbitals in the staggered structure. However, the overall 7 ACS Paragon Plus Environment


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hyperconjugation energy increases in the order of F < H < Cl < Br. We note here that Eq. 4 accounts all

and

interactions. For ethane, the

strength thus should be halved. For the others, the the

interaction

interaction is much stronger than

interaction which increases in the order X = H < F < Cl < Br based on their

electronegativities and NBO computations.3 This can be proved by the 1H NMR spectra of CH3CX3 determined experimentally. For X=H, F and Cl, the experimental chemical shifts are 0.86, 1.87 and 2.75, respectively.37-39 Computationally, we can “visualize” the electron transfer with the electron density difference (EDD) map between the delocalized state ( ΨD in Eq. 3) and the localized state ( ΨL in Eq. 2), as shown in Fig. 3, where the red/blue color refers to the increase/decrease of the electron density. Fig. 3 shows that on one hand the electron density moves from the methyl group to the C-C region, leading to the significant enhancement of the CC bond. On the other hand, the CF3 group has little change while the CCl3 group loses a little electron density with more from the CBr3 group in staggered structures. But in the eclipsed structures, there is no electron density loss from the CX3 (X = F, Cl, Br) groups.

(1a)

(1b)

(2a)

(2b)


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(3a)

(3b)

(4a)

(4b)

Fig. 3. The electron density difference (EDD) maps showing the electron delocalization between CH3 and CX3 groups which strengthens the central C-C bond in (a) staggered structures and (b) eclipsed structures (1-4 refer to F, Cl, Br and H, with isodensity value 0.001 a.u.).

The MP2 energy difference between the staggered (s) and eclipsed (e) structures can be further decomposed into three components, namely steric effect (∆Es), hyperconjugation effect (∆Ehc), and electron correlation (∆Ecorr) as ∆EMP2

= E(e,MP2) – E(s,MP2) = E(e,HF) – E(s,HF) + ∆Ecorr = E(e,BLW) – E(s,BLW) + ∆Ehc + ∆Ecorr = ∆Es + ∆Ehc + ∆Ecorr

(5)

Fig. 4 shows the energy components for the systems studied in this work at the MP2 level. The electron correlation plays a negligible role in both 1,1,1-trifluoroethane and ethane, but slightly favors the eclipsed (crowded) structures of 1,1,1-trichloroethane and 1,1,1tribromoethane, partially due to the dispersion effect. It is interesting to observe that the conventional steric effect dominates the energy differences (rotation barriers) in all species, but



the hyperconjugation effect plays a secondary yet important role, and contributes to the rotation barrier from 24% in ethane to 40% in 1,1,1-trifluoroethane.

8

∆Es b ∆E hc a

Energy (kcal/mol)

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6

c

4

∆Ecorr

2 0 -2

X=F 1

Cl 2

Br 3

H 4

Fig. 4. BLW energy decomposition analyses for the rotation barriers in CH3CX3 (X=F, Cl, Br, H).

Conclusion In summary, the hyperconjugative interaction in 1,1,1-trihaloethane, largely from with minor contribution from

, decreases in the order Br > Cl > F and rangs

from 9.59 to 7.25 kcal/mol in the staggered structures. The hyperconjugation effect is weakened in the eclipsed structures due to the reduced overlap between

and

, and thus accounts for

35-40% of the rotation barriers which are dominated by the conventional steric effect. This is consistent with both the 1H NMR spectra of CH3CX337-39 and the NMR experiment with 1,2difluoroethane8 showing that the variation of 1JCF with the FCCF torsional angle cannot be well explained by the hyperconjugation model.

ACKNOWLEDGEMENTS We thank US National Science Foundation under the grants CHE-1055310 and CNS-1126438 (YM) and the Sandoz family foundation, the Swiss NSF grant (200021_121577/1) and EPFL (CC) for financial support.

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Table of Contents graphic

σ*CF C

σCH

H

C

F


Direct Evaluation of the Hyperconjugative Interactions in 1,1,1

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