An Interacting Quantum Atoms (IQA) - ACS Publications - American

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Article Cite This: J. Phys. Chem. A 2018, 122, 1439−1450

pubs.acs.org/JPCA

Fluorine Gauche Effect Explained by Electrostatic Polarization Instead of Hyperconjugation: An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study Published as part of The Journal of Physical Chemistry virtual special issue “Manuel Yáñez and Otilia Mó Festschrift”. Joseph C. R. Thacker†,‡ and Paul L. A. Popelier*,†,‡ †

Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain

‡

S Supporting Information *

ABSTRACT: We present an interacting quantum atoms (IQA) study of the gauche effect by comparing 1,2-difluoroethane, 1,2-dichloroethane, and three conformers of 1,2,3,4,5,6-hexafluorocyclohexane. In the 1,2-difluoroethane, the gauche effect is observed in that the gauche conformation is more stable than the anti, whereas in 1,2-dichloroethane the opposite is true. The analysis performed here is exhaustive and unbiased thanks to using the recently introduced relative energy gradient (REG) method [Thacker, J. C. R.; Popelier, P. L. A. Theor. Chem. Acc. 2017, 136, 86], as implemented in the in-house program ANANKE. We challenge the common explanation that hyperconjugation is responsible for the gauche stability in 1,2-difluoroethane and instead present electrostatics as the cause of gauche stability. Our explanation of the gauche effect is also is seen in other molecules displaying local gauche conformations, such as the recently synthesized “all-cis” hexafluorocyclohexane and its conformers where all the fluorine atoms are in the equatorial positions. Using our extension of the traditional IQA methodology that allows for the partitioning of electrostatic terms into polarization and charge transfer, we propose that the cause of gauche stability is 1,3 C···F electrostatic polarization interactions. In other words, if a number of fluorine atoms are aligned, then the stability due to polarization of nearby carbon atoms is increased. Since these initial findings, the gauche effect has been defined by IUPAC as follows: 1. The stabilization of the gauche (synclinal) conformation in a two-carbon unit bonded vicinally to electronegative elements, e.g., 1,2-difluoroethane. 2. The destabilization of the gauche (synclinal) conformation in a two-carbon unit bonded vicinally to large, soft and polarizable elements such as sulfur and bromine. A recent review5 of the fluorine gauche effect discussed the importance of the gauche effect as a conformational control strategy. The review highlights its importance in the construction of functional small molecules, which are in turn particularly important for drug design and enantioselective catalysis. Recently the gauche effect was used to facilitate acyclic conformational control in iminium systems.6 This work was done in an effort to emulate enzyme catalysis using small molecules. It is postulated that small molecules can be used as efficient catalysts if they can display the same dynamic conformational changes that occur in enzymes upon substrate

1. INTRODUCTION 1

The gauche effect was coined by Wolfe in a paper that observed the stability of the gauche conformation in X−CH2− CH2−X when the electronegativity of the substituent (X) increases. Wolfe partially attributed this phenomenon to “size” or “steric” factors of the substituent atoms. He also stated “the importance of the gauche effect becomes less as the distance between the interacting ligands [X] increases” and that this observation displayed a “subtle balance between attractive and repulsive interactions”. In fact, prior to Wolfe’s work, the gauche effect was already observed in 1960 by Klaboe and Nielsen2 who studied 1,2-difluoroethane using infrared and Raman spectroscopy at variable temperatures. They concluded that the anti and gauche conformations were of comparable stability. In 1973, Van Schaick et al.3 showed, using electron diffraction in the gas phase, that the preferred conformation of 1,2difluoroethane was gauche. This finding corroborated the 1971 microwave spectroscopy results of Butcher et al.4 who had shown the dihedral angle in 1,2-difluoroethane to be ϕFCCF = 73 ± 4°. Despite being a well-acknowledged chemical phenomenon, there was still no conclusive explanation as to what causes the gauche effect in substituted ethanes. © 2018 American Chemical Society

Received: December 1, 2017 Revised: January 12, 2018 Published: January 30, 2018 1439

DOI: 10.1021/acs.jpca.7b11881 J. Phys. Chem. A 2018, 122, 1439−1450

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The Journal of Physical Chemistry A binding. The gauche ef fect allows for control of the configuration of a small molecule and is therefore used to emulate conformations in enzymes. Goodman et al.7 provided evidence through a natural bond order (NBO)8 analysis that the preference for the gauche conformation in 1,2-difluoroethane is due to the “vicinal hyperconjugative interaction between anti C−H bonds and C− F* antibonds”. They also stated that “the cis C−H/C−F* interactions are substantial”. Within the same paper they showed moreover that stabilization due to so-called “bent bonds” (as proposed by Wiberg et al.9,10) is minimal and does not contribute with any significance to gauche conformation stability. Despite the popularity of hyperconjugation as an explanation for the gauche effect, Goodman et al. stated in their paper that their results were inconclusive and that electrostatics had not been “logically eliminated” as an explanation for gauche stability. The inconclusive nature of those results calls for an exhaustive analysis using an energy partitioning method called interacting quantum atoms (IQA),11 which was inspired by earlier work12 carried out in 2001 introducing the topological atoms of the quantum theory of atoms in molecules (QTAIM).13−16 As an orbital-free and parameter-free energy partitioning scheme, IQA allows for each type of energy contribution (kinetic, exchange−correlation, and electrostatics) of a system to be calculated in a well-defined manner. Admittedly, at a practical level, QTAIM brings in a numerical error caused by the quadrature executing the integration over the volumes of the topological atoms. However, this error is of the order of 1 kJ mol−1 such that the sum of all energy contributions recovers to a sufficient degree the total energy of the wave function. The well-separated nature of the various IQA energy contributions is an asset compared to the state-ofaffairs in the NBO approach. This advantage makes it possible to study the electrostatic, exchange, correlation,17,18 and even kinetic energy terms on an equal footing. In contrast, the NBO approach is unable to properly represent electrostatic interactions, as they appear in the so-called Lewis-type energy, which includes both “steric” and electrostatic contributions, the decomposition of which can only be approximated.19,20 Moreover, NBO charges are also known to be heavily contaminated by basis set superposition error making them almost meaningless in the context of molecular interactions.21 In contrast, the QTAIM charges22 are compatible with the IQA energies because both quantities are derived from the same spatial (i.e., real-space or topological) partitioning. Indeed, the QTAIM charges, together with the corresponding atomic multipole moments, recover23 the exact IQA electrostatic energy provided the multipole expansion converges.24 There is a second reason to investigate the gauche effect with IQA rather than with NBO. In 2009, Martiń Pendás et al.25 published a comparison of NBO and IQA in the context of stereoelectronic effects in 1,2-difluoroethane. They found that despite good agreement between the hyperconjugation model (determined using NBO) prevalent in the literature and IQA delocalization indices, NBO was unable to detect all effects in this system. In particular, NBO was unable to spot significant “through-space” F−F delocalization in the gauche conformation and therefore cannot be complete in its analysis. Considering that NBO is unable to offer well-defined and independent electrostatics, and is moreover unable to detect “through-space” interactions, there is a clear case to proceed with IQA.

More recently, further support appeared for including electrostatics in the study of the gauche effect. In 2014, Baranac-Stojanovic published a paper26 using energy decomposition analysis (EDA) to highlight the importance of electrostatics in the gauche stabilization of 1,2-difluoroethane. It would be chemically intuitive to analyze the electrostatics of a system that contains highly electronegative fluorine atoms, which are known to dramatically polarize electron density in molecules. This paper also alluded to a feature not often considered in an investigation of the gauche effect in 1,2difluoroethane: “structural changes accompanying the rotation should not be neglected”. This final sentence is crucial considering the electrostatic nature of 1,2-difluoroethane, highlighting the r−1 dependence of electrostatic interactions and the stretching of the central C−C bond. The literature on the gauche effect often discusses a large number of “system dependent” explanations for the effect, which in reality are not the same phenomenon as described by the IUPAC definition (and seen in 1,2-difluoroethane), which we consider to be the intrinsic gauche ef fect. For example, Sasanuma and Sugita27 studied the gauche effect in 1,2dimethoxyethane where they altered the dihedral angles around three separate bonds, which allowed for possible intramolecular hydrogen bonding to stabilize the gauche conformation of the central C−C bond, which is evidently not the same gauche effect as the intrinsic gauche effect observed in 1,2-difluoroethane. Similarly, when discussing 3-fluoropiperidinium and βfluoroethylammonium, Gooseman et al.28 stated: “it is not possible to deconvolute the intrinsic gauche effect from the intra-molecular electrostatic hydrogen bonds”. Using Mulliken charges, they also asserted that systems with formal cationic charges (X−CH2−CH2−X+) generally show a greater gauche preference than their neutral counterparts. This finding is attributed to stabilizing (i.e., less destabilizing) X···X+ electrostatic interactions. Despite the concept of the intrinsic gauche effect being referred to by Gooseman et al., the cause of the gauche effect in neutral compounds (such as 1,2-difluoroethane) was not considered. Only the added stabilization due to the presence of a formal charge was concluded to further stabilize the already present intrinsic gauche effect. The results presented by Yahai-Ouahmed et al.29 in their 2014 study of perhalogenated ethanes showed a distinct difference between fluorine and the other halogens. Using the IQA methodology, as we do here, they were able to show that the F−F interactions are much more electrostatic in nature than other halogen−halogen interactions. Their work showed the unique behavior of fluorine and constitutes evidence for its often-called “hard-sphere” behavior. Similarly, we recently studied model SN2 reactions30 in halogenated methane using the IQA coupled with the relative energy gradient (REG) method (details in section 2.2). We found that electrostatic interactions between fluorine and carbon played a much larger role in stabilizing the products and reagents compared to the transition state than in stabilizing molecules containing heavier halogens. In the current work, we build upon these results, showing again that in fluorinated hydrocarbons electrostatic effects dominate. However, unlike the previous papers,30,31 we are able to understand electrostatics in terms of chargetransfer/monopolar interactions and polarization. This greater understanding of electrostatics allows us to give deeper and more robust chemical insight. We will thus gain a better understanding of how atoms behave in molecules. 1440


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The Journal of Physical Chemistry A

overlap, so no “overcounting” corrections are necessary. As a result, the space-filling nature of topological atoms leads to their properties being additive. The total energy of the system is then simply recovered, with a small integration error, by adding the various atomic energy components. In principle, IQA considers four components as defined in eq 1,

The intrinsic gauche effect is what we consider in the present article. To reiterate, intrinsic gauche stability is that which stabilizes the gauche conformation in formally neutral compounds and is due to the atoms in the structure X− CH2−CH2−X (as seen in 1,2-difluoroethane). Other stabilization effects due to additional atoms and groups are to be considered to play a role in extrinsic gauche stability. This distinction between intrinsic and extrinsic gauche stability is crucial, as they should be considered as two, distinct chemical phenomena. Intrinsic gauche stability (although often shown to be a weaker than extrinsic gauche stability) is more “system independent” and also agrees with the IUPAC definition(s) of the gauche effect (whereas factors considered in extrinsic gauche stability do not). To summarize, an authentic understanding of the cause of the gauche effect in 1,2-difluoroethane can be obtained from IQA and QTAIM. Both approaches share the idea of real-space partitioning by a gradient vector field,14 which together are part of the overarching approach of quantum chemical topology (QCT).32−34 IQA has been successfully used to gain meaningful insight into a growing number of chemical systems ranging from proton-transfer reactions35 to intramolecular bond paths between electronegative atoms36 to hydrogen− hydrogen interactions with respect to the torsional barrier in biphenyl37 over short-range electrostatic potentials across torsional barriers38 to CO2 trapping by adduct formation,39 atom−atom repulsion,40 and the diastereoselective allylation of aldehydes,41 to name a few.

atoms

Etotal =

∑

E intra(A) +

A

1 2

atoms

∑

(Vcl(A,B) + Vx(A,B)

B≠A

+ Vc(A,B))

(1)

where Eintra contains all the energetic contributions within an atomic basin. The term Vx(A,B) is the exchange energy between atoms A and B and Vc(A,B) is the correlation energy between the two atoms A and B. The latter has been derived17,45 and calculated, for the first time, for Møller− Plesset theory (MP2, MP3, and MP4) wave functions. However, in the current study, this computationally very expensive route is not followed. Instead, we proceeded with a density functional route, taking advantage of the first IQAB3LYP implementation46 that correctly sums all IQA energy contributions to the original energy of the overall wave function. Density functional theory typically makes the exchange energy join the correlation energy in a single term Vxc(A,B), which is the energy we proceed with in the current study. Hence only 3 IQA components of eq 1 will appear from hereon. The IQA energy term Vcl(A,B) represents the classical (cl) electrostatic energy between the atoms A and B (we will refer to “electrostatics” henceforth). The Vcl(A,B) term can be further partitioned into a charge-transfer (Vct(A,B)) term and a polarization (Vpl(A,B)) term, defined in eqs 2 and 3, respectively,

2. BACKGROUND 2.1. Interacting Quantum Atoms (IQA). IQA11,42 is based on the QTAIM15,43 atomic partitioning scheme. QTAIM partitions the calculated electron density into atomic basins, which are also called topological atoms. Figure 1 shows the topological atoms in the gauche conformation of 1,2-difluoroethane as visualized by a finite element algorithm.44

Vct(A,B) =

where

QA00

A B Q 00 Q 00

rAB

(2)

is the monopole moment of atom A, and

Vpl(A,B) = Vcl(A,B) − Vct(A,B)

(3)

Three important comments need to be made. First, the chargetransfer energy can be safely associated with only the monopolar electrostatic energy is because the monopole moment rigorously expresses charge transfer. In other words, the QTAIM monopole should not be regarded47 as a topological equivalent to a RESP charge, for example. Such a charge has been designed, to the best of its limited ability, to reproduce the full electrostatic potential, whereas the QTAIM monopole only is known48 to do this poorly, unless at long range. Put differently yet again, the QTAIM monopole’s task is to quantify charge transfer, rather than artificially approximate the electrostatic potential; higher QTAIM atomic multipole moments can achieve the latter. Second, as explained before,49 charge transfer is a special case of polarization. In general, the term polarization refers to a change in a multipole moment caused by an external field or a geometric change. Typically, polarization refers to dipolar polarization but, as explained above, it can refer to quadrupolar polarization, or to charge transfer, if monopole moments are affected. Third, the charge transfer and polarization described by eqs 2 and 3 are induced by the entire system. Therefore, these equations describe how the pairwise interactions respond to a change in the total system rather than describe the charge transfer or polarization

Figure 1. Topological atoms in the gauche conformation of 1,2difluoroethane.

The IQA approach calculates energetic terms by integrating the appropriate quantum mechanical densities over the topological atoms. When carried out in 3D, over a single atom, then intra-atomic energies emerge. When carried out in 6D, simultaneously over two topological atoms, interatomic energies are obtained. Note that the QTAIM partitioning is space-filling, which means that there are no gaps between the atoms. Second, space-filling also means that atoms do not 1441


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The Journal of Physical Chemistry A induced by atom A on atom B or vice versa. In other words, at no point do we claim that any charge lost by atom A would be completely taken up by atom B or vice versa. Indeed, any given atom is always part of the total system and hence interacts with any other atom. In summary, the IQA terms Eintra(A), Vcl(A,B),and Vxc(A,B) represent the internal atomic energy, the pairwise electrostatic energy, and the pairwise covalent energy of the molecular system. 2.2. The Relative Energy Gradient (REG) Method. We recently published31 the REG method and applied it to study the water dimer. Here we only review salient elements. As the number of energy terms in IQA increases as the square of the number of atoms, it soon becomes unfeasible to study systems by hand, even for reasonably small systems. The REG method was therefore developed to automate the analysis of potential energy surfaces (PES) with the aim of: 1. determining subsets of partitioned energies that best describe how the total energy changes over the PES and 2. extracting chemical insight from an energetically partitioned system. The REG method is exhaustive and requires no arbitrary parameters. It allows for the study of energy-partitioned systems up to an arbitrarily large size and is able to extract chemically relevant information as ordered lists (see below). This makes the output of the REG method intuitive and easy to understand. The REG method is so named because it is based on a comparison of energy gradients, one associated with the IQA-partitioned energy Ei, and one with the total energy Etot (which is the sum over all Ei values allowing for a small numerical discrepancy). An example of such an Ei value is the exchange−correlation energy between the two carbons denoted Vxc(C,C). These energy gradients can only be seen if there is a configurational evolution of the system and its atoms. Hence a coordinate s is introduced, which controls this configurational evolution and marks the M discrete snapshots included in a REG analysis. An equivalent way of putting the above explanation is that a partitioned energy at a given point in the evolution, Ei(s), is a fixed fraction of the total energy at that same point, Etotal(s), or Ei(s) = REGi ·Etotal(s) + ci

over each barrier (i.e., PES interval) is then calculated using ordinary least-squares linear regression as shown in eq 5, REGi =

(E translated )T ·Eitranslated total (E translated )T ·E translated total total

(5)

where = [Etotal(s1) − Etotal E translated ̅ total Etotal(s2) − Etotal ̅ ⋯Etotal(sM ) − Etotal ̅ ] Eitranslated = [Ei(s1) − Ei̅

Ei(s2) − Ei̅ ⋯Ei(sM ) − Ei̅ ]

where T marks the transpose, s1 to sM define the coordinates of the given barrier, and E̅ i and E̅total represent the mean value of the given partitioned energy term and the total energy over a given barrier. Equation 5 represents the contribution of a given energy (Ei) term to the gradient of the total energy (Etotal) over a given barrier. In essence, this equation quantifies the stability of an energy term at the minimum value of the barrier compared to the maximum value. It is crucial to check that such a comparison is valid using the Pearson correlation coefficient for the ith IQA-energy contribution, Ri defined in eq 6, Ri =

(E translated )T ·Eitranslated total ∥E translated ∥2 ∥Eitranslated∥2 total

(6)

Finally, we discuss the appropriate interpretation of REG values, starting with the sign and then moving on to the magnitude. Positive REG values indicate that Ei and Etotal have the same gradient direction across the barrier. Therefore, Ei contributes to the formation of the barrier. Conversely, negative REG values indicate that Ei has the opposite gradient direction compared to Etotal across a barrier, such that Ei stabilizes while Etotal destabilizes. In other words, Ei now works against the formation of the barrier. The magnitude of the REG value can be thought of as the ratio of gradients, such that if Ei has a REG magnitude of |1| its gradient is equal to that of Etotal. A REG magnitude less than |1| indicates that the gradient is smaller than that of Etotal (e.g., a magnitude of |0.8| indicates the gradient of Ei is 20% smaller than that of Etotal). A REG magnitude greater than |1| indicates that the gradient is larger than that of Etotal (i.e., a magnitude of |1.5| indicates the gradient of Ei is 50% larger than that of Etotal). Therefore, and in summary, by ordering the REG values from largest to smallest, a list is formed in which the Ei terms that most contribute to the barrier behavior are at the top and those that oppose the barrier are at the bottom.

(4)

where ci is the intercept and REG is the slope or gradient. Note that the index i refers to the ith IQA-energy contribution, for example Vxc(C,C). Such a contribution is characterized by both a locality (e.g., carbon and carbon interaction) and an energy type (e.g., exchange−correlation or “xc”), both of which are counted together by the single index i. The fact that the single index i is used to define both the energy type and the associated atom(s) means that all IQA energies are treated identically and are therefore directly comparable within the REG method. The more linear the relationship between Ei and Etotal over the M data points, the more the concept of the REG makes sense. This is why the linearity of eq 4 is assessed by means of the Pearson correlation coefficient (see below). The first step of the REG method is to dissect the total energy PES into segments, which is usually done energy-barrierwise. In other words, a REG analysis is performed independently for each interval of the PES bounded by the edge of the PES and/or one or two of its turning points. However, it is possible for barriers to be dissected further if greater resolution is required. The REG value for a particular Ei

3. COMPUTATIONAL DETAILS To evaluate the intrinsic gauche effect, two systems were considered and compared: 1,2-difluoroethane and 1,2-dichloroethane. The global minimum of each structure can be seen in Figure 2: 1,2-difluoroethane shows global gauche stability, whereas 1,2-dichloroethane shows global anti stability. Both molecules (1,2-difluoroethane and 1,2-dichloroethane) were rotated about the central dihedral angle (about the C1− C4 bond) from 0° (where the two halogen atoms are eclipsed) to 180° (where the two halogen atoms are anti) in increments of 10°. Upon rotation the dihedral angle was fixed and a geometry optimization was run allowing for all coordinates to relax except the fixed (i.e., controlled) dihedral angle. The wave function obtained for each geometry (marked by a restrained 1442


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maximum in 1,2-dichloroethane exists instead at 120° rather than at 130°. Furthermore, the energy difference between the anti and the maximum at 130° is about 7.3 kJ mol−1 in 1,2difluoroethane, whereas the energy difference between the anti conformation and the maximum in 1,2-dichloroethane (at 120°) is 17.6 kJ mol−1. Next we discuss the total energy differences between the gauche and anti conformations in 1,2-difluoroethane and 1,2dichloroethane. This total energy difference is not IQA based, in that all atoms are summed over to give molecular kinetic, exchange−correlation, and electrostatic energies. We start with this coarse analysis, that is, one that lacks atomic resolution but instead looks at how the various energy types act together, over the whole system to acquire chemical insight based on molecular energy to show our conclusions do not require atomic definitions to be corroborated. To obtain molecular energies, we partition the energy into three components: kinetic, exchange−correlation, and electrostatics, as shown in eqs 7, 8, and 9, respectively. As the kinetic energy of a system is a one-electron property, the kinetic energy of the system is contained in the intra-atomic terms only. Conversely, as the exchange−correlation and electrostatic contributions to the energy are two-electron based energies, they are a sum of both inter- and intra-atomic terms,

Figure 2. Global energy minima of (left) 1,2-difluoroethane and (right) 1,2-dichloroethane with the atomic labeling for each molecule.

dihedral angle) was then partitioned using the IQA energy partitioning scheme. The output potential energy surfaces were then analyzed using the REG method.31 To analyze the interactions in 1,2,3,4,5,6-hexafluorocyclohexane, the energetic differences between three geometry-optimized configurations (“all-cis”, equatorial, and axial) were compared using IQA. All wave functions were obtained by the program GAUSSIAN0950 using the B3LYP functional in conjunction with the Dunning basis set aug-cc-pVTZ.51 All IQA calculations were performed using the program AIMAll52 version 16.01.09. All REG calculations were carried out by the in-house program ANANKE.

atoms

4. RESULTS AND DISCUSSION 4.1. Analysis of 1,2-Difluoroethane and 1,2-Dichloroethane. Figure 3 compares the full energy profiles 1,2-

∑

E ke =

E intra,ke(A)

(7)

A

atoms

Vxc =

∑

E intra,xc(A) +

A atoms

Vcl =

∑

E intra,cl(A) +

A

1 2

1 2

atoms atoms

∑ ∑

Vxc(A,B) (8)

B≠A

A

atoms atoms

∑ ∑ A

Vcl(A,B) (9)

B≠A

Table 1 shows the energy differences (ΔE = Eanti − Egauche) between the three energy contributions in the total system. The Table 1. Energy Differences (in Terms of Eke, Vvx, and Vcl) between the Anti and the Gauche Conformations (ΔE = Eanti − Egauche)a system

Figure 3. PES of 1,2-dichloroethane and 1,2-difluoroethane as the dihedral angle X−C−C−X is evolved, where the dotted lines bound the barriers over which ANANKE performs its separate analyses. In both compounds the gauche conformation appears at 70°, the eclipsed at 0°, and the anti conformation at 180°. All energies are shown relative to the minimum energy ever found (transposed to 0 kJ mol−1).

1,2difluoroethane 1,2dichloroethane

ΔEke/ kJ mol−1

ΔVxc/ kJ mol−1

ΔVcl/ kJ mol−1

−11.6

2.1

14.5

5.0

2.8

0.4

−12.7

−9.5

sum/ kJ mol−1

a

As a result of this subtraction convention, a positive entry reinforces the gauche stabilization (because then Egauche < Eanti).

difluoroethane and 1,2-dichloroethane as a function of the dihedral angle, showing a number of similarities between the two molecules as well as dissimilarities. In terms of similarity, in 1,2-difluoroethane the height of the energy barrier between the gauche conformation and the eclipsed conformation (at 0°) is 31.5 kJ mol−1, and the energy barrier between the gauche and the energy maximum (at 130°) is 11.4 kJ mol−1. In 1,2dichloroethane these two barriers have similar energies relative to the gauche conformation, namely, 30.1 and 11.0 kJ mol−1, respectively. However, in terms of dissimilarity, in 1,2difluoroethane the gauche conformation (at 70°) is 4.2 kJ mol−1 more stable that the anti conformation (at 180°), whereas in 1,2-dichloroethane the anti conformation is 6.7 kJ mol−1 more stable than the gauche conformation. Also, the

sum of all three energy differences in 1,2-difluoroethane is 5.0 kJ mol−1, which gives the error of 0.8 kJ mol−1 compared to the calculated B3LYP energy (of 4.2 kJ mol−1; see before). For 1,2dichloroethane, this error is 2.8 kJ mol−1 (−9.5 vs −6.7 kJ mol−1). These errors are due to the numerical integration of the electron density and increased due to the summation of the two errors that are included in the difference. Considering 1,2difluoroethane, it is evident that the kinetic energy destabilizes the gauche conformation by −11.6 kJ mol−1 compared to the anti conformation, whereas the exchange−correlation energy stabilizes the gauche conformation by 2.1 kJ mol−1 compared to the anti conformation, and so does the electrostatic energy, by 14.5 kJ mol−1. The magnitudes of these three energy differences 1443


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are more stable in the gauche than in the anti, whereas the negative energy differences relate to terms more stable in the anti than in the gauche. First we note the symmetry of energy terms across the molecule, such that equivalent IQA terms have very similar energetic values, allowing for a small deviation of the order of 0.1 kJ mol−1 caused by the integration error. When 1,2difluoroethane and 1,2-dichloroethane are compared, it is evident that individual electrostatic energies change the most between the anti and gauche conformations in 1,2-difluoroethane but individual exchange−correlation energies change most in 1,2-dichloroethane. This information (when corroborated with Table 1) shows that despite the largest individual energy changes in 1,2-dichloroethane being in exchange− correlation terms, large energetic cancellations in such terms between the gauche and anti conformations must occur that do not exist in the electrostatic components. Our discussion of Tables 1 and 2 challenges the common explanation of the gauche stability due to hyperconjugation effects put forward by Goodman et al.7 because both tables show the importance of the electrostatic terms in stabilizing the gauche conformation over the anti conformation in 1,2difluoroethane. To understand the gauche effect further, Table 2 will be discussed in detail. In total, this table actually contains 64 entries given that the number of IQA terms is the square of the number of atoms. However, Table 2 only shows the 20 entries with the largest magnitude energy differences. In 1,2difluoroethane the largest IQA energies that stabilize the gauche conformation over the anti are the 1,3 electrostatic interactions between C and F. In total they stabilize the gauche conformation by 50.2 kJ mol−1 over the anti conformation. In 1,2-dichloroethane, the equivalent 1,3 C···Cl interactions only stabilize the gauche conformation by (1.1 kJ mol−1 × 2=) 2.2 kJ mol−1 compared to case for the anti conformation (Table S1 in the Supporting Information). In 1,2-dichloroethane, the terms that most stabilize the gauche compared to the anti conformation are the 1,2 C−Cl exchange−correlation terms, which sum to 23 kJ mol−1. By comparison, in 1,2-difluoroethane these two terms sum to 4 kJ mol−1 (again see Table S1 in the Supporting Information). The second largest energy contribution in both 1,2-difluoroethane and 1,2-dichloroethane is the exchange−correlation between the two carbon atoms. In 1,2-difluoroethane this interaction stabilizes the gauche over the anti by 19.8 kJ mol−1 compared to 6.4 kJ mol−1 in 1,2dichloroethane. It is therefore evident that the 1,3 C···F electrostatic interactions stabilize the gauche most over the anti in 1,2-difluoroethane. It is also evident that the equivalent 1,3 C···Cl electrostatic interactions are not large enough to cause gauche stability in 1,2-dichloroethane. As the discussion of Table 2 showed that the 1,3 C···F electrostatic interactions were the most important in stabilizing the gauche conformation, we study these interactions further, alongside the 1,2 C···F electrostatic interactions in Figure 4. In this figure we separate the two energies into their charge-transfer and polarization contributions as shown in eqs 2 and 3. The first aspect to note is that the 1,3 C···F polarization term (red triangle, Vpl(C1,F7)) shows the largest change in energy over the whole dihedral angle range and stabilizes when going from 180° to 0°, by 44.9 kJ mol−1. Because there are two equivalent 1,3 energy terms (Vpl(C1,F7) and Vpl(C4,F8)), the overall stabilization due to these interactions is ∼90 kJ mol−1. This large energy shows that the 1,3 C···F polarization interactions stabilize as the fluorine atoms become more eclipsed, which

are not compatible with the traditional explanation of gauche stability being due to hyperconjugation. Indeed, hyperconjugation is associated with the exchange−correlation energy, which is about 7 times smaller than the electrostatic contribution. The kinetic energy of the system represents steric interactions between atoms in a system, as shown by Wilson and Popelier40 (and in related unpublished results). It could be hypothesized that this kinetic instability in the gauche conformation is due to the fluorine atoms being closer to each other in the eclipsed conformation than in the anti conformation. Despite the kinetic energy destabilizing the gauche conformation compared to the anti, the electrostatics of the system have a greater preference for the gauche conformation over the anti. Thus, the electrostatics are more dominant than the kinetic energy. For 1,2-dichloroethane, the kinetic energy stabilizes the gauche conformation over the anti conformation by 2.8 kJ mol−1, and exchange−correlation by 0.4 kJ mol−1. Importantly (and in contrast to 1,2-difluoroethane) the electrostatic energy destabilizes the gauche conformation compared to the anti conformation in 1,2-dichloroethane by −12.7 kJ mol−1. In summary, we have learned from the coarse (nonatomistic) analysis in Table 1 that electrostatics are dominant in both systems but acting in opposite ways between the fluoroand chloro-substituted ethane. Second, in 1,2-difluoroethane, the change in exchange−correlation energy is about an order of magnitude smaller than the change in electrostatic energy, thereby jeopardizing the role of hyperconjugation. To reveal the fine structure of the energy contributions in Table 1, we partition the energy further using IQA. Table 2 shows the IQA energy terms with the largest difference between the gauche and anti conformations for 1,2-difluoroethane and 1,2-dichloroethane. The positive energy differences Table 2. Largest Magnitude IQA Energy Differences between the Anti and Gauche Conformations (ΔE = Eanti − Egauche)a 1,2-difluoroethane term Vcl(C4,F8) Vcl(C1,F7) Vxc(C1,F4) Vcl(C4,F7) Vcl(C1,F8) Vcl(H3,F8) Vcl(H5,F7) Vcl(C1,H2) Vcl(C4,H6) Vxc(F7,F8) Vxc(C1,H2) Vxc(C4,H6) Vxc(C1,F7) Vxc(C4,F8) Vcl(C1,H3) Vcl(C4,H5) Vxc(C4,H5) Vxc(C1,H3) Vcl(C1,H4) Vcl(F7,F8)

1,2-dichloroethane −1

ΔE/kJ mol 25.1 25.1 19.8 5.6 5.5 3.9 3.9 3.6 3.6 3.5 −3.7 −3.8 −4.1 −4.1 −4.4 −4.4 −4.7 −4.7 −20.9 −39.2

term

ΔE/kJ mol−1

Vxc(C4,Cl7) Vxc(C1,Cl8) Vxc(Cl7,Cl8) Vxc(C1,C4) Vcl(C1,H2) Vcl(C4,H6) Vxc(H2,C4) Vxc(C1,H6) intra(H6) intra(H2) Vcl(C4,Cl7) Vcl(C1,Cl8) Vxc(C4,H6) Vxc(C1,H2) intra(C4) intra(Cl7) intra(Cl8) Vcl(Cl7,Cl8) Vxc(C1,Cl7) Vxc(C4,Cl8)

11.5 11.4 10.8 6.4 2.5 2.5 2.4 2.4 1.9 1.9 −3.7 −3.7 −4.0 −4.0 −4.1 −5.9 −5.9 −6.1 −6.5 −6.5

a

A positive entry reinforces the gauche stabilization (because then Egauche < Eanti). 1444


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smaller energy change about dihedral rotation than the equivalent C···F terms in 1,2-difluoroethane. By considering Table 2, we also note that the 1,3 C···Cl electrostatic interaction is not one of the terms with one of the largest magnitudes of energy difference between the anti and gauche conformations. However, the 1,2 C−Cl electrostatic interaction does have a relatively large magnitude but prefers the anti over the gauche by 2 × −3.7 = −7.4 kJ mol−1. In Figure 5, the difference between the anti and gauche conformation for the Vpl(C1,C17) energy is 2.2 kJ mol−1, which is an order of magnitude smaller than the equivalent interaction in 1,2difluoroethane, despite favoring the gauche conformation. The charge-transfer term (Vct(C1,C17)) energy difference between the anti and gauche conformations is −1.1 kJ mol−1. Similarly, this charge-transfer term is smaller than its equivalent interaction in 1,2-difluoroethane and favors the anti conformation. The observations highlighted in this paragraph show that the electrostatic terms crucial for gauche stability in 1,2fluoroethane are not prevalent in 1,2-dichloroethane, which evidence why the former is more stable in the gauche conformation whereas the latter is not. Considering Figures 4 and 5 conclusively shows that the gauche effect in 1,2-difluoroethane is due to the electrostatic interactions between C and F atoms. In particular, we show that it is the polarization interaction between the 1,3 C···F atoms that stabilizes the gauche conformation over the anti conformation, and that this interaction is an order of magnitude smaller in 1,2-dichloroethane. We have also shown that exchange−correlation interactions do stabilize the gauche configuration in 1,2-difluoroethane (in particular between the two central carbon atoms). However, exchange−correlation interactions are not the largest cause of gauche stability in 1,2difluoroethane, as they are ∼7 times smaller than the electrostatic interactions. With this in mind, we state that the gauche effect is primarily an electrostatic effect and rather than a hyperconjugation effect. In particular, we have shown the 1,3 C···F polarization interactions are crucial to gauche stability in 1,2-difluoroethane. To further understand the stability of the gauche effect, we now perform the REG method on the PES formed by dihedral rotation. The REG method allows for the independent study of each energy barrier (leading from an energy minimum to an energy maximum). We are therefore not directly comparing the stabilities of the anti and gauche conformations but are instead understanding the formation of each minima with respect to the local energy barrier. Table 3 shows the energy terms of the largest magnitude REG values for each barrier in 1,2difluoroethane. Each barrier is defined via turning points in the total energy such that barrier 1 is defined from 0° to 70°, barrier 2 from 70° to 130°, and barrier 3 from 130° to 180° (Figure 3). We systematically discuss each of the three energy barriers occurring in 1,2-difluoroethane as shown in Figure 3. We will draw all values from Table 3 and discuss the positive REG values separately from the negative REG values. The largest positive REG value in barrier 1 is that of the exchange− correlation between the two carbon atoms (Vxc (C1,C4)) with a value of 1.43, which shows that this energy contributes most to the barrier when going from 0° to 70°. The reason behind this preference is due to C−C bond elongation, which reduces the exchange between the atoms. The next two largest energy terms are the intra-atomic energies of the fluorine atoms (F7 and F8, each with values of 0.71), which indicate a large internal

Figure 4. Electrostatic charge-transfer (square) and polarization (triangle) energy terms of a 1,3 C···F interaction (red) and a 1,2 C−F interaction (green) varying in 1,2-difluoroethane upon rotation of the dihedral angle. Note that only one of each the two (symmetric) 1,3 C···F or 1,2 C−F polarization/charge-transfer terms is shown.

helps in making the gauche more stable than the anti because the 1,3 C···F polarization energy difference between the anti and gauche conformations for this molecule is 28.1 kJ mol−1 (2 × 28.1 = 56.2 kJ mol−1 in total). The Vpl(C1,F7) 1,3 energy contribution displays a much larger difference between the anti and gauche conformations than the corresponding chargetransfer term Vct(C1,F7) does, which shows an energy difference of only −3.0 kJ mol−1 between the anti and gauche conformations. Clearly the polarization interaction of the 1,3 C···F favors the gauche conformation but the charge-transfer term does not. Moreover, the polarization energy term is close to an order of magnitude larger than the charge-transfer term and therefore dominates. Evidently, considering Figure 4, the 1,2 C···F terms do not change as much as the 1,3 C···F terms. The charge-transfer energy difference for a single 1,2 C···F (Vct(C1,F8)) interaction is −0.2 kJ mol−1 between the anti and the gauche, and the polarization term (Vpl(C1,F8)) shows an energy difference of 5.7 kJ mol−1. This finding again demonstrates that the interaction due to molecular charge transfer between C and F prefers the anti conformation, whereas polarization prefers the gauche conformation. However, for the 1,2 C···F interactions the energy differences are not as great as for the 1,3 C···F interactions. In Figure 5, we consider the charge-transfer and polarization energy terms for 1,2-dichloroethane, and thus Figure 5 is the counterpart of Figure 4. It is immediately clear that the C···Cl electrostatic components in 1,2-dichloroethane display a much

Figure 5. Electrostatic charge-transfer (square) and polarization (triangle) energy terms of a 1,3 C···Cl interaction (red) and a 1,2 C−Cl interaction (green) varying in 1,2-dichloroethane upon rotation of the dihedral angle. 1445


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Table 3. Largest Magnitude REG Values and Pearson Correlation Coefficients (R) for the Three Barriers in 1,2-Difluoroethane barrier 1 term

REG

barrier 2 R

Vxc(C1,C4) Vintra(F8) Vintra(F7) Vct(F7,F8) Vintra(C4) Vintra(C1)

1.43 0.71 0.71 0.66 0.63 0.61

1.00 0.99 0.99 0.93 0.96 0.94

Vpl(C4,F7) Vpl(C1,F8) Vct(C4,H5) Vct(C1,H3) Vpl(C4,F8) Vpl(C1,F7) Vxc(F7,F8)

−0.35 −0.36 −0.42 −0.42 −0.45 −0.46 −0.66

−0.96 −0.97 −0.91 −0.91 −0.94 −0.94 −0.98

term

REG

barrier 3 R

Vxc(C1,C4) Vpl(C1,F7) Vpl(C4,F8) Vct(C4,H5) Vct(C1,H3) Vct(C4,F7) Vct(C1,F8)

1.92 1.65 1.64 0.61 0.61 0.58 0.57

0.99 0.98 0.98 0.82 0.82 0.92 0.91

Vct(C1,C4) Vpl(C1,C4) Vintra(C1) Vintra(C4) Vct(F7,F8)

−1.29 −1.35 −1.38 −1.44 −2.36

−0.95 −0.99 −0.92 −0.93 −0.98

term

REG

R

Vct(C1,H3) Vct(C4,H5) Vintra(H3) Vintra(H5) Vct(F7,F8) Vct(C4,F7) Vct(C1,F8) Vct(C4,F8) Vct(C1,F7)

1.69 1.69 1.07 1.07 0.97 0.94 0.94 0.93 0.92

1.00 1.00 1.00 1.00 0.98 0.97 0.97 0.99 0.99

Vct(C1,C4) Vintra(C1) Vintra(C4)

−1.84 −2.04 −2.13

−0.99 −0.98 −0.98

atoms prefers the eclipsed conformation, as do the 1,3 C···F polarization interactions. Second, we study barrier 2 using the REG method. The terms with positive REG values are those that have the largest contribution forming the barrier from 70° to 130° (i.e., these terms have an energetic preference for a dihedral angle of 70° over 130°). The term with the largest REG value (of 1.92) is the exchange−correlation between the two carbon atoms. This term shows that the carbon bond weakens as the system becomes eclipsed at 130°, which is again due to an increase in bond length between these two atoms in the 130° eclipsed conformation. The next two largest terms are again the 1,3 C··· F interactions (with REG values of ∼1.65), which show the importance of such interactions in stabilizing the gauche conformation. As there are two of these terms and REG values are additive, the sum of these terms actually makes them more important than the Vxc (C1,C2) term in stabilizing the gauche conformation over the 130° conformation, overall. These large REG values associated with 1,3 C···F polarization again show the importance of electrostatics in stabilizing the gauche conformation in 1,2-difluoroethane over exchange−correlation. The energy terms with negative REG values favor the 130° conformation over the gauche conformation. The monopolar electrostatic (charge-transfer) term between the two fluorine atoms has the largest negative magnitude REG value of −2.36 and shows that the repulsion between these atoms most favors the 130° conformation. Again this effect is due to the increased separation of these two atoms as the dihedral angle increases and again shows the “hard-sphere”-like behavior of fluorine− fluorine electrostatic interactions. It is also important to note that this repulsion is not as large as the sum of the two 1,3 C···F polarization REG terms and therefore shows that the F···F repulsion is not large enough to prevent the gauche conformation from being more stable than the eclipsed conformation at 130°. Finally, barrier 3 is investigated. The REG values of this barrier do not indicate why the gauche conformation is stable but instead show why the anti conformation is stable over the 130° conformation. Therefore, we will not study this barrier in as much detail as barriers 1 and 2. We do see that the largest REG values relate to 1,2 C···H interactions and intra-atomic energies of the H atoms. We see that the monopolar electrostatics (charge transfer) between the two F atoms are

change of electron density within the atoms upon dihedral rotation. The third term is the charge transfer between the two fluorine atoms (Vct(F7,F8), with a value of 0.66). Equation 2 shows that this term is the interaction energy between atomic monopole moments (net charges, more precisely) of the two atoms. Thus, as the dihedral angle increases from 0° to 70°, the distance between these two negative fluorine atoms also increases. As a result, the (positive) charge-transfer energy term decreases and therefore this term favors the dihedral angle being at 70° (compared to being at 0°). The fact that this monopolar/charge-transfer energy term is more important than the polarization term also suggests that the fluorine atoms behave like “hard-spheres” in their electrostatic interactions, in that the interaction is similar to that of a point charge. The two next largest REG terms are the intra-atomic energies of the two central carbon atoms C1 and C4, with REG values of ∼0.6. This is evidence of a large electron density change within the atomic basins, which could relate to the central C−C bond stretching which in turn alters the electrostatic field caused by the change in nuclear separation within this region of electron density. From this discussion of the positive REG values in barrier 1, it is evident that the preference of the gauche conformation over the eclipsed conformation is due to a strengthening of the central C−C bond and the point charge (charge transfer) between the two F atoms. The preference of the gauche conformation over the eclipsed conformation is also due to electron density changes within the atomic basins of the carbon and fluorine atoms. The terms with negative REG values are terms that show a preference for fluorine atoms in the eclipsed conformation over the gauche conformation. The largest of these terms is the exchange−correlation between the two fluorine atoms (Vxc(F7,F8)), showing that, when this interaction increases, the dihedral is eclipsed. Note that this interaction is the same one that was discussed by Martiń Pendás et al.,25 and which is a “through-space” interaction that NBO cannot spot. The second largest negative terms in Table 3 are those of the 1,3 C···F polarization interactions (with REG values of ∼−0.45), this reflects the observations made in Figure 4 that these term stabilize as the fluorine atoms eclipse. However, as there are two 1,3 C···F polarization terms, they have a larger REG value (when summed) than the F−F exchange− correlation term, showing that these terms are more important in stabilizing the eclipsed conformation. In conclusion, it is evident that the exchange−correlation between the two fluorine 1446


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The Journal of Physical Chemistry A Table 4. Largest Magnitude REG Values for the Three Barriers in 1,2-Dichloroethane barrier 1

barrier 2

barrier 3

term

REG

R

term

REG

R

term

REG

R

Vxc(C1,C4) Eintra(Cl7) Eintra(Cl8) Vxc(C4,Cl8) Vxc(C1,Cl7) Vpl(C1,C4) Vxc(C4,Cl7) Vxc(C1,Cl8) Vxc(Cl7,Cl8)

1.31 0.71 0.70 0.23 0.23 −0.31 −0.36 −0.37 −0.78

1.00 0.98 0.98 0.98 0.98 −1.00 −0.96 −0.96 −0.94

Vxc(C1,C4) Vxc(Cl7,Cl8) Eintra(H3) Eintra(H5) Vxc(C1,Cl8) Vxc(H5,Cl8) Vxc(H3,Cl7) Eintra(C1) Eintra(C4)

1.88 1.12 0.74 0.74 0.43 −0.71 −0.71 −0.78 −0.78

1.00 0.92 0.99 0.99 0.97 −0.99 −0.99 −0.98 −0.97

Vxc(C1,C4) Eintra(H5) Eintra(H3) Vxc(C1,Cl7) Vxc(C4,Cl8) Eintra(C4) Eintra(C1) Vxc(H3,Cl7) Vxc(H5,Cl8)

0.89 0.54 0.54 0.28 0.27 −0.40 −0.43 −0.49 −0.50

1.00 0.98 0.98 1.00 1.00 −0.95 −0.96 −0.96 −0.96

Figure 6. Three conformations of 1,2,3,4,5,6-hexafluorohexane studied. In the “all-cis” conformation two possible 1,3 C···F interactions per carbon atom can be seen.

ethane (for the 1,3 C···Cl interactions). These polarization terms stabilize the gauche over the anti conformation in 1,2difluoroethane and also stabilize the gauche conformation over the barrier at ∼130°. We also showed that exchange− correlation effects are present in stabilizing the gauche conformation 1,2-dichloroethane but do not lead to overall gauche stability. Thus, hyperconjugation does not lead to gauche stability in 1,2-haloethanes generally. 4.2. Analysis of 1,2,3,4,5,6-Hexafluorocyclohexane. In this section we study three conformations of 1,2,3,4,5,6hexafluorocyclohexane and 1,2,3,4,5,6-hexachloroethane, recently synthesized by Keddie et al.53 In this paper they also performed a NBO analysis to show that the same hyperconjugation interactions occur in “all-cis” hexafluorohexane as in 1,2-difluoroethane. The purpose of our study is to show that the 1,3 C···F polarization interactions exist in molecules generally and are more important than hyperconjugation in 1,2,3,4,5,6-hexafluorohexane. We also strive to understand in more detail the relative stability of the “all-cis” hexafluorohexane molecule by comparing it to two other conformations. For brevity in notation we shall refer to the three conformations as “all-cis”, axial, and equatorial, as shown in Figure 6. It is evident that the vicinal (i.e., 1,4) fluorine atoms in the “all-cis” and equatorial conformations have similar dihedral angles to those in the gauche conformation in 1,2-difluoroethane, whereas the axial vicinal fluorine atoms more closely resemble the anti conformation in 1,2-difluoroethane. The stability of these conformations is such that the equatorial conformation is the most stable with a total energy at B3LYP/aug-cc-pVTZ level of −2 183 403.4 kJ mol−1. The axial conformation is the second most stable, being 23.0 kJ mol−1 less stable than the equatorial conformation. The least stable conformation is the “all-cis” conformation, which is 32.2 kJ mol−1 less stable than the equatorial conformation. To understand the “all-cis” conformation, we compare its energy

also important, which again is understood as the distance between the two fluorine atoms has increased. Here we summarize the discussion of Table 3. The first point to note is the importance of the exchange−correlation of the central C−C atoms in stabilizing the gauche conformation compared to the barriers adjacent to this minimum. However, the multiple 1,3 C···F polarization interactions favor the conformations with smaller dihedral angles and, overall, these polarization terms dominate over the central C−C exchange− correlation. The second (similar) point is the greater importance of the 1,3 C···F polarization interactions in stabilizing structures as the dihedral angle approaches 0°. The 1,3 C ···F polarization energies are the reason for global gauche stability as is also shown in the discussion of Figures 4 and 5. The third point is that the most important electrostatic interaction between the two fluorine atoms is the monopolar/ charge-transfer electrostatic term (not polarization). Hence fluorine atoms do not polarize and instead act like “hard spheres”. This F−F electrostatic repulsion in gauche conformation is not as destabilizing as the 1,3 C···F interactions are stabilizing. For comparison, Table 4 shows the REG analysis of 1,2dichloroethane. The first point to note when Table 4 is compared to Table 3 is that there are fewer electrostatic terms, the only one being the fourth most negative term in barrier 1. However, a similarity between 1,2-difluoroethane and 1,2dichloroethane appears in the importance of the Vxc (C1,C4) term, which is the most single important term for barrier 1 and barrier 2 for both molecules. This observation proves that this term also stabilizes the gauche conformation in 1,2-dichloroethane but does not cause global gauche stability. If the gauche ef fect was due to hyperconjugation, then the gauche conformation should be globally stable but alas it is not. The above discussions show that the 1,3 C···F polarization interactions in 1,2-difluoroethane do not exist in 1,2-dichloro1447


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The Journal of Physical Chemistry A differences between the axial and equatorial conformations. The largest magnitude energy differences can be seen in Table 5.

Table 6. Energy Difference between the Axial and Equatorial Conformationsa term

Table 5. Energy Differences between the Axial and “All-Cis” Conformations and between Equatorial and “All-Cis” Conformationsa term

ΔEaxial−“all‑cis”/ kJ mol−1

FEq−Feq Ceq−Fax Cax−Feq Ceq−Ceq

213.2 199.8 189.6 136.3

Eintra Fax Eintra Ceq Eintra Cax Vct 1,4 Ceq−Feq Vct 1,4 Feq−Fax

−78.6 −97.9 −125.3 −148.2 −248.2

Vct Vpl Vpl Vct

1,5 1,3 1,3 1,3

term

ΔEequatorial−“all‑cis”/ kJ mol−1

Cax−Fax Cax−Fax Ceq−H Ceq−Fax Cax−Fax

240.0 150.5 82.5 68.7 51.5

Eintra Fax Eintra Cax Vpl 1,3 Cax−Cax Vct 1,5 Fax−Fax

−81.6 −92.9 −140.7 −237.8

Vct Vpl Vct Vct Vct

1,4 1,4 1,2 1,5 1,2

Vct Vpl Vpl Vpl Vpl Vpl Vct Vpl

1,5 1,3 1,3 1,4 1,2 1,4 1,4 1,4

F−F (same face) C−F C−C C−C C−C C−F F−F (opposite faces) C−F

ΔEaxial‑equatorial/kJ mol−1 419.4 346.7 236.7 63.8 −126.5 −236.5 −244.8 −330.7

a

The energy differences are the sum of all terms in the molecule of equivalent interactions. A positive value means that equatorial is more stable than axial.

the F atoms act as “hard-spheres” as the charge-transfer/ monopolar electrostatic terms (Vct 1,5 F−F) contribute most (412.4 kJ mol−1) to the stability of the equatorial conformation over the axial conformation. This again can be explained due to the increase in interatomic distance (going from the same face axial positions to the equatorial positions). Considering Table S2 in the Supporting Information, it is evident that the equivalent electrostatic interactions in 1,2,3,4,5,6-hexachlorohexane (particularly the Vpl 1,3 C−Cl interactions) are not dominant in understanding the conformational preference of the molecule. By studying 1,2,3,4,5,6hexafluoroethane and 1,2,3,4,5,6-hexachloroethane in the “allcis”, axial, and equatorial conformations, we have shown that the 1,3 C···X polarization interactions stabilize the conformations when the dihedral angle is closer to gauche than anti when X = F. We have also shown that the F−F monopolar electrostatics have an energetic preference to have increased bond lengths. Conversely, when X = Cl such stabilization of gauche-like conformations due to 1,3 C···X polarization does not exist. It is also evident that the F atoms act as “hard spheres” because the energies that are most repulsive when closer to the eclipsed conformation are those of chargetransfer/monopolar interactions.

a

The energy differences are the sum of all terms in the molecule that make up equivalent interactions. A positive energy difference means that all-cis is more stable than either axial or equatorial.

The notation used indicates the atoms as they appear in the “all-cis“ conformation, such that Fax is the axial fluorine atom and its neighboring carbon atom is denoted Cax (as seen in Table 2 there is no need to define hydrogen atoms in such a way as the atom is implicit from the carbon to which it is bonded). The lack of exchange−correlation terms in Table 5 indicates that the largest energy differences between the “all-cis” and the two other conformations are electrostatic in nature, or due to an internal change of electron density within the atomic basins (i.e., Eintra). Considering the energy differences between the axial and “all-cis” conformations, the interactions that most stabilize the “all-cis” conformation over the axial conformation are the Vct 1,5 Feq−Feq interactions (with a total energy difference of 213.2 kJ mol−1). This term indicates that the monopolar repulsion between the fluorine atoms decreases when moving from the axial to equatorial positions. This is understandable as the internuclear distance between fluorines increases when going from axial to equatorial. The second and third largest terms represent the polarization of the carbon atoms by the fluorine on the neighboring carbon (i.e., 1,3 C···F polarization). Note how these terms reflect the observation made in 1,2-difluoroethane, such that in the axial conformation of 1,2-difluoroethane the F−C−C−F dihedral angle (with a value of −159°) is similar to the anti conformation and in the “all-cis” conformation has a dihedral angle (with a value of −57°) similar to that for the gauche conformation. Table 5 shows that in the “all-cis” conformation (where the dihedral angle is similar to that of the gauche confirmation) these 1,3 C···F polarization terms stabilize the conformation by 199.8 + 189.6 = 389.4 kJ mol−1 compared to the case for the axial conformation in which the F−C−C−F dihedral angle is similar to that of the anti conformation. When the axial and equatorial conformations are compared as shown in Table 6, it is again evident that when the F−C−C− F dihedral angles are closer to the gauche conformation (as in the equatorial conformation) the 1,3 C−F polarization energies contribute dramatically to the stabilization of the configuration. This is seen as they stabilize the equatorial conformation over the axial conformation by 346.7 kJ mol−1. It is also evident that

5. CONCLUSION We have shown the importance of 1,3 C···F polarization interactions in stabilizing the gauche (and gauche-like) conformations. By exhaustively studying all energy terms (by type and locality) and the barriers to rotation of the F−C−C− F dihedral angle, we have shown conclusively that the 1,3 C−F polarization interactions are the cause of gauche stability in 1,2difluoroethane. This finding challenges the traditional and outdated idea that hyperconjugation is the cause of gauche stability. With this new knowledge we hope to give synthetic and structural chemists a deeper understanding of the gauche effect, thereby allowing them to exploit the phenomenon based on its true physical properties. The mechanism of gauche stability is that of 1,3 C···F polarization, and these energy terms are found in more systems than just 1,2-difluoroethane. Indeed, they are important in the global stability of the equatorial conformation of 1,2,3,4,5,6hexafluorohexane and also the local stability in the “all-cis” conformation of this molecule compared to that of the axial conformation. Overall, it can be stated that fluorine atoms prefer facial (or near-facial) conformations due to the additional polarization stabilization with the vicinal carbon neighbors. 1448


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b11881. Tables of energy differences and atomic numbering scheme (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(P.L.A.P.) E-mail: [email protected]. ORCID

Paul L. A. Popelier: 0000-0001-9053-1363 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Gratitude is also expressed to the EPSRC for the award of an Established Career Fellowship (EP/K005472/1) to one of us (P.L.A.P.) and to the EPSRC for a PhD studentship to J.C.R.T.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on January 30, 2018, with errors in equations 8 and 9. The corrected version was reposted on January 31, 2018.

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