Abstract
We have quantum chemically investigated the rotational isomerism of 1,2‐dihaloethanes XCH2CH2X (X = F, Cl, Br, I) at ZORA‐BP86‐D3(BJ)/QZ4P. Our Kohn‐Sham molecular orbital (KS‐MO) analyses reveal that hyperconjugative orbital interactions favor the gauche conformation in all cases (X = F−I), not only for X = F as in the current model of this so‐called gauche effect. We show that, instead, it is the interplay of hyperconjugation with Pauli repulsion between lone‐pair‐type orbitals on the halogen substituents that constitutes the causal mechanism for the gauche effect. Thus, only in the case of the relatively small fluorine atoms, steric Pauli repulsion is too weak to overrule the gauche preference of the hyperconjugative orbital interactions. For the larger halogens, X⋅⋅⋅X steric Pauli repulsion becomes sufficiently destabilizing to shift the energetic preference from gauche to anti, despite the opposite preference of hyperconjugation.
Keywords: activation strain model, bond theory, conformational analysis, energy decomposition analysis, gauche effect
Beyond hyperconjugation! State‐of‐the‐art quantum chemical analyses reveal that, in 1,2‐dihaloethanes, hyperconjugation always favors the gauche conformation. It is the steric (Pauli) repulsion that is behind the trend known as the gauche effect: weak repulsion (X = F) leaves the gauche preference intact, whereas stronger repulsion (X = Cl, Br, I) shifts the preference to anti.
1. Introduction
The energy profile for rotation around the C−C bond in 1,2‐disubstituted ethanes features four stationary points, that is, two staggered conformers (gauche and anti) connected via two eclipsed transition states (syn and anticlinal), as schematically illustrated in Figure 1a. [1] Depending on the nature of the substituted groups, the equilibrium can shift to favor either the gauche or the anti‐conformer. [2] The so‐called gauche effect, a term coined by Wolfe in 1972, [3] is the phenomenon that the gauche conformer is energetically more favorable than the anti‐conformer in cases where X is an electron‐withdrawing group (usually containing atoms from the second period of the periodic table, such as nitrogen, oxygen, or fluorine). [4] The gauche effect has been observed in a variety of molecules (especially those containing an organic fluorine) [5] and has been used as a tool for controlling the conformational preference in the design of organic compounds towards specific molecular properties. [6]
Figure 1.
a) Stationary points in the energy profile for rotation around the C−C bond of 1,2‐dihaloethanes and b) main orbital interactions affecting the gauche‐anti equilibrium.
In the currently accepted model, the gauche effect arises from stabilizing hyperconjugative [7] interactions between antiperiplanar σ orbitals (see Figure 1b). [8] This picture was developed to explain experimental evidences on the conformational behavior of the 1,2‐difluoroethane, [9] the simplest molecule that exhibits the gauche preference. [10] In this hyperconjugation model, the higher stability of the gauche conformer is attributed to the antiperiplanar charge‐transfer from the filled σC−H orbital to the empty σ* C−F orbital, which is stronger than the corresponding charge‐transfer from the filled σC−F to the empty σ* C−F in the anti‐conformer. [8] For heavier halogens, it is argued that this trend should be reversed, because of the better electron‐donor and electron‐acceptor capabilities of σC−X and σ* C−X orbitals as X goes from F to Cl, Br, or I. [11] However, recent reports have shed more light on the role of other forces behind this effect. Baranac‐Stojanović [12] pointed out that stabilization of the gauche conformer is caused by orbital and also electrostatic interactions, Thacker and Popelier [13] attributed it solely to electrostatics, while Martín‐Pendás and coworkers [14] explained it based on both electrostatic and exchange‐correlation interactions. [15]
In view of this ongoing and highly relevant controversy, we have investigated the origin of the gauche effect within the framework of quantitative Kohn‐Sham molecular orbital (KS‐MO) theory using the series of 1,2‐dihaloethanes XH2C−CH2X (X = F, Cl, Br, I, see Figure 1). Herein, we show that, at variance to the currently prevailing model, the switch in preference from gauche for X = F to anti for X = Cl−I, is caused by the increasing steric demand of the substituent X, as the latter descends down a group in the periodic table. This trend does not originate from hyperconjugation, which we show to always favor gauche but only overrule steric (Pauli) X⋅⋅⋅X repulsion in the gauche conformation for the smallest substituent X, in our model systems, the second‐row fluorine atom. We also highlight how geometrical relaxation, in particular, the effect of the variation of the C−C bond length, upon internal rotation around this bond can mask the change in the various orbital and electrostatic interactions and needs to be taken into consideration to properly identify causalities.
2. Results and Discussion
To understand how the XH2C−CH2X bonding mechanism determines conformational preferences, we have analyzed this bond explicitly for all four 1,2‐dihaloethanes in terms of two open‐shell CH2X. fragments forming a C−C electron‐pair bond in various conformations. The MO diagram with the valence orbitals of the CH2X. fragments is provided in Figure 2 (see Figure S1 for more details of CH2X. and the better known CH3X molecular orbitals). The overall bond energy ΔE has been divided into two major components using the activation strain model (ASM): [16] the strain (ΔE strain) that results from the distortion of the two CH2X. radicals from their equilibrium structure to the geometry they acquire in the XH2C−CH2X molecule and the actual interaction (ΔE int) between the deformed radical fragments. The interaction energy ΔE int was further decomposed using our canonical energy decomposition analysis for open‐shell fragments (EDA) [17] into four energy terms that can be associated with the following physical factors: classical electrostatic interaction (ΔV elstat), Pauli repulsive orbital interactions (ΔE Pauli) between closed‐shell orbitals which is responsible for steric repulsion, stabilizing orbital attractions (ΔE oi) that account, among others, for electron‐pair bonding as well as donor‐acceptor interactions, and corrections for dispersion interactions (ΔE disp). For the purpose of clarity, the above‐mentioned energy terms along the internal rotation around the C−C bond are considered relative to the syn conformation (i. e., represented as a ΔΔE), since the latter represents the global energy maximum conformation in all cases. All calculations were performed using ZORA‐BP86‐D3(BJ)/QZ4P [18] as implemented in the Amsterdam Density Functional (ADF) program, [19] and PyFrag 2019 to facilitate all ASM and EDA analyses. [20]
Figure 2.
MO diagram for the formation of the 1,2‐dihaloethanes XH2C−CH2X (X = F, Cl, Br, I) from two open‐shell CH2X. fragments, along with the fragment molecular orbitals (FMO) depicted as quantitative 3D plots (isovalue = 0.04) for CH2Cl., computed at ZORA‐BP86‐D3(BJ)/QZ4P.
Our rotational energy profiles of 1,2‐difluoro and 1,2‐diiodoethanes are given in Figure 3 (full data on all model systems can be found in Figure S2 in the Supporting Information). Firstly, we note the well‐known energy profile of 1,2‐dihaloethanes XH2C−CH2X, [11] that is, for 1,2‐difluoroethane (X = F), the gauche conformer is the global energy minimum, whereas the anti‐conformer is the global energy minimum for all heavier 1,2‐dihaloethanes (X = Cl, Br, I). The torsion angle ϕX−C−C−X (where X = F, Cl, Br, I) of the gauche conformer is shifted from 60° to ca. 70°, in good agreement with the experimental value of 71.0(3)° for 1,2‐difluoroethane (X = F). [21] The C−C bond length directly correlates with conformational stabilities and is shorter in the energy minima and longer in the energy maxima (see Figure 3). For example, in 1,2‐difluoroethane (X = F), the C−C bond shortens from syn (1.556 Å) to gauche (1.506 Å), then lengthens going towards the anticlinal conformation (1.526 Å) and shortens again at the anti‐conformer (1.520 Å). Similar, though less pronounced effects are observed for the heavier halogens.
Figure 3.
Rotational energy profile and C−C bond length variation as a function of the ϕX−C−C−X dihedral angle of the 1,2‐difluoro and 1,2‐diiodoethanes. Computed at ZORA‐BP86‐D3(BJ)/QZ4P.
Thus, the variation in C−C bond length along internal rotations is significant (e. g., for 1,2‐difluoroethane, it spans 0.05 Å). In the following, we address the question of where this breathing in C−C bond distance between short in minima and long in maxima comes from, and how it affects the individual interaction mechanisms and their EDA energy terms.
2.1. Geometrical Relaxation and Rotational Energy Profile
Our analyses reveal an interesting interplay of effects in which steric Pauli repulsion is the dominant term behind both the raise in energy and the expansion of the C−C bond at eclipsed conformations. The results of these analyses also highlight the importance of separating changes in bonding mechanism, and thus in EDA terms, associated with the internal rotation from further changes in bonding, and thus in EDA terms, due to the further geometrical relaxation (in particular, C−C bond‐length variation) that occurs in response to the internal rotation, because this further geometrical relaxation again modifies and thus hides the original causal factors.
Figure 4 shows how the different energy components (i. e., Pauli repulsion, electrostatics and orbital interactions) vary as a function of C−C separation for the syn and gauche conformations of 1,2‐difluoro and 1,2‐diiodoethanes (full data on all model systems can be found in Figure S3 in the Supporting Information). Note that, in a fully relaxed rotation around the C−C bond, not only the C−C bond length changes, but also the geometry of the CH2X. fragments which becomes increasingly pyramidalized in the eclipsed conformation to mitigate the buildup of steric Pauli repulsion (vide infra). Therefore, to separate the effect of C−C bond length variation from the effect of CH2X. bending, we first focus on the curves with fixed CH2X. geometry as in the gauche conformer CH2X(g) (solid lines, red for syn and black for gauche). Note that the upward slope of the ΔE Pauli curve is larger than the downward slopes of the ΔV elstat and ΔE oi curves in all cases, which means that ΔE Pauli changes faster as a function of the C−C distance. Also, the Pauli repulsion is strongest in the syn conformation for all distances shown and the gradient of the red line is larger than of the black line, that is, the increase of ΔE Pauli with the shortening of the C−C bond length is greater in the syn case (see Figure S4 in the Supporting Information for the derivative of the different energy terms with respect to the C−C bond length). The larger gradient of the ΔE Pauli curve in the syn conformation will drive the molecule towards a longer equilibrium C−C bond length. [22] Therefore, steric Pauli repulsion is the reason why the C−C bond is longer at the syn conformation. The picture remains essentially the same if we consider the effect of CH2X. bending to the syn geometry CH2X(s) (dotted lines, red for syn and black for gauche). The magnitude of all energy terms is however smaller since, in its syn geometry, CH2X. is more bent away from the C−C bond region which reduces the Pauli repulsion (but also other interactions) between the fragments.
Figure 4.
EDA of the interaction between two open‐shell CH2X. fragments in 1,2‐difluoro and 1,2‐diiodoethanes as a function of the C−C separation, computed at ZORA‐BP86‐D3(BJ)/QZ4P. Vertical dashed lines denote the equilibrium bond distances of the syn and gauche conformations.
Next, we analyze how geometrical relaxation, in particular, the change in C−C bond length, affects the interpretation of the energy profile for internal rotation around this bond of the 1,2‐dihaloethanes. Our results reveal that all energy components are strengthened in the global energy minima because of the shorter C−C bond in these conformations, that is, the observed trends in ΔΔV elstat, ΔΔE Pauli, and ΔΔE oi are simply a function of the C−C distance. Thus, care should be exercised when analyzing relaxed rotational barriers (i. e., when all geometrical parameters are flexible to optimize during rotation). The key to understand the trends in the interacting terms is to first take a closer look at the fully relaxed rotation around the C−C bond. As can be seen from Figure 5a for the 1,2‐difluoro and 1,2‐diiodoethanes (full data on all model systems can be found in Figure S5 in the Supporting Information), the ΔΔE originates primarily from a more stabilizing ΔΔE int that favors the gauche conformer for X = F and the anti‐conformer for X = Cl, Br, I. The ΔΔE strain, stemming from the bending of the CH2X. fragments, is much smaller and more uniform along the rotation of the C−C bond. Since the interaction energy plays such a critical role in the observed trends, the different contributors to the interaction energy were analyzed in more detail using our EDA. [17] Figure 5b shows that, in all cases, the trends in the interaction energy are equally dictated by the stabilizing orbital and electrostatic interactions (the ΔΔE oi and ΔΔV elstat curves nearly coincide in all points of the rotation around the C−C bond). On first glance, these findings are, indeed, in line with a previous report that attributed the gauche effect to both orbital and electrostatic stabilization. [12] However, owing in particular to the C−C bond lengthening (which is caused by a higher steric Pauli repulsion at any given C−C distance, vide supra), the ΔΔE Pauli term is lowest along this curve in the syn conformation. This observation is counterintuitive, as already shown in Figure 4 and stressed in the analysis of the rotation barrier of ethane, [22] in that the steric repulsion is least destabilizing in the eclipsed conformation where the two C−X bonds are pointing in the same direction and the halogen lone‐pairs on each fragment are in closest proximity (see 2π and 3π* orbitals in Figure 2). The trends observed in Figure 5b are dominated by consequence of the C−C bond shortening and stretching, that is, all energy terms are maximized when the C−C bond is shorter (i. e., in the staggered conformers, ΔΔE oi and ΔΔV elstat are more stabilizing, and ΔΔE Pauli is more destabilizing) whereas the opposite occurs when the C−C bond is longer (i. e., in eclipsed conformers; see Figures 3 and 5b). [23] Figure 6 confirms that the changes in the C−C bond length (ΔrC−C) correlate with both ΔΔE Pauli and ΔΔE oi terms.
Figure 5.
Activation strain (ASA) and energy decomposition analyses (EDA) as a function of the ϕX−C−C−X dihedral angle of the 1,2‐difluoro and 1,2‐diiodoethanes. a) ASA and b) EDA for fully relaxed rotation, c) EDA and d) key closed‐shell‐closed‐shell overlaps for rigid rotation with CH2X. fragments in gauche geometry but with C−C distance set to 1.52 Å. Computed at ZORA‐BP86‐D3(BJ)/QZ4P.
Figure 6.
Correlation between the C−C bond stretching with steric Pauli repulsion and orbital interactions during rotation around the C−C bond. Computed at ZORA‐BP86‐D3(BJ)/QZ4P.
Therefore, to obtain an unbiased picture, it is necessary to perform a numerical experiment in which the strong effect of C−C bond length variation on the energy terms has been eliminated. This can be achieved by performing a rigid rotation around the C−C bond while all geometry parameters but the torsion angle ϕX−C−C−X are kept unchanged. To this end, let us take the gauche conformer of each 1,2‐dihaloethane at its optimum geometry and rotate it from the syn to the anti‐conformation. To compare all molecules on a more equal footing, we rotate all 1,2‐dihaloethanes from the same C−C bond distance set to 1.52 Å (as in the staggered geometry with the longest C−C bond length, i. e., the anti‐conformer of the 1,2‐difluoroethane; see Figure 5c). Note that the conformational preferences in the ΔΔE int curve shown in Figure 5c remain the same as in the fully relaxed rotational profiles, that is, ΔΔE int favors gauche for X = F and anti for X = Cl, Br, and I. The ΔΔE Pauli is a minimum at the staggered conformations and goes to a maximum at the eclipsed conformations, as would be expected. Note that the other energy components have a smaller contribution to the trends in ΔΔE int. The ΔΔV elstat term is more stabilizing at the eclipsed conformations (see ref. [22] for a detailed discussion on the behavior of ΔΔV elstat in rotation barriers), and the ΔΔE oi only slightly changes upon rotation around the C−C bond. The same overall trend is found if we rotate all 1,2‐dihaloethanes from their optimum gauche or anti (Figure S6) as well as syn geometries (Figure S7). Note that the strain energy ΔE strain vanishes in this analysis because it is constant for geometrically frozen fragments; therefore, ΔΔE strain is zero and ΔΔE int = ΔΔE.
The smallest ΔΔE Pauli for syn observed in the flexible rotation (Figure 5b) is, therefore, a result of the elongation of the C−C bond and the bending of the CH2X. fragments, that reduces the overlap between the orbitals of the vicinal C−X bonds. Note, for example, that the rigid rotation from the equilibrium gauche conformer of the 1,2‐difluoroethane to the syn orientation leads to 4.0 kcal mol−1 more Pauli repulsion (Figure 7). Then, when we keep the molecule in the syn conformation but relax the other geometry parameters, the Pauli repulsion lowers almost 40 kcal mol−1, much more than the initial rise of 4.0 kcal mol−1. Similar effects can be observed for other 1,2‐dihaloethanes (see Figure S7 for the connection of each EDA term between a staggered and an eclipsed rigid rotation of all 1,2‐dihaloethanes). This highlights that analyses over relaxed rotational barriers, or final equilibrium geometries, only reflect the consequences but not the reason that leads to a given structural preference in the first place. The importance of taking into account the strong effect of geometrical relaxation in the course of a chemical phenomenon when elucidating the physical factors underlying it has already been nicely pointed out in the literature.[ 22 , 24 ] Therefore, detailed analyses of the rotational profiles of 1,2‐dihaloethanes performed herein clearly demonstrate that ΔΔE Pauli is the dominant, causal term that determines the observed trends in the variation of the C−C bond length and in the overall rotational energy profile. [25]
Figure 7.
Pauli repulsion as a function of the ϕX−C−C−X dihedral angle of the 1,2‐difluoro and 1,2‐diiodoethanes. Computed at ZORA‐BP86‐D3(BJ)/QZ4P.
2.2. Steric Pauli Repulsion and the Gauche Effect
In the following, we discuss how the above analysis of the rotational energy profiles affects the interpretation of the gauche effect observed in the 1,2‐difluoroethane. We show that the fluorine atoms in FCH2CH2F are too small to cause significant steric Pauli repulsion in the gauche conformation and, for this reason, hyperconjugation dominates for X = F.
The most significant closed‐shell−closed‐shell overlaps between the two CH2X. fragments contributing to the trend in ΔΔE Pauli (shown in Figure 5c) arise between the well‐known C−X π‐bonding and π*‐antibonding CH2X. FMOs, [26] 2π and 3π*, respectively, each of which possesses both, X lone‐pair character as well as carbon 2p amplitude (see Figure 8). ΔΔE Pauli is a maximum at the syn because of a larger ⟨2π|2π⟩ overlap, which decreases as the C−C bond is rotated to the anti‐conformer (see Figure 5d). This effect is more pronounced for heavier halogens because of the larger spatial extension of their valence np atomic orbitals. Note that the difference in ⟨2π|2π⟩ between gauche and anti‐conformers also increases as X goes from F to I. For example, for X = F, the ⟨2π|2π⟩ is the same in the gauche and anti, whereas, for X = Cl, Br, and I, it is larger in the gauche (see Figure 8). A similar behavior is found for the ⟨2π|3π*⟩ overlap integral. Thus, the trend in Pauli repulsion determines that the conformational equilibrium gradually shifts to the anti‐conformer as the halogen increases in size. [11] Interestingly, only for 1,2‐difluoroethane, the ΔΔE Pauli is slightly larger for anti than gauche (see Table S1). This can be ascribed to the ⟨3π*|3π*⟩ overlap, in which the amplitude of the 3π* orbital is larger on the less electronegative carbon atom because of the out‐of‐phase mixing of C 2p and F 2p orbitals, resulting in a larger ⟨3π*|3π*⟩ for anti than gauche (see Figure 8). As the atomic p orbital of the halogen atom goes up in energy (and becomes more diffuse) going down group 17 in the periodic table, the amplitude of the 3π* orbital increases on the halogen atom and, thus, the ⟨3π*|3π*⟩ overlap is smaller for anti than gauche for X = Cl, Br, and I. At variance to the heavier and effectively larger halogens, the fluorine orbitals are too compact to cause significant overlap and steric Pauli repulsion and, therefore, cannot shift the conformational equilibrium to anti.
Figure 8.
MO diagram and the most significant occupied‐occupied orbital overlaps between the CH2X. fragments (where X = F, Cl, Br, I), along with ⟨2π|2π⟩ (isovalue = 0.04) and ⟨3π*|3π*⟩ (isovalue = 0.02) in the gauche and anti‐conformers of the 1,2‐difluoro and 1,2‐diiodoethane. Analysis in rigid rotation in gauche geometry but with C−C distance set to 1.52 Å, computed at ZORA‐BP86‐D3(BJ)/QZ4P.
The important role played by steric Pauli repulsion is not surprising for heavier 1,2‐dihaloethanes (X = Cl, Br, I), [11] but it constitutes an unprecedented physical factor behind the gauche effect in 1,2‐difluoroethane (X = F). [27] In contrast to the widespread belief that the fluorine atoms would repel each other in the gauche conformation, our analysis at the consistent geometries (i. e., all conformations at the same C−C bond length of 1.52 Å) shows that ΔΔE Pauli slightly favors (by 0.4 kcal mol−1) the gauche over the anti‐conformer for X = F (Figure 5d). In this way, any subtle attractive interaction can effectively determine its conformational preference, which is the case of the hyperconjugative interactions used to explain the gauche effect in the 1,2‐difluoroethane.
The hyperconjugative orbital interactions are more favorable in the gauche conformer, in line with the current view of the gauche effect. [8] However, this is the case for all 1,2‐dihaloethanes analyzed herein, not only for X = F, because the orbital energy gap of the donor‐acceptor interaction favoring gauche (i. e., 3π* → 4σ*) is smaller than the one favoring anti (i. e., 2π → 4σ*; see MO diagram in Figure 2). Thus, the stabilization due to the ΔΔE oi results predominantly from a charge‐transfer from the occupied 3π* orbital of one fragment into the unoccupied 4σ* orbital of the other fragment (see Figure 9, or Figure S8 for the full data along the rotation of the C−C bond). This is more stabilizing for the 1,2‐difluoroethane solely because of the larger orbital overlap (⟨3π*|4σ*⟩ = 0.15 and 0.02 for X = F and I, respectively). Again, due to the difference in electronegativity in the C−F bond, the amplitude of both antibonding orbitals, 3π* and 4σ*, is larger on the less electronegative atom, that is, on carbon (see Figure 9). Thus, as the difference in electronegativity decreases on going towards heavier halogens, the orbital overlap between the two CH2X. fragments also decreases. For the same reason, the orbital energy gap is always bigger when X = F (Δϵ = 9.2 eV for X = F and Δϵ = 4.6 eV for X = I), that is, it shows a trend opposite to that of ΔΔE oi. This is interesting because previously the strength of hyperconjugative interactions in substituted ethanes has been typically attributed to the orbital energies alone. [28] Note that the contribution from the 3σ → 4σ* is less important for the conformational preferences because of a larger orbital energy gap and the associated overlap is similar for gauche and anti (see Figures 2 and S8).
Figure 9.
MO diagram for the donor‐acceptor interaction between the occupied 3π* orbital of one fragment and the unoccupied 4σ* orbital of the other fragment, along with 3π* overlapping with 4σ* as 3D plots (isovalue = 0.04) in the gauche conformers of the 1,2‐dihaloethanes. Analysis in rigid rotation in gauche geometry but with C−C distance set to 1.52 Å, computed at ZORA‐BP86‐D3(BJ)/QZ4P.
The above agrees well with the fact that the orbital interactions have the strongest preference for the gauche conformer of 1,2‐dihaloethanes in the case of X = F. Nevertheless, the reason that this preference of the orbital interactions for gauche can become decisive for X = F, is the very small difference in Pauli repulsion ΔΔE Pauli, in that case, between gauche and anti‐conformers.
3. Conclusions
At variance with the current model, the gauche effect in 1,2‐dihaloethanes (X = F, Cl, Br, I) is not caused by hyperconjugation alone, but also by steric Pauli repulsion between substituents X, as follows from our quantum chemical analysis based on relativistic dispersion‐corrected density functional theory. The gauche effect refers to the phenomenon that the gauche conformer is energetically favored for X = F while, in all other cases (X = Cl, Br, I), the preferred conformer is anti. The current model ascribes the gauche effect to hyperconjugative orbital interactions that favor gauche in case of X = F. Our Kohn‐Sham molecular orbital (KS‐MO) analyses, however, reveal that such hyperconjugative orbital interactions favor the gauche conformation in all cases, not only for X = F but also for X = Cl, Br, and I. The analyses show that it is Pauli repulsion between lone‐pair‐type orbitals on the halogen substituents that constitutes the causal mechanism for the gauche effect. Thus, only in the case of the relatively small fluorine atoms, steric Pauli repulsion is small enough to not overrule the gauche preference of the hyperconjugative orbital interactions. For the larger halogens, X⋅⋅⋅X steric Pauli repulsion destabilizes the gauche conformer and, in this way, shifts the energetic preference from gauche to anti, despite the inverse preference of hyperconjugation.
Conflict of interest
The authors declare no conflict of interest.
Supporting information
As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.
Supplementary
Acknowledgements
This work was supported by the Netherlands Organization for Scientific Research (NWO), the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and the Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG). This work was carried out on the Dutch national e‐infrastructure with the support of SURF Cooperative.
D. Rodrigues Silva, L. de Azevedo Santos, T. A. Hamlin, C. Fonseca Guerra, M. P. Freitas, F. M. Bickelhaupt, ChemPhysChem 2021, 22, 641.
Contributor Information
Prof. Dr. Célia Fonseca Guerra, Email: c.fonsecaguerra@vu.nl.
Prof. Dr. Matheus P. Freitas, Email: matheus@ufla.br.
Prof. Dr. F. Matthias Bickelhaupt, Email: f.m.bickelhaupt@vu.nl.
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