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Turn: Weak Interactions and Rotational Barriers in Molecules – Insights from Substituted Butynes Oluwarotimi Omorodion, Matthew Bober, and Kelling J. Donald J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09155 • Publication Date (Web): 07 Oct 2016 Downloaded from http://pubs.acs.org on October 10, 2016

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The Journal of Physical Chemistry

Turn: Weak Interactions and Rotational Barriers in Molecules – Insights from Substituted Butynes Oluwarotimi Omorodion, Matthew Bober, and Kelling J. Donald* Department of Chemistry, Gottwald Center for the Sciences, 28 Westhampton Way, University of Richmond, Richmond, Virginia 23173, United States.

ABSTRACT: The nature of the bonding and a definite preference for an eclipsed geometry in several substituted but-2-ynes, including certain novel derivatives, are uncovered and examined. In particular, we consider the molecular species R3C-C≡C-CR3 (where R= H, F, Cl, Br, I, and CN), their R3C-B≡N-CR3 analogues, and a few novel exo-bridge systems with intra-molecular hydrogen bonds running parallel to the C-C≡C-C chain. In some cases, the potential energy surfaces are remarkably flat - so flat, in fact, that free rotation is predicted for those molecules at very low temperatures. A systematic investigation of the bonding in the halogenated butynes demonstrates that the eclipsed conformation actually becomes more stable relative to the staggered form as R becomes larger and less electronwithdrawing. The rotational barriers (the differences in energy between the eclipsed and staggered geometries) are magnified significantly, however, in a special case where selected R groups at the ends of the R3C-C≡C-CR3 molecule form hydrogen bonds parallel to the C-C≡C-C core. In those systems, the hydrogen bonds serve as a weak locking mechanism that favors the eclipsed conformation. A comparison of HF and uncorrected DFT methods versus the MP2(full), CCSD(T), and other dispersion corrected methods confirm that correlation accounts to a significant extent for barriers in substituted butyne compounds. In the hydrogen-bonded systems, the barriers are comparable to and larger in some cases than the barriers observed for the far more extensively studied ethane molecule.

*Corresponding Author: Tel.: 804-484-1628; Fax: 804-287-1897; E-mail: [email protected]

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Introduction Understanding the geometrical preferences in simple alkanes, alkenes, and alkynes is important because small organic molecules can serve as model systems for fragments of larger species. But predicting and rationalizing the bonding in even simple organic molecules can be difficult. The historic struggles to determine and explain the structure of benzene and the (re)assessments of the bonding in ethane are two examples.1 - 4 2

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In this work, we consider the but-2-yne molecule (also called dimethylacetylene, or crotonylene) and a range of substituted forms, which may be viewed as a modification of the wellstudied ethane system, with a triple bond (C≡C) inserted into the C-C single bond. Alkyne subunits occur within several organic systems of current interest, and butyne specifically serves as either a reactant or an intermediate in certain organic reactions including cycloadditions.5 It has been pointed out in references 6 and 7 that an analysis of the infrared bands alone is insufficient for determining the preferred geometry for but-2-yne (R3C-C≡C-CR3; R = H), since the terminal methyl groups exhibit essentially free rotation against a barrier (E = E(D3h) – E(D3d)) that is lower apparently than 0.1 kcalmol-1. A more recent investigation (using both experimental and theoretical methods)8 has provided additional evidence, however, that the eclipsed (D3h) form (Figure 1(a)) is the lowest energy structure for that (CH3-CC-CH3) molecule.

(a)

(b)

Figure 1: (a) Eclipsed, D3h, and (b) staggered, D3d, but-2-yne structures. In this work, we consider the structure and the stability of R3C-CC-CR3 where R = H, F, Cl, Br, I, At, and CN.

Hexafluoro-but-2-yne (R = F), the perfluorinated derivative of but-2-yne, is used in some cases as a dienophile.9 It was initially determined via infrared spectroscopy to have a staggered


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D3d orientation in the gas phase10 (Figure 1(b)), but gas-phase electron diffraction was used some seventeen years later to show that “the molecule exhibits essentially free internal rotation.”11 It appears, therefore, that although the ethane and perfluoroethane molecules are known experimentally and theoretically to prefer identical staggered arrangements with a somewhat higher rotational barrier for the latter,12,13 a similar parallel (between the unsubstituted and fluorinated forms) has not been established unequivocally for butynes. We have not found in the literature, for instance, any systematic analysis of the chemical bonding preferences for any of the butyne isomers (but-1-yne or but-2-yne) relative to their halogen-substituted analogues. In this work, we investigate the bonding preferences and rotational barriers in substituted but-2-ynes (R3C-C≡C-CR3), for R = H, F, Cl, Br, I, At, and CN. The influence of the size and electron withdrawing power of R and the influence of dynamic correlation as incorporated into certain computational ab initio and density functional methods are examined. CN was an appealing option as a non-monoatomic candidate for R in this context because it is small and is known to be an electron withdrawing substituent. Additionally, the linear (-CC≡N) arrangements in the -CR3 terminal groups minimize steric congestion and any secondary interaction that could arise among the R substituents themselves within the -CR3 fragment. The discourse on rotational barriers is broadened here as well by an examination of (i) isoelectronic species in which the central -C≡C- triple bonds is replaced by -N≡B-,14 and (ii) the influence of dispersion interactions (dynamic correlation) on the barriers to rotation about the -CC- bridge in butynes. We examine, too – along with the simpler R substituents mentioned above – a class of butyne isomers in which intra-molecular bonding interactions (specifically hydrogen bonding) serve as weak locks (see Figure 2) that stabilize one conformation of the R3CCC-CR3 molecule substantially relative to another.


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Figure 2: Model of an eclipsed substituted but-2-yne molecule with intra-molecular hydrogen bond(s) where W = NH or NCH3. In the monosubstituted cases (where the number of substituents, n, = 1), R and R are H atoms. For trisubstituted cases (n = 3), R = CHW, R = CHCHF, and three hydrogen bonds are parallel to the central -CC- bond. The latter investigation is also of interest to our research group because of our related work on the structural and electronic compression of chemical bonds,15 and our interest in hindered molecular rotors.16 We find that in some cases the rotational barriers in the hydrogen-bonded systems discussed in this work are higher than those obtained for ethane. Computational Methods Computational ab initio Møller-Plesset (MP2(full))17 and density functional (B3PW91)18,19 methods were used throughout this work for geometry optimization. We selected the B3PW91 method as our primary density functional theoretical (DFT) approach instead of the commonly used B3LYP alternative because, in our experience, the former gives slightly superior results for optimized bond distances and angles. The correlation-consistent triple zeta (cc-pVTZ) basis sets20 were used for the elements in periods one to three. For the heavier elements, Br, I, and At, we employed scalar-relativistic (MDF) energy consistent small core pseudopotentials (ECPs) with 10e-, 28e-, and 60e- cores, respectively, and the associated cc-pVTZ quality basis sets.21,22 The rotational energy barriers on the potential energy surfaces of but-2-yne and its perhalogenated and CN substituted analogues were determined by rotating the -CR3 units in 5o increments relative to each other. A 10o interval was accepted, however, for the more elaborate hydrogen bonded systems depicted in Figure 2. In each case, the dihedral angle, , is defined herein such that  is equal to 0o for the eclipsed conformation. Although that single dihedral angle was


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fixed at each step in modeling the potential energy surfaces, the geometry optimizations for each value of  were otherwise unconstrained. All of the geometrical optimizations and computational analyses mentioned above were carried out using the Gaussian 03 suite of programs.23 The 09 version of the Gaussian program,24 which we acquired subsequently, was employed specifically for a more detailed examination of the influence of dispersion on rotational barriers. The latter version of the program was employed because it includes the more recent D3 dispersion correction25 as well as the B97D3 method, which we have employed in this study as part of our assessment of the role of dispersion on the energy barriers in the title compounds. Single point energy calculations have been carried out as well for all of the structures optimized at the MP2(full)26 level of theory in order to obtain relative energies (between eclipsed and staggered geometries) at higher levels of theory. That list includes the simpler MP2 method (with core electrons excluded from correlation calculations),26 the MP3, MP4(D, DQ, and SDQ), CCSD, and the so-called gold-standard CCSD(T)27 levels of theory using the same triple zeta quality basis sets and pseudo-potentials mentioned above. A comparative analysis of the contributions to the bonding identified by competing energy partition schemes (such as hyperconjugation and steric interactions) is not attempted in this work. We wish in this contribution to identify and assess systematically the overall extent of the barriers to rotation and the nature of the bonding in the distinct classes of substituted butyne compounds mentioned above, which have not been considered (or even posited, in some cases) to date in the literature. We examine in detail the influence of correlation on those rotational barriers. The nature of the charge transfer between fragments within the R3C-C≡C-CR3 systems is examined as well using the natural bond orbital (NBO) analysis as implemented in the Gaussian program in order to improve our understanding of trends in the geometrical parameters in those compounds.


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Results and Discussion At the B3PW91 level of theory, the eclipsed D3h conformation of the R3C-C≡C-CR3 molecules for R = F, Cl, Br, I and At becomes more stable as the halides get larger (see Figure S1 in the supporting information). The difference in energy between the D3h and D3d conformations is never more than 0.26 kcalmol-1, however, which would allow for free rotation of the -CR3 groups relative to each other at temperatures above ~130 K. The MP2(full) method (Figure 3) yields the same general trends in the rotational barriers as those obtained at the B3PW91 level (see Figures S1 and Table S1). Astatine was not considered at the MP2(full) level due to computational costs, but the bromo- and (in particular) the iodobutyne molecules have noticeably higher energy barriers at the MP2(full) level. For R = I, for example, the barrier is 0.42 kcalmol-1 compared to 0.23 kcalmol-1 at the B3PW91 level of theory. Overall, however, our results confirm that at both levels of theory the rotational barriers in the butyne compounds are quite low compared to the barrier in ethane. At the B3PW91 and MP2(full) levels of theory the computed barriers for ethane are 2.6 kcalmol-1 and 3.1 kcalmol-1, respectively, which are both within a few tenths of the experimental value of ~2.8 kcalmol-1.5,28

Figure 3: Computed MP2(full) energies of the possible orientations of but-2-yne and several of its derivatives. R = At was excluded at the MP2(full) level of theory due to computational costs for the optimizations at that level.


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Of particular interest for us here are the increasing deviations in the computed rotational barriers at the two levels of theory, and the reasons for those deviations. The significant differences between the barriers obtained at the MP2(full) and B3PW91 levels of theory for the larger halides betray, we find (as we show more clearly later on), an increasing role of dispersion interactions (as the halides become more polarizable) in determining the energy barriers of these substituted organic systems. The results confirm, as well, the relative insignificance of steric interactions between the two terminal CR3 groups in these compounds; the eclipsed geometry actually becomes more stable as the halides get larger (see Figure 3). The staggered geometry is preferred for R = F and CN, but in both cases the potential energy surface is so flat as to make that apparent geometrical preference of no practical consequence. Our results are in line, therefore, with the experimental evidence mentioned above for free rotation in perfluorobutyne, and we predict the same for R = CN. The eclipsed conformation is preferred for butyne itself (R = H in Figure 3), but the rotational barrier is again so low that essentially free rotation is predicted for that molecule as well in the gas phase. Substituent Effects and Geometry: The influence of halogenation and CN substitution on the carbon-carbon bond distances in the butyne structure are summarized in Figure 4.

Figure 4: Internal carbon-carbon single and triple bond lengths in substituted but-2-ynes, all obtained at the MP2(full) level of theory. The corresponding values at the B3PW91 level are shown in Figure S2 in the supporting information. The dashed lines pass through the data points for R = H. They serve only as references for the influence of substitution on the bond lengths in the butyne molecule.


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In general, the C-C single bonds become shorter and the C≡C triple bonds become a bit longer as the halides get larger. Put another way, substituting for R = Cl, Br, and I (using R = H as our reference – see the green dashed lines in Figure 4), lengthens the triple bond and compresses the single bonds, but the most electron withdrawing substituents – both F and the CN group – have the very opposite effect. The correspondence in Figure 4 between the compression of the C-C single bonds and the expansion of the triple bond as the halides get larger suggests that one of these effects is a consequence of or arises in tandem with the other. That is, the trends are structural manifestations of a single phenomenon – a systematic redistribution of the electron density in the molecule as the size and electron withdrawing power of the substituents (R) change. A natural bond orbital (NBO) analysis provides evidence, for instance, that the ‘donoracceptor’ stabilization energy (E(2)) (an estimate from 2nd order perturbation theory) for the delocalization of electron density from the C≡C bonding to the (C-R)* antibonding orbitals and from the C-R bonding to (C≡C)* antibonding orbitals become more substantial going from R = F to R = I (see Table 1). Both of those sets of donor-acceptor interactions across the C-C single bonds are expected to destabilize the C≡C and C-R bonds and to compress the C-C single bonds. C≡C  (C-R)* charge transfers reduce the bond order of the triple bond directly, and C-R  (C≡C)* interactions reduce that ‘triple’ bond order as well by adding electron density to CC anti-bonding orbitals. These kinds of hyperconjugative interactions are similar qualitatively to those observed in ethane, except that in this case the terminal CR3 units interact primarily through the mediating C≡C group and not directly via C-R  (C-R)* interactions. Through-bond interactions between


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the two terminal CR3 groups via the shared C≡C bridge appear to promote, therefore, the preference in the chlor-, bromo-, and iodo-butynes, for the high symmetry eclipsed geometry. Table 1: Natural Bond Orbital (NBO) analysis data for interactions between occupied and unoccupied CC and C-R bond orbitals for R3C-C≡C-CR3 for R = CN, H, F, Cl, Br, and I (all in the eclipsed geometry)× optimized at the MP2(full) level of theory. Antibonding bond orbitals (the electron acceptors) are indicated by a ‘*’ symbol.

Donor Acceptor Total E(2) / kcalmol-1 (C—C(N))* 4.12 CC CN× C—C(N) 8.89 (CC)* (C—H)* 4.8 CC H C—H 12.58 (CC)* (C—F)* 6.09 CC F× C—F 3.30 (CC)* (C—Cl)* 8.34 CC Cl 8.69 C—Cl (CC)* (C—Br)* CC 8.62 Br C—Br (CC)* 11.83 (C—I)* 9.47 CC I 16.84 C—I (CC)* † These results are for the eclipsed form, which is not a minimum for R = CN and F at the MP2(full) level of theory. This eclipsed form is used for comparison with all of the other cases for which the eclipsed structure is preferred. For the C-CN fragment, The influence of the CN bond is ignored. It is in each case < 1.0 kcalmol-1. R

For perfluorobutyne, the short C-F bond distance, the significant polarity of the C-F bond, and repulsive interactions between the F centers in each CF3 group vs. the -C≡C- -system, may explain why the E(2) values are so small for C-F donations to (C≡C)* (3.30 kcalmol-1 in Table 1). And that observation (that the C-F  C≡C interactions are weak) helps us to understand, too, both the instability of the eclipsed geometry for perfluorobutyne, and the longer C-C single bond distances that we find (Figure 4) for that fluorinated molecule. At the MP2(full) level, the C-C single bonds in the optimized structures for R = F and I are 1.459 Å, and 1.410 Å, respectively. For R = CN (Table 1), the computed E(2) values are also smaller than the values for R = Cl, Br, and I. After perusing the data in Table 1, therefore, it is hardly surprising that the electronwithdrawing CN substituent and F (see Figure 3) have similar bonding preferences. In both of those cases, the staggered geometry is preferred! The potential energy surfaces in Figure 3 are


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remarkably flat, and calculations at even higher levels of theory (using the MP2(full) optimized geometries) agree completely with the preference for the staggered geometry for R = CN and F, even if there is some disagreement on the actual sizes of the barriers (Figure 5).

Figure 5: Energy differences (E = E(D3h) – E(D3d)) at several levels of theory (through to the CCSD(T) level) between the eclipsed (D3h) and staggered (D3d) conformation of the substituted butyne molecules, using the optimized MP2(full) geometries. The actual energies in Hartree units for the eclipsed and staggered conformations are given in the supporting information (Table S2).

The MP2 method (blue unbroken line in Figure 5)26 exaggerates and the MP3 method (green unbroken line) underestimate the barriers somewhat relative to the CCSD(T) method for Br and I on the right in Figure 5, but the post-HF methods all agree qualitatively on the geometrical preferences in all of the molecules. To two decimal places, all of the methods predict barriers of 0.01 kcalmol-1 and 0.00 kcalmol-1 (no barrier) for R = H and R = F, respectively (see Figure 5 and Table S2 in the Supporting Information). For the larger halides, it is clear from Figure 5 that the HF method dramatically underestimates the barriers for the eclipsed structures (R = Cl, Br, and I), and overestimates the barrier for R = CN. The actual energies used in computing these barriers and the E values themselves are listed for readers in the Supporting Information (Table S2).


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The computed Wiberg bond indices for the C≡C and C-C bonds in the butyne molecules (Table 2) align very well with the trend in their bond lengths in Figure 4. Table 2: Computed Wiberg bond indices for the C-C single and C≡C triple bonds in R3C-C≡C-CR3 for R = CN, H, F, Cl, Br, and I. R = CN†

CC C—C

2.83 0.98

R = Cl

R=H

CC C—C

2.82 1.07

R = Br

R = F†

CC C—C

2.89 0.98

R=I

2.60 CC 2.75 CC 2.68 CC C—C 1.04 C—C 1.07 C—C 1.12 † These results are for the eclipsed form, which is apparently not the minimum energy geometry for R = CN or F. This eclipsed form is used for comparison with all of the other cases for which the eclipsed structure is preferred.

The bond order for the C-C single bond (Tables 2 and S3) increases from 0.98 for R = F to 1.04, 1.07, and 1.12 for R = Cl, Br, and I, respectively, which is consistent with the observed incremental shrinkage in the C-C bond going from R = F to R = I in Figure 4a. For the triple bond, the changes in the bond order run in the opposite direction – from 2.89 for R = F to 2.77, 2.68, and 2.60 for R = Cl, Br, and I, which is in excellent agreement as well with the slight expansion of that bond going from R = F to R = I in Figure 4b. The perturbation of the C-R bonds in R3C-C≡C-CR3 (due to their interactions with the triple bond in the butyne molecule) is exposed if we compare the C-R bonds with those of the simple CR3H molecule, where the -C≡C-CR3 fragment is replaced by -H. As we show in Table 3, the C-F bond distance is identical (to three decimal places) in both F3C-H and F3C-C≡C-CF3 (at the MP2(full) level), but the C-R distances in R3C-C≡C-CR3 are longer relative to those in CR3H in all of the other cases (for R = CN, H, Cl, Br, and I). For the halides, this expansion in the C-R bond goes incrementally from 0.000 Å for R = F to 0.029 Å for R = I (Table 3), which is in line with the evidence for an increased destabilization of the C-R bonds (due to C-R  (C≡C)* and C≡C  (C-R)* charge transfers (Table 1)) as the halide gets larger.


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Table 3: C-R bond distance (in angstrom units) for the simple CR3H substituted methane molecule and in the relevant R3C-CC-CR3 molecule. All of the data were obtained at the MP2(full) level of theory. The optimized eclipsed R3C-CC-CR3 geometries were considered in each case. The difference between the two sets of distances, r, are given in the last column. R CN H F Cl Br I

C-R Bond Distances / Å (a) C-R in R3CH (b) C-R in R3C-CC-CR3 1.462 1.469 1.083 1.086 1.331 1.331 1.759 1.773 1.910 1.930 2.127 2.156

r = r(b) - r(a) 0.007 0.003 0.000 0.014 0.020 0.029

For completeness, the C≡C  (C-C)* and C-C  (C≡C)* ‘donor-acceptor’ stabilization energies are included in the supporting information as well (Table S3). But those interactions weaken both the C≡C and the C-C bonds, so it is difficult to assess their significance for the bond length variations in the C-CC-C subunit as a function of R. A Correlation Corollary: We carried out a series of calculations on the eclipsed and staggered conformations of the periodobutyne molecule using ab initio and density functional methods that account for dispersion systematically or as a correction (MP2(full), B97D3, B3PW91+D3, and B3LYP+D3). And we compared those results (Figure 6) with data that we obtained using both the Hartree-Fock (HF) and the uncorrected density functional B3PW91, and B3LYP methods.

Figure 6: Relative energies, E, between the unfavourable staggered (D3d) geometry and the stable eclipsed (D3h) form (using the Gaussian 09 suite of programs) for I3C-C≡C-CI3.


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The rotational barriers obtained with the corrected DFT methods are much closer to the MP2(full) value (-0.42 kcalmol-1) than those derived from the uncorrected DFT (B3PW91 and B3LYP), and HF methods (Figure 6). The largest difference is between the HF and the MP2(full) levels of theory, where the rotational barrier (E from Figure 6) is raised by 0.24 kcalmol-1 at the MP2(full) level – an increase of more than 100% – compared to the HF result where E = 0.18 kcalmol-1. The impact of dispersion corrections on the DFT data is significant. The B3PW91 and B3LYP energy barriers favor the eclipsed geometry, but the barriers increase by over 40% when dispersion is included in the form of the B3PW91+D3 and B3LYP+D3 variants (Figure 6). The stand-alone B97D3 method gives an energy difference E = 0.38 kcalmol-1, which is between the values obtained using those two DFT+D3 methods and the ab initio MP2(full) method (see Figure 6). The data summarized in Figure 6 indicates in a straightforward way the relative significance of dynamic correlation on the rotational barriers, E, in periodobutyne, an example of a simple organic molecule with polarizable substituents. The origins of the correlation effects are not traced out in this work, but we decided to look closely at iodobutyne because it has the largest barrier to rotation compared to all of the other cases that we have considered so far. With its large and soft terminal I atoms, iodobutyne offers us some important insights into the significance of dispersion in substituted organic compounds. The sensitivity of the potential energy surface of that system to the selected model chemistry makes it, we think, an excellent test system for assessing the quality of novel post-HF methods. We have illustrated already in Figure 5 (using the fixed MP2(full) optimized structures) the importance of correlation, even for systems with less polarizable halides. All of the methods


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that account for correlation follow the same general trend (see Figure 5), but the HF method fails badly on almost all counts as a quantitative tool. In general, the HF method tends to underestimate the barriers for the most polarizable halides and exaggerates it for R = CN. One success for the HF method, however, is the prediction of the staggered form for R = CN and the eclipsed geometry for the heavier halides. So, although the barrier heights are affected significantly by dispersion interactions, fundamental bonding interactions such as those identified above using the NBO method tend to favor as well the overall geometrical trends observed at the highest levels in Figure 5. Overall (going from the HF to the CCSD(T) level), correlation lowers the rotational barrier for the staggered R = CN case, but tends to enhance the barriers for eclipsed cases (Figure 5), especially for the systems with the most polarizable terminal atoms (i.e. for R = Br and I). An Alternative Bridge: Replacing the central -C≡C- fragment with the isoelectronic -N≡B- unit14 offers some insight into the influence of asymmetry in the triple bond on the rotational barriers. The Substitution causes a very small net increase (by only 0.07 Å) in the distance between the terminal CR3 groups in R3C-C≡C-CR3, but it leads in certain cases to a significant decrease in the rotational barrier. In Figure 7, these decreases in E show up as shifts towards the zero line of the y-axis (from the parent CR3-C≡C-CR3 molecule (black markers) to CR3-B≡N-CR3 (red markers)). The overall structural preferences are unaffected in most cases, however, when C≡C is replaced by B≡N. For R = H, Cl, Br, and I, the barrier is lower (the brown markers in Figure 7 are closer to the zero line), but the eclipsed structure is still favored. For F3C-C≡C-CF3 and (CN)3CC≡C-C(CN)3 for which the staggered conformation is preferred (Figures 3 and 5), substituting for B≡N causes a reversal at the MP2(full) level of theory in the conformational preferences and the eclipsed form is actually preferred, but with even less significant barriers to rotation.


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Figure 7: MP2(full) Energy differences between the eclipsed and staggered conformations for the normal substituted butynes and their CR3-N≡B-CR3 analogues. In this graph, a shift toward the horizontal y (E) = 0 line going from the black to the red markers corresponds to a decrease in the barrier to the alternative conformer. The eclipsed structure is preferred if E is negative.

Figure 8: Energy differences (E = E(D3h) – E(D3d)) at several levels of theory (through to the CCSD(T) level) between the eclipsed (D3h) and staggered (D3d) conformation for CR3-N≡B-CR3, using the optimized MP2(full) geometries. The actual energies in Hartree units for the eclipsed and staggered conformations are given in the supporting information (Table S4). The eclipsed structure is preferred at a given level of theory if E is negative. Indeed, the energy barriers between the eclipsed and staggered conformations are marvelously tiny for R = CN and F, whether C≡C or B≡N is in the middle of the molecule (Figures 5 and 8). But, as we show in Figure 8, an improvement in the treatment of correlation (see the post-


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HF data for R = CN in Figure 8) lowers the HF barrier to rotation noticeably for C(CN)3-N≡BC(CN)3. So it appears that the MP2 (full) method actually favors the eclipsed structure in Figure 7 only because it overcorrects for correlation. That artificial lowering is remedied in Figure 8 such that the CCSD(T) value in Figure 8 for R = CN is between the HF and the MP2 values.26,29 Notice that all of the methods in Figure 8 (including the HF method) actually agree on the basic structural preferences in the six molecules that we considered. They even concur that the flattest potential energy surface is obtained when R = F. Indeed, a reversal of the structural preference (from staggered to eclipsed) is apparent when we replace C≡C by B≡N (comparing Figures 5 and 8) but the E values are so low (see Tables S2 and S4) that the actual location of the global minimum for R = F is essentially irrelevant. The difference between Figure 5 and 8 for R = H is almost imperceptible at all of the levels of theory that we have considered. So, the biggest consequence of the isoelectronic modification of the core triple bond going from C≡C to B≡N appears to be the noticeable decrease in the barrier heights (less negative E values) for the larger halides in the series (Figures 5 and 8). Intra-Molecular Hydrogen Bonding and Energy Barriers: A Proposal. The stabilization of one conformation vs. another in a molecule can be decisive for the direction of chemical reactions and product ratios in organic chemistry. For the systems considered in this work so far, the potential energy surfaces are quite flat, however, and free rotation is expected at rather low temperatures in many cases. A question that we asked, therefore, was whether it would be possible to identify a practical (that is, experimentally accessible) structural strategy for heightening rotational barriers in butyne systems. How to gain, we wondered, some control at low temperatures over the rotation of terminal CR3 groups about the -C≡C- bond? A general structural strategy that we posit for that purpose is depicted in Figure 2, where a hydrogen bond (in blue in Figure 2) is formed by an electron rich center (W) and an opposing H


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atom in the molecule. In the geometrically optimized cases shown in Figure 9, the hydrogen bonds serve as weak tethers that stabilize the molecules in the eclipsed conformation. The substituents that we consider in this work are R = CHW, where -W (= -NH or -NCH3) is an electron donor – a hydrogen bond acceptor – at one end of the CR3-C≡C-CR3 molecule and R = -CHCHF at the other (Figure 9). In each species the lone pair on the N atom (dark blue site in Figure 9) is oriented towards the H atom in the –CH=CHF substituent on the opposite end of the molecule.

Figure 9: Sample structures. The mono- and tri-substituted forms have been considered for both W = NH, and W = NCH3. The sample pictures shown here are for (a) the monosubstituted (n = 1) case for W = NH, and (b) the trisubstituted (n = 3) case for W = NCH3. The geminal electron withdrawing F atom was included in the –CH=CHF group in order to strengthen the positive electrostatic potential on H and promote H---N hydrogen bonding. The influence of the -CH3 substitution at the N center in the molecules was considered because CH3 (being a good  donor) tends to enhance the availability of the N lone pair, which promotes bonding as well. Donald et al. have demonstrated, for example, that the F3C—I---N(CH3)3 halogen bond is stronger than the F3C—I---NH3 analogue.30,31 The relative energies obtained at the B3PW91 levels of theory on a slice of the potential energy surface for the mono- and tri- H-bond bridged butyne systems are shown in Figure 10. The eclipsed forms – those in which the N lone pair and the opposing C—H bond are aligned (see Figure 9) – are preferred for both of the ‘monosubstituted’32 (n = 1) cases. For the ‘trisubstituted’ (n = 3) systems, the eclipsed geometry is even more strongly favoured. The relative energies in Figure 10 for those n = 3 structures are noticeably less than three times the relative energies of the monosubstituted forms, but that may be explained by the costs for the rehybridization and


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structural changes in the molecules going from the mono- to the symmetrized tri-substituted structures. The hydrogen bonds are stretched in the latter n = 3 structures, for example, by about 0.1 Å relative to the n = 1 cases (see Figure S3).

Figure 10: Computed B3PW91 energies of the mono- and tri- hydrogen bonded structures (see Figure 2) with W = NH, and NCH3. The energies are plotted relative to the staggered conformations  = 180o (see Figure 9). For the tri-substituted cases, the potential energy curve repeat every 120o. The curves from  = 60o (staggered) to  = 180o (staggered) (i.e. a full cycle) are shown here. The eclipsed form is achieved at  = 120o (shown), and at  = 0o. Dynamic correlation is expected to be even more important for the bonding in these systems that form hydrogen bonds than those mentioned above that do not. So we supplemented the full potential energy curves obtained at the B3PW91 level of theory (which are shown in Figure 10) by optimizing both the eclipsed and staggered structures independently at the HF, B97D3, and MP2(full) levels of theory and comparing the relative energies (i.e. the negative of the barrier heights) for all four methods (see Figure 11). For cases where n = 3 at the B97D3 level of theory (for both W = NH and W = NCH3), the staggered conformers repeatedly collapsed to the eclipsed form, which is the global minimum, so we were unable to obtain direct E values for those two cases at the B97D3 level.33 To obtain approximate values, however, we generated staggered structures by changing the relevant dihedral angle for the optimized eclipsed B97D3 species (keeping all other parameters fixed) and we computed the B97D3 energies for the resulting structure. The resulting relative energy data are


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included in Figure 11 (as grey triangles under n = 3) along with the other data points (E = E(eclipsed) – E(staggered)) that were all obtained by full independent optimizations of the eclipsed and staggered forms at the stated levels of theory.

Figure 11: Relative energies of the optimized eclipsed vs staggered forms for the substituted but2-yne compounds (CHW)R2C-C≡C-CR2(CHCHF) where W = -NH and -NCH3. Note: For n = 3 at the B97D3 level, we could not generate optimize staggered forms – staggered starting structures reverted repeatedly to the eclipsed forms. The E values in grey are estimates obtained using the energy of (B97D3) optimized eclipsed structures and single point (B97D3) energies for staggered forms generated by changing only the dihedral angle of the eclipsed forms. The results in Figure 11 confirm that dispersion plays a decisive role in the sizes of the barriers in both the mono- and tri-substituted forms of the compounds. Relative to the HF level of theory, the barriers are higher by about 1.5 – 2.0 kcalmol-1 at the MP2(full) level of theory. The B3PW91 method hardly does any better than the HF method, especially for the monosubstituted cases, but the B97D3 method, which accounts explicitly for dispersion, shows a noticeably better agreement with the MP2(full) values (Figure 11). Correlation and Weak Inductive Effects: Changing W in Figure 11 from NH to NCH3 has only a very small effect on the actual rotational barriers, but an assessment of the nature of those effects affords us a few important insights. Replacing the H atom on N with the more electron donating CH3 group is expected to increase the availability of the lone pair on the N center31 and stabilize the N---H hydrogen bond slightly. That is precisely what we find for both the mono- and tri-


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substituted cases at the B97D3 and MP2(full) levels of theory that account for dispersion. The E values become more negative in Figure 11 when we replace H with CH3 for those two methods, while the opposite behavior is seen with the HF and B3PW91 methods (Figure 11). That extra stabilization that is achieved (for W = NCH3 compared to W = NH) when dispersion is included is not dramatic at all, but it reaffirms, we think, the need to account for correlation if we are to compute accurately any trend (in hydrogen bonded species, in this case) that relies on inductive effects and weak interactions. Compared to the simple but-2-yne molecule and its halide and CN analogues, the eclipsed hydrogen bonded structures have very high barriers to rotation. The mono-substituted case with W = NH in Figure 11 at the MP2(full) level of theory, for example, has a barrier to the staggered conformation (-2.68 kcalmol-1) that is over six times higher than that obtained at the same level of theory (Figure 6) for periodobutyne (-0.42 kcalmol-1). For the tri-substituted H-bonded case with W = NCH3, the E value (-4.51 kcalmol-1) is an entire order of magnitude larger than that periodobutyne barrier. Even though we borrowed the geometrical parameters from the eclipsed form at the B97D3 level (except for changing the value of ) for computing the energy of the staggered structures for n = 3, all of the E values obtained at that level of theory are noticeably closer to the MP2(full) values than the HF and B3PW91 values. Moreover, the slight stabilization of the system in the case where W = NCH3 (relative to the case where W = NH) is actually recovered very well with the B97D3 method (Figure 11), which indicates again the significance of correlation in reproducing subtle trends in the bonding and thermodynamics for these hydrogen bonded systems. And other cases where inductive effects are potentially important (as they are here for the -H vs. -


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CH3 substitution at N) are expected to require, too, an explicit accounting of electron correlation beyond the HF level. On the advice of one reviewer, we computed the barriers for these systems at levels of theory beyond MP2, including the CCSD(T) level. The results of those energy calculations (all obtained using structures obtained at the MP2(full) level) are shown in Figure 12. The relative energies obtained at the range of other high level methods computed along with the CCSD(T) values agree completely with the claims made above. As we saw in Figure 11 and emphasize in Figure 12, the subtle CH3 substituent effect is denied at HF level of theory. But it – the incremental extra stabilization predicted above when W = NCH3 – is confirmed in Figure 12 for all of the postHF methods through to the CCSD(T) level, underscoring the importance of correlation calculations for reproducing substituent effects.

Figure 12: Computed relative energies, E = Eeclipsed - Estaggered, of the mono- and tri- hydrogen bonded structures (Figure 2) with W = NH, and NCH3 obtained at high levels of theory for structures optimized at the MP2(full) level. Values were obtained at CCSD(T) level only for the less demanding monosubstituted structures for which the resources available proved adequate. The actual energies in Hartree units for the eclipsed and staggered conformations are given in the supporting information (Table S5).


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We show in Figure 12 that the barriers are underestimated drastically at the HF level relative to all of the other ab initio methods. The MP2 method26 used in Figure 12 seems to exaggerate the barriers, however, such that the CCSD(T) values fall neatly between the MP2 and the MP3 values in Figure 12 – which reflects the typical ordering observed for those three postHF levels of theory.34 Although we were unable to compute the CCSD and CCSD(T) energies for the much more demanding n = 3 cases, one might assume with some confidence that the CCSD(T) values fall within the narrow range between the MP2 and MP3 values on the right hand side in Figure 12 for both W = NH and W = NCH3. - Some Notes on Structure: For the mono-substituted cases (n = 1) for W = NH and W = NCH3 at the MP2(full) level, the C-C≡C bond angles are actually a few degrees less than 180o (Figure S3) arching in a bit towards the hydrogen bond, and the N---H hydrogen bond distances are 2.470 Å and 2.451 Å, respectively (see Figure S3). When the additional two pairs of substitutions are made going from n = 1 to n = 3, the systems symmetrize, however, such that the H bonds are stretched by just over 0.1 Å to give 2.581 Å and 2.583 Å, respectively for W = NH and NCH3. Relative to the simple butyne H3C-C≡C-CH3 molecule, the presence of the parallel intramolecular hydrogen bond(s) influences the covalent single and triple bonds within the central linear C-C≡C-C chain in different ways (Figure 13). For the C-C single bonds, for example, C1-C2 in Figure 13 contracts only slightly in the presence of the hydrogen bonds and the other C-C bond (C3-C4) is even less sensitive to the presence of the hydrogen bonds (Figure 13a). At the MP2(full) level, the triple bond is unresponsive. To three decimal places, the triple bond is the same length (1.211 Å) in all five cases in Figure 13. There is a slight decrease at the B3PW91 level (Figure S4), but not by much at all. It is clear from Figure 13 in fact that three hydrogen bonds working together are still too weak to compress a carbon-carbon triple bond to any significant extent.


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Figure 13: Internal carbon-carbon single and triple bond lengths in substituted but-2-ynes, all obtained at the MP2(full) level of theory. The overall outcome of the various small modifications in the interatomic separations in the carbon chain, therefore, is that the long C1---C4 separation is hardly affected by the presence of the hydrogen bonds. But the barriers to rotation increase dramatically relative to the simpler systems considered in previous sections of this work. Indeed, the rotational barrier at the MP2(full) level when W = NCH3 for n = 3 (i.e. 4.5 kcalmol-1), exceeds the corresponding MP2(full) barrier in ethane (3.1 kcalmol-1) by 50%. Without an adequate accounting for dispersion, however, (at the HF or uncorrected DFT levels) a substantial fraction of that stabilization in the hydrogenbonded systems is lost (Figures 11 and 12). - A Closing Remark on Rotors. One of the reasons that we converged on the proposed hydrogen bonded systems considered in this work is an interest in our group in molecular motors and hindered rotations in molecules. We have not used molecular dynamic methods in this study, but the presence of a noticeable barrier in the hydrogen bonded butynes are of interest to us because of the possibility of the thermal control of the rotation about the -C≡C- bonds. That prospect brings to mind for us the boron wheels, for example, that have been cited as molecular versions of socalled Wankel motors.35 We find that the barriers to rotation here are comparable to those found for systems of concentric boron rings.16,35 We have been gratified to find that hydrogen bonding


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is in fact achievable in these unprecedented butyne systems without disrupting the structural integrity of the -C-C≡C-C- core, while increasing significantly, though not exorbitantly, the sizes of the energy barriers in the structures. Alternative structures with comparable or stronger hydrogen or even halogen bonds may be contemplated as well. Summary and Outlook The conformational preferences of but-2-yne, its halogen and CN substituted analogues (R3C-C≡C-CR3), plus R3C-BN-CR3, and a set of novel derivatives exhibiting intra-molecular hydrogen bonding have been examined. We find that the insertion of a non-innocent C≡C or BN spacer into the ethane C-C bond stabilizes the eclipsed geometry over the staggered form for the hydrocarbon and several of its substituted variants. Among the perhalogenated butynes, R3C-C≡C-CR3, where R = F, Cl, Br, I and At, the preference for the eclipsed geometry increases as the atom gets larger and less electron withdrawing. The staggered geometry is actually preferred for the cases where R = F and CN, but it is increasingly unstable relative to the eclipsed form for R = Cl, Br, I, and At. Those general patterns in the bonding preferences in that set of substituted butyne systems have been determined using density functional methods, MP2 and higher levels of theory. The results are accounted for by an increase in the extent of fragment orbital interactions along the length of the butyne chain and an increasingly substantial role for electron correlation as the atom gets larger. A direct partitioning in terms of Coulomb interactions vs. charge transfer, exchange, and so forth to the overall barrier heights in the compounds has not been attempted here. In the case of ethane, that discourse has lingered for several years (emerging, fading, and re-emerging) spawning several contested contributions.4,36 - 41 A comparative assessment of that sort for popular 3738

3940


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energy decomposition strategies for the systems considered in this work may be in order, however, as one reviewer has suggested, for the next phase of this work. We find, nonetheless, that an NBO analysis of the interactions among the CR3 and CC fragments in the title compounds indicates that the triple bond in the middle of the R3C-C≡C-CR3 molecules effectively mediates certain orbital interactions between the terminal CR3 groups. Those interactions, along with dispersion, become increasingly important for the rotational barriers as the terminal R atoms become larger and more polarizable. And those bonding interactions between the triple bond and the C-R bonds, which intensify as R gets larger (for the set of halides), explains an observed decrease in the lengths of the C-C single bonds and an associated expansion (very slight) in the central triple bond going from R = F to R = Cl, Br, and I in Figure 4. A novel class of compounds in which adjacent intra-molecular hydrogen bonds provide a locking mechanism is investigated as a strategy for raising and controlling the barrier to rotation about the principal axis of the butyne molecule. The presence of the hydrogen bonds raises the energy barriers to rotation from less than 0.5 kcalmol-1 in periodobutyne to 4.5 kcalmol-1 for the triply hydrogen bonded systems. It should be possible, therefore, to determine experimentally the conformation and to control the hindered rotation of the terminal groups in these hydrogen bonded compounds much more easily than it has proven to be for butyne and perfluorobutyne.6-11 The importance of correlation corrections for simple substituted butynes and intramolecular hydrogen-bonded species is emphasized here. Over 1.5 kcalmol-1 is gained, for example, going from the HF to the CCSD(T) level of theory in one case (Figure 12), and noticeable differences are observed as well for uncorrected vs. dispersion corrected density functional methods.


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More work has to be done to understand the relative contribution (in quantitative terms) of charge transfer and non-covalent interactions in these structurally and thermodynamically interesting systems. It would be useful to assess as well the quality of alternative dispersion corrected density functional methods – a set of tools in quantum chemistry that continues to proliferate and to improve. More (and more accurate) experimental data on the rotational barriers in the substituted butynes examined in this work will be very helpful, too, for that assessment. The synthesis of the hydrogen-bonded species may be the most challenging first step in that direction.

ASSOCIATED CONTENT Supporting Information: Tables of optimized geometries discussed in this work. MP2(full) and B3PW91 structures, and data for graphs mentioned in this work, and long references for the Gaussian 03 and 09 suites of programs used in this work. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author: * Tel.: 804-484-1628; E-mail: [email protected]. Author Contributions: The manuscript was written through contributions of all three authors. All three authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT Our work was supported by the National Science Foundation (NSF-CAREER award (CHE1056430) and NSF-MRI Grants (CHE-0958696 (University of Richmond (UR)) and CHE1229354 (the MERCURY consortium). Omorodion and Bober are grateful to the Department of Chemistry and the School of Arts and Sciences at the University of Richmond as well for funding. We are grateful to the reviewers for their helpful comments and suggestions.


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References and Notes (1) Kikuchi, S. A History of the Structural Theory of Benzene—The Aromatic Sextet Rule and Hückel’s Rule. J. Chem. Ed. 1997, 74, 194-201. (2) Rocke, A. J. It Began with a Daydream: The 150th Anniversary of the Kekulé Benzene Structure. Angew. Chem. Int. Ed., 2015, 54, 46-50. (3) Kemp, J.; Pitzer, K. Hindered Rotation of the Methyl Groups in Ethane. J. Chem. Phys. 1936, 4, 749. (4) Mo, Y.; Gao, J. Theoretical Analysis of the Rotational Barrier of Ethane. Acc. Chem. Res. 2007, 40, 113-119. See also references therein. (5) Schore, N. E. Transition-Metal-Mediated Cycloaddition Reactions of Alkynes in Organic Synthesis. Chem. Rev. 1988, 88, 1081-1119. (6) Kopelman R. Far Ir Spectrum of Dimethylacetylene: Internal Rotation and Evidence for a D6h Effective Symmetry. J. Chem. Phys. 1964, 41, 1547-1553. (7) Bunker, P.R.; di Lauro C. Dimethylacetylene: The Theory Required to Analyse the Infrared and Raman Perpendicular Bands. Chem. Phys. 1995, 190, 159-169. (8) Palmer, M.; Walker I. The Electronic States of But-2-yne Studied by VUV Absorption, NearThreshold Electron Energy-Loss Spectroscopy and Ab Initio Configuration Interaction Methods. Chem. Phys. 2007, 340, 158-170. (9) Essers, M.; Haufe, G. e-EROS: Encyclopedia of Reagents for Organic Synthesis, last accessed July 15, 2015. http://onlinelibrary.wiley.com/doi/10.1002/047084289X.rn00669/abstract. (10) Miller, F.; Bauman R. Vibrational Spectrum of Hexafluoro 2 butyne. J. Chem. Phys. 1954, 22, 1544-1548.


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(11) Kveseth K.; Seip H.M., Stolevik R. The Molecular Structure of Hexafluoro 2 butyne Determined by Gas Electron Diffraction Acta Chemica Scandinavica. 1971, 25, 2975-2982. (12) Hirota, E.; Saito, S.; Endo, Y., Barrier to Internal Rotation in Ethane from the Microwave Spectrum of CH3CHD2 J. Chem. Phys. 1979, 71, 1183-1187. (13) Parra, R.; Zeng, X.C. Staggered and Eclipsed Conformations of C2F6: A Systematic Ab Initio Study J. Fluor. Chem 1997, 83, 51-60. (14) We use the ‘-BN-’ resonance structure throughout this paper. It reflects our bias, since we use –BN- as a substitute here for the isoelectronic -CC- unit. Moreover, the ‘sp3’ C atoms of the -CR3 fragments that are bonded to -BN- are saturated, so delocalization from N to -CR3 or from -CR3 to an empty valence p orbital on B are not expected to be especially large. The computed ‘BN’ Wiberg bond index in H3C-BN-CH3 is 2.02, while to corresponding C-B and N-C bond orders are 0.93 and 1.05, respectively. That the B-N bond order is greater than 2.00 confirms that the bond has some, however small, triple bond character. Similarly, the N-C bond order (.i.e. 1.05, which is too large for a simple σ bond) suggests that electron density from N delocalizes a bit onto that C center as well. The linear geometries of the R3CBN-CR3 compounds support the claim, too, that the triple bond character of the BN bond is substantial. (15) Martínez-Guajardo, G.; Donald, K. J.; Wittmaack, B K.; Vazquez, M. A.; and Merino, G. Shorter Still: Compressing C-C Single Bonds. Org. Lett. 2010, 12, 4058-4061. (Additions: ibid. 2011, 13, 172.) (16) Cervantes-Navarro, F.; Martínez-Guajardo, G.; Osorio, E.; Moreno, D.; Tiznado, W.; Islas, R.; Donald, K. J. and Merino, G. Stop rotating! One Substitution Halts the B19- Motor Chem. Comm. 2014, 50, 10680-10682. ACS Paragon Plus Environment

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(17) Head-Gordon, M.; Head-Gordon, T. Analytic MP2 Frequencies without Fifth-Order Storage. Theory and Application to Bifurcated Hydrogen Bonds in the Water Hexamer. Chem. Phys. Lett. 1994, 220, 122-128, and references therein. (18) K. Burke, J. P. Perdew, Y. Wang, Electronic Density Functional Theory: Recent Progress and New Directions (Eds.: J. F. Dobson, G. Vignale, M. P. Das), Springer, New York, 1998. (19) Perdew, J. P.; Burke, K.; Wang, Y. Generalized Gradient Approximation for the ExchangeCorrelation Hole of a Many-Electron System. Phys. Rev. B 1996, 54, 16533-16539 and references therein. (20) Dunning’s correlation consistent basis sets: Kendall, R. A.; Dunning Jr., T. H.; Harrison, R. J. Electron Affinities of the First Row Atoms Revisited. Systematic Basis Sets and Wavefunctions. J. Chem. Phys. 1992, 96, 6796‐6806. (21) Peterson, K.A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the post-d Group 16–18 Elements. J. Chem. Phys. 2003, 119, 1111311123. (22)

Peterson, K.A.; Shepler, B.C.; Figgen, D.; Stoll, H. On the Spectroscopic and

Thermochemical Properties of ClO, BrO, IO, and Their Anions. J. Phys. Chem. A 2006, 110, 13877-13883. (23) Gaussian 03, Revision E.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C. et al. The full reference for this method is in the supporting information.


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(24) Gaussian 09, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al. The full reference for this method is in the supporting information. (25) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements HPu. J. Chem. Phys., 2010, 132, 154104. (26) MP2(full) and MP2 calculations are distinguished by the exclusion of core electrons from the (post-SCF) correlation calculations in the latter (MP2) version of the method, following the designations for the Gaussian 03 and 09 suites of program. MP2(full) calculations consider both core and valence electrons. See the website http://www.gaussian.com/g_tech/g_ur/k_fc.htm (last accessed Sept. 1, 2016). (27) Pople, J. A.; Head Gordon, M.; Raghavachari K. Quadratic Configuration Interaction. A General Technique for Determining Electron Correlation Energies. J. Chem. Phys. 1987, 87, 5968-5975, and references therein. (28) Liu, S. J. Phys. Chem. A. Origin and Nature of Bond Rotation Barriers: A Unified View. 2013, 117, 962-965. (29) Incidentally, the version of the MP2 method that ignores correlation for the core electrons does better here (for R = CN) than the MP2(full) form, which overcorrects even more extremely than the former for correlation for some systems. (30) Donald, K. J.; Wittmaack, B. K.; Crigger, C. Tuning σ-Holes: Charge Redistribution in the Heavy (Group 14) Analogues of Simple and Mixed Halomethanes Can Impose Strong Propensities for Halogen Bonding. J. Phys. Chem. A 2010, 114, 7213-7222.


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(31) Tawfik, M.; Donald, K. J. Halogen Bonding: Unifying Perspectives on Organic and Inorganic Cases. J. Phys. Chem. A 2014, 118, 10090-10100. (32) ‘Monosubstituted’ refers in this context to the case in which both terminal carbon atoms have a single substituent such that a single intra-molecular hydrogen bond can be formed. In the ‘trisubstituted’ case, the terminal carbon atoms each have three complementary substituents such that three hydrogen bonds can be formed. (33) The optimization of that staggered systems at the B97D3 level of theory proved to be very problematic. The staggered forms converged inevitably to the eclipsed conformer during unconstrained optimization calculations, or failed to converge in cases where constraints were employed to maintain the staggered geometry. (34) For a description of the tendencies in MPn data to oscillate between over and under-estimating correlation for n = 2 to 4 relative to the correct or some limiting value, see: Jensen, F. Introduction to Computational Chemistry; John Wiley & Sons: West Sussex, 2007; pp 162168. (35) Merino, G. and Heine, T., And Yet It Rotates: The Starter for a Molecular Wankel Motor. Angew. Chem. Int. Ed., 2012, 51, 10226‐10227. (36) Pitzer, R. The Barrier to Internal Rotation in Ethane. Acc. Chem. Res. 1983, 16, 207-210. (37) Pophristic V., Goodman L., Hyperconjugation Not Steric Repulsion Leads to the Staggered Structure of Ethane. Nature 2001, 411, 565-568. (38) Bickelhaupt, F. M.; Baerends, E. J. The Case for Steric Repulsion Causing the Staggered Conformation of Ethane. Angew. Chem. Int. Ed., 2003, 42, 4183-4188. (39) Weinhold, F. Rebuttal to the Bickelhaupt–Baerends Case for Steric Repulsion Causing the Staggered Conformation of Ethane. Angew. Chem. Int. Ed., 2003, 42, 4188-4194.


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(40) Liu, S.; Govind, N. Toward Understanding the Nature of Internal Rotation Barriers with a New Energy Partition Scheme: Ethane and n-Butane. J. Phys. Chem. A 2008, 112, 6690-6699. (41) Cortés-Guzmán, F.; Cuevas, G.; Pendás, Á. M.; Hernandez-Trujillo, J. The Rotational Barrier of Ethane and Some of its Hexasubstituted Derivatives in Terms of the Forces Acting on the Electron Distribution. Phys. Chem. Chem. Phys., 2015, 17, 19021-19029.


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