Tunneling by 16 Carbons: Planar Bond Shifting in [16]Annulene

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Tunneling by 16 Carbons: Planar Bond Shifting in [16]Annulene Cameron S. Michel, Philip P. Lampkin, Jonathan Z. Shezaf, Joseph F. Moll, Claire Castro, and William L. Karney J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b13131 • Publication Date (Web): 08 Mar 2019 Downloaded from http://pubs.acs.org on March 8, 2019

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Journal of the American Chemical Society

Tunneling by 16 Carbons: Planar Bond Shifting in [16]Annulene Cameron S. Michel, Philip P. Lampkin, Jonathan Z. Shezaf, Joseph F. Moll, Claire Castro,* and William L. Karney* Department of Chemistry, University of San Francisco, 2130 Fulton Street, San Francisco, California 94117 United States Email: [email protected], [email protected]

Abstract Mid-sized annulenes are known to undergo rapid p-bond shifting. Given that heavy-atom tunneling plays a role in planar bond shifting of cyclobutadiene, we computationally explored the contribution of heavy-atom tunneling to planar π-bond shifting in the major (CTCTCTCT, 5a) and minor (CTCTTCTT, 6a) known isomers of [16]annulene. UM06-2X/cc-pVDZ calculations yield bond-shifting barriers of ca. 10 kcal/mol. The results also reveal extremely narrow barrier widths, suggesting a high probability of tunneling for these bond-shifting reactions. Rate constants were calculated using canonical variational transition state theory (CVT) as well as with small curvature tunneling (SCT) contributions, via direct dynamics. For the major isomer 5a, the computed SCT rate constant for bond shifting at 80 K is 0.16 s–1, corresponding to a half-life of 4.3 s, and indicating that bond shifting is rapid at cryogenic temperatures despite a 10 kcal/mol barrier. This contrasts with the CVT rate constant of 8.0 x 10–15 s–1 at 80 K. The minor isomer 6a is predicted to undergo rapid bond shifting via tunneling even at 10 K. For both isomers, bond shifting is predicted to be much faster than competing conformation change despite lower barriers for the latter process. The preference for bond shifting represents cases of tunneling control in which the preferred reaction is dominated by heavy-atom motions. At all temperatures below –50 °C, tunneling is predicted to dominate the bond shifting process for both 5a and 6a. Thus, [16]annulene is predicted to be an example of tunneling by 16 carbons. Bond shifting in both isomers is predicted to be rapid at temperatures accessible by solution-phase NMR spectroscopy, and an experiment is proposed to verify these predictions.

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Introduction The importance and prevalence of hydrogen atom tunneling in chemistry has been long established;1,

2

such tunneling is now known to play a significant role in many enzymatic

reactions.3-5 Evidence of tunneling by heavier atoms is much less common. Since the landmark paper of Carpenter on carbon atom tunneling in planar bond shifting of cyclobutadiene (1),6 the number of heavy-atom tunneling (usually by C or N) processes has gradually increased.7, 8 Of the cases that have been observed experimentally9-16 or predicted computationally,17-27 most are such that the significant motions comprising the reaction are focused on one or two atoms. Some notable exceptions, some of which are shown in Scheme 1, include computational work on (1) the Cope rearrangement of semibullvalene (2),17 for which tunneling has since been confirmed experimentally;15 (2) π-bond shifting in pentalene (3);21 π-bond shifting in heptalene (4);21 and (3) a group of 11 organic reactions including the Diels-Alder reaction.28 Scheme 1 1

2

3

4

The reactions of 2 and 3 were predicted to be fast at cryogenic temperatures and to be dominated by carbon tunneling. For example, for Cope rearrangement in 2, the computed rate constant including small curvature tunneling at 10 K was 1.4 x 10–3 s–1, which was 84 orders of magnitude larger than that without tunneling (7.1 x 10–88 s–1).17 Bond shifting in the 12-carbon system heptalene (4), with a 13 kcal/mol computed barrier, was predicted to be dominated by carbon tunneling, with tunneling-inclusive rate constants of 0.36 s–1 at 100 K and 1.2 x 10–38 s–1 at 10 K.21

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Significant conformational motion along the reaction coordinate for 4 was the reason for the small rate constant at cryogenic temperature. It is noteworthy that the reactions in Scheme 1 do not allow for probing the possibility of tunneling control29 (vide infra), as there is no other competing reaction in each case. In contrast to the bridged systems pentalene (3) and heptalene (4), planar π-bond shifting in monocyclic [4n]annulenes occurs via a singlet diradical transition state. The rich work on cyclobutadiene6,

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raises the question of whether facile, planar π-bond shift in larger

[4n]annulenes can be explained by carbon atom tunneling. Bond shifting in cyclooctatetraene (COT) occurs after flattening of the ring, and the overall bond-shift barrier (ca. 14 kcal/mol) is due mostly to the barrier for flattening, i.e. ring inversion (10-12 kcal/mol).35-38 Thus, the role of tunneling in COT dynamics is unclear. In larger [4n]annulenes, particularly those with trans C=C bonds, the competition between multiple intramolecular processes such as bond shifting and conformation change can lead to the possibility of tunneling control, in which a system preferentially passes through a higher but narrower barrier, rather than over a lower but wider barrier.29, 39 There is no evidence that the main isomer of [12]annulene undergoes planar bond shifting.40 Thus, our work here focuses on [16]annulene. The observation of only one peak (a singlet) in the 1H NMR of spectrum of [16]annulene at temperatures above -50 °C indicates that multiple processes occur rapidly at those temperatures: planar bond shifting, degenerate conformational change, and configuration change.37 Scheme 2 summarizes these processes. The two main configurational isomers of [16]annulene, 5a (CTCTCTCT) and 6a (CTCTTCTT), can both undergo planar degenerate bond shift as well as conversion to their corresponding conformational minima, 5b and 6b. The conformation change consists of rotation of a trans C=C bond so that inner and outer hydrogens switch positions. Oth explained that a series of bond shift and conformation change steps in 5 would render all 16 protons magnetically equivalent. (Only the first conformation change step is shown.) The same applies to isomer 6.41 The nonplanar nature of 5 and 6 (due to sterics between inner hydrogens) distinguishes these systems from cyclobutadiene (1) and pentalene (3), which are completely planar, and the competition between bond shift and conformation change distinguishes 5 and 6 from 1, 3, and heptalene (4), which have no competing unimolecular processes. In addition, bond shifting in 5 and 6 is distinct from that in heptalene in that the heptalene bond-shifting transition state has a closed-shell electronic structure, whereas the bond-shift transition states for 5 and 6 are singlet diradicals. Isomerization of 5a to 6a is a multistep process that occurs via Möbius bond shift

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between 5b and 6b, and not directly between 5a and 6a.42 On the basis of dynamic NMR measurements combined with line-shape simulation, Oth derived activation energies (Ea) of 8.2 to 9.2 for all four processes: 5a

5a’, 5a

5b, 6a

6a’, and 6a

6b.37,43

If, as in cyclobutadiene, bond shifting in [16]annulene requires only small displacements of the carbons, then [16]annulene may be a case involving simultaneous tunneling by 16 heavy atoms. In addition, depending on the relative barrier heights of the competing bond shift and conformation change processes, the possibility arises that the system may preferentially tunnel through the higher barrier rather than pass over the lower barrier––a phenomenon that Schreiner has termed “tunneling control.”29, 39 Scheme 2 Ha

conform. change Hb

Hb

Ha

TS5b

5b

π-bond shift Hb

TS5a

5a CTCTCTCT

Ha 5a’

Möbius bond shift

conform. change

Hc Hd 6b

TS6b

Hd

π-bond shift

Hc

TS6a

6a CTCTTCTT

Hd

Hc 6a’

Here we report computational results on the competing processes of bond shifting and conformation change in the two major configurational isomers of [16]annulene, 5 and 6. We predict bond shifting to be rapid at cryogenic temperatures due to tunneling by 16 carbons at once, providing the first example of tunneling control39, 44-46 in annulenes. To our knowledge these are the first examples of heavy-atom tunneling in systems where multiple pathways are possible. Moreover, our results reveal tunneling systems where the motion is concentrated on the largest number of heavy atoms to date.

Computational Methods Geometries of all stationary points were optimized at the (U)M06-2X/cc-pVDZ level.47-49 Vibrational analyses were performed at the same level, to confirm the nature of stationary points and obtain zero-point vibrational energies. The M06-2X method was chosen for several reasons. 4


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First, for the CTCTCTCT-[16]annulene minimum, it provides C–C bond lengths in good agreement with the crystal structure,50 reflecting an accurate degree of bond-length alternation. It also gives geometries close to those obtained with the BHandHLYP method, which is considered reliable for annulenes.51,

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Second, broken-spin symmetry UM06-2X provides a correct

qualitative description of the potential surface for planar bond shifting, in that it predicts the bondequalized structures to be transition states. Such behavior is essential for the direct dynamics calculations to work. In contrast, UBHandHLYP predicts that the bond-equalized form of [16]annulene is a minimum (i.e. no imaginary frequencies), rendering that method unsuitable. Third, UM06-2X yields reaction energetics for the systems of interest in reasonable agreement with higher-level methods such as CASPT2. UM06-2X was also used for intrinsic reaction coordinate (IRC) calculations to evaluate barrier widths and obtain reactant and product geometries for subsequent rate calculations. To check the reliability of the UDFT energies, energies were also computed with the CASPT2 method,53 which applies second-order perturbation theory (and hence dynamic electron correlation54) to a CASSCF reference wave function. The active space for CASPT2 calculations consisted of all 16 π electrons, and all 16 π/π* molecular orbitals. The CASPT2 calculations employed the cc-pVDZ basis set,48 and the default IPEA shift of 0.25 hartrees was used. Rate constants were computed by direct dynamics, using canonical variational transition state theory (CVT),55 and also with inclusion of multidimensional tunneling in the form of small curvature tunneling (SCT).4, 56-59 The normal step size used in these calculations was 0.01 bohr (with a scaling mass of 1 amu), but for the bond shifting reactions 40 initial steps of 0.001 bohr step size were used to accurately capture the narrow barrier shape near the top of the barrier. NMR chemical shifts and coupling constants were computed with the GIAO-B3LYP/6311+G** method60 at the M06-2X/cc-pVDZ geometries. Computed shieldings were subtracted from the shielding computed for tetramethylsilane (TMS) to obtained chemical shifts in ppm. Geometry optimizations, frequency calculations, IRC, and NMR chemical shift and coupling constant calculations were performed with Gaussian 09.49 CASPT2 calculations were performed with Molcas 8.2.61 Direct dynamics calculations for rate constants employed Gaussrate62 as the interface between Gaussian 09 and Polyrate 2010-A.63 Vibrations and molecular orbitals were visualized with Molden.64

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Results and Discussion Energetics, Geometries, and Reaction Coordinates. The M06-2X relative energies in Table 1 indicate that for both 5a and 6a the barrier for degenerate π-bond shift is predicted to be higher than that for conformation change. Because unrestricted DFT yields a 50:50 wave function for the singlet diradical transition states TS5a and TS6a, single point energies for all species were also computed at the CASPT2(16,16)/cc-pVDZ level.53, 61 Due to systematic errors in the CASPT2 method when comparing open- vs. closed-shell species, the computed energies of TS5a and TS6a in Table 1 are likely too low, but it is difficult to know by how much.65 Overall, however, the finding that the UM06-2X relative energies of TS5a and TS6a are within 1-2 kcal/mol of the energies obtained with CASPT2 suggests that the UM06-2X results are reasonably trustworthy, despite the 50:50 nature of the wave functions. Table 1. Relative Energies (in kcal/mol) of Stationary Points for Bond Shifting and Conformation Change in [16]Annulene Isomers 5 and 6a M06-2X species sym rel E 5a S4 0.0 TS5a C2v 9.6b TS5b C1 8.3 5b C1 5.3 6a TS6a TS6b 6b a

C1 Cs C1 C1

1.1 11.4c 7.5 4.6

CASPT2 rel E 0.0 8.8 10.9 8.4 3.5 9.6 9.5 6.9

All calculations performed with the cc-pVDZ basis set on (U)M06-2X optimized geometries.

Unrestricted DFT calculations on TS5a and TS6a employed broken spin symmetry. All relative energies are referenced to 5a and are corrected for M06-2X ZPE differences. b = 1.22. c

= 1.22. Figure 1 shows the DFT optimized geometries of 5a and 6a as well as the bond shift

transition states. Geometries of conformational minima 5b and 6b and the corresponding transition states are given in Supporting Information. Prior to bond shifting, bond-alternating 5a must

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undergo a significant amount of conformational flattening. In this respect 5a is similar to cyclooctatetraene and heptalene (4), which must flatten before bond shifting can occur (vide infra). In contrast, 6a and TS6a differ much less from each other in their degree of nonplanarity.

1.349 H H

H

1.400

1.461 1.350 1.454

H

H

1.402

H

H

H

5a (S4) ∆r = 0.112 Å

TS5a (D2d) ∆r = 0.002 Å

1.452

1.350 1.465 1.349 1.456 1.354

1.466 1.350 1.350 1.457 1.453

6a (C1) ∆r = 0.117 Å

1.399

1.407 1.402 1.395 1.412

1.404 1.3991.403

TS6a (Cs) ∆r = 0.017 Å

Figure 1. (U)M06-2X/cc-pVDZ optimized structures of [16]annulene isomers 5a (CTCTCTCT) and 6a (CTCTTCTT) and corresponding bond-shift transition states TS5a and TS6a. Selected C– C bond lengths in Å. Edge views show degree of nonplanarity. ∆r = difference between the longest and shortest C–C bonds. The probability of tunneling depends on barrier height, barrier width, and the mass of the particle. For example, for a simplified parabolic barrier, the tunneling probability is given by eq 1, where P is the tunneling probability, w is the barrier width, m is the mass of the particle, and V0– E is the height below the top of the barrier.7 Equation 1 shows that the exponential function for probability is affected linearly by barrier width and by the square root of the mass. 𝑃 = exp&−𝜋 ) 𝑤+2𝑚(𝑉0 − 𝐸)/ℎ5

(1)

In a more sophisticated treatment––one that accounts for small-curvature tunneling along a multidimensional reaction path, as in the calculations employed here––the tunneling transmission probability at energy E is given by 𝑃6 (𝐸) in equation 2, where 𝜃(𝐸) is the imaginary action integral evaluated along the tunneling path, defined according to equation 3.59 In eq 3, 𝜇9:: is the

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effective reduced mass, s is the value of the reaction coordinate, and 𝑉;6 is the vibrationally adiabatic ground state potential (vide infra). 𝑃6 (𝐸) = 1⁄{1 + exp[−2𝜃(𝐸)]} F

𝜃(𝐸) = (2𝜋/ℎ) ∫F G +2𝜇9:: (𝑠)|𝐸 − 𝑉;6 (𝑠)| 𝑑𝑠 H

(2)

(3)

Whether one uses equation 1 or the combination of equations 2 and 3, the same qualitative conclusions result. Reactions involving large motions by hydrogen atoms can still have high tunneling probability due to the small mass of hydrogen. Large motions associated with conformation change, especially of the type involving rotation of a trans C=C bond about the flanking single bonds, involve large motions by atoms with large masses (carbons), suggesting lower tunneling probabilities. The plots of potential energy vs. reaction coordinate s (where s is the distance along the path in mass-weighted coordinates) for 5a (Figure 2) and 6a (in Supporting Information) show the striking difference between the taller but narrower barrier for bond shifting (e.g. 5a

5a’) and the lower but wider barrier for conformation change (e.g. 5a

5b). The

dotted curve in Figure 2 depicts the potential energy along the minimum energy path (Vmep), exclusive of zero-point energies, whereas the solid curve shows the vibrationally adiabatic ground state potential (𝑉;6 ), which includes zero-point contributions.66 Notice that the units on the abscissae contain the square root of the mass because we use mass-scaled coordinates. In other words, the effect of mass (i.e. the contribution of mass to barrier width) is already included in Figure 2. In particular, the 𝑉;6 vs. s curve in Figure 2 shows that 5a exhibits the potential for “tunneling control,” i.e., preferential passage through the higher but narrower barrier rather than passage over the lower barrier. There are several prior examples of this in the literature.29, 39, 44-46 14 12

Vmep VaG

TS5b

10 V (kcal/mol)

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TS5a

8 6 4

5b

2 0 -20

5a’

5a -15

-10

-5

0

5

10

15

20

s (bohr•amu1/2)

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Figure 2. (U)M06-2X/cc-pVDZ potential energy as a function of reaction coordinate s, where s is the distance along the path in mass-scaled coordinates, for bond shifting and conformation change in CTCTCTCT-[16]annulene isomer 5a. Solid curve is the minimum-energy (Vmep) path (exclusive of zero-point energy). Dotted curve is the vibrationally adiabatic ground-state potential VaG, set to 0 kcal/mol for the energy of 5a. The VaG curve includes the effect of zero-point energy, whereas the Vmep curve does not. The 5a minimum corresponds to zero on the s-axis, with conformation change to the left and bond shift to the right. Separate from the process of isomerization to a different conformer, the need for annulenes to flatten somewhat before bond shifting can also affect the barrier width and hence the tunneling probability. The plot for 5a

5a’ is reminiscent of that for bond shifting in heptalene (4),1 as the

latter system also exhibits a long portion of low-slope curve that corresponds mainly to conformational flattening that precedes bond shift. Figure 3 depicts superimposed Vmep plots for degenerate bond shifting in 5a, 6a, and heptalene (4).67 Despite the similarity in overall barriers for bond shifting, the heptalene curve in Figure 3 exhibits a significantly higher shoulder than that for 5a, due to the greater energetic cost of conformational flattening in 4. In contrast, 6a requires very little conformational reorganization before bond shifting. 14 12 Vmep (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5a bond shift

10

6a bond shift 4 bond shift

8 6 4 2 0 -10

-8

-6

-4

0 4 -2 2 s (bohr•amu1/2)

6

8

10

Figure 3. (U)M06-2X/cc-pVDZ plots of potential energy along the minimum-energy path as a function of reaction coordinate s, where s is the distance along the path in mass-scaled coordinates. (a) Bond shifting and conformation change in CTCTCTCT-[16]annulene isomer 5a. The 5a minimum corresponds to zero on the s-axis, with conformation change to the left and bond shift to the right. (b) Comparison of potential energy along the minimum energy path for bond shifting in 5a (solid line), CTCTTCTT isomer 6a (dashed line), and heptalene (4, dotted line). The transition state for each process corresponds to zero on the s-axis. The circles on the heptalene curve illustrate how much wider the heptalene bond shifting barrier is compared to the barriers for bond shifting in 5a and 6a, at a point 3 kcal/mol above the minima.

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The contrast between 4 on the one hand, and 5a and 6a on the other hand, with respect to necessary conformational motions preceding bond shifting, can be understood by evaluating distances moved by carbons. Table 2 shows the average distance moved by the carbon atoms as each molecule goes from one point on the Vmep curve to a symmetrical point on the other side (as exemplified by the two circles in Figure 3), as well as the maximum distance moved by a carbon atom. From one potential minimum to the equivalent bond-shifted minimum (“0.0 kcal” in Table 2), the carbons of heptalene (4) move an average of 0.48 Å, those of 5a 0.44 Å, and those of 6a 0.14 Å, indicating that overall 6a requires the least motion. By a point 2 kcal/mol above the minima, the carbons of 5a and 6a have to move an average of less than 0.10 Å to reach a symmetrical point on the other side of the barrier. By 3 kcal above the minimum, the carbons of 5a and 6a must move less than 0.08 Å, whereas the carbons of 4 still have to move an average of more than 0.15 Å (Table 2, and circles in Figure 3), indicating that at that energy 4, unlike 5a and 6a, still has not reached the “narrow” part of the barrier. Indeed, even at 3 kcal/mol above the minimum, the difference between the longest and shortest C–C bonds (∆r) in 4 is 0.134 Å, the same as in the 4 minimum; that is, bond shifting has not progressed at all. That flattening and bond shifting are largely but not completely separate in 5a is evident from how little ∆r changes between the optimized geometry of 5a (0.112 Å) and the geometry at a point 3.0 kcal/mol up the minimumenergy path for bond-shifting (0.103 Å). Table 2. Distances Moved (in Å) by Carbons in π-Bond Shift Reactionsa 0.0 2.0 3.0 kcal/molb cpd

avg

max

kcal/molb avg

max

kcal/molb avg

max

4

0.479 0.851

0.243 0.458

0.159 0.301

5a

0.440 0.909

0.081 0.107

0.067 0.076

6a

0.144 0.303

0.071 0.099

0.063 0.078

a Values for 5a and 6a taken from M06-2X/cc-pVDZ

results. Values for heptalene are from M06-2X/6-31G* results. Average values are taken over all carbons in each molecule. Max = maximum distance moved by a carbon. bV mep relative to the energy of the reactant.

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Kinetics. Rate constants for the processes of interest for 5a computed with canonical variational transition state theory (CVT) as well as those including small curvature tunneling (CVT/SCT) are provided in Table 3. The corresponding rate constants for 6a are given in Table 4. At all temperatures, the quasiclassical68 (CVT) rate constants for conformation change are larger than the CVT rate constants for bond shifting, due to the lower computed barrier for the former process. Thus, conformation change should be faster if the system were governed solely by transition state theory. When tunneling contributions are included, however, bond shifting is faster than conformation change of 5a at all temperatures up to 240 K. At 100 K, for example, bond shifting is predicted to be more than 106 times faster than conformation change. Even at 80 K bond shifting of 5a is predicted to be rapid; the computed CVT/SCT rate constant of 0.16 s–1 corresponds to a half-time of 4.3 s for the process. Moreover, tunneling overwhelmingly dominates the rates of bond shifting, accounting for >95% of the rate at 240 K and 99.99% of the rate at 160 K.

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Table 3. (U)M06-2X/cc-pVDZ Barrier Heights (in kcal/mol) and Computed Rate Constants (in s–1) for Bond Shifting and Conformation Change in CTCTCTCT-[16]Annulene 5a 5a bond shift 5a conform. chgb (5a 5a’) (5a 5b) ‡ c ‡ V = 12.9 kcal/mol V = 9.2 kcal/molc T (K) kCVT kCVT/SCT kCVT kCVT/SCT 10 1.1x10–199 9.6x10–21 1.1x10–170 2.7x10–126 20 3.1x10–94 6.9x10–14 9.5x10–80 2.3x10–67 40 2.3x10–41 1.2x10–6 3.9x10–34 1.7x10–32 –15 –1 80 8.0x10 1.6x10 3.5x10–11 8.5x10–11 100 1.7x10–9 3.9x100 1.5x10–6 2.6x10–6 110 1.5x10–7 1.4x101 7.2x10–5 1.2x10–4 –6 1 –3 120 6.2x10 4.3x10 1.8x10 2.7x10–3 140 2.2x10–3 2.8x102 3.0x10–1 4.0x10–1 160 1.8x10–1 1.3x103 1.4x101 1.7x101 0 3 2 180 5.7x10 5.1x10 2.7x10 3.3x102 200 8.9x101 1.7x104 3.0x103 3.4x103 220 8.6x102 4.8x104 2.1x104 2.4x104 3 5 5 240 5.7x10 1.3x10 1.1x10 1.2x105 260 2.8x104 3.4x105 4.3x105 4.7x105 a CVT= canonical variational transition state theory. SCT = small curvature tunneling. CVT/SCT includes both overbarrier and tunneling contributions. b If one includes symmetry considerations, the rate constants for conformation change in 5a should be doubled.69 c V‡ refers to the V mep barrier height.

The influence of tunneling on bond shift in 5a can also be seen from the tunneling transmission coefficient, k, which relates to the rate constant k according to eq 2, where R is the 𝑘≈𝜅

MN O

𝑒 Q∆6

‡ /MN

(2)

gas constant, T is the absolute temperature, h is Planck’s constant, and ∆G‡ is the free energy of activation. In the absence of tunneling, k = 1, whereas when tunneling contributes, k > 1. The k values for 5a bond shifting at 10 K and 100 K are 8.7 x 10178 and 2.3 x 109, respectively. Even at 240 K (–33 °C), k is 23.2, indicating that tunneling dominates the process. In contrast, tunneling contributes far less to the rate of conformation change in 5a, as reflected by, for example, k = 1.77 at 100 K.

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The rate constant results for the CTCTTCTT isomer 6a are shown in Table 4. Without tunneling, conformation change in 6a is faster than bond shifting in 6a by at least three orders of magnitude at all temperatures, but with inclusion of tunneling, bond shift is faster below about 140 K. Most striking is the large computed kCVT/SCT of 0.36 s–1 for bond shifting of 6a at 10 K. This contrasts sharply with the computed kCVT/SCT value of 9.6 x 10–21 s–1 for bond shifting of 5a at the same temperature. Thus, bond shifting in 6a, via tunneling, is predicted to be rapid even at 10 K. This is presumably due to the narrower barrier at low energies for bond shifting in 6a compared to 5a (Figure 3). Table 4. (U)M06-2X/cc-pVDZ Barrier Heights (in kcal/mol) and Computed Rate Constants (in s–1) for Bond Shifting and Conformation Change in CTCTTCTT-[16]Annulene 6a 6a bond shift 6a conform. change (6a 6a’) (6a 6b) ‡ b ‡ V = 13.8 kcal/mol V = 7.4 kcal/molb T (K) kCVT kCVT/SCT kCVT kCVT/SCT –215 –1 –130 10 1.5x10 3.6x10 1.6x10 1.4x10–86 20 3.5x10–102 8.3x10–1 1.2x10–59 3.5x10–47 40 2.3x10–45 2.3x100 4.6x10–24 2.7x10–22 –17 1 80 7.6x10 1.7x10 4.2x10–6 1.1x10–5 100 4.0x10–11 5.2x101 1.8x10–2 3.2x10–2 110 4.9x10–9 9.3x101 3.7x10–1 6.1x10–1 –7 2 0 120 2.7x10 1.7x10 4.7x10 7.1x100 140 1.5x10–4 5.1x102 2.6x102 3.5x102 160 1.7x10–2 1.5x103 5.2x103 6.7x103 –1 3 4 180 6.8x10 3.9x10 5.5x10 6.6x104 200 1.3x101 9.9x103 3.6x105 4.2x105 220 1.5x102 2.4x104 1.7x106 1.9x106 3 4 6 240 1.2x10 5.7x10 6.2x10 6.9x106 260 6.5x103 1.3x105 1.9x107 2.0x107 a CVT= canonical variational transition state theory. SCT = small curvature tunneling. CVT/SCT includes both overbarrier and tunneling contributions. b V‡ refers to the V mep barrier height. One of the most dramatic manifestations of tunneling is the temperature independence of rate constants for some systems at low temperature. Figure 4 depicts Arrhenius plots of the computed rate constants. The plots show graphically how bond shifting for both 5a and 6a is influenced much more by tunneling than is conformation change. For 5a (Figure 4a), the CVT/SCT 13



curve for bond shifting does not level off at low temperature, suggesting that tunneling for that process is thermally activated.70 In this respect bond shifting in 5a is similar to the case of heptalene (4), which also requires significant conformational motion.21 On the other hand, the CVT/SCT curve for bond shifting in 6a (Figure 4b) levels off below about 50 K to a fairly high value (ln k ~ –1.0 for k = 0.36 s–1 at 10 K), suggesting that bond shifting via tunneling can occur from the lowest quantum state of 6a.10,71

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-40 CVT, 5a bond shift CVT/SCT, 5a bond shift

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Figure 4. Arrhenius plots of M06-2X/cc-pVDZ rate constants for bond shifting and conformation change in (a) CTCTCTCT-[16]annulene isomer 5a and (b) CTCTTCTT isomer 6a. Blue = bond shifting, red = conformation change. Dashed lines = without tunneling, canonical variational transition state theory (CVT). Solid curves = with small-curvature tunneling (CVT/SCT). Our results suggest that bond shifting is favored over conformation change below 240 K for 5a, and below 140 K for 6a, despite higher barriers for bond shifting in both cases. Such “tunneling control” arises because of narrow barrier widths.39 Previously reported examples of tunneling control have all involved movement of a light atom (hydrogen) in the preferred reaction.39, 44-46 To our knowledge, planar bond shifting processes in the two main isomers of [16]annulene represent the first examples of tunneling control in which the preferred process is dominated by heavy-atom motions. Moreover, these processes entail significant movement by all 16 carbons of the molecule. 14


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There are key discrepancies between our results and the earlier conclusions of Oth.37 For example, based on NMR line shape analysis, Oth proposed rate constants of 55 s–1 and 40 s–1 at – 100 °C (173 K) for bond shifting and conformation change, respectively, in 5a. With tunneling included, we predict corresponding rate constants of 2700 s–1 and 82 s–1 for bond shifting and conformation change, respectively. For 6a, Oth derived values of 2800 s–1 for both processes at – 100 °C, compared to our values of 2400 s–1 and 22000 s–1 for bond shift and conformation change, respectively.72 The rate constants for bond shift in 6a agree reasonably well. In contrast, our rate constant for bond shift in 5a is ca. 50 times that obtained by Oth. The results allow us to make a testable prediction involving NMR spectroscopy.27, 73 The major isomer 5a predominates in solution; thus, one can focus on what the NMR spectrum of 5a would look like. The computed 1H NMR chemical shifts and coupling constants for 5a are shown in Figure 5. If both bond shifting and conformation change in 5a are slow, then the Hb and Hd protons should give separate signals differing by about 0.10 ppm, with each being a doublet of doublets. In addition, the Ha signal should appear as a doublet of doublets, with coupling constants of approximately 14 Hz and 10 Hz. However, if bond shifting is rapid and conformation change is slow, the Hb and Hd protons become magnetically equivalent, and as a result the Ha protons should appear as a triplet, and the Hc protons should also appear as a triplet. Assuming a 500 MHz spectrometer,74 we estimate that in the temperature range 110-140 K, bond shifting in 5a should be rapid, whereas conformation change should be slow, yielding an NMR spectrum with triplets for Ha and Hc rather than doublets of doublets. Given the practical realities of NMR spectroscopy, this prediction should be considered a guideline. Nevertheless, as current NMR technology is far improved relative to the 60 MHz instrument used by Oth,37 a reexamination of the spectrum of [16]annulene should provide evidence of tunneling in planar bond shifting in [16]annulene.

15



5.68 5.43 H 5.78

Hd

Hd

Hb

c

Ha 12.90 ppm

J(Ha-Hb) = 9.7 Hz J(Ha-Hd) = 13.7 Hz J(Hb-Hc) = 11.5 Hz J(Hc-Hd) = 6.4 Hz

Figure 5. GIAO-B3LYP/6-311+G**//M06-2X/cc-pVDZ 1H NMR chemical shifts (in ppm d) and coupling constants for S4-symmetric CTCTCTCT-[16]annulene (5a).

Conclusions In summary, we have performed multidimensional tunneling calculations, using density functional theory, on competing dynamic processes in the two lowest energy isomers of [16]annulene. Based on the rate constants obtained with and without inclusion of small curvature tunneling, planar π-bond shifting is predicted to be dominated by heavy-atom tunneling and to be rapid at cryogenic temperatures––e.g. kCVT/SCT = 0.16 s–1 at 80 K for the major (CTCTCTCT) isomer 5a and kCVT/SCT = 0.36 s–1 at 10 K for the minor (CTCTTCTT) isomer 6a. Despite higher barriers for bond shifting than for conversion to the nearest conformational minima, the predicted kinetic preference for bond shifting in both 5a and 6a constitutes a rare example (the first, we think) of tunneling control in which the atomic motions are concentrated on multiple carbons rather than on hydrogen. Building on Carpenter’s prescient study of carbon tunneling in cyclobutadiene and on recent work on heavy-atom tunneling, our results extend the scope of such tunneling to systems that tunnel rapidly despite significant motions of 16 carbon atoms. Our results also indicate that, due to tunneling, there is a temperature range for which NMR spectroscopy on [16]annulene should show rapid planar bond shifting but slow conformation change. Efforts to test this prediction are underway.

Acknowledgements. This work was generously supported by the National Science Foundation (CHE-1565793) and the University of San Francisco Faculty Development Fund. We thank Dr. David Hrovat (University of North Texas) and Prof. Charles Doubleday (Columbia University) for helpful discussions.

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Supporting Information Available: Absolute energies, zero point energies, structures of species involved in conformation change reactions, potential energy profile along the reaction coordinate for bond shift and conformation change in 6a, a sample Polyrate input file, tables of computed rate constants, discussion of QRST calculations, optimized Cartesian coordinates for all stationary points, and complete citations for software used. This material is available free of charge via the Internet at http://pubs.acs.org.

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71.

Our computed rate constants for bond shifting do not completely level off because the

results were obtained without using the quantized reactant state tunneling (QRST) method. Using the QRST method gives similar results to those in Tables 3 and 4 for bond shifting, though rate constants may differ by a factor of two at very low temperatures. QRST was found to be inappropriate for the conformation change reactions. See Supporting Information for details. 72.

Degenerate conformation change in 6a is a three-step process, or at least it requires

rotation of three trans C=C bonds. Here we have computed only the first step, and it is uncertain whether this is the rate-determining step. Degenerate conformation change in 5a requires four steps, and the first step (the one computed here for 5a to 5b) is predicted to be the ratedetermining step. See ref. 42. 73.

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23



TOC Graphic conformation change

relative energy

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ha

Hb Hb

π-bond shift

Ha heavy-atom tunneling

reaction coordinate

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Tunneling by 16 Carbons: Planar Bond Shifting in [16]Annulene

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