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WIREs Comput Mol Sci
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Reactions that involve tunneling by carbon and the role that calculations have played in their study

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Chemical reactions can proceed either by passage of the reactants over the reaction barrier or by tunneling through the barrier. During the past 40 years, it has become clear that tunneling, not only by hydrogen but also by carbon, can occur, provided that the reaction barrier is narrow and that tunneling occurs at energies that are not too far below the top of the barrier. This review discusses those reactions in which tunneling by carbon has been predicted to occur by calculations and/or been found to occur by experiments. WIREs Comput Mol Sci 2016, 6:20–46. doi: 10.1002/wcms.1235 This article is categorized under: Structure and Mechanism > Molecular Structures
The ring closure of triplet cyclopentane‐1,3‐diyl to bicyclo[2.1.0]pentane.
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Electrocyclic ring opening of 41 to 42 is calculated to occur rapidly by temperature‐independent tunneling at temperatures below 30 K.
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Electrocyclic ring opening of benzazarines 39a and b to ketenimines 40a and b. The latter reaction occurs at 10 K; the former does not.
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The automerization of semibullvalene (38a) and the bond shifting reaction in semibullvalene‐d1 (38b).
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The automerization of cyclopropenyl anion (37a) and four derivatives (37b–d).
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The automerization of 1,3,5‐tri‐tert‐butylpentalene (36a) and two models (36b and c) used to simulate this reaction computationally. The rotations of the CR3 groups that must accompany double bond shifting are shown.
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Pentalene (33), heptalene (34), and acepentalene (35).
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Bergman cyclization of enediyne 31 to diradical 32.
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Reaction of p‐anisaldehyde (29) with Roush's reagent (30).
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Deuterium abstraction from C‐11 of linoleic acid‐11,11‐d2 (28) by Fe(III)OH in the reaction of 28 with soybean lipoxygenase‐1 (SLO‐1).
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Arrhenius plots of the ln 12C/13C KIEs versus 1/T in the ring opening of 25 to 26 and 27. The experimental ratio of the two radicals formed was obtained by James and Singleton by chemically trapping the radicals with (C4H9)3SnH and then measuring the ratio of 13C at C3 and C4 of the 1‐butene formed by natural abundance 13C NMR. The predicted ratio of 26 to 27 was obtained by CVT calculations for reaction over the barrier and by CVT + SCT calculations for tunneling through the barrier. (Reprinted with permission from Ref. . Copyright 2010 American Chemical Society)
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Determination of the 12C/13C KIEs in the ring opening of 25, labeled in natural abundance with 13C at one ring carbon (red asterisk). Measuring the ratio of the two products, 26 and 27, gives the ratio of the 12C/13C KIEs on which ring bond in 25 cleaves.
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Ring opening of cyclopropylcarbinyl radical (18) to 3‐buten1‐yl radical (19).
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The two possible products, 23 and 24, formed by ring opening of disubstituted cyclopropylcarbinyl radical 22a–c.
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Photolysis of matrix‐isolated cyclopropylcarbinyl iodide (20) leads to the formation of 1,3‐butadiene (21). No trace of radical 18 or 19 was detected,
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The linear Arrhenius plot for ring opening of cyclopropylcarbinyl radical (18) to 3‐buten1‐yl radical (19), obtained with rate constants computed by canonical variational transition state theory (CVT) for passage over the reaction barrier (blue points), and the curved Arrhenius plot, obtained with rate constants (red points) computed with the inclusion of small‐curvature tunneling (SCT). The CVT + SCT plot is curved, because the ring‐opening reaction goes from a high‐temperature region, where passage over the barrier dominates, to a lower‐temperature region, where thermally activated tunneling occurs with a lower Ea, to a very low‐temperature region, where the tunneling reaction occurs from the lowest vibrational level of 18, so that the rate of reaction becomes temperature‐independent. (Reprinted with permission from Ref. . Copyright 2008 American Chemical Society)
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Ring expansion of noradamantylmethylcarbene (13d) to 2‐methyladamantene (14d) and competing 1,2‐hydrogen shift to form 1‐vinylnoradamantane (17).
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Bisnoradamanylcarbenes (15) and adamantylcarbenes (16).
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Ring expansion of noradamantylcarbenes (13) to adamantenes (14)
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Ring expansion of cyclopropylfluorocarbene (11) to 1‐fluorocyclobutene (12).
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Tunneling (red line) through a parabolic barrier of width, w = 1.0 Å, at its base and at an energy of (a) V0 − E = 6 kcal/mol and (b) V0 − E = 3 kcal/mol below the top of the barrier. As shown, at V0 − E = 3 kcal/mol, the effective width is only w = 0.7 Å. The dotted line represents the potential energy of a harmonic oscillator, with a frequency of ca. 1000 cm−1, that has its n = 0 and 1 vibrational levels at, respectively, V0 − E = 6 and 3 kcal/mol. The dotted and solid lines do not connect properly, because, at energies far below the top of the barrier a parabolic barrier provides a poor approximation to the actual shape of the reaction barrier.
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Ring expansion of 1‐methylcylobutylfluorocarbene (9a) and 1‐methylcylobutylchlorocarbene (9b) to, respectively, 1‐fluoro‐2‐methylcyclopent‐1‐ene (10a) and 1‐chloro‐2‐methylcyclopent‐1‐ene (10b).
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Ring opening of 1H‐bicyclo[3.1.0]‐hexa‐3,5‐dien‐2‐one (7) to singlet 4‐oxocyclohexa‐2,5‐dienylidene (S‐8), which is followed by intersystem crossing (ISC) to the triplet ground state (T‐8). The reason for the difference between the bonding in S‐8 and T‐8 is discussed in the text.
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Schematic potential energy surface for tunneling in a linear A − B + C→A + B − C reaction. The dashed blue line represents the minimum energy path (MEP), which passes under the transition state (TS). The dashed green line represents a tunneling path that minimizes the imaginary action by ‘corner cutting.’ The green tunneling path is higher in energy than the MEP, but the green path provides a shorter tunneling pathway through the barrier in the mass‐weighted coordinates used in the diagram.
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Tunneling through a parabolic barrier of width, w, at an energy V0 − E below the top of the barrier.
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Tunneling through a rectangular barrier of width, w, at an energy V0 − E below the top of the barrier.
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Isomerization of cyclobutadiene‐1,4‐d2 to cyclobutadiene‐1,2‐d2.
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The ring closure of triplet cyclobutane‐1,3‐diyl to bicyclo[1.1.0]butane.
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