Bond Memory in Dynamically Determined Stereoselectivity

Abstract

The carboborative ring contraction of cyclohexenes exhibits an abnormal selectivity pattern in which a formally concerted double migration gives rise to predominant but not exclusive inversion products. In dynamic trajectories, the inversion and retention products are formed from the same transition state, and the trajectories accurately account for the experimental product ratios. The unusual origin of the selectivity is the dynamically retained non-equivalence of newly formed versus pre-existing bonds after the first bond migration.

Graphical Abstract

Much of the understanding of molecular structure in chemistry implicitly assumes time-averaged geometries and statistical distributions of energy in molecules. For example, symmetry-linked bonds to atoms are considered equivalent, even though in individual molecules at any instant the positions and energies of the atoms may be inequivalent. CH₂FCl is not viewed as being chiral in any meaningful sense, because no ordinary experiment can detect the ephemeral positional and energetic differences between the hydrogen atoms¹. On sufficiently short time scales, however, the de facto dynamical asymmetry of structures with symmetrical connectivity can influence experimental observations, either through bond breaking in specifically energized fragments of molecules^2,3 or through dynamic matching^4–9. We describe here how the combination of energetic non-equivalence in newly formed versus pre-existing bonds and the initial geometrical non-equivalence of the two bonds on the slope of an energy surface can direct high stereoselectivity at an adjacent reactive center.

The Larionov group recently reported the photoinduced carboborative ring contraction of cyclohexenes to afford chiral cyclopentanes.¹⁰ The reaction was proposed to occur by a sensitized cis/trans isomerization, giving rise to a strained trans-cyclohexene nucleophile (1). Electrophilic addition by a tertiary borane via 2^‡ then forms the zwitterionic adduct 3. Ring contraction through 4^‡ leads to the betaine structure 5. The nature of 5 and its dynamics will be of central importance here. Stereodivergent alkyl migrations via 6-R or 6-I quench the charge separation and give the product cyclopentanes 7-R and 7-I. The stereochemistry of the combination of ring contraction and boron–alkyl migration steps cannot be determined with cyclohexene itself, but a strong preference for inversion was previously seen with complex substrates. Here, we have carefully assigned and quantitated the relatively simple (+)-limonene reaction (Figure 1).

Figure 1.

Stereochemistry of the photoinduced carboborative ring contraction of (+)-limonene. See the SI for the determination of the experimental ratios.

An unusual observation is that the two rearrangement steps are stereochemically linked, but not completely so. That is, if the bond to C₆ lost in the ring-contraction step is viewed as the “leaving group” and the migrating boron–alkyl is the “nucleophile”, the combination of steps converting 3 to 7 occurs with preferential, but not exclusive, inversion of configuration at C₁ (see 9-I/10-I versus 9-R/10-R in Figure 1). If the two migrations occurred simultaneously, stereospecific inversion would be expected, as in any S_N2 step. If the ring-contraction step were complete before the boron–alkyl migration, equal inversion and retention might be expected. The high stereoselectivity but absence of S_N2-like stereospecificity then appears inconsistent with either a concerted or a two-step process.

Our hypothesis was that this unexpected stereoselectivity pattern is associated with dynamics on a bifurcating energy surface.^11–14 The trajectory study here supports this idea but uncovers an origin for the selectivity that is uniquely dynamical in nature. The results complicate the mechanistic interpretation of stereoselectivity in reactions.

M11/6-31+G** calculations were chosen here based on a comparison of diverse DFT methods versus DLPNO-CCSD-(T)/aug-cc-pVTZ energies for a series of geometries along a minimum energy path (MEP) from 1 to 7 (see the Supporting Information (SI)). The ring contraction of 3 is barrierless,¹⁵ and the MEP has C₆ migrate from C₁ to C₂ to pass into the area of structure 5, though 5 is not an energy minimum. The MEP then continues downhill by a boron—alkyl shift to C₁ through 6-I to afford 7-I. The energy surface for the ring contraction and boron—alkyl migration is steeply declining, going downhill by 61 kcal/mol overall and 45 kcal/mol from 5 to 7-I.

The stereochemically tractable (+)-limonene/triethylborane reaction of Figure 1 was the focus of the calculations here. Unlike the model reaction, this system is configurationally and conformationally complex. The initial cis/trans isomerization can occur in two ways, leading to a distorted chair with the isopropenyl group either equatorial (8-eq) or axial (8-ax). For each, the isopropenyl group and the attacking triethylborane can adopt multiple conformations, and the possibilities were explored systematically (see the SI). Importantly, the conformation of the triethylboryl group later in the mechanism is established in the transition state for its attack on the alkene. The structures subsequent to the initial addition step are extremely short-lived. As a result, their conformations are in a non-Curtin—Hammett regime,¹⁶ and they cannot interconvert prior to the final product formation.

Figure 2 outlines the calculated mechanism. The lowest-energy TS 11^‡ for the addition of triethylborane to 8-eq involves a low barrier (8.0 kcal/mol in free energy) despite the steric hindrance. The resulting zwitterion 12 exists in a shallow energy well of only 0.3 kcal/mol versus the subsequent ring-contraction TS 13^‡. The MEP forward from 13^‡ faces no further barrier before arriving at the inversion product 9-I, so in this respect the two rearrangement steps are concerted. However, the ring contraction is complete in the MEP before any significant motion of a boron—ethyl group, and the MEP passes through the shoulder structure 14 (the limonene analog of 5, not an energy minimum). Because of the tertiary cation at C₂ in 12, the ring contraction is less favored than in the unsubstituted model, and it is only ~2.8 kcal/mol downhill from 12 to 14. The final boron—alkyl migration is extremely exothermic. No TS leading by MEP to 9-R could be located, and the same was true for the other conformations explored. This absence of TSs leading to retention means that conventional stationary-point calculations cannot account for the experimentally observed minor product.

Figure 2.

Lowest-energy calculated mechanism for the reaction of 8-eq with triethylborane. Relative free energies are shown in parentheses in kcal/mol. The energy for non-minimum 14 is based on when the C₂–C₆ distance is 1.6 Å.

To explore whether the retention product could arise from dynamic motions after the ring contraction, trajectory studies were conducted. Quasiclassical direct-dynamics trajectories were initiated from the area of 13^‡, a conformational analog of 13^‡, and a configurational analog derived from 8-ax. The choice of TSs used was based on the two lowest-energy 11^‡ analogs for addition to 8-eq and the lowest-energy analog for addition to 8-ax. Each normal mode was given its zero-point energy, a Boltzmann-random distribution of thermal energy appropriate for 298.15 K, and a random phase. The trajectories were integrated in 1 fs steps forward and backward in time using a Verlet algorithm, and were continued until they terminated at 9/10 or returned to intermediate 12.

A striking feature of the trajectories is that the ring contraction and boron—alkyl shifts are separated in time, eschewing any degree of synchronicity.¹⁷ An average time of 216 fs was required to traverse from 13^‡ to 9-I/9-R This includes on average 78 fs to get to 14 (defined as C₂–C₆ < 1.6 Å with C₁–C_ethyl > 2.3 Å), 107 fs in the area of 14, and 31 fs for the final highly exothermic boron–alkyl shift (defined by the C₁–C_ethyl distance reaching an approximate no-return threshold of <2.3 Å). Only 5% of the trajectories involve temporal overlap between the ring contraction and boron—alkyl shifts, as judged by a C₁–C_ethyl distance of less than 2.3 Å before the C₂–C₆ distance reaches <1.6 Å. The remaining 95% of trajectories involve well-separated stages for the ring contraction and boron–alkyl shift, remaining on the edge of an energy cliff near 14 for a remarkable 113 fs on average.

Table 1 summarizes the stereochemical results. For both 8-eq and 8-ax, the inversion products (9-I and 10-I) were strongly favored, but in each case significant amounts of the retention products were formed. Due to the practicality-limited number of trajectories, the 95% confidence limits on the trajectory ratios are 2.0% and 3.0% for 8-eq and 8-ax, respectively. The trajectories overestimate slightly the amount of inversion, but the predicted ratios are within error of the experimental observations.

Table 1.

Trajectory Results Starting from 13^‡, a Low-Energy Conformational Analog, and an 8-ax-Derived Analog^a

system	inversion (9-I/10-I)	retention (9-R/10-R)	ratio
8-eq, TS 13‡	360	30	92.3:7.7
second-lowest TS	328	32	91.1:8.9
		weighted: 91.7:8.3 (±2.0)
		experiment: 90:10
8-ax, lowest-energy TS	373	42	89.9:10.1 (±3.0)
		experiment: 87:13

^aSee the SI for the TS structures and error analysis.

The trajectory results and their close fit with experimental observations support our hypothesis that the reaction involves a bifurcating energy surface and that the inversion and retention products arise from the same ring-contraction transition state. After the ring contraction, a sharply downward-sloping energy surface can lead from 14 to either product. The interesting question then is not why some retention is observed, but rather why inversion is so strongly favored.

We considered first whether the inversion-engendering ethyl group (Et_i, Figure 3) was initially better aligned with the empty p-orbital of C₁ than the alternative ethyl group leading to retention (Et_r). The migration of Et_i would then be favored by a steeper, least-motion path. Trajectories, however, initially place the Et_i and Et_r in nearly equivalent positions with respect to C₁ in the area of 14. A continuation of C₁ and C₂ motions in the transition vector for 13^‡ (Figure 3) brings the C₁–C₂ bond and the non-migrating ethyl group (Et_n) into a surprisingly encumbered eclipsed conformation (average C₂–C₁–B–Et_n dihedral angle −4° with σ = 11°) as the trajectories reach 14. The slightly advantageous alignment of Et_i is ephemeral as conformational twisting continues, so that the 93% of the trajectories at some point in the area of 14 have Et_r better aligned. Dihedral alignment then cannot account for predominant inversion.

Figure 3.

Composite conformational motion as 13^‡ descends to 14 and 14 evolves with time.

The crux of the problem of understanding inversion is that the nominal structure of 14 (or 5) is misleading. The symmetry of the bond connections to C₂ makes the C₂–C₆ and C₂–C₃ bonds appear equivalent. (See the SI for evidence that the distant isopropenyl group has a negligible effect on the stereoselectivity.) However, 14 is actually highly asymmetric in three subtle but mutually reinforcing ways: (1) the newly formed C₂–C₆ bond is initially vibrationally excited, similarly to what has been seen in the acetone cation radical,³ and it maintains this local excitation with a time constant of ~50 fs, with some energy retained for up to 160 fs (see the SI); (2) the empty p-orbital of C₁ is initially lined up with the C₂–C₆ bond, and donation from the electrons of the excited bond to C₁ is retained for an extended time; (3) the Et₃B group as a whole is initially much closer to C₆ than C₃ (C₆–B averages ~3.1 Å, C₃–B averages ~4.1 Å) and the inertial effect of the Et₃B holds C₁ closer to the C₂–C₆ bond.

These effects and their dissipation can be seen in the slow evolution of the average C₁–C₂–C₆ and C₁–C₂–C₃ angles after the formation of 14 (Figure 4). For trajectories that lead to the inversion product, the average C₁–C₂–C₆ angle increases and the C₁–C₂–C₃ angle decreases over time, but the system never reaches approximate symmetry, even after 200 fs. In contrast, the retention product is associated with trajectories that symmetrize the connections to C₂ more rapidly. A low C₁–C₂–C₆ angle prevents formation of the retention product. This is understandable as a short-lived steric effect in which the C₆ methylene blocks a migrating Et_r. Inversion is then favored because ~80% of the trajectories retain asymmetric geometries throughout their time in the area of 14.

Figure 4.

Evolution of the average C₁–C₂–C₆ and C₁–C₂–C₃ angles in inversion and retention trajectories after formation of 14.

Symmetry and time are intimately intertwined. Chiral atropisomers are defined by the long time required for their racemization, while the rapidly inverting ethylmethylamine is “operationally” achiral.¹ Most “memory effects” impact stereoselectivity through the time persistence of conformations.¹⁸ On shorter, sub-picosecond time scale, dynamic matching arises when the symmetry of a short-lived formally symmetrical intermediate is broken by the retained non-symmetrical momentum of the atoms as they enter the area of the intermediate. The general idea here is the same, but it is taken to its logical extreme since 14 is not an intermediate and since the molecular asymmetry is both energetic and geometrical.¹⁹

When the products of a reaction are selected within a sufficiently short time, symmetry all but disappears. As a result, molecular events that are separated in time can be interconnected by short-lived dynamical differences. This possibility is not new,^2,3 but here it affects the stereochemistry of an ordinary reaction in solution. This dynamical asymmetry complicates the understanding of stereochemical observations and their origin, since stereospecificity in formally concerted concomitant bonding changes would not necessary require any degree of temporal overlap. We are continuing to explore the impact of dynamical effects on the understanding of selectivity in reactions.