Ping-pong tunneling reactions, part 2: boron and carbon bell-clapper rearrangement

Introduction

A good deal of attention has been paid to the established chemistry of hypercoordinated compounds [1], [2], [3], [4], [5], [6] (also called, controversially, hypervalent systems) by both experimentalists and theoreticians, due to their unique reactivity and properties. These molecules are usually described by a three-center four-electron bond [6], [7], and are typical within main group elements in and below the third row of the periodic table. Pentacoordinated bond formation by second row elements such as carbon and boron are, due to their low polarizability and high relative electronegativity, very scarce (though the trigonal bipyramidal geometry is common in the transition state of S_N2 reactions). Still, they are possible, as many computational and experimental studies have shown [4], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. For example, Akiba et al. [19], [20] used an anthracene scaffold to synthesize potentially pentacoordinated carbocation and boron containing compounds (see C_R,Y and B_R,Y in Fig. 1). Although some species have very loose bonding between the boron or the carbocation to the lateral Lewis bases, and therefore cannot be considered as hypercoordinative (for instance B_OMe,OMe or C_OMe,OMe), other molecules have tight symmetrical binding, showing a clear symmetrical pentacoordinated geometry (such as B_F,OMe) [20].

Fig. 1:

(a) Bell-clapper degenerate reactions for B_R,Y and C_R,Y (X=B or C⁺). In many cases the symmetrical structure is sufficiently stabilized to produce a single pentacoordinated species instead of the degenerate double-well system. (b) Optimized structures of B_H,NCl2 at C_s (stable geometry) and C_2v (transition state) symmetry.

Yet, other species prefer an unsymmetrical geometry, with the central atom leaning to one or the other donor group (for example B_Me,NMe2 or B_Cl,NMe2) [20]. These almost symmetrical molecules are of particular interest for the present research, as they can undergo a very fast intramolecular degenerate bond-making and breaking between the sp³ central atom and the lateral substituents. This rearrangement occur through a symmetrical S_N2 mechanism, as was shown by ¹H NMR and DFT studies, in what was called a “bell-clapper” mechanism (Fig. 1) [3], [21], [22]. The energy barrier for this rearrangement reaction was found to be too small to measure by the NMR coalescence method. Encouraged by the low barrier and small displacement of the central carbon or boron, we envisaged that these reactions may occur by heavy atom tunneling, analogous to a quantum ping-pong game [23].

Quantum mechanical tunneling (QMT) of hydrogen is a well-known effect that has been widely studied both experimentally and theoretically [24], [25]. The extent to which tunneling occurs in a chemical reaction depends on the barrier width (w), barrier height (ΔE^‡), and atomic masses (m) of the moving parts of the molecule, according to:

where P is the tunneling probability (“barrier permeability”), and x is a factor that depends on the shape of the potential energy curve [24]. It can be seen from eq. 1 that the tunneling probability is particularly sensitive to the barrier width (a variable with no significance in semi-classical transition state theory), making the amplitude of the atomic movements the most critical factor for a swift tunneling. In this sense, it was recently shown that “heavy” atom tunneling (i.e. atoms from the second row of the periodic table) is indeed possible, as long as the barrier height is low and, more important, the barrier width is markedly narrow [24], [26]. The first experimental evidence of such kind of tunneling was found in the automerization (aka π-bond shifting) of cyclobutadiene [27], [28], [29]. From there, several other documented reactions emerged, such as the ring expansion of methyl-cyclobutyl-fluorocarbene [30], ring opening of cyclopropyl-carbinyl radical [31], [32], degenerate rearrangement of semibullvalene [33], [34], ketenimine ring expansion [35], and ring closure of cyclopentane-1,3-diyl [36], [37] (see also Refs. [26], [38], [39] and references within). All these examples share the already cited characteristics: a low and narrow activation barrier. To the best of our knowledge, the heaviest atom predicted to tunnel from the ground state in a realistic (albeit theoretical) reaction involves a fluorine, in another case of a quantum ping-pong mechanism [23]. We can divide all these reactions in two groups, the exothermic ones (asymmetric reaction profiles such as the cited ring expansion, opening or closing), and the isothermic ones (degenerate rearrangements with symmetric reaction coordinates, such as the cyclobutadiene and semibullvalene cases). In the latter group, which includes our current bell-clapper reaction, we can also find many examples of H-transfer, such as proton sponges and formic acid dimer [40], [41], [42].

In this work, through computational tools we predict the boron and carbon atom tunneling by rapid bond switching on the bell clapper mechanism (Fig. 1). Additionally, we propose an experimental test to check the QMT effect by NMR spectroscopy.

Results and discussion

Figure 1 shows the key intramolecular S_N2 reaction (bell-clapper mechanism) for B_R,Y and C_R,Y. This reaction undergoes a bond switching between the central X and lateral Y groups via a C_2v trigonal bipyramidal transition state structure which resembles a pentacoordinated bonding pattern, with a symmetrical double-well potential energy surface. Table 1 lists the activation energy, the bond length of the bonded (r₁) and non-bonded (r₂) X–Y bond, the effective barrier width (w_½) and the tunneling limit (T_L) for B_R,Y and C_R,Y studied systems.

In the original B_Cl,NMe2 system reported by Akiba et al. our computed activation energy is 39.7 kJ·mol⁻¹, with bond distances of 1.675 and 3.137 Å for the shorter (r₁) and longer (r₂) B–N distances (see Table 1 and Fig. 1), in good agreement with the X-ray diffraction analysis (r₁=1.664 and r₂=3.129 Å) [20]. The effective barrier width (w_½=0.73 Å) is significantly narrower than the complete movement that the boron must travel, but it is a more accurate proxy to use for the T_L; close to the minima the displacement of the atom requires a negligible energy, and therefore those sections of the reaction coordinate are kinetically irrelevant for tunneling. Still, the high T_L value of 24.4 for B_Cl,NMe2 indicates that the reaction will not occur by QMT from the ground state. We therefore tuned the system by attempting various substitutions that would shrink both the barrier height and width, thus giving better candidates for tunneling. Due to clashing effects, this process is more trial an error than a systematic search. For instance, a weaker Y electron donor will make the short X–Y bond (r₁) more labile and longer (with a lower ΔE^‡), but it will make the long X–Y bond (r₂) longer as well, compensating the effect; therefore, a weaker Y nucleophile may or may not lower w_½ and T_L. Similarly, a strong σ electron withdrawing atom in the R groups may also act as a π donor (as in the case of halogens), blurring the possibility of predictions. In addition, some steric hindrance pushes the Y groups inside (for instance when comparing Y=NH₂ and NMe₂), changing the potential energy surface exclusively by brute force. Still, a couple of rules of thumb can be grasped: the asymmetric potential with higher activation energy tends to be favored by stronger Y electron donors (compare B_H,NH2 to B_H,NCl2) or by weaker R π donors (B_H,NF2 vs. B_Cl,NF2, the latter being a symmetrical pentacoordinated species, and therefore not included in Table 1). These effects strengthen the charge transfer interaction between X and Y.

Analyzing the trends between similar systems in Table 1 we can still find one clear, expected trend. Narrower w_½ correlates with lower ∆E^‡, hence both of them correlate with a smaller T_L. This can be explained by considering the harmonic potentials of the reactant and product states being closer, which puts the crossing point in a lower position [23]. Since our objective is to find systems with a fast QMT, low activation barriers should produce the desired outcome (as long as it is not so low that the system will prefer the C_2v geometry!). Therefore, we carried out accurate QMT computations (SCT) on the most promising systems, B_H,NCl2 and B_H,NBr2 (T_L=7.4 and 7.7, respectively). To our delight, we obtained quite fast tunneling rate constants of 590 and 61 s⁻¹ (t_½=1 and 11 ms), respectively, close to the absolute zero (that is, QMT from the ground state, where it is completely independent of the temperature). Considering that the computed semi-classical rates (CVT, without any tunneling correction) have the “impossible” values of k=5×10⁻⁴⁵ and 5×10⁻⁵⁴ s⁻¹, we can ascertain that in cryogenic conditions the reaction occurs exclusively by a QMT mechanism. This might be, to the best of our knowledge, the first predicted case of a boron atom tunneling.

In parallel to the boron bell-clapper, also the isoelectronic carbocation-based reaction has been thoroughly studied in previous works [19], [20], [21], and therefore it is de rigueur to include it here. However, we must take into consideration that the necessary inclusion of a counterion in most experimental setup will change the reaction [56], and therefore our computational results will only match the experiment where the carbocation can be isolated at low temperature (for instance in a supersonic expansion equipment). Due to the much stronger interactions with Y, carbocations have much higher activation energies, with very stable C_s geometries. Hence, all the studied systems based on amine substituents were unsuitable for QMT (T_L ≫10, see for example, C_H,NH2 in Table 1). However, with much weaker Y groups there is a slim chance, as can be seen in Table 1 for halides, with T_L=11.5 and 11.7 for C_H,Cl and C_H,Br, respectively (C_H,F prefers the C_2v geometry). The ensuing SCT computations yielded k=7×10⁻¹¹ s⁻¹ when approaching the zero Kelvin regime for C_H,Br (with a semi-classical value of k_CVT=3×10⁻¹³⁹ s⁻¹ at 6 K), which can hardly be considered a realistic tunneling (t_½=300 years). But C_H,Cl gave k=6×10⁻⁵ s⁻¹ (t_½=3 h, with k_CVT=7×10⁻¹²² s⁻¹ at 6 K), well within what can be considered “experimental time”. Therefore, this molecule can be included in the pantheon of systems that can react by carbon atom tunneling [26].

Figure 2a shows the Arrhenius plot of B_H,NCl2 and C_H,Cl. In the low temperature region, the SCT rate constants deviates from the classical CVT rates reaching a clear plateau where the rates become independent of temperature, a distinct signature of tunneling from the ground state. For B_H,NCl2, at ~50 K the tunneling rate becomes dominant (k_SCT=4×10⁵ s⁻¹, k_CVT=9×10⁴ s⁻¹), while at ~30 K the semi-classical rate is negligible (k_SCT=3×10³ s⁻¹, k_CVT=3 s⁻¹). Below ~10 K the rate is entirely dominated by heavy atom tunneling from the ground state (note that in the case of hydrogen tunneling the vibrational states are usually more separated, showing larger independence from the temperature compared to heavy atom QMT). For C_H,Cl we start to see QMT dominance at ~75 K (k_SCT=98 s⁻¹, k_CVT=38 s⁻¹), negligible semi-classical reaction at ~40 K (k_SCT=4×10⁻⁴ s⁻¹, k_CVT=10⁻⁸ s⁻¹), and exclusive tunneling from the ground state again at ~10 K.

Fig. 2:

(a) Arrhenius graph of the CVT (dashed lines) and CVT+SCT (curved lines) natural logarithms of the rate constants versus T⁻¹ for the bell-clapper reaction of B_H,NCl2 (in red) and C_H,Cl (in blue) systems. (b) Kinetic isotope effects including QMT of B_H,NCl2 for the boron (¹⁰B/¹¹B), the two hydrogens connected to B (H/D) and the two nitrogens (¹⁴N/¹⁵N).

Considering the fast tunneling rate of the B_H,NCl2 at cryogenic conditions, we decided to check the possibilities of QMT by substituting the lower carbon at the central anthracene ring. We expected that by having there a bulkier hetero atom, it will push out the lateral rings, bringing closer the Y groups and producing a narrower and lower rearrangement barrier. For this purpose we introduced a Si atom forming a 10-silaanthracene scaffold for B_H,NCl2 (Scheme 1). Preliminary results suggested a large influence of the Si atom on the w_½ (0.41 Å) and ΔE^‡ (8.2 kJ·mol⁻¹), producing a T_L of only 6.2. However, and to our surprise, the rate constant for this system was extremely slow (k_SCT=5×10⁻⁰⁷ s⁻¹, with t_½=15 days) at 6 K, which can barely be considered as a viable tunneling mechanism. This stark disparity between the accurate SCT rate constants and the T_L can be explained based on the displacement vectors of the imaginary frequency at the TS. In contrast to B_H,NCl2, where the movement is basically centralized at the boron, the 10-silaanthracene structure leads to a more collective motion in the molecular reorganization. As the T_L approximation depends on only one TDA, a system with several atoms moving concertedly interfere in the correct T_L interpretation. This acts as a warning in the use of the simple tunneling limit model.

Scheme 1:

10-silaanthracene scaffold for B_H,NCl2.

Conclusions

In this paper, we have investigated intramolecular degenerate S_N2 rearrangement reactions of the “bell-clapper” type, where a central boron atom (or its isoelectronic carbocation) switches bond alternatively with its lateral Lewis bases placed at one and eight position of the anthracene molecule. This rapid ping-pong like reaction can be accompanied by low activation energy and relatively narrow barrier width. Tuning of the systems by introducing relatively weak bases (such as nitrogen dihalides for the boron and halogens in the carbocation systems) at the lateral “Y” positions can significantly reduce the effective barrier width along with lowering in the energy barrier, making them an ideal system for heavy atom tunneling. Calculation including the small curvature tunneling (SCT) approximation reveals that the reaction on B_H,NCl2 occurs exclusively by boron atom tunneling close to absolute zero, while the classical thermal over the barrier reaction is virtually non-existence. The remarkably high KIE for the B atom is also a witness of the QMT effect. To the best of our knowledge, this is the first example of reaction involving boron atom tunneling. Other promising candidates that are found to be driven by heavy atom tunneling are B_H,NBr2 and C_H,Cl, where the latter involves carbon atom tunneling. Additionally, we postulate an experimental test to probe the QMT mechanism by cryogenic NMR spectroscopy.