The effect of force on a chemical reaction has been visited in three different molecular environments. The results reveal a unifying framework that enables predictions of force-induced reactivity.
Chemists tend to think about the ways in which molecules behave — the shapes they are most likely to adopt, the molecular partners with which they are most likely to bind, or the rates and outcomes of their reactions — in terms of energies. But in the light of reports that applied forces can direct new chemical transformations1,2,3,4, or induce unusual stress responses in materials5,6, it is becoming increasingly profitable to consider molecular behaviour in terms of forces. Writing in the Journal of the American Chemical Society, Akbulatov et al.7 provide a crucial benchmark for force-induced reactivity (chemomechanics) by uniting internally and externally stress-induced chemical behaviour across time- and length-scales of several orders of magnitude.
The authors' study centres on the reactivity of gem-dibromocyclopropane, a chemical group that contains a ring of three carbon atoms (Fig. 1). This ring can be pulled open mechanically to give a product (known as an alkene) that is both longer and more stable than its precursor.
The force required for the reaction can be applied through several mechanisms. For example, micrometre-long polymers consisting of thousands of sequentially connected cyclopropanes have been stretched by the miniature 'tweezers' of an atomic force microscope8. In a second scenario, cyclopropanes could be incorporated into larger rings known as strained macrocycles, so that the larger ring pulls on the smaller one in much the same way that a bow pulls its bowstring taut. A third scenario, in which an isolated, small cyclopropane-containing molecule is pulled by a force, can be simulated using computational models.
In these three scenarios, the force is transmitted to the cyclopropane across distances ranging from 10−10 metres (for the small molecules) to 10−6 metres (for the polymer). What's more, the force is applied directly in the simulations (to the point of attachment of one of the R groups in Fig. 1), but indirectly through a variety of chemical bonds in the other cases. Despite these differences, it is reasonable to expect that a common basis underpins the chemical behaviour resulting from these otherwise disparate contexts.
Finding such commonality by considering energy is difficult, because the amount of energy associated with the strain in each system varies greatly with the size of the system. For example, it takes around 1,000 times more energy to distort the polymer than to distort a macrocycle to a comparable extent, because in the polymer there are about 1,000 times as many degrees of freedom into which the strain can be distributed. In contrast to energy, however, the local force acting on a cyclopropane provides a potentially convenient and useful basis for comparison.
Enter Akbulatov et al., who neatly 'close the loop' on chemomechanical coupling — the correlation between the rate of a chemical reaction and the force applied to induce it — by comparing the strain in cyclopropane-containing small molecules, macrocycles and polymers. Using a combination of computational and experimental approaches, the authors show that the stress-induced behaviour of the macrocycles and small molecules can be used to quantitatively model the microscopic behaviour of the polymer. Their result is crucial for the burgeoning field of mechanochemistry because it unites the current thinking about different ways of applying tension to molecules: internal versus external forces, applied directly or indirectly.
Proper accounting of local forces in a molecule is often difficult when a restoring force is applied across a sequence of nuclei, as is the case in the strained polymer and macrocycles. Unlike temperature, which is the same for any and all subsets of atoms in a system at equilibrium, the local forces that are 'felt' between different sets of nuclei are not identical to each other, and are not the same as the constraining forces applied elsewhere in the molecule. For example, if a stretching force is applied at the ends of a polymer chain, the resulting local forces within the molecule differ from the applied force. The distribution of restoring forces is quite nuanced, and recent computational work9 has shown that different atomic connections can affect local chemomechanical coupling, independently of the source of the tension.
Akbulatov et al. used a clever strategy to assess the forces acting on the nuclei in the cyclopropane groups. Molecular geometries, such as bond lengths and bond angles, are somewhat pliable, and the authors recognized that the distortion of a cyclopropane from its equilibrium geometry reflects the local force acting on its nuclei. By calculating such distortion — specifically, the distances between nuclei — they were able to determine the local forces acting on cyclopropanes in the three different scenarios. This approach for calibrating tension was highly effective as a method for evaluating the effect of the surrounding chemical structure on local force: using a single formalism, the authors accurately modelled the reactivity of cyclopropanes in molecules of lengths ranging from ångströms to micrometres, and at timescales ranging from months to milliseconds.
It should be pointed out that Akbulatov and colleagues' approach for assessing chemomechanics relies on extensive computational methods, particularly to assess the local forces in molecules. The calculations required are quite involved, and so might limit the broad use of the authors' strategy. Looking ahead, it will be interesting to see whether similar methods that require more minimal calculations can be developed to reproduce experimental benchmarks of chemomechanics with comparable success.
Nevertheless, the ability to predict force-induced reactivity has several implications. First, the molecular view of chemomechanics can now be directly related to problems on even greater length scales than those addressed by Akbulatov et al., such as mechanically active functional groups embedded within proteins10 or a macroscopic material under load5. Second, the authors' approach lends itself to predicting new behaviours, such as how different chemical attachments might enhance the mechanical reactivity of a molecule.
Finally, because energy = force × distance, evaluating reactivity as a function of force rather than of energy allows otherwise inaccessible details of molecular structure (the 'distance' in the equation) to be determined, both for complicated reaction mechanisms that are resistant to conventional experimental probes and for 'mechanical-only' mechanisms that are otherwise impossible to work out. It is therefore a particular strength of Akbulatov and co-workers' study that not only are chemomechanical relationships between molecules of different sizes shown to be valid, but that the authors also demonstrate how such relationships might be determined and applied.
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