On the calculation of internal forces in mechanically stressed polyatomic molecules.

We discuss how to define and to compute internal forces in a molecule subjected to mechanical stress. Because of the inherently many-body character of intramolecular interactions, internal forces cannot be uniquely defined without specifying a set of internal coordinates used to describe the molecular structure. When such a set is comprised of 3N - 6 interactomic distances (N being the number of atoms) and includes the bond lengths of interest, we show that the associated forces, while satisfying the equation F = ∂V/∂R (where R is the bond length, F is the internal force in this bond, and V is the potential energy of the molecule), can be determined from the molecular geometry alone. We illustrate these ideas using several toy models ranging from small molecules to a graphene sheet and show that the magnitude of the internal force in a bond is not necessarily a good predictor of its strength in response to mechanical loading. At the same time, analysis of internal forces reveals interesting phenomena such as the force multiplication effect, where weak external forces may, e.g., be used to break strong bonds, and offers insight into the catch-bond phenomenon where chemical reactivity is suppressed through application of a force.

Exploring the topography of the stress-modified energy landscapes of mechanosensitive molecules.

We propose a method for computing the activation barrier for chemical reactions involving molecules subjected to mechanical stress. The method avoids reactant and transition-state saddle optimizations at every force by, instead, solving the differential equations governing the force dependence of the critical points (i.e., minima and saddles) on the system's potential energy surface (PES). As a result, only zero-force geometry optimization (or, more generally, optimization performed at a single force value) is required by the method. In many cases, minima and transition-state saddles only exist within a range of forces and disappear beyond a certain critical point. Our method identifies such force-induced instabilities as points at which one of the Hessian eigenvalues vanishes. We elucidate the nature of those instabilities as fold and cusp catastrophes, where two or three critical points on the force-modified PES coalesce, and provide a classification of various physically distinct instability scenarios, each illustrated with a concrete chemical example.

Molecular catch bonds and the anti-Hammond effect in polymer mechanochemistry.

While the field of polymer mechanochemistry has traditionally focused on the use of mechanical forces to accelerate chemical processes, theoretical considerations predict an underexplored alternative: the suppression of reactivity through mechanical perturbation. Here, we use electronic structure calculations to analyze the mechanical reactivity of six mechanophores, or chemical functionalities that respond to mechanical stress in a controlled manner. Our computational results indicate that appropriately directed tensile forces could attenuate (as opposed to facilitate) mechanochemical phenomena. Accompanying experimental studies supported the theoretical predictions and demonstrated that relatively simple computational models may be used to design new classes of mechanically responsive materials. In addition, our computational studies and theoretical considerations revealed the prevalence of the anti-Hammond (as opposed to Hammond) effect (i.e., the increased structural dissimilarity between the reactant and transition state upon lowering of the reaction barrier) in the mechanical activation of polyatomic molecules.

Computation of transit times using the milestoning method with applications to polymer translocation.

Milestoning is an efficient approximation for computing long-time kinetics and thermodynamics of large molecular systems, which are inaccessible to brute-force molecular dynamics simulations. A common use of milestoning is to compute the mean first passage time (MFPT) for a conformational transition of interest. However, the MFPT is not always the experimentally observed timescale. In particular, the duration of the transition path, or the mean transit time, can be measured in single-molecule experiments, such as studies of polymers translocating through pores and fluorescence resonance energy transfer studies of protein folding. Here we show how to use milestoning to compute transit times and illustrate our approach by applying it to the translocation of a polymer through a narrow pore.

Regiochemical effects on molecular stability: a mechanochemical evaluation of 1,4- and 1,5-disubstituted triazoles.

Poly(methyl acrylate) chains of varying molecular weight were grown from 1,4- as well as 1,5-disubstituted 1,2,3-triazoles. Irradiating acetonitrile solutions of these polymers with ultrasound resulted in the formal cycloreversion of the triazole units, as determined by a variety of spectroscopic and chemical labeling techniques. The aforementioned reactions were monitored over time, and the rate constant for the cycloreversion of the 1,5-disubstituted triazole was measured to be 1.2 times larger than that of the 1,4-disubstituted congener. The difference was attributed to the increased mechanical deformability of the 1,5-regioisomer as compared to the 1,4-isomer. This interpretation was further supported by computational studies, which employed extended Bell theory to predict the force dependence of the activation barriers for the cycloreversions of both isomers.

Chemical reactions modulated by mechanical stress: extended Bell theory.

A number of recent studies have shown that mechanical stress can significantly lower or raise the activation barrier of a chemical reaction. Within a common approximation due to Bell [Science 200, 618 (1978)], this barrier is linearly dependent on the applied force. A simple extension of Bell's theory that includes higher order corrections in the force predicts that the force-induced change in the activation energy will be given by -FΔR - ΔχF(2)∕2. Here, ΔR is the change of the distance between the atoms, at which the force F is applied, from the reactant to the transition state, and Δχ is the corresponding change in the mechanical compliance of the molecule. Application of this formula to the electrocyclic ring-opening of cis and trans 1,2-dimethylbenzocyclobutene shows that this extension of Bell's theory essentially recovers the force dependence of the barrier, while the original Bell formula exhibits significant errors. Because the extended Bell theory avoids explicit inclusion of the mechanical stress or strain in electronic structure calculations, it allows a computationally efficient characterization of the effect of mechanical forces on chemical processes. That is, the mechanical susceptibility of any reaction pathway is described in terms of two parameters, ΔR and Δχ, both readily computable at zero force.

Congenitally absent superior mesenteric artery in an asymptomatic adult.

Congenitally absent superior mesenteric artery is an extremely rare anatomic anomaly with only one other case reported in an adult. We have described an elderly patient who presented with complete absence of the superior mesenteric artery found incidentally on computed tomography imaging. The patient had no abdominal pain, nausea, or other gastrointestinal symptoms. An abnormally enlarged inferior mesenteric artery provided collateral circulation to the midgut. No intervention was performed at the time given the patient's adequate circulation and lack of symptoms. The present case highlights consideration of anatomic mesenteric vascular anomalies before procedures involving inferior mesenteric artery ligation or coverage.