Assessment of theoretical methods for the determination of the mechanochemical strength of covalent bonds

Oriented External Electric Field Controls the Rupture Forces in Mechanophores

Controlling the reactivity of molecules under a mechanical pull has generated significant interest in organic and polymer chemistry. Inducing mechano-lability for otherwise rigid molecules has been possible through structural alterations like adjusting the pulling group, ring strain, and electron density of the scissile bond. In this article, we report that an oriented external electric field (OEEF) can significantly assist in mechanochemical transformations. Using a structurally diverse set of ring-opening reactions, 1(a)-4(a), we show that the critical force required for bond-cleavage, Frup, gets appreciably reduced when the OEEF acts in-phase with the bond-polarity direction. The primary condition for utilizing OEEF along with mechanochemistry is the requirement of structural asymmetry along the target bond. Effectively therefore, any polar ring-opening reaction might be manipulated by OEEF. The versatility of the strategy of using OEEF and mechanical force together can also be appreciated by the enhanced rupture force when the direction of the OEEF is flipped. We show that mechanical pulling and electric field can act as entwined twins toward mechano-lability.

Force Dependent Barriers from Analytic Potentials within Elastic Environments

Bond rupture under the action of external forces is usually induced by temperature fluctuations, where the key quantity is the force dependent barrier that needs to be overcome. Using analytic potentials we find that these barriers are fully determined by the dissociation energy and the maximal force the potential can withstand. The barrier shows a simple dependence on these two quantities that allows for a re-interpretation of the Eyring-Zhurkov-Bell length Δ x ‡ and the expressions in theories going beyond that. It is shown that solely elastic environments do not change this barrier in contrast to the predictions of constraint geometry simulate external force (COGEF) strategies. The findings are confirmed by explicit calculations of bond rupture in a polydimethylsiloxane model.

Implementing the mechanical force into the conceptual DFT framework: understanding and predicting molecular mechanochemical properties

Studying mechanochemical properties through the implementation of the mechanical force into the conceptual DFT framework (E = E[N,v,F_ext]).

Mechanical Switching of Aromaticity and Homoaromaticity in Molecular Optical Force Sensors for Polymers

The sensing of mechanical stress in polymers is indispensable for investigating the origin and propagation of cracks that lead to material failure and for designing mechanically responsive polymers. Here the unique approaches of using the force-induced switching of aromaticity and homoaromaticity in molecular optical force sensors for the real-time measurement of mechanical forces acting in stretched polymers are suggested. The mechanical switching of aromaticity in Dewar benzene is an irreversible event, whereas the degree of π-orbital overlap in homoaromatic compounds like homotropylium can be adjusted progressively over a wide range of forces. Using computational methods, it is demonstrated that both approaches lead to significant changes in the visible part of the UV/Vis spectra of the force sensors upon application of weak forces (pN-nN). Polymers that incorporate such molecular force sensors therefore change their color well before material failure occurs.

Ab initio simulations of bond breaking in sulfur crosslinked isoprene oligomer units

Sulfur crosslinked polyisoprene (rubber) is used in important material components for a number of technical tasks (e.g., in tires and sealings). If mechanical stress, like tension or shear, is applied on these material components, the sulfur crosslinks suffer from homolytic bond breaking. In this work, we have simulated the bond breaking mechanism of sulfur crosslinks between polyisoprene chains using Car-Parrinello molecular dynamic simulations and investigated the maximum forces which can be resisted by the crosslinks. Small model systems with crosslinks formed by chains of N = 1 to N = 6 sulfur atoms have been simulated with the slow growth-technique, known from the literature. The maximum force can be thereby determined from the calculated energies as a function of strain (elongation). The stability of the crosslink under strain is quantified in terms of the maximum force that can be resisted by the system before the crosslink breaks. As shown by our simulations, this maximum force decreases with the sulfur crosslink length N in a step like manner. Our findings indicate that in bridges with N = 1, 2, and 3 sulfur atoms predominantly, carbon-sulfur bonds break, while in crosslinks with N > 3, the breaking of a sulfur-sulfur bond is the dominant failure mechanism. The results are explained within a simple chemical bond model, which describes how the delocalization of the electrons in the generated radicals can lower their electronic energy and decrease the activation barriers. It is described which of the double bonds in the isoprene units are involved in the mechanochemistry of crosslinked rubber.

Theoretical simulation of the infrared signature of mechanically stressed polymer solids

Mechanical stress leads to deformation of strands in polymer solids, including elongation of covalent bonds and widening of bond angles, which changes the infrared spectrum. Here, the infrared spectrum of solid polymer samples exposed to mechanical stress is simulated by density functional theory calculations. Mechanical stress is described with the external force explicitly included (EFEI) method. The uneven distribution of the external stress on individual polymer strands is accounted for by a convolution of simulated spectra with a realistic force distribution. N-Propylpropanamide and propyl propanoate are chosen as model molecules for polyamide and polyester, respectively. The effect of a specific force on the polymer backbone is a redshift of vibrational modes involving the C-N and C-O bonds in the backbone, while the free C-O stretching mode perpendicular to the backbone is largely unaffected. The convolution with a realistic force distribution shows that the dominant effect on the strongest infrared bands is not a shift of the peak position, but rather peak broadening and a characteristic change in the relative intensities of the strongest bands, which may serve for the identification and quantification of mechanical stress in polymer solids.

Force-induced retro-click reaction of triazoles competes with adjacent single-bond rupture

The highly controversial force-induced cycloreversion of 1,2,3-triazole, its well-known retro-click reaction, is shown to be possible only for 1,5-substituted triazoles, but competes with rupture of an adjacent single-bond. We draw this conclusion from both static and dynamic calculations under external mechanical forces applied to unsubstituted and 1,4- and 1,5-substituted triazoles. The JEDI (Judgement of Energy DIstribution) analysis, a quantum chemical tool quantifying the distribution of strain energy in mechanically deformed molecules, is employed to identify the key factors facilitating the force-induced retro-click reaction in these systems. For 1,4-substituted triazoles it is shown to be impossible, but the parallel alignment of the scissile bond in 1,5-substituted triazoles with the acting force makes it generally feasible. However, the weakness of the carbon-nitrogen bond connecting the triazole ring to the linker prevents selective cycloreversion.

Analysis of the Acting Forces in a Theory of Catalysis and Mechanochemistry

The theoretical description of a chemical process resulting from the application of mechanical or catalytical stress to a molecule is performed by the generation of an effective potential energy surface (PES). Changes for minima and saddle points by the stress are described by Newton trajectories (NTs) on the original PES. From the analysis of the acting forces we postulate the existence of pulling corridors built by families of NTs that connect the same stationary points. For different exit saddles of different height we discuss the corresponding pulling corridors; mainly by simple two-dimensional surface models. If there are different exit saddles then there can exist saddles of index two, at least, between. Then the case that a full pulling corridor crosses a saddle of index two is the normal case. It leads to an intrinsic hysteresis of such pullings for the forward or the backward reaction. Assuming such relations we can explain some results in the literature. A new finding is the existence of roundabout corridors that can switch between different saddle points by a reversion of the direction. The findings concern the mechanochemistry of molecular systems under a mechanical load as well as the electrostatic force and can be extended to catalytic and enzymatic accelerated reactions. The basic and ground ansatz includes both kinds of forces in a natural way without an extra modification.

Advances in Quantum Mechanochemistry: Electronic Structure Methods and Force Analysis

In quantum mechanochemistry, quantum chemical methods are used to describe molecules under the influence of an external force. The calculation of geometries, energies, transition states, reaction rates, and spectroscopic properties of molecules on the force-modified potential energy surfaces is the key to gain an in-depth understanding of mechanochemical processes at the molecular level. In this review, we present recent advances in the field of quantum mechanochemistry and introduce the quantum chemical methods used to calculate the properties of molecules under an external force. We place special emphasis on quantum chemical force analysis tools, which can be used to identify the mechanochemically relevant degrees of freedom in a deformed molecule, and spotlight selected applications of quantum mechanochemical methods to point out their synergistic relationship with experiments.

A density functional theory model of mechanically activated silyl ester hydrolysis

To elucidate the mechanism of the mechanically activated dissociation of chemical bonds between carboxymethylated amylose (CMA) and silane functionalized silicon dioxide, we have investigated the dissociation kinetics of the bonds connecting CMA to silicon oxide surfaces with density functional calculations including the effects of force, solvent polarizability, and pH. We have determined the activation energies, the pre-exponential factors, and the reaction rate constants of candidate reactions. The weakest bond was found to be the silyl ester bond between the silicon and the alkoxy oxygen atom. Under acidic conditions, spontaneous proton addition occurs close to the silyl ester such that neutral reactions become insignificant. Upon proton addition at the most favored position, the activation energy for bond hydrolysis becomes 31 kJ mol(-1), which agrees very well with experimental observation. Heterolytic bond scission in the protonated molecule has a much higher activation energy. The experimentally observed bi-exponential rupture kinetics can be explained by different side groups attached to the silicon atom of the silyl ester. The fact that different side groups lead to different dissociation kinetics provides an opportunity to deliberately modify and tune the kinetic parameters of mechanically activated bond dissociation of silyl esters.

Mechanochemistry: the effect of dynamics

Dynamical effects on the mechanochemistry of linear alkane chains, mimicking polyethylene, are studied by means of molecular dynamics simulations. Butane and octane are studied using density-functional theory (DFT), whereas higher homologues are studied using a simple one-dimensional model in which the molecules are represented by a linear chain of Morse potentials (LCM). The application of a fixed external force to a thermodynamically pre-equilibrated molecule leads to a preference for cleavage of the terminal C-C bonds, whereas a sudden application of the force favors bond breaking in the central part of the chain. In all cases, transition-state theory predicts higher bond-breaking rates than found from the more realistic molecular dynamics simulations. The event of bond dissociation is related to dynamic states involving symmetric vibrational modes. Such modes do in general have lower frequencies of vibration than antisymmetric modes, which explains the deviation between the statistical theory and the dynamics simulations. The good qualitative agreement between the DFT and LCM models makes the latter a useful tool to investigate the mechanochemistry of long polymer chains.

Mechanically induced silyl ester cleavage under acidic conditions investigated by AFM-based single-molecule force spectroscopy in the force-ramp mode

AFM-based dynamic single-molecule force spectroscopy was used to stretch carboxymethylated amylose (CMA) polymers, which have been covalently tethered between a silanized glass substrate and a silanized AFM tip via acid-catalyzed ester condensation at pH 2.0. Rupture forces were measured as a function of temperature and force loading rate in the force-ramp mode. The data exhibit significant statistical scattering, which is fitted with a maximum likelihood estimation (MLE) algorithm. Bond rupture is described with a Morse potential based Arrhenius kinetics model. The fit yields a bond dissociation energy D_e = 35 kJ mol⁻¹ and an Arrhenius pre-factor A = 6.6 × 10⁴ s⁻¹. The bond dissociation energy is consistent with previous experiments under identical conditions, where the force-clamp mode was employed. However, the bi-exponential decay kinetics, which the force-clamp results unambiguously revealed, are not evident in the force-ramp data. While it is possible to fit the force-ramp data with a bi-exponential model, the fit parameters differ from the force-clamp experiments. Overall, single-molecule force spectroscopy in the force-ramp mode yields data whose information content is more limited than force-clamp data. It may, however, still be necessary and advantageous to perform force-ramp experiments. The number of successful events is often higher in the force-ramp mode, and competing reaction pathways may make force-clamp experiments impossible.

Single-molecule force-clamp experiments reveal kinetics of mechanically activated silyl ester hydrolysis

We have investigated the strength of silyl ester bonds formed between carboxymethylated amylose (CMA) molecules and silane-functionalized silicon oxide surfaces using AFM-based single-molecule force spectroscopy in the force-clamp mode. Single tethered CMA molecules were picked up, and bond lifetimes were determined at constant clamp forces of 0.8, 1.0, and 1.2 nN at seven temperatures between 295 and 320 K at pH 2.0. The results reveal biexponential rupture kinetics. To obtain the reaction rate constants for each force and temperature individually, the results were analyzed with a biexponential kinetic model using the maximum likelihood estimation (MLE) method. The force-independent kinetic and structural parameters of the underlying bond rupture mechanisms were extracted by fitting the entire data set with a parallel MLE fit procedure using the Zhurkov/Bell model and, alternatively, an Arrhenius kinetics model combined with a Morse potential as an analytic representation of the binding potential. With activation energies between 37 and 40 kJ mol(-1), and with Arrhenius prefactors between 5 × 10(4) and 2 × 10(6) s(-1), the results point to the hydrolysis of the silyl ester bond.

Influence of external force on properties and reactivity of disulfide bonds

The mechanochemistry of the disulfide bridge--that is, the influence of an externally applied force on the reactivity of the sulfur-sulfur bond--is investigated by unrestricted Kohn-Sham theory. Specifically, we apply the COGEF (constrained geometry simulates external force) approach to characterize the mechanochemistry of the disulfide bond in three different chemical environments: dimethyl disulfide, cystine, and a 102-atom model of the I27 domain in the titin protein. Furthermore, the mechanism of the thiol-disulfide reduction reaction under the effect of an external force is investigated by considering the COGEF potential for the adduct and transition-state clusters. With the unrestricted Becke-three-parameter-Lee-Yang-Parr (UB3LYP) exchange-correlation functional in the 6-311++G(3df,3pd) orbital basis, the rupture force of dimethyl disulfide is 3.8 nN at a disulfide bond elongation of 35 pm. The interaction with neighboring groups and the effect of conformational rigidity of the protein environment have little influence on the mechanochemical characteristics. Upon stretching, we make the following observations: the diradical character of the disulfide bridge increases; the energy difference between the singlet ground state and low-lying triplet state decreases; and the disulfide reduction is promoted by an external force in the range 0.1-0.4 nN. Our model of the interplay between force and reaction mechanism is in qualitative agreement with experimental observations.

Chemomechanics: chemical kinetics for multiscale phenomena

The purpose of this critical review is to introduce the reader to an increasingly important class of phenomena: enormous changes in rates of simple chemical reactions within macromolecules as they are stretched by interactions with the environment. In these chemomechanical, or mechanochemical, phenomena the effect of the macromolecular environment can be visualized as a spring (harmonic or anharmonic) bridging and pulling apart a pair of atoms of the macromolecule. Being able to predict how the parameters of this spring affect the kinetics of the reactions occurring between the constrained atoms may create revolutionary opportunities for designing new reactions, molecules and materials that would capture large-scale deformations to drive useful chemistry or, conversely, that would propel autonomous micro- and nanomechanical devices by coupling them to the concerted motion of atoms that convert reactants into products. Although chemists have long studied and exploited coupling between molecular strain and reactivity in small molecules, a quantitative understanding of the relationship between large-scale (>50 nm) strain and localized reactivity presents unique conceptual and experimental challenges. Below we discuss both the phenomenology and the interpretive framework of chemomechanical phenomena (102 references).