A mechanochemical study of the effects of compression on a Diels-Alder reaction

Calculating high-pressure vibrational frequencies analytically with the extended hydrostatic compression force field approach

We report the implementation of the analytical Hessian for the mechanochemical extended hydrostatic compression force field method in the Q-Chem program package. To verify the implementation, the analytical Hessian was compared with finite difference calculations. In addition, we calculated the pressure dependency of the Raman active vibrational modes of methane, ethane, and hydrogen, as well as all IR and Raman active modes of Buckminsterfullerene, and compared the results with experimental and theoretical data. Our implementation paves the way for the analysis of geometric points on a pressure-deformed potential energy surface and provides a straightforward model to calculate the vibrational properties of molecules under high pressure.

Studying and exploring potential energy surfaces of compressed molecules: a fresh theory from the eXtreme Pressure Polarizable Continuum Model

We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the XP-PCM framework. The effective potential energy surface is defined by the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform, in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining of the optimized geometry of compressed methane and the transition state of electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.

High-Pressure Reaction Profiles and Activation Volumes of 1,3-Cyclohexadiene Dimerizations Computed by the Extreme Pressure-Polarizable Continuum Model (XP-PCM)

Quantum chemical calculations are reported for the thermal dimerizations of 1,3‐cyclohexadiene at 1 atm and high pressures up to the GPa range. Computed activation enthalpies of plausible dimerization pathways at 1 atm agree well with the experiment activation energies and the values from previous calculations. High‐pressure reaction profiles, computed by the recently developed extreme pressure‐polarizable continuum model (XP‐PCM), show that the reduction of reaction barrier is more profound in concerted reactions than in stepwise reactions, which is rationalized on the basis of the volume profiles of different mechanisms. A clear shift of the transition state towards the reactant under pressure is revealed for the [6+4]‐ene reaction by the calculations. The computed activation volumes by XP‐PCM agree excellently with the experimental values, confirming the existence of competing mechanisms in the thermal dimerization of 1,3‐cyclohexadiene.

Theoretical Studies of Furan and Thiophene Nanothreads: Structures, Cycloaddition Barriers, and Activation Volumes

This theoretical study examines the formation, structure, and stability of two of the most ordered nanothreads produced yet, those derived from furan and thiophene. The energetic consequences and activation barriers of the first two steps of oligomerization via a Diels-Alder mechanism were examined. The ca. 20 GPa difference in the synthetic pressures (lower for furan) is explainable in terms of the greater loss of aromaticity by the thiophene. The effects of pressure on the reaction profiles, operating through a volume decrease along the reaction coordinate, are illustrated. The interesting option of polymerization proceeding in one or two directions opens up the possibility of polymers with opposing, cumulative dipole moments. The computed activation volumes are consistently more negative for furan, in accordance with the lower onset pressure of furan polymerization. The energetics of three ordered polymer structures were examined. The syn polymer, with all O/S atoms on the same side, if not allowed to distort, is at a high energy relative to the other two due to the O/S lone pair repulsion, understandably greater for S than for O at the 2.8/2.6 Å separation. Set free, the syn isomers curve or arch in two- or three-dimensional (helical) ways, whose energetics are traced in detail. The syn polymer can also stabilize itself by twisting into zig-zag or helical energy minima. The release of strain in a linear thread as the pressure is relaxed to 1 atm, with consequent thread curving, is a likely mechanism for the observed loss of the crystalline order in the polymer as it is returned to ambient pressure.

The activation efficiency of mechanophores can be modulated by adjacent polymer composition

The activation efficiency of mechanophores in stress-responsive polymers is generally limited by the competing process of unspecific scission in other parts of the polymer chain. Here it is shown that the linker between the mechanophore and the polymer backbone determines the force required to activate the mechanophore. Using quantum chemical methods, it is demonstrated that the activation forces of three mechanophores (Dewar benzene, benzocyclobutene and gem-dichlorocyclopropane) can be adjusted over a range of almost 300% by modifying the chemical composition of the linker. The results are discussed in terms of changes in electron density, strain distribution and structural parameters during the rupture process. Using these findings it is straightforward to either significantly enhance or reduce the activation rate of mechanophores in stress-responsive materials, depending on the desired use case. The methodology is applied to switch a one-step "gating" of a mechanochemical transformation to a two-step process.

Modeling Molecules under Pressure with Gaussian Potentials

The computational modeling of molecules under high pressure is a growing research area that augments experimental high-pressure chemistry. Here, a new electronic structure method for modeling atoms and molecules under pressure, Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) approach, is introduced. In this method, a set of Gaussian potentials is distributed evenly on the van der Waals surface of the investigated chemical system, leading to a compression of the electron density and the atomic scaffold. Since no parameters other than pressure need to be specified, GOSTSHYP allows straightforward geometry optimizations and ab initio molecular dynamics simulations of chemical systems under pressure for nonexpert users. Calculated energies, bond lengths, and dipole moments under pressure fall within the range of established computational methods for high-pressure chemistry. A Diels-Alder reaction and the cyclotrimerization of acetylene showcase the ability of GOSTSHYP to model pressure-induced chemical reactions. The connection to mechanochemistry is pointed out.

A mechanochemical model for the simulation of molecules and molecular crystals under hydrostatic pressure

A novel mechanochemical method for the simulation of molecules and molecular crystals under hydrostatic pressure, the eXtended Hydrostatic Compression Force Field (X-HCFF) approach, is introduced. In contrast to comparable methods, the desired pressure can be adjusted non-iteratively and molecules of general shape retain chemically reasonable geometries even at high pressure. The implementation of the X-HCFF approach is straightforward, and the computational cost is practically the same as for regular geometry optimization. Pressure can be applied by using any desired electronic structure method for which a nuclear gradient is available. The results of the X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods. Experimental spectroscopic data of a molecular crystal under pressure are reproduced accurately.

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.

Experimental Polymer Mechanochemistry and its Interpretational Frameworks

Polymer mechanochemistry is an emerging field at the interface of chemistry, materials science, physics and engineering. It aims at understanding and exploiting unique reactivities of polymer chains confined to highly non-equilibrium stretched geometries by interactions with their surroundings. Macromolecular chains or their segments become stretched in bulk polymers under mechanical loads or when polymer solutions are sonicated or flow rapidly through abrupt contractions. An increasing amount of empirical data suggests that mechanochemical phenomena are widespread wherever polymers are used. In the past decade, empirical mechanochemistry has progressed enormously, from studying fragmentations of commodity polymers by simple backbone homolysis to demonstrations of self-strengthening and stress-reporting materials and mechanochemical cascades using purposefully designed monomers. This progress has not yet been matched by the development of conceptual frameworks within which to rationalize, systematize and generalize empirical mechanochemical observations. As a result, mechanistic and/or quantitative understanding of mechanochemical phenomena remains, with few exceptions, tentative. In this review we aim at systematizing reported macroscopic manifestations of polymer mechanochemistry, and critically assessing the interpretational framework that underlies their molecular rationalizations from a physical chemist's perspective. We propose a hierarchy of mechanochemical phenomena which may guide the development of multiscale models of mechanochemical reactivity to match the breadth and utility of the Eyring equation of chemical kinetics. We discuss the limitations of the approaches to quantifying and validating mechanochemical reactivity, with particular focus on sonicated polymer solutions, in order to identify outstanding questions that need to be solved for polymer mechanochemistry to become a rigorous, quantitative field. We conclude by proposing 7 problems whose solution may have a disproportionate impact on the development of polymer mechanochemistry.

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.