Theoretical Mechano-chemistry: Stressing Molecules in the "Virtual Lab"
What is "Mechanochemistry"?
Most chemical reactions must be activated by applying some form of excess energy. Certainly the oldest approach consists of using fire, i.e. thermal energy, leading to what is commonly known as thermochemistry. Other well–known “chemistries” are triggered by light or electricity, i.e. photochemistry or electrochemistry. A general observation is that different ways of activating chemical reactions might lead to different reaction pathways – including different products in extreme cases. In contrast and despite pioneering macroscopic experiments by Matthew Carey Lea at the end of the 19th century, the field of mechanically induced covalent chemistry, which is dubbed here “mechanochemistry”
in analogy to photochemistry, electrochemistry etc., still remains largely unexplored when it comes to a theoretical understanding at the fundamental molecular level.
Clearly this lack of understanding is at odds with the fantastic current experimental possibilities to use mechanical nano–Newton forces as a tool to induce, alter, or control chemical reactions by manipulating atoms or olecules [1,2]. This is typically achieved within setups relying on atomic force microscopy (AFM), using individual molecules that are covalently anchored to tips, or sonication experiments carried out in solution, using an ensemble of mechanophores with long polymer chains attached that act as force transducers.
On the other hand it is obvious that mechanical forces almost certainly will lead to different reaction pathways and thus different products much alike what is know from e.g. photochemistry or electrochemistry. This implies a growing gap between the ever increasing potential of experimental nanomanipulation techniques and a missing theoretical framework to understand such experimental observations. Finally, it
is noted that understanding mechanochemistry will not only be important within the realm of chemistry as such, but it will impact as well on getting insights into mechanical aspects of such diverse issues as molecular friction, nanoscale machines, enzymatic reactions, or targeted delivery to name but a few.
The aim of the project “Mechanochemistry of Covalent Bond Breaking from First Principles” is to complement experiments in the real laboratory by those carried out in the “Virtual Lab” , thus advancing the emerging field of theoretical mechanochemistry . In particular, mechanically-induced ringopening reactions have been in the focus of these investigations so far. Relying on ab initio simulations  at its heart, this study yielded unprecedented insights into the molecular details of the influence of constant external mechanical forces on reaction mechanisms. Before presenting our representative results on ring-opening of cyclopropane derivatives a few words on our simulation approach are in order.
Isotensional Stretching of Molecules in the "Virtual Lab"
Most quantum-chemical calculations or ab initio simulations of stretched molecules are carried out using so-called “isometric” conditions. Such setups are easily accessible in any conventional program package that has holonomic constraints available. This is either done by fixing an internal distance between two atoms in a molecule, or by constraining the two atoms to specified positions along a space-fixed axis. The latter approach is mostly used in periodic codes, where the former in quantum chemistry codes that have been optimized to treat finite systems. A comprehensive review on theoretical mechanochemistry can be found in Ref. . In contrast to this approach, the mechanochemical simulations presented in the following draw on our previously devised conceptual framework based on force-transformed potential energy surfaces (FT–PES) . In this “isotensional” formalism, the FT–PES, given an external constant force F0, is rigorously defined as
VEFEI (x, F0 )=VBO (x)-F0 q(x),
where VBO (x) is the usual Born–Oppenheimer (BO) PES as a function of all nuclear cartesian coordinates x, and q is the mechanical coordinate, i.e. a structural parameter (a generalized coordinate in terms of x) on which the force acts. By locating the stationary points of this function, in which the “External Force is Explicitly Included” (EFEI), one can evaluate, without invoking any approximation, properties such as reactant and transition state (TS) structures as functions of F0.
It is certainly instructive to analyze the FT–PES, which provides a static zero– temperature perspective of mechano-chemical reaction mechanisms [6,7,8,9], but this approximation clearly lacks the inclusion of thermal, entropic, dynamical and solvation effects except for crude modeling of these.
Using the power of capability platforms such as the Blue Gene/P machine JUGENE at Forschungszentrum Jülich allows us to go a major step beyond computing the FT–PES. The natural generalization is to carry out finite-temperature simulations using the FT–PES, i.e. VEFEI (x, F0 ), as input instead of
the usual BO–PES, VBO (x). Clearly, this calls for ab initio simulations  where the electronic structure and thus the forces acting on the nuclei is computed “on the fly” to move the nuclei under the influence of a constant external mechanical force, instead of precalculating and fitting VBO (x) and thus VEFEI (x, F0 ). This combination enables us to map multi-dimensional free energy landscapes at constant force, which we call force-transformed free energy surface (FT–FES) .
However, following this avenue requires the computation of free energy surfaces for several constant forces, which is a daunting task. This is made possible using the powerful ab initio metadynamics technique developed by Laio and Parrinello as reviewed in Ref. . At the technical level, using the so-called “multiple walker” sampling in conjunction with the CPMD software package  greatly improves the efficient use of the Blue Gene architecture, see our inSiDE contribution on prebiotic peptide synthesis  for technical background and scaling assessment. Together, this package of methods allows us to carry out efficiently ab initio simulations 
of mechanochemical reactions on Blue Gene platforms.
Enforced Ring-Opening of Cyclopropanes
Cyclobutene-based mechanophores have received a lot of attention recently, whereas cyclopropane systems, such as gem-dihalogencyclopropane derivatives, are under-researched in the realm of covalent mechanochemistry [2,4]. Yet, the force-induced electrocyclic ring-opening of these compound classes has furnished striking results [2,4]. Indeed, the mechanochemical activation of cis benzocyclobutenes
has been shown, both experimentally and computationally, to promote a thermally forbidden disrotatory ringopening process. The application of
a transient tensile force on gem-difluorocyclopropanes, in its turn, has been shown experimentally to lead to an unexpected isomerization of trans species into their less stable cis isomers via a mechanochemical trapping of a diradical TS. Even more enigmatic are gem-dichlorocyclopropane (gDCC) systems, which feature a counterintuitive
lack of selectivity in the mechanically assisted ring-opening reactions of cis versus trans isomers: while one expects the external forces to promote the ring-opening of cis gDCC more efficiently (due to a better coupling between the mechanical coordinate and the reaction coordinate), the experimental observations indicate that both isomers undergo force-induced ring-opening processes with approximately the same probability.
|Figure 1: Left: Scheme showing the involved chemical species, i.e. all reactants (cis; trans–I and trans–II being enantiomers), transition states (TS–I to TS–IV; S–TS–I to S–TS–IV), and products (Z,R; Z,S; E,S; E,R). The arrows connecting the reactants with the distinct products via the corresponding TSs represent the reaction paths obtained from IRC mapping and ab initio trajectory shooting starting from the TSs (see text). The second set of TSs (S–TS) belongs to interconversion reactions between selected products as indicated. For simplicity all structures correspond to the stationary points at zero force, the Z,R product is reproduced twice for clarity, and the Cl atoms are colored violet. Right: Force–dependence of activation energies ΔE‡ (F0) (open symbols) and free energies ΔA‡ (F0) at 300 K (filled symbols) of the disrotatory ring–opening of cis (red circles for the “outward” pathway) and trans (blue squares) 1,1–dichloro–2,3– dimethylocyclopropanes. The stretching force is applied to the C atoms of the two terminal methyl groups as indicated in the inset.
In our project the mechanochemical reactivity and force-induced stereochemistry of gDCCs has been scrutinized based on isotensional ab initio metadynamics simulations . Our thermodynamic approach is supplemented by ab initio trajectory shooting simulations operating on the FT-PESs in order to dissect genuinely dynamical effects on branching ratios as a function of force (the details of this technique are provided in the Supporting Information
of Ref. ). Based on these methods
we have unveiled the mechanisms of force-induced ring-openings of cis versus trans gDCCs, which rationalizes puzzling experimental findings. Even more importantly, we have discovered an unprecedented complex mechanostereo-chemical behavior, whereby the ring-opening of trans isomers of 1,3-disubstituted gDCCs can lead to two different diastereomers, with the probabilities of obtaining them featuring an intricate dependence on the force exerted onto the system.
The model system chosen to explore the mechanochemistry of gDCCs is 1,1-dichloro-2,3-dimethylcyclopropane: its cis and trans isomers and the four possible distinct reaction products of the corresponding ring-opening processes are depicted in Fig.1. In the first stage of our study, the thermal chemistry (i.e. the chemistry at zero force) of gDCCs was dissected. Our simulations (both at 0 K and at 300 K) have revealed that the ring-opening
of these molecules, which yield the corresponding 2,3-dichloroalkenes, proceeds via a concerted disrotatory mechanism, whereby the breaking
of the C-C bond takes place in concert with the C-Cl bond cleavage and the subsequent Cl migration. For cis gDCC there are two possible pathways as indicated in Fig. 1: the “outward pathway” which passes through TS-I and the “inward pathway” via TS-III. On the basis of the difference between the activation energies of both pathways (about 5 kcal/mol, see Fig.1), it has been concluded that the thermal ringopening of cis gDCC occurs via a “disrotatory outward mechanism”, whose BO-PES features a TS of Cs symmetry (TS-I) and a bifurcation point along the intrinsic reaction coordinate (IRC) after the TS is left behind. By virtue of this topological feature, the migrating Cl atom can move either to the C atom on the right side (thus yielding the Z,Ralkene) or to the left (leading to Z,Salkene), see Fig.1. Given the topology of the underlying PES, the ring-opening of cis gDCC is expected to yield the two enantiomeric alkenes with equal probability. The disrotatory ring-opening of trans gDCC at zero force, in its turn, implies either the TS-II or the TS-IV according to Fig.1, with neither of these two TSs featuring symmetry. Trajectory shooting simulations initiated from TS-II have brought to light the fact that the ring-opening of trans gDCC can yield either the E,S-alkene or the Z,S-alkene in the absence of external forces. The probabilities of obtaining these two diastereomers were calculated to be 0.76 and 0.24, respectively. The branching ratio of obtaining E,Rversus Z,R-alkenes via TS-IV are identical because of symmetry. The computed activation free energies were found to be lower (by about 4 kcal/mol) for the ring-opening of cis gDCC than trans gDCC, as shown in Fig.1.
After having set the stage by describing the thermal chemistry of gDCCs, we will now focus on the mechanochemical behavior of these molecules. As explained in Ref. , of all the reaction pathways depicted in Fig. 1 only two are relevant for fully describing the mechanochemistry of gDCCs: the disrotatory outward mechanism of cis gDCC and the disrotatory ring-opening of trans gDCC passing through TS-II. As shown in Fig. 1, the force-dependence featured by the activation free energy, ΔA‡, and the activation energy, ΔE‡, for the two considered pathways follows
a similar general trend. The values of
ΔA‡ (F ) have been obtained from the 0
FT-FESs displayed in Fig. 2. Despite the similar trends, the values of ΔA‡ (F0) are much lower by about 6-7 kcal/mol over the whole range of forces, which results in a dramatic rate acceleration due to finite-temperature and entropy effects not accounted for when computing only ΔE‡ (F0). With reference to the selectivity with which the tensile load might promote preferentially the ring-opening of one isomer, both the qualitatively different shapes of the energy curves associated with the cis and trans reactants and the corresponding rupture forces (1.5 nN and 2.5 nN, respectively, at 300 K) reflect the fact that the external forces enhance the ring-opening of cis gDCCs more efficiently. This is somehow contradictory to the experimentally found lack of selectivity. As argued in Ref. , the most plausible suggestion for resolving such apparent contradiction would be to speculate that sufficiently large forces (forces on the order of 2 nN would suffice, according to the data in Fig. 1) were generated in the sonochemical experiments as to reach the barrierless regime for the ring-opening reactions of both isomers.
|Figure 2: Force-transformed free energy surfaces (FT-FESs) for ring-opening for the cis reactant of 1,1-dichloro-2,3-dimethylcyclopropane in the absence of any external force and with three different external forces (F0 = 0.5, 1.0, and 1.25 nN as indicated). These FT-FESs have been obtained by means of isotensional ab initio metadynamics simulations performed in a reaction subspace spanned by two collective variables: CV1 is the C C distance associated with the bond that yields upon the ring-opening process. CV2 is the difference CN1 - CN2 of the coordination numbers of both chlorine atoms with respect to the left (CN1) or right (CN2) carbon atom in the cyclopropane ring.
Last but not least, our exploration of the mechanochemistry of gDCCs has unveiled a most surprising feature: the force-dependent selectivity of the ring-opening of trans reactant to yield either the Zor the E-diastereomer of the corresponding dichloroalkene.
As clearly displayed in Fig. 3, the corresponding branching ratio changes dramatically and non-monotonically as a function of F0. This intricate switching behavior obviously implies that a ratio of about 50:50 is expected to be observed only close to some specific critical forces (0.7 nN, 1.9 nN and 2.2 nN). Importantly, in the limit of large forces the majority product is the Z,S-product, which is just opposite to the situation encountered at zero force. To the best of our knowledge, this is the first time that such an intricate mechanochemical behavior of a reaction resulting from intrinsically dynamical effects but determining its stereochemistry is reported.
The theoretical mechanochemistry presented so far has been carried out in the gas phase. Clearly, this is only a first step as each and every experiment is carried out in the condensed phase - be it a liquid phase in sonication or a protein matrix in AFM experiments. Although initial work along these lines has been carried out on JUGENE, we are looking very much forward to using the Blue Gene/Q platform JUQUEEN at Forschungszentrum Jülich to push theoretical mechanochemistry
in much more realistic environments such as solutions and biomolecules.
|Figure 3: Force-dependence of the probability of obtaining the E,S-products (red) versus Z,S-products (black) upon ring-opening of trans reactant as computed from dynamical trajectory shooting simulations. The range of forces with yellow and white backgrounds correspond to the forces at which the majority product of the ringopening process is the E,S-alkene or the Z,S-alkene, respectively.
It gives us pleasure to thank Motoyuki Shiga, Janos Kiss, Martin Krupicka, Miriam Wollenhaupt, Matthias Rückert, and Marcus Böckmann for fruitful discussions.
We are grateful to Deutsche Forschungsgemeinschaft (Reinhart Koselleck Grant MA 1547/9 to D.M.), Alexander von Humboldt Stiftung (Humboldt Fellowship to J.R.A), Catalan Government (Beatriu de Pinós Fellowship to J.R.A.), as well as Spanish Government (“Ramón y Cajal” contract to J.R.A.) for having supported financially our research on theoretical mechanochemistry.
Last but not least, the excellent and significant computational support by John von Neumann Institute for Computing (NIC) and Jülich Supercomputing Centre (JSC) is most gratefully acknowledged.
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inSiDE 6:30–35, 2008
• Przemyslaw Dopieralski
• Padmesh Anjukandi
• Jordi Ribas-Arino
• Dominik Marx
Lehrstuhl für Theoretische Chemie Ruhr-Universität Bochum