• computational chemistry;
  • conformation analysis;
  • cyclobutenes;
  • force distributions;
  • mechanochemistry


Internal molecular forces can guide chemical reactions, yet are not straightforwardly accessible within a quantum mechanical description of the reacting molecules. Here, we present a force-matching force distribution analysis (FM-FDA) to analyze internal forces in molecules. We simulated the ring opening of trans-3,4-dimethylcyclobutene (tDCB) with on-the-fly semiempirical molecular dynamics. The self-consistent density functional tight binding (SCC-DFTB) method accurately described the force-dependent ring-opening kinetics of tDCB, showing quantitative agreement with both experimental and computational data at higher levels. Mechanical force was applied in two different ways, namely, externally by a constant pulling force and internally by embedding tDCB within a strained macrocycle-containing stiff stilbene. We analyzed the distribution of tDCB internal forces in the two different cases by FM-FDA and found that external force gave rise to a symmetric force distribution in the cyclobutene ring, which also scaled linearly with the external force, indicating that the force distribution was uniquely determined by the symmetric architecture of tDCB. In contrast, internal forces due to stiff stilbene resulted in an asymmetric force distribution within tDCB, which indicated a different geometry of force application and supported the important role of linkers in the mechanochemical reactivity of tDCB. In addition, three coordinates were identified through which the distributed forces contributed most to rate acceleration. These coordinates are mostly parallel to the coordinate connecting the two CH3 termini of tDCB. Our results confirm previous observations that the linker outside of the reactive moiety, such as a stretched polymer or a macrocycle, affects its mechanochemical reactivity. We expect FM-FDA to be of wide use to understand and quantitatively predict mechanochemical reactivity, including the challenging cases of systems within strained macrocycles.