Development and Application of Quantum Chemical Methods for the Description of Molecules Under Mechanical Stress

In mechanochemistry, forces are used to initiate chemical reactions. Although mechanochemical reactions have been conducted for millennia, a fundamental understanding of the relevant processes at the molecular level is still unavailable. Nevertheless, mechanochemistry is a lively field with an extraordinarily wide range of applications. Several approaches to apply forces to single molecules are commonly used today. One such approach is Single-Molecule Force Spectroscopy, where forces are transmitted from the cantilever of an Atomic Force Microscope to a macromolecule that is anchored to a glass surface. Moving the cantilever away from the surface exerts a pulling force on the molecule. In another class of mechanochemical experiments, ultrasound baths are used to rupture polymers mechanically or to transduce forces to a mechanically susceptible moiety. This capability of ultrasound baths is due to the collapse of cavitational bubbles in the liquids, which generates tensile forces. Furthermore, ball milling or grinding techniques can be used to crush solids, thereby applying forces to molecules. This procedure can be applied to make and break covalent bonds. Due to the lack of solvent, mechanochemical synthesis in a ball mill shows enormous potential as a sustainable and environment-friendly alternative to thermochemistry. Despite this rich body and long history of experimental mechanochemical procedures, the underlying processes are not well understood at the molecular level. However, such a comprehension is desperately needed for the optimization of mechanochemical syntheses. The use of quantum chemical methods to describe mechanochemical processes, which is called quantum mechanochemistry, has proven to be of tremendous value in understanding mechanochemistry at its most fundamental level. Quantum chemical methods for the description of molecules under external forces afford predictions on force-induced changes in molecular geometry, reactivity and spectroscopic properties. Moreover, force analysis tools are available that can be used to identify the mechanically relevant degrees of freedom in a molecule or its force-bearing scaffold, thereby rationalizing mechanochemical reactivity. During my PhD work, I have developed the JEDI (Judgement of Energy DIstribution) analysis, which is a quantum chemical force analysis tool for the distribution of stress energy in a mechanically deformed molecule. Based on the harmonic approximation, an energy is calculated for each bond, bending and torsion in a molecule, thus allowing the identification of the mechanically most strained regions in a molecule as well as the rationalization of mechanochemical processes. When a molecule is stretched, some internal modes store more energy than others. This leads to particularly large displacements of certain modes and to the preconditioning of selected bonds for rupture. Using the JEDI analysis I investigated the mechanochemical properties of polymer strands that are tangled into knots. In analogy to ropes, polymer strands are weakened by the ubiquitous overhand knot by approximately 50% and the point of bond rupture is located at the “entry” or “exit” of the knot. The JEDI analysis revealed the reason for this behavior. Upon stretching, most stress energy is stored in the torsions of the curved part of the knot and only a remarkably small amount of energy is used to stretch the bonds that ultimately break. This observation leads to the physical picture that the knot “chokes off” the chain in its immediate vicinity. In this process, the torsions act as work funnels that effectively localize the mechanical energy in the knot, thus preconditioning the covalent bonds at its entry and exit for bond rupture. Besides the description of mechanical deformation in the ground state, the JEDI analysis can be used in the electronically excited state to quantify the energy gained by relaxation on the excited state potential energy surface (PES). For this, the harmonic approximation needs to be applicable on the excited state PES of interest. The physical process that is described by the excited state JEDI analysis is fundamentally different from the ground state variant. While in the ground state JEDI analysis the distribution of stress energy in a mechanically deformed molecule is analyzed, i.e. energy is expended for deformation, the excited state JEDI analysis quantifies the energy gained by the relaxation of each internal mode upon relaxation on the excited state PES, i.e. energy becomes available. With the excited state JEDI analysis, the mechanical efficiency of molecular photoswitches can be calculated. The spatial extension of a photoswitch that undergoes, e.g., cis-trans-photoisomerization, changes significantly during this process and forces are exerted on the environment. However, other internal modes of the photoswitch that do not contribute to the change in spatial extension change as a side effect of the relaxation on the excited state PES and a certain amount of energy is wasted on them. This effect limits the mechanical efficiency of photoswitches. Using the excited state JEDI analysis, I investigated the mechanical efficiency of the stiff-stilbene photoswitch, which had been used in an experiment in literature to accelerate the electrocyclic ring opening of cyclobutene by photoisomerization. I found that the mechanical efficiency of stiff-stilbene is much too low to account for the observed enhancement of the reaction. A much more reasonable physical explanation is that excess energy from absorption of a photon is dissipated as heat, which accelerates the rupture of the thermally labile bond in cyclobutene. Furthermore, I used the JEDI analysis to investigate methods for the stabilization of strained hydrocarbons. Angle-strained cycloalkynes with a ring size smaller than eight carbon atoms are highly unstable under normal laboratory conditions, since the C≡C−C bond angles deviate substantially from linearity. Applying an external force in an appropriate direction partially linearizes these bond angles, thus leading to a stabilization of the cycloalkyne. Incorporating cycloheptyne into a macrocycle with stiff-stilbene, however, does not lead to a significant stabilization, since the mechanical efficiency of stiff-stilbene is low. Coupling cycloheptyne to another strained hydrocarbon, on the other hand, stabilizes the molecule tremendously. In particular, cycloheptyne was coupled to a strained cyclophane in a condensed macrocycle and I found that appropriate linking leads to a loss of strain in both hydrocarbons. In addition to the development of the JEDI force analysis tool, I used existing quantum mechanochemical methods to develop molecular force probes. This class of molecules can be incorporated into larger systems like polymers and proteins and can be used to monitor forces acting in different regions of the macromolecules in real-time via force-induced changes in the spectroscopic signals of the force probes. I found that the reduction of point group symmetry upon mechanical deformation of the molecular force probe is a profitable feature, since electronically excited states that are degenerate in the unperturbed state can split up upon application of an external force. This effect can lead to the generation of new peaks in the spectrum, thus allowing the precise identification of the force probe signal. Additionally, I incorporated molecular force probes into the backbone of proteins without disturbing their natural fold. The formation of hydrogen bonds between the force probe and neighboring strands in a β-sheet preserves the secondary and tertiary structure of the protein and allows the identification of the pulling direction. The application of forces along and perpendicular to the backbone yields pronounced and clearly distinguishable signals of the force probes in the infrared and Raman spectra. Advantageously, the intensities of these signals are proportional to the external force at selected points of the spectrum, which makes the molecules “force rulers”. The signals of the force probes can be intensified and shifted to a transparent window in the protein spectrum by isotopic substitution.