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Force probes allow reaction rates to be measured as a function of the restoring force in a molecule that has been stretched or compressed. Unlike strain energy, approaches based on restoring force allow quantitative molecular understanding of phenomena as diverse as translation of microscopic objects by reacting molecules, crack propagation and mechanosensing. Conceptually, localized reactions offer the best opportunity to gain fundamental insights into how rates vary with restoring forces, but such reactions are particularly difficult to study systematically using microscopic force probes. Here, we show how a molecular force probe, stiff stilbene, simplifies force spectroscopy of localized reactions. We illustrate the capabilities of our approach by validating the central postulate of chemomechanical kinetics--force lowers the activation barrier proportionally to the difference in a single internuclear distance between the ground and transition states projected on the force vector--on a paradigmatic unimolecular reaction: concerted dissociation of the C-C bond.

We report a method to estimate the restoring force of a constrained small molecule and relate changes in its reactivity to this force. Restoring force is a size-invariant measure of molecular strain and offers a conceptual framework to bridge studies of macromolecular reactions by force spectroscopies with those of strained small molecules. We illustrate our method by showing that E stiff stilbene (1,1'-Delta-biindan) with up to 700 pN of force along its C6,C6' axis is accessible by photoisomerization. It reverts thermally to the Z isomer with tau(1/2) approximately 100 ms, probably long enough to be useful for microscale actuation. The quantum yield of photoisomerization and the activation barrier of thermal isomerization of constrained stiff stilbene increase sharply as the restoring force decreases.

Sensitized photolysis: We describe a series of macrocyclic disulfides containing stiff stilbene (see scheme) as the intramolecular photosensitizer designed for fundamental mechanistic studies of sensitized photolysis of the S-S bond. Preliminary studies revealed weak temperature dependence of the quantum yields, which decreased exponentially with Boltzmann-weighted average separation between the S-S bond and stiff stilbene.

We investigated the effect of several computational variables, including the choice of the basis set, application of symmetry constraints, and zero-point energy (ZPE) corrections, on the structural parameters and predicted ground electronic state of model 5-coordinate hemes (iron(II) porphines axially coordinated by a single imidazole or 2-methylimidazole). We studied the performance of B3LYP and B3PW91 with eight Pople-style basis sets (up to 6-311+G*) and B97-1, OLYP, and TPSS functionals with 6-31G and 6-31G* basis sets. Only hybrid functionals B3LYP, B3PW91, and B97-1 reproduced the quintet ground state of the model hemes. With a given functional, the choice of the basis set caused up to 2.7 kcal/mol variation of the quintet-triplet electronic energy gap (DeltaEel), in several cases, resulting in the inversion of the sign of DeltaEel. Single-point energy calculations with triple-zeta basis sets of the Pople (up to 6-311G++(2d,2p)), Ahlrichs (TZVP and TZVPP), and Dunning (cc-pVTZ) families showed the same trend. The zero-point energy of the quintet state was approximately 1 kcal/mol lower than that of the triplet, and accounting for ZPE corrections was crucial for establishing the ground state if the electronic energy of the triplet state was approximately 1 kcal/mol less than that of the quintet. Within a given model chemistry, effects of symmetry constraints and of a "tense" structure of the iron porphine fragment coordinated to 2-methylimidazole on DeltaEel were limited to 0.3 kcal/mol. For both model hemes the best agreement with crystallographic structural data was achieved with small 6-31G and 6-31G* basis sets. Deviation of the computed frequency of the Fe-Im stretching mode from the experimental value with the basis set decreased in the order: nonaugmented basis sets, basis sets with polarization functions, and basis sets with polarization and diffuse functions. Contraction of Pople-style basis sets (double-zeta or triple-zeta) affected the results insignificantly for iron(II) porphyrin coordinated with imidazole. Poor performance of a "locally dense" basis set with a large number of basis functions on the Fe center was observed in calculation of quintet-triplet gaps. Our results lead to a series of suggestions for density functional theory calculations of quintet-triplet energy gaps in ferrohemes with a single axial imidazole; these suggestions are potentially applicable for other transition-metal complexes.

In weakly coordinating solvents FeII meso-(N-methylimidazol-2-yl)porphine Fe exists as a stable dimer (Kd=50+/-30 nM) that binds ligands without undergoing dissociation and is presently the simplest complex in which the mono-imidazole ligation of a ferroheme is enforced without excess imidazole in solution.