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How mechanical forces speed up chemical reactions: The quantum Bell formula

Tuesday, September 20, 3:30PM – 5PM
POB 6.304

Dmitrii E Makarov, ICES and Department of Chemistry and Biochemistry

Mechanical force applied to an individual molecule can be used to enhance or suppress its conversion to other chemical species or change its reactivity with respect to other molecules. This effect is commonly described by the empirical formula popularized by Bell [Science, v. 200, p. 618], which predicts that the reaction rate should be exponentially sensitive to the force, k(f) ~ exp(f/f0). The force scale f0 quantifies the sensitivity of a reaction to the force and, for thermally activated processes, can be estimated as kT/a, where a is a length scale associated with the process. Although far from exact, Bell’s formula is widely used to describe a variety of mechanochemical phenomena. For example, biophysicists commonly use it to describe cell adhesion or the coupling of mechanical and chemical processes in living organisms. In this talk, I will explore the sensitivity of chemical reactions to mechanical forces in the regime, where quantum mechanical effects, particularly tunneling, are significant. I will derive a quantum-mechanical analog of the Bell formula, provide simple estimates for f0 in the quantum regime, and, more generally, describe how to numerically compute the force dependence of a quantum reaction rate using a semiclassical “instanton” method. Mechanical force applied to an individual molecule can be used to enhance or suppress its conversion to other chemical species or change its reactivity with respect to other molecules. This effect is commonly described by the empirical formula popularized by Bell [Science, v. 200, p. 618], which predicts that the reaction rate should be exponentially sensitive to the force, k(f) ~ exp(f/f0). The force scale f0 quantifies the sensitivity of a reaction to the force and, for thermally activated processes, can be estimated as kT/a, where a is a length scale associated with the process. Although far from exact, Bell’s formula is widely used to describe a variety of mechanochemical phenomena. For example, biophysicists commonly use it to describe cell adhesion or the coupling of mechanical and chemical processes in living organisms. In this talk, I will explore the sensitivity of chemical reactions to mechanical forces in the regime, where quantum mechanical effects, particularly tunneling, are significant. I will derive a quantum-mechanical analog of the Bell formula, provide simple estimates for f0 in the quantum regime, and, more generally, describe how to numerically compute the force dependence of a quantum reaction rate using a semiclassical “instanton” method.

Hosted by Leszek Demkowicz