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WIREs Comput Mol Sci
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Theory and simulation of atom tunneling in chemical reactions

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Quantum tunneling of atoms, the penetration of energy barriers higher than the total energy of the system, plays a role in many chemical systems. While any chemical reaction is dominated by tunneling at low enough temperature, there is evidence for hydrogen atom tunneling even in enzymatic reactions at ambient conditions. The smaller the mass of the atoms, the lower and thinner the barrier is, the stronger the tunneling effect increases the reaction rate. Different methods to calculate tunneling rates are available. They range from full solutions of the time‐dependent Schrödinger equation via the semiclassical method to ad hoc corrections of classical transition state theory. The basis of different methods, their accuracy, and applicability is discussed in the present overview, with a particular focus on instanton theory, a Feynman‐path‐based approach using the semiclassical approximation.

Instantons in more dimensions: Instanton paths for different temperatures in the Müller–Brown potential. At low enough temperature, the system tunnels through two barriers directly from the reactant state (RS) to the product state (PS), blue line.
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Typical instantons of a one‐dimensional energy barrier. The energy is shown by a thin black line, representative images of the instanton path as purple dots. The instanton path stretches over the barrier and ends at equal energies at both sides, the tunneling energy Eb. Right: the lower the temperature, the longer the instanton becomes (graphs shifted along the energy axis). At Tc, the instanton collapses to a point on the saddle point and the theory becomes inapplicable.
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Arrhenius plot of the logarithm of the rate constant plotted versus the inverse temperature. The classical over‐the‐barrier reaction results in a straight line. The rate becomes constant at low temperature when tunneling dominates.
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Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

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