Tunneling, path-integral quantum dynamics

Path-integral statistical mechanics is obtained in strict analogy to path-integral quantum dynamics [71]. The path-integral version of quantum dynamics focuses on the fact that a quantum mechanical system is allowed to violate Hamilton s principle. For example, tunneling (a nonclassical motion) is possible within quantum mechanics. Seizing on a comment by Dirac [72] on the relationship between S and the quantum propagator... 

Hwang et al.131 were the first to calculate the contribution of tunneling and other nuclear quantum effects to enzyme catalysis. Since then, and in particular in the past few years, there has been a significant increase in simulations of QM-nuclear effects in enzyme reactions. The approaches used range from the quantized classical path (QCP) (e.g., Refs. 4,57,136), the centroid path integral approach,137,138 and vibrational TS theory,139 to the molecular dynamics with quantum transition (MDQT) surface hopping method.140 Most studies did not yet examine the reference water reaction, and thus could only evaluate the QM contribution to the enzyme rate constant, rather than the corresponding catalytic effect. However, studies that explored the actual catalytic contributions (e.g., Refs. 4,57,136) concluded that the QM contributions are similar for the reaction in the enzyme and in solution, and thus, do not contribute to catalysis. 

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