Centroid methods molecular dynamics

The Feynman-Hibbs and QFH potentials have been used extensively in simulations examining quantum effects in atomic and molecular fluids [12,15,25]. We note here that the centroid molecular dynamics method [54, 55] is related and is intermediate between a full path integral simulation and the Feynman-Hibbs approximation ... 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

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. 

A disadvantage of using Car-Parrinello path integral methods is that the molecular dynamics is used only to compute averaged properties, the simulation dynamics having no direct physical meaning. A recently developed, albeit approximate method for generating fully quantum mechanical dynamics is the ab initio centroid molecular dynamics method (Marx et al., 1999 Pavese et al., 1999). Tlie application of Car-Parrinello methods to... 

General Time Correlation Functions Centroid Molecular Dynamics Method... 

Perez, A. Tuckerman, M. E. Muser, M. H., A Comparative Study of the Centroid and Ring-Polymer Molecular Dynamics Methods for Approximating Quantum Time Correlation Eunctions from Path Integrals. J. Chem. Phys. 2009,130,184105. 

Takayanagi T, Shiga M. (2003) Photodissociation of CI2 in helium clusters an application of hybrid method of quantum wavepacket d5uiamics and path integral centroid molecular dynamics. Chem. Phys. Lett. 372 90-96. 

Much work has been recently done in extending path integral and centroid molecular dynamics (CMD) methods to include nuclear quantum effects in classical MD simulations [230-233]. Tachikawa etal [230] studiedp-CH O) (n= 1-3) by ab initio hybrid Monte Carlo and ab initio path integral simulations. Their simulation showed that, due to quantum effects, the average hydrogen-bonded... 

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