Monte Carlo simulation path integrals approach

The computation of quantum many-body effects requires additional effort compared to classical cases. This holds in particular if strong collective phenomena such as phase transitions are considered. The path integral approach to critical phenomena allows the computation of collective phenomena at constant temperature — a condition which is preferred experimentally. Due to the link of path integrals to the partition function in statistical physics, methods from the latter — such as Monte Carlo simulation techniques — can be used for efficient computation of quantum effects. 

The calculation of the potential of mean force, AF(z), along the reaction coordinate z, requires statistical sampling by Monte Carlo or molecular dynamics simulations that incorporate nuclear quantum effects employing an adequate potential energy function. In our approach, we use combined QM/MM methods to describe the potential energy function and Feynman path integral approaches to model nuclear quantum effects. 

As a final example in this subsection we mention the recent study of Zillich and Whaley who examined LiH solvated in He clusters with up to 100 atoms. The authors used a path integral Monte Carlo simulation approach, whose details shall not be discussed further here. The LiH-He interaction potential was found to be highly anisotropic with attractions for He approaching the molecule in a direction parallel to the molecular axis, but with strong repulsions for He approaching the molecule in a direction perpendicular to the molecular bond. Despite these repulsions, the authors found that LiH prefers to occupy central regions of the LiH He clusters for n larger than 10-15. 

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