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Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques-which is based on re-weighted sampling-is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average. © 2011 The Royal Society.

Progress in the atomic-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born-Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code (Ceriotti et al., 2014) was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives., Program summary, Program Title: i-PI, Program Files doi: http://dx.doLorg/10.17632/x792grbm9g.1, Licensing provisions: GPLv3, MIT, Programming language: Python, External routines/libraries: NumPy, Nature of problem: Lowering the implementation barrier to bring state-of-the-art sampling and atomistic modeling techniques to ab initio and empirical potentials programs., Solution method: Advanced sampling methods, including path-integral molecular dynamics techniques, are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic coordinates from the Python interface, and to return the forces and energy that are used to integrate the equations of motion, optimize atomic geometries, etc., Restrictions: This code does not compute interatomic potentials, although the distribution includes sample driver codes that can be used to test different techniques using a few simple model force fields. (C) 2018 Elsevier B.V. All rights reserved.

The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (1% of the studied structures) lie between the values of C60 and C70, the two most abundant fullerenes. Interestingly, buckminsterfullerene is the only fullerene with zero information entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.