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We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time correlation functions are conveniently computed via reweighted averages along a single trajectory and kinetic rates are accessed at no additional cost. These abilities are illustrated analyzing a model potential and the umbrella inversion of NH$_3$ in water. The algorithm allows a parallel implementation and promises to be a powerful tool for the study of rare events.
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We show how standard Metadynamics coupled with classical Molecular Dynamics can be successfully ap- plied to sample the configurational and free energy space of metallic and bimetallic nanopclusters via the implementation of collective variables related to the pair distance distribution function of the nanoparticle itself. As paradigmatic examples we show an application of our methodology to Ag147, Pt147 and their alloy AgshellPtcore at 1:1 and 2:1 chemical compositions. The proposed scheme is not only able to reproduce known structural transformation pathways, as the five and the six square-diamond mechanisms both in pure and core-shell nanoparticles but also to predict a new route connecting icosahedron to anti-cuboctahedron.
Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is function of a selected number of collective variables. We propose here a change in perspective that shifts the focus from the bias to the probability distribution reconstruction, while keeping some of the key characteristics of metadynamics, such as the flexible on-the-fly adjustments to the free energy estimate. The result is an enhanced sampling method that presents a drastic improvement in convergence speed, especially when dealing with suboptimal and/or multidimensional sets of collective variables. The method is especially robust and easy to use, in fact it requires only few simple parameters to be set, and it has a straightforward reweighting scheme to recover the statistics of the unbiased ensemble. Furthermore it gives more control on the desired exploration of the phase space, since the deposited bias is not allowed to grow indefinitely and it does not push the simulation to uninteresting high free energy regions. We demonstrate the performance of the method in a number of representative examples.
Sampling complex potential energies is one of the most pressing challenges of contemporary computational science. Inspired by recent efforts that use quantum effects and discretized Feynmans path integrals to overcome large barriers we propose a replica exchange method. In each replica two copies of the same system with halved potential strengths interact via inelastic springs. The strength of the spring is varied in the different replicas so as to bridge the gap between the infinitely strong spring, that corresponds to the Boltzmann replica and the less tight ones. We enhance the spring length fluctuations using Metadynamics. We test the method on simple yet challenging problems.
We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of alanine dipeptide free energy landscape.
We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the path followed during the transition is needed. The only requirement is to know the fluctuations of the system while in the two metastable states. With this information in hand we build the collective variable using a modified version of Fishers linear discriminant analysis. The usefulness of this approach is tested on the metadynamics simulation of two representative systems. The first is the freezing of silver iodide into the superionic $alpha$-phase, the second is the study of a classical Diels Alder reaction. The collective variable works very well in these two diverse cases.
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