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 drastic change in perspective that shifts the focus from the bias to the probability distribution reconstruction, leading to an improvement in usability and convergence speed. The resulting enhanced sampling method can be seen as a combination of metadynamics and adaptive umbrella sampling approaches, that aims at taking the best from the two worlds. This new method has a straightforward reweighting scheme and allows for efficient importance sampling, avoiding uninteresting high free energy regions. Thanks to a compressed kernel density estimation it can handle a higher dimensional collective variable space, and does not require any prior knowledge of the boundaries of such space. The new method comes in two variants. The first aims at a quick convergence, avoiding oscillations and maximizing the quasi-static bias regime, while in the second the main focus is on a rapid exploration of the free energy landscape. We demonstrate the performance of the method in a number of representative examples.Enhanced sampling plays a crucial role in modern simulation techniques, and is a very active area of research [1]. Of particular importance has been the work of Torrie and Valleau [2]. They consider a system with an interaction potential U (R), where R denotes the atomic coordinates. Sampling is accelerated by adding a bias potential V (s) that depends on R via a set of collective variables (CVs), s = s(R). The CVs are chosen so as to describe the modes of the system that are more difficult to sample. The choice of a proper set of CVs is critical, as it determines the efficiency of the method. The properties of the unbiased system are then calculated by using a reweighting procedure. In fact the unbiased probability densitycan be written as an average over the biased ensemble:where β is the inverse temperature. Since this work, a large number of CV based methods have been proposed. Adaptive umbrella sampling[3] (AUS) was the first to build iteratively V (s) so that it would compensate for the free energy surface (FES), F (s) = − 1 β log P (s). At the n-th iteration the bias is given by:where the probability estimate P n (s) can be obtained via a weighted histogram, with weights w k = e βV k , or some more elaborate estimator [4], and can be updated iteratively or on the fly [5,6]. At convergence one has V (s) = −F (s). A different approach has been introduced by metadynamics[7, 8] (MetaD). Here one builds V (s) directly, instead of first reconstructing the probability distribution. The bias is updated on the fly by adding a Gaussian centered at every new point sampled s k :

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SignificanceSilica is one of the most abundant minerals in Earth’s crust and since the dawn of civilization its use has accompanied mankind’s technological evolution. Understanding crystallization is crucial in many industrial processes as well as in geology. Although experiments and simulations are difficult, we are able to perform an atomistic simulation of the β-cristobalite crystallization using an enhanced sampling method that uses as input only the intensity of the highest X-ray diffraction peak of β-cristobalite.