A new Lagrangian formulation is introduced. It can be used to make molecular dynamics (MD) calculations on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamical equations given by this Lagrangian. This new MD technique is well suited to the study of structural transformations in solids under external stress and at finite temperature. As an example of the use of this technique we show how a single crystal of Ni behaves under uniform uniaxial compressive and tensile loads. This work confirms some of the results of static (i.e., zero temperature) calculations reported in the literature. We also show that some results regarding the stress-strain relation obtained by static calculations are invalid at finite temperature. We find that, under compressive loading, our model of Ni shows a bifurcation in its stress-strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. It is suggested that such a transformation could perhaps be observed experimentally under extreme conditions of shock.

We present a new molecular dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains constant during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. We illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liquid phases. Its performance is excellent and largely independent on the thermostat parameter also with regard to the dynamic properties.

We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework. Here (Ri) indicate the nuclear coordinates and (n"} are all the possible external constraints imposed on the system, like the volume fl, the strain e"", etc. The ing with the size of the cedure has to be repeat functional U contains the internuclear Coulomb repulguration, the theoretical sion and the effective electronic potential energy, ingeometries, when these eluding external nuclear, Hartree, and exchange and ment, still remains an u correlation contributions.In the conventional formulation, minimization ofWe adopt a quite diff the energy functional [Eq. (1)] with respect to the orminimization of the KS bitals p;, subject to the orthonormality constraint, ization problem which c leads to the self-consistent KS equations, i.e. , concept of simulated an

We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the FES, allowing the efficient exploration and accurate determination of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.M olecular dynamics (MD) and the Monte Carlo simulation method have had a very deep influence on the most diverse fields, from materials science to biology and from astrophysics to pharmacology. Yet, despite their success, these simulation methods suffer from limitations that reduce the scope of their applications. A severe constraint is the limited time scale that present-day computer technology and sampling algorithms explore. In particular, there are many circumstances where the free energy surface (FES) has several local minima separated by large barriers. Examples of these situations include conformational changes in solution, protein folding, first-order phase transitions, and chemical reactions. In such circumstances a simulation started in one minimum will be able to move spontaneously to the next minimum only under very favorable circumstances. A host of methods have been suggested to lift this restriction and explore the FES (1-13) or to characterize the transition state (14, 15). Here we propose a solution to this problem by combining the ideas of coarse-grained dynamics (16, 17) on the FES (10, 12) with those of adaptive bias potential methods (2, 11), obtaining a procedure that allows the system to escape from local minima in the FES and, at the same time, permits a quantitative determination of the FES as a byproduct of the integrated process. MethodologyWe shall assume here that there exists a finite number of relevant collective coordinates s i , i ϭ 1,n where n is a small number, and we consider the dependence of the free energy Ᏺ(s) on these parameters. Practical examples of appropriate choices of these variables will be given below. The exploration of the FES is guided by the forces F i t ϭ ϪѨᏲ͞Ѩs i t . To estimate these forces efficiently, we introduce an ensemble of P replicas of the system, each obeying the constraint that the collective coordinates have a preassigned value s i ϭ s i t , and each evolved independently at the same temperature T. Since the P replicas are statistically independent, the estimate of thermodynamic observables (e.g., the forces on the constraints) is improved with respect to an evaluation on a single replica, and it can be parallelized in a straightforward manner. The constraints are imposed on each replica via the standard methods of constrained molecular dynamics (18) by adding to the Lagra...

We present the Gaussian and plane waves (GPW) method and its implementation in QUICKSTEP which is part of the freely available program package CP2K. The GPW method allows for accurate density functional calculations in gas and condensed phases and can be effectively used for molecular dynamics simulations. We show how derivatives of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calculations for single molecules and plane wave based calculations in the condensed phase is excellent. Wave function optimisation with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the density matrix. We illustrate these findings with calculations using commodity PCs as well as supercomputers.

The accurate description of chemical processes often requires the use of computationally demanding methods like density-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems.

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