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Daniel V. Schroeder
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Physics students now have access to interactive molecular dynamics simulations that can model and animate the motions of hundreds of particles, such as noble gas atoms, that attract each other weakly at short distances but repel strongly when pressed together. Using these simulations, students can develop an understanding of forces and motions at the molecular scale, nonideal fluids, phases of matter, thermal equilibrium, nonequilibrium states, the Boltzmann distribution, the arrow of time, and much more. This article summarizes the basic features and capabilities of such a simulation, presents a variety of student exercises using it at the introductory and intermediate levels, and describes some enhancements that can further extend its uses. A working simulation code, in HTML5 and JavaScript for running within any modern Web browser, is provided as an online supplement.
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We perform nonadiabatic simulations of warm dense aluminum based on the electron-force field (EFF) variant of wave-packet molecular dynamics. Comparison of the static ion-ion structure factor with density functional theory (DFT) is used to validate the technique across a range of temperatures and densities spanning the warm dense matter regime. Focusing on a specific temperature and density (3.5 eV, 5.2 g/cm3), we report on differences in the dynamic structure factor and dispersion relation across a variety of adiabatic and nonadiabatic techniques. We find the dispersion relation produced with EFF is in close agreement with the more robust and adiabatic Kohn-Sham DFT.
Met-enkephalin, one of the smallest opiate peptides and an important neurotransmitter, is a widely used benchmarking problem in the field of molecular simulation. Through its range of possible low-temperature conformations separated by free-energy barriers it was previously found to be hard to thermalize using straight canonical molecular dynamics simulations. Here, we demonstrate how one can use the recently proposed population annealing molecular dynamics scheme to overcome these difficulties. We show how the use of multi-histogram reweighting allows one to accurately estimate the density of states of the system and hence derive estimates such as the potential energy as quasi continuous functions of temperature. We further investigate the free-energy surface as a function of end-to-end distance and radius-of-gyration and observe two distinct basins of attraction.
To take into account nuclear quantum effects on the dynamics of atoms, the path integral molecular dynamics (PIMD) method used since 1980s is based on the formalism developed by R. P. Feynman. However, the huge computation time required for the PIMD reduces its range of applicability. Another drawback is the requirement of additional techniques to access time correlation functions (ring polymer MD or centroid MD). We developed an alternative technique based on a quantum thermal bath (QTB) which reduces the computation time by a factor of ~20. The QTB approach consists in a classical Langevin dynamics in which the white noise random force is replaced by a Gaussian random force having the power spectral density given by the quantum fluctuation-dissipation theorem. The method has yielded satisfactory results for weakly anharmonic systems: the quantum harmonic oscillator, the heat capacity of a MgO crystal, and isotope effects in 7 LiH and 7 LiD. Unfortunately, the QTB is subject to the problem of zero-point energy leakage (ZPEL) in highly anharmonic systems, which is inherent in the use of classical mechanics. Indeed, a part of the energy of the high-frequency modes is transferred to the low-frequency modes leading to a wrong energy distribution. We have shown that in order to reduce or even eliminate ZPEL, it is sufficient to increase the value of the frictional coefficient. Another way to solve the ZPEL problem is to combine the QTB and PIMD techniques. It requires the modification of the power spectral density of the random force within the QTB. This combination can also be seen as a way to speed up the PIMD.
In this work we investigate the transient solidification of a Lennard-Jones liquid using non-equilibrium molecular dynamics simulations and continuum heat transfer theory. The simulations are performed in slab-shaped boxes, where a cold thermostat placed at the centre of the box drives the solidification of the liquid. Two well-defined solid fronts propagate outwards from the centre towards the ends of the box until solidification is completed. A continuum phase change model that accounts for the difference between the solid and the liquid densities is formulated to describe the evolution of the temperature and the position of the solidification front. Simulation results for a small and a large nanoscale system, of sizes $30.27$,nm and $60.54$,nm, are compared with the predictions of the theoretical model. Following a transient period of $sim$20-40 ps and a displacement of the solidification front of 1-2.5 nm we find that the simulations and the continuum theory show good agreement. We use this fact to combine the simulation and theoretical approaches to design a simple procedure to calculate the latent heat of the material. We also perform simulations of the homogeneous freezing process, i.e. in the absence of a temperature gradient and at constant temperature, by quenching the liquid at supercooled temperatures. We demonstrate that the solidification rate of homogenous freezing is much faster than the one obtained under a thermal gradient for systems of the same size subject to the same thermostat temperature. Our study and conclusions should be of general interest to a wide range of atomistic solids.
Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may distort such assumption. Fortunately, backward error analysis allows us to identify the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which coincides with the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refine
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