A method that numerically integrates Newton's equations of motion for many atoms, using forces obtained from interatomic potentials, to calculate atomic motion over time.
Japanese name: 分子動力学法
Molecular dynamics appears in 8 practice questions across 1 topic, including Computational materials science.
In molecular dynamics, the initial positions of the atoms and velocities following the Maxwell–Boltzmann distribution at the target temperature are given first. Next, the force on each atom is found from an interatomic potential, and the equations of motion are integrated step by step with the Verlet method or similar to update positions and velocities. Repeating this hundreds of thousands to millions of times gives the trajectories of the atoms. To represent the interior of a crystal or liquid, periodic boundary conditions that join opposite faces of the simulation box are used to remove surface effects. The method was begun by Alder and Wainwright in 1957 with a system of hard spheres and is now widely used in materials, chemistry and biomolecules.
Averaging the atomic trajectories over time gives a wide range of properties. The diffusion coefficient, for example, is found from the fact that the mean of the squared distance moved by atoms (the mean square displacement) grows as 6Dt in three dimensions. If it grows by 0.6 nm² in 100 ps, D = 1×10⁻⁹ m²/s, of the same order as in liquid metals. The radial distribution function, which describes the distribution of distances between atoms, reveals the structure of liquids and amorphous materials and can be compared with X-ray and neutron diffraction results. Thermal expansion, elastic constants, melting points, thermal conductivity and the energies of grain boundaries and dislocations can also be calculated.
Solving the equations of motion as they are calculates a state in which the number of atoms, volume and total energy are constant (the NVE ensemble). To hold temperature or pressure constant as in experiments, a thermostat representing energy exchange with a heat bath, or a barostat that changes the size of the box, is added to calculate the NVT or NPT ensemble. Nosé's method, the basis of the widely used Nosé–Hoover method, was proposed in 1984. At first the system is not in equilibrium, so the part before temperature and energy settle is excluded from averages, and averages are taken over a sufficiently long time afterward.
The times that molecular dynamics can follow are usually nanoseconds to microseconds. A simulated tensile test therefore runs at a strain rate of about 10⁸ s⁻¹ (10% strain in 1 ns), more than ten orders of magnitude faster than the roughly 10⁻³ s⁻¹ of experiments. Dislocations have no time to overcome obstacles with the help of thermal activation, so strengths tend to come out higher than in experiments. Rarely occurring events, such as diffusion in solids, are also hard to follow directly, and kinetic Monte Carlo and similar methods are combined. Because the calculation is classical, quantum effects also cause deviations in heat capacity and other properties well below the Debye temperature.
Answer: C. 5×10⁵
Since 1 ns = 10⁻⁹ s and 2 fs = 2×10⁻¹⁵ s, the number of steps is 10⁻⁹/(2×10⁻¹⁵) = 5×10⁵. The time step must be small enough to divide the period of atomic vibration (around 100 fs) into several tens of steps, and for systems containing light hydrogen it is set to 1 fs or less. If the step is too large, errors in numerical integration such as the Verlet method destroy energy conservation and the calculation breaks down. 5×10² takes fs as 10⁻¹² s (ps), and 5×10⁸ takes ns as 10⁻⁶ s (µs). Because forces on all atoms are calculated at every step, nanoseconds to microseconds is the rough limit of the time that molecular dynamics can follow.
Answer: B. The embedded atom method (EAM) potential adds an embedding energy that depends on the electron density created by the surrounding atoms, describing the many-body nature of metallic bonding
The Lennard-Jones potential is a pair potential depending only on the distance between two atoms; it describes weak, non-directional bonding such as that of the noble gases well, but not the properties of metals or covalent bonds. In metals, the many-body effect, in which the bond strength of an atom changes with the number of surrounding atoms, is large, and EAM adds this as a function of the electron density created by the surrounding atoms. With pair potentials alone, the Cauchy relation C₁₂ = C₄₄ between the elastic constants always holds for an unstressed FCC or BCC crystal, in which every atom sits at a center of symmetry, but many metals do not satisfy it. In covalent bonding the bond angle matters, so the Stillinger–Weber and Tersoff potentials, which include angular terms, are used. Machine-learning potentials trained on DFT results are also widely used.
Molecular dynamics solves the equations of motion, so it follows atomic motion along real time and also gives dynamic properties such as diffusion and vibrations. Monte Carlo methods such as the Metropolis method choose states according to probabilities to find equilibrium averages; they carry no information about time but can also handle slow changes such as the exchange of atoms.
It is molecular dynamics in which the forces on the atoms are obtained at each step not from an interatomic potential but from electronic structure calculations such as density functional theory. It can also handle the breaking and forming of chemical bonds, but the computational cost is high, and it handles only a few hundred atoms over times of a few tens of picoseconds.
The biggest factor is the accuracy of the interatomic potential: properties the potential cannot describe will not come out correctly. Size effects from too small a simulation box, statistical scatter from short averaging times and integration errors from the time step also matter, so one checks that results do not change when these conditions are varied.
Because forces on all atoms are calculated at every step, nanoseconds to microseconds is the rough limit of the time that molecular dynamics can follow.
In molecular dynamics, you want to integrate the equations …In molecular dynamics the instantaneous temperature is found from the atomic velocities in this way, and when the temperature is to be held constant, the velocities are adjusted by coupling to a heat bath (a thermostat).
In a molecular dynamics calculation of a monatomic system, …Classical molecular dynamics, which uses interatomic potentials, can follow thousands to millions of atoms for times of the order of nanoseconds.
Which pairing of a materials computation method with the ra…Solving equations of motion with an empirical interatomic potential is classical molecular dynamics.
Which statement about the ideas behind density functional t…Ordinary DFT is a calculation of the ground state at 0 K, so obtaining finite-temperature properties requires combining it with calculations of lattice vibrations (phonons) or molecular dynamics.
Which is a correct tendency of the results of standard DFT …Density functional theory Interatomic potential Phase-field method Finite element method Phonon Monte Carlo method Vacancy CALPHAD method Materials informatics