A Hands-On Introduction to Molecular Dynamics

Abstract

We present an introduction to the chemical and computational aspects of the molecular dynamics (MD) simulation technique. Using just a few elementary ideas from classical mechanics and numerical analysis, and linear chains of identical particles as example systems, we take the reader through the steps required for the design and analysis of a simple molecular dynamics experiment. We employ the Hooke's law model for the interactions between the particles since its visualization in terms of masses and springs provides a natural model for chemical bonds. We derive the classical equations of motion in detail for the three-particle chain. We then introduce two simple methods for numerically integrating the equations of motion, one based on Euler's method for differential equations, and the other a more accurate algorithm developed by Verlet. We analyze the dynamics of the three-particle system in terms of its normal modes of vibration. Finally, exploiting the closed-form solution admitted by the Hooke's law potential, we compare the errors generated by the two integration algorithms. As supplemental material, we provide a basic MD implementation using the Euler algorithm in both Fortran and C and a set of suggested exercises.

Computer simulations of fluid flow over catalytic surfaces for water splitting

“…The dynamics of each bead i can be determined by the following equations − i U = m i a i = m i (d 2 r i /dt 2 ) = m i (dv i /dt) and v i = dr i /dt, where r i and v i are the position and velocity vectors of bead i, respectively. The equations of motion will be integrated using the Velocity Verlet method [7] which has greater stability, time reversibility and preserves the symplectic form on the phase space compared to the Euler method [8]. The position r i and velocity v i of a bead i using the Velocity Verlet algorithm are calculated as follows: v i (t + t) = v i (t) + (1/2)(a i (t) + a i (t + t)) t and r i (t + t) = r i (t) + v i (t) t + (1/2)a i (t) t 2 , where r i (t), r i (t + t), v i (t) and v i (t + t) are respectively the position and velocity vectors at time t and t + t ( t is the integration time step).…”

Facilitating Students’ Interaction with Real Gas Properties Using a Discovery-Based Approach and Molecular Dynamics Simulations

“…As the use of MD simulations has become increasingly important in the chemical and biological sciences, it has also seen increased use in chemical and biological pedagogy, both to expose students to this increasingly important tool, and to leverage some of its unique capabilities to achieve specific learning goals. − Molecular dynamics simulations, and molecular modeling techniques more generally, have been integrated into many aspects of the undergraduate science curricula with a variety of positive outcomes. ,− Two common features of many of these activities are that they: (i) leverage visualization capabilities to help students refine mental models and develop an intuition for underlying physical and chemical phenomena and (ii) permit students to study observable quantities that would be difficult to measure experimentally. For example, Speer et al described activities where physical chemistry students used the Amber MD suite to simulate water, ethanol, and benzene to illustrate connections between intermolecular forces and temperature on liquid structure as quantified by the radial distribution function, a quantity whose experimental determination via X-ray scattering would not be feasible in many undergraduate laboratories .…”

“…Hati and Bhattacharyya have described the use of MD simulations in discovery-driven laboratories that help students connect protein structure to protein function via their dynamical behaviors . Several reports in this Journal have also discussed the use of MD simulations to explore intermolecular and intramolecular forces from a microscopic point of view − while other authors have discussed ways to involve undergraduates in the development of MD simulations tools. , …”

New Computational Physical Chemistry Experiments: Using POGIL Techniques withab Initioand Molecular Dynamics Calculations

“…A number of uses of MD in physical chemistry lab exercises have been reported over the past 20 years. While exercises can focus on having students understand MD techniques (28,29), more published works emphasize using MD simulations to develop understanding of a specific system or chemical concept. Specific applications have included studies of intermolecular forces (27), conformational analyses (30,31) hydrogen bonding (32), and modeling of liquid and gas motions (24).…”