Numerical integration of the equations of motion for rigid polyatomics: The matrix method

We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, we can perform a MD simulation mo...

Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of calculations. An approach for constructing symmetric simplectic numerical schemes with given approximation accuracy in relation to integration step, for solving molecular dynamics Hamiltonian equations, is proposed in this paper. Numerical experim...

We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations, and is limited in accuracy only by the numerical methods for solving small systems of linear equations. As a result of the non-iterative and exact (within numerical accuracy) nature of the procedure there is no drift in the constrained geometry, and the method is theref...

This paper invites the reader to experiment with an easy-to-use MATLAB implementation of Metropolis integrators for Molecular Dynamics (MD) simulation. These integrators are analysis-based, in the sense that they can rigorously simulate dynamics along an infinitely long MD trajectory. Among explicit integrators for MD, they seem to be the only ones that satisfy the fundamental requirement of stability. The schemes can handle stiff or hard-core potentials, and are straightforw...

In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on initial conditions is explicit and the equations governing the orientation of the body involve only real numbers. Based on these results, an efficient method to calculate the location and orientation of the rigid body at arbitrary times is ...

A parallelized quantum dynamics package using the Smolyak algorithm for general molecular simulation is introduced in this work. The program has no limitation of the Hamiltonian form and provides high flexibility on the simulation setup to adapt to different problems. Taking advantage of the Smolyak sparse grids formula, the simulation could be performed with high accuracy, and in the meantime, impressive parallel efficiency. The capability of the simulation could be up to te...

A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and interaction rules are derived from Lagrangian mechanics in the presence of constraints. This approach is most suitable when the body is composed of relatively few point masses or is semi-flexible. In the second method, the equations of rigid b...

Elegant integration schemes of second and fourth order for simulations of rigid body systems are presented which treat translational and rotational motion on the same footing. This is made possible by a recent implementation of the exact solution of free rigid body motion. The two schemes are time-reversible, symplectic, and exactly respect conservation principles for both the total linear and angular momentum vectors. Simulations of simple test systems show that the second o...

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [Ingebrigtsen et al., J. Chem. Phys. 135, 104101 (2011); ibid, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algori...

Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on the basis of taking the nuclei as classical particles.