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

A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This allows to resolve the rigidity problem rigorously using constraint forces. It is shown that the procedure for preservation of molecular rigidity can be realized particularly simply within the Verlet algorithm in velocity form. We demonstrat...

A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration, whereas orientational positions are expressed in terms of either principal axes or quaternions. As a result, the rigidness of molecules appears to be an integral of motion, despite the atom trajectories are evaluated approximately. The alg...

A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and orientational coordinates are decoded by processing transformations. This allows to overcome the barrier on the order of precision of the integration at a given number of force-torque evaluations per time step. Testing in dynamics of water versus ...

A very simple explicit integrator for the rotational motion of rigid linear molecules is presented which can preserve the rigidity of the molecules without requiring any constraint force. The integrator is time-reversible and symplectic, thus preserving volume in phase space. It also conserves angular momentum. As expected, having all these virtues, it remains stable for large time-steps. Both the leap-frog and velocity-Verlet versions of the integrator are described. Since i...

A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational positions. Contrary to the standard implicit method by Fincham [Mol. Simul., 8, 165 (1992)], the revised angular momentum approach presented corresponds completely to the leapfrog idea on interpolation of dynamical variables without using any e...

We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that demand a careful analysis when discretized: first, the treatment of periodic boundary conditions; second, the formulation of approximations of systems with three-body interaction forces; third, their extension to atomic systems with functional...

New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the new algorithms appear to be more efficient than the original Verlet versions which correspo...

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in the literature to further split up the kinetic part of the Hamiltonian, which lowers the accuracy. The goal of this note is to comment on the best combination of optimized splitting and gradient methods that avoids splitting the kinetic energ...

In ab initio molecular dynamics simulations of real-world problems, the simple Verlet method is still widely used for integrating the equations of motion, while more efficient algorithms are routinely used in classical molecular dynamics. We show that if the Verlet method is used in conjunction with pre- and postprocessing, the accuracy of the time integration is significantly improved with only a small computational overhead. The validity of the processed Verlet method is de...

In condensed matter physics, particularly in perovskite materials, the rotational motion of molecules and ions is associated with important issues such as ion conduction mechanism. Constrained Molecular Dynamics (MD) simulations offer a means to separate translational, vibrational, and rotational motions, enabling the independent study of their effects. In this study, we introduce a rotational and roto-translational constraint algorithm based on the Velocity Verlet integrator...