A New Time-Reversible Integrator for Molecular Dynamics Applications

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...

We point out that two of Milne's fourth-order integrators are well-suited to bit-reversible simulations. The fourth-order method improves on the accuracy of Levesque and Verlet's algorithm and simplifies the definition of the velocity $v$ and energy $e = (q^2 + v^2)/2$ . ( We use this one-dimensional oscillator problem as an illustration throughout this paper ). Milne's integrator is particularly useful for the analysis of Lyapunov ( exponential ) instability in dynamical sys...

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show how to bootstrap easily to higher order accuracy.The method, first shown for a single particle in one dimension, is then neatly extended to many dimensions and many particles.

Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The algorithm used in MD was originally formulated by I. Newton at the beginning of his book $Principia$. Newton's discrete dynamics is exact in the same sense as Newton's analytic counterpart Classical Mechanics. Both dynamics are time-reversible, ...

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...

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...

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...

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...

We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are obtained by eliminating the dominant terms in the error. These new methods can be viewed as a generalization of the impulse method. In the implementation of these methods, the long-range forces only need to be computed on the slow time sca...

A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are integrated within the Verlet framework in velocity form. It is shown that, contrary to previous methods, in the approach introduced the rigidity of molecules can be conserved automatically without any additional transformations. A comparison of...