http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/Constraints/Shake1977.pdf

Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes

The application of the computer simulation method of molecular dynamics to macromolecules is investigated. The protein trypsin inhibitor (BPTI), consisting of 454 united atoms, is used as an example. Different algorithms for integrating the equations of motion are compared, both theoretically and in practice. It is examined to what extent the chain structure of a macromolecule allows a reduction of the computational effort by the introduction of constraints in the dynamics of the chain. A calculational scheme is proposed, by which constraints can be incorporated in predictor-corrector algorithms. The optimum choice of an algorithm depends on the desired accuracy of the solution and on the character of the forces acting on the molecule, viz. whether these are noisy or not. For nonconstraint dynamics a Gear predictor-corrector algorithm yields the best results, whereas for constraint dynamics the Gear and Verlet algorithms produce comparable results. The application of bond-length constraints reduces the re...

Algorithms for macromolecular dynamics and constraint dynamics

Molecular Dynamics

Using a transformation of the rigid body equations of motion due to Evans [4], a new algorithm is presented for the molecular dynamics simulation of rigid polyatomic molecules. The algorithm consists of solving the eulerian rigid body equations, using quaternions to represent orientations, by a fifth-order predictor corrector method. Compared to previous methods, it is shown that this algorithm leads to an order of magnitude increase in computing speed.

Singularity free algorithm for molecular dynamics simulation of rigid polyatomics

DEM/CFD-DEM Modelling of Non-spherical Particulate Systems: Theoretical Developments and Applications

The molecular-dynamic method was used to simulate a fluid of 500 rigid diatomic homo-nuclear molecules interacting by a double Lennard-Jones potential. The equilibrium and time-dependent properties are calculated in the liquid phase. The computed pressure and the internal energy agree quantitatively to a few percent with experimental values for nitrogen. The reorientational and the velocity of the center-of-gravity self-correlation functions are also discussed. The memory-function formalism and the extended-diffusion models are used to interpret the reorientational self-correlation functions. The analysis reveals that these self-correlation functions have an exponential behavior for times larger than 5 \ifmmode\times\else\texttimes\fi{} 1${0}^{\ensuremath{-}13}$ sec. In this model, considering present computing precision, there is no observable hydrodynamic-type relaxation in the reorientational self-correlation functions.

B. Quentrec

Papers

Simulation of Diatomic Homonuclear Liquids