Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes
A numerical algorithm integrating the 3 N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method is applied to a molecular dynamics simulation of a liquid of 64 n-butane molecules and compared to a simulation using generalized coordinates. The method should be useful for molecular dynamics calculations on large molecules with internal degrees of freedom.