A new algorithm for rigid body molecular dynamics

The molecular dynamics of a completely rigid molecule is described in terms of external coordinates, namely translations and rotations, and a new algorithm is proposed, which is faster than other known methods and satisfies the constraints up to a desired accuracy. The procedure dispenses with the adoption of Lagrange multipliers and it is derived from an expression previously proposed for the motion of a semirigid molecule, when constraints are imposed to any selected number of intramolecular parameters. The latter need not to be specified for a rigid body but cannot be altogether ignored since it is necessary to guarantee that internal and external coordinates form a complete set of independent variables. This requirement is met by the familiar Eckart-Sayvetz conditions which provide with an iterative procedure for the evaluation, through symmetric orthogonalization, of a matrix of rotation. It turns out that only a first approximation of this matrix is necessary, therefore a final algorithm is proposed, based on the definition of infinitesimal angles of rotation about the mass center.