Internal Coordinate Molecular Dynamics Based on the Spectroscopic B-Matrix

Internal coordinate molecular dynamics (ICMD) has been used in the past in simulations for large molecules as an alternative way of increasing step size with a reduced operational dimension that is not achievable by MD in Cartesian coordinates. A new MD formalism in nonredundant generalized (internal and external) coordinates for flexible molecular systems is presented, which is based on the spectroscopic B-matrix rather than the A-matrix of previous methods. The proposed formalism does not require a direct inversion of a large matrix as in the recursive formulations based on robot dynamics, and takes advantage of the sparsity of the spectroscopic B-matrix, ensuring computational efficiency for flexible molecules. Each molecule’s external rotations about an arbitrary atom center, which may differ from its center of mass, are parameterized by the SU(2) Euler representation, giving singularity free parameterization. Based on the clear separability in the generalized coordinates between fast varying degrees of freedom and slowly varying ones, a multiple time step algorithm is introduced that avoids the nontrivial interaction distance classification inherent in the method in Cartesian coordinates.