A new formalism for molecular dynamics in internal coordinates

Abstract 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 ICMD formalism 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 an inversion of a large matrix as in the recursive formulations based on robot dynamics, and takes advantage of the sparsity of the 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. Although the formalism is based on the use of nonredundant generalized (internal and external) coordinates, an MD simulation in linearly dependent coordinates can be done by finding a transformation to a new set of independent coordinates. 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 previous nontrivial interaction distance classification. Also presented is a recursive method for computing nonzero A -matrix elements that is much easier to apply to a general molecular structure than the previous method.