SHAKE, rattle, and roll: Efficient constraint algorithms for linked rigid bodies - Forester, Timothy R.; Smith, William (Journal of computational chemistry, 1998)
We present an iterative constraint algorithm, QSHAKE, for use with semirigid molecules in molecular dynamics simulations. The algorithm is based on “SHAKE‐ing” bond constraints between rigid bodies, whose equations of motion are solved in the quaternion framework. The algorithm is derived and its performance compared with SHAKE for liquid octane. QSHAKE is significantly more efficient whenever SHAKE requires triangles (or tetrahedra) of constraints to maintain molecular shape. Efficiencies are gained because QSHAKE reduces the number of holonomic constraints that must be solved iteratively and requires fewer iterations to obtain convergence. The gains in efficiency are most noticeable when a high degree of precision is imposed on the constraint criteria. QSHAKE is also stable at larger time steps than SHAKE, thus allowing for even more efficient exploration of phase space for semirigid molecules. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 102–111, 1998