A fast SHAKE algorithm to solve distance constraint equations for small molecules in molecular dynamics simulations

TLDR

The SHAKE algorithm is a widely used iterative method for enforcing distance constraints in molecular dynamics by linearizing and decoupling the coordinate equations. This study proposes M‑SHAKE, which solves the coupled constraint equations simultaneously via matrix inversion. The authors benchmarked M‑SHAKE against SHAKE in simulations of water, dimethyl sulfoxide, and chloroform. M‑SHAKE was found to be significantly faster than SHAKE when molecules have few constraints or when high accuracy is needed. © 2001 John Wiley & Sons, Inc., J Comput Chem 22:501–508.

Abstract

A common method for the application of distance constraints in molecular simulations employing Cartesian coordinates is the SHAKE procedure for determining the Lagrange multipliers regarding the constraints. This method relies on the linearization and decoupling of the equations governing the atomic coordinate resetting corresponding to each constraint in a molecule, and is thus iterative. In the present study, we consider an alternative method, M-SHAKE, which solves the coupled equations simultaneously by matrix inversion. The performances of the two methods are compared in simulations of the pure solvents water, dimethyl sulfoxide, and chloroform. It is concluded that M-SHAKE is significantly faster than SHAKE when either (1) the molecules contain few distance constraints (solvent), or (2) when a high level of accuracy is required in the application of the constraints. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 501–508, 2001