A comparative study of molecular dynamics in Cartesian and in internal coordinates: Dynamical instability in the latter caused by nonlinearity of the equations of motion

• Published in: Journal of computational chemistry Vol. 28; no. 6; pp. 1107 - 1118
• Main Authors: Lee, Sang-Ho, Palmo, Kim, Krimm, Samuel
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 30.04.2007; Wiley Subscription Services, Inc
• Subjects: Algorithms; Atoms & subatomic particles; Computer Simulation; constrained dynamics; Energy; external rotation; internal coordinate; Kinetics; Mathematical Computing; Matrix; Mechanics; Molecular Conformation; molecular dynamics; Nonlinear equations; numerical integration; Octanes - chemistry; Organic Chemicals - chemistry; Rotation; Simulation; Spectrum analysis; Velocity
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.20627

The stability of a general molecular dynamics (MD) integration scheme is examined for simulations in generalized (internal plus external) coordinates (GCs). An analytic expression is derived for the local error in energy during each integration time step. This shows that the explicit dependence of the mass‐matrix on GCs, which makes the system's Lagrange equations of motion nonlinear, causes MD simulations in GCs to be less stable than those in Cartesian coordinates (CCs). In terms of CCs, the corresponding mass‐matrix depends only on atomic masses and thus atomistic motion is subject to the linear Newton equations, which makes the system more stable. Also investigated are two MD methods in GCs that utilize nonzero elements of the vibrational spectroscopic B‐matrices. One updates positions and velocities in GCs that are iteratively adjusted so as to conform to the velocity Verlet equivalent in GCs. The other updates positions in GCs and velocities in CCs that are adjusted to satisfy the internal constraints of the new constrained WIGGLE MD scheme. The proposed methods are applied to an isolated n‐octane molecule and their performances are compared with those of several CCMD schemes. The simulation results are found to be consistent with the analytic stability analysis. Finally, a method is presented for computing nonzero elements of B‐matrices for external rotations without imposing the Casimir–Eckart conditions. © 2007 Wiley Periodicals, Inc.J Comput Chem 2007