Multiscale Modeling and Simulation

Materials and Process Simulation Center (MSC)

California Institute of Technology










bulletO(n) and O(Log n) Constrained Molecular Dynamics

O(n) and O(Log n) Constrained Molecular Dynamics

Funding Agencies

Leveraged partially from different grants

Program Managers


Start date

(initial development started on September, 1996)

June 2006






Andres Jaramillo-Botero


William A. Goddard, III


Past collaborators:

Tahir Cagin (now at Texas A&M)


Amir Fijany (JPL)


In the study of molecular systems using Molecular Dynamics (MD) simulations it is often desired to impose relative or absolute motion constraints on atoms or groups of atoms. This offers several different advantages depending on the type of constraint involved, i.e. absolute or relative, and on the type of generalized coordinates used to describe the equations of motion (EOM) of the system, i.e. Cartesian or internal. Indistinctively, both approaches involve the formulation of mixed systems of differential EOM and nonlinear algebraic equations of constraint.

Our approach involves the use of internal coordinates, even though this  increases the complexity of the solution to the EOM (mainly because we now have a highly coupled molecular system with highly non-linear, non inertial terms in velocity, a dense mass matrix operator and potential numerical conditioning of the formulation solution) hence requiring efficient algorithms to compute the algebraic differential solution in linear, or better, computation time, it offers several advantages over the conventional Cartesian constrained dynamics methods (the Figure to the left depicts an NVT@300K of a polymer chain that results in an order of magnitude increase in simulation time-step in comparison to conventional atomistic Cartesian MD). 

We have successfully demonstrated its use in large-scale, long-term dynamics of complex systems in polymer and protein science [see Publication list].  Current research involves addressing challenges in closed loop kinematics systems and correcting bad contact dynamics without time penalties.

Related Publications
bulletJaramillo-Botero, A. "Molecular Nanomanipulator Dynamic Design Criteria" In: Dekker Encyclopedia of Nanoscience and Nanotechnology. 1st Ed. New York : Marcel Dekker Publ., 2004.
bulletJaramillo-Botero, A., Matta, A., Correa, JF, Perea, W. Software platform for robot modeling and simulation, Vol. 3, No. 1, December 2004
bulletJaramillo-Botero, A. "Computational Nanotechnology in the Design of Nanoscale Molecular Positional Devices", NASA Jet Propulsion Laboratory Seminar (invited talk), Pasadena, California (US) November 23, 2004
bulletJaramillo-Botero, A. and Crespo, A. "A Unified Formulation For Massively Parallel Rigid Multibody Dynamics Of O(Log2 N) Computational Complexity", Journal of Parallel and Distributed Computing, Academic Press, Vol. 62, No. 6, June 1, 2002.
bulletJaramillo-Botero, A "Design Criteria for a 3 DOF positional nanomanipulator based on a Constrained Molecular Dynamics Model" In: Mathematics in Nanoscale Science and Engineering 2004 Reunion Conference (invited talk), 2004, University of California at Los Angeles, Lake Arowhead Conference, California (US) January 2004.
bulletMassively Parallel Algorithms for Long-term Simulations of Large-scale Molecular Systems, Universidad Politecnica de Valencia, Doctoral Thesis, (spanish) ISBN: 958-8162-60-2, 1998.
bulletFijany, A., Jaramillo-Botero, A., Cagin, T., and Goddard, W.A. III, A Fast Algorithm for Massively Parallel, Long Term Simulations of Complex Molecular Dynamics Systems, pp 505-515 (1998), in Parallel Computing: Fundamentals, Applications and New Directions, Eds. E. H. D'Hollander, G. R. Joubert, F. J. Peters and U. Trottenberg.
bulletFijany, A., Cagin, T., A., Jaramillo-Botero, and Goddard, W. A. III. Novel Algorithms for massively parallel, long term simulation of molecular dynamics systems, Advances in Engineering Software, 29, 441-450 (1998).
bulletFijany, A., T. Cagin, A. Jaramillo-Botero, S. Gulati, and W.A. Goddard,"Novel Algorithms for Massively Parallel, Long-Term, Simulation of Molecular Dynamics Systems," 4th NASA National Symposium on Large-Scale Analysis and Design on High-Performance Computers and Workstation, Williamsburg, VA, October 1997.
bulletFijany, A., T. Cagin, A. Jaramillo-Botero, and W.A. Goddard, "Massively Parallel Constraint Force Algorithm for MD Simulation of Polymers and Dendrimers," Presented at the 1997 American Physical Society (APS) Int. Conf. on Computational Physics (PC97), Santa Cruz, CA, Aug. 1997.
bulletFijany, A. A. Jaramillo -Botero, T. Cagin, and W.A. Goddard, "A Fast Algorithm for Massively Parallel, Long-Term, Simulation of Complex Molecular Dynamics Systems," Proceedings Parallel Computing 97 (PARCO 97), Bonn, Germany, September 1997.
bulletFijany, A., T. Cagin, A. Jaramillo -Botero, T. Coley, and W.A. Goddard, "A Massively Parallel Algorithm for Solution of Constrained Equations of Motion with Application to Large-Scale Long-Time Molecular Dynamics Simulations," Presented at the 2nd Parallel Computational Chemistry Symposium, American Chemistry Society (ACS), San Francisco, CA, April 1997.
bulletFijany, A., T. Cagin, A. Jaramillo -Botero, and W.A. Goddard,"A Massively Parallel Algorithm for Solution of Constrained Equations of Motion in Molecular Dynamics," Presented at the American Physical Society Meeting, Kansas City, MO, March 1997.
bulletRigid Multibody Molecular Dynamics: Strictly Parallel Computations, ISBN: 958-33-4988-7, TR-RAG-1996 - Robotics and Automation Group (RAG), 1996. online:


 (C) Materials and Process Simulation Center, Caltech, 2007.
Contact: Andres Jaramillo-Botero [ajaramil at].
Last updated: 04/04/12.