Commun. Comput. Phys., 6 (2009), pp. 231-246.

Decomposition of Molecular Motions into Translational, Rotational, and Intramolecular Parts by a Projection Operator Technique

F. Y. Hansen 1*, H. Taub 2

1 Department of Chemistry, Technical University of Denmark, IK 207 DTU, DK-2800 Lyngby, Denmark.
2 Department of Physics and Astronomy and the University of Missouri Research Reactor, University of Missouri, Columbia, Missouri 65211, USA.

Received 18 June 2008; Accepted (in revised version) 14 August 2008
Available online 15 December 2008


The motion of the atoms in a molecule may be described as a superposition of translational motion of the molecular center-of-mass, rotational motion about the principal molecular axes, and an intramolecular motion that may be associated with vibrations and librations as well as molecular conformational changes. We have constructed projection operators that use the atomic coordinates and velocities at any two times, t=0 and a later time t, to determine the molecular center-of-mass, rotational, and intramolecular motions in a molecular dynamics simulation. This model-independent technique facilitates characterization of the atomic motions within a system of complex molecules and is important for the interpretation of experiments that rely on time correlation functions of atomic and molecular positions and velocities. The application of the projection operator technique is illustrated for the inelastic neutron scattering functions and for the translational and rotational velocity autocorrelation functions.

AMS subject classifications: 81V55
PACS: 34.30.+h, 34.50.Dy, 68.03.Hj, 71.15.Pd
Key words: Molecular dynamics, projection operator, correlation functions, scattering functions, translational motion, rotational motion, intramolecular motion.

*Corresponding author.
Email: (F. Y. Hansen), (H. Taub)

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