Molecular dynamics simulations with constrained roto-translational motions: Theoretical basis and statistical mechanical consistency

Journal of Chemical Physics

Volumn 112, Issue 1, 2000, Pages 9-23

  Amadei, A ^a   Chillemi, G ^a   Ceruso, M A ^a   Grottesi, A ^a   Di Nola, A ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002178685     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.480557     Document Type: Article

References (22)

1. A. D. Mc Lachlan, J. Mol. Biol. 49, 128 (1979).
2. G. Gallavotti, The Elements of Mechanics (Springer-Verlag, New York, 1983).
3. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics. Vol. 1, 3rd ed. (Pergamon, New York, 1980).
4. D. J. Evans and G. P. Morris, Comput. Phys. Rep. 1, 297 (1984).
5. D. Brown and J. H. R. Clarke, Mol. Phys. 51, 1243-1252 (1984).
6. S. Nosé, Mol. Phys. 52, 255 (1984).
7. W. G. Hoover, Phys. Rev. A 31, 1695 (1985).
8. C. Eckart, Phys. Rev. 47, 552 (1935).
9. Note that for N particles confined in a line, once the center of mass defined in the line by one coordinate is set in the origin, there are only N-1 independent coordinates left among the 3N-5 possible internal coordinates. In the case of N particles confined in a plane, once the center of mass defined in the plane by two coordinates is set in the origin and the rotational angle in the plane is defined, there are only 2N-2-1 independent coordinates left among the 3N-6 possible internal coordinates. In the paper, according to the standard analytical mechanical definition, for internal coordinates we mean only the independent ones.
10. J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comput. Phys. 23, 327-341 (1977).
11. T. Mulders and W. Swegat, Mol. Phys. 94, 395-399 (1998).
12. Note that when the total linear momentum is fixed at zero during the dynamics and no explicit constraints for this are used, such a condition implies the presence of three implicit holonomic constraints for the center of mass position. These implicit constraints can be used for the definition of the ξ coordinates and hence in the ξ, π phase space no constants of motion due to the center of mass constraints are present. The case where the total linear momentum is a nonzero constant can be reduced to the previous one using in the definition of the full phase-space Cartesian co-ordinates relative to the center of mass position and their conjugated momenta.
13. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5, 3rd ed. (Pergamon, New York, 1980).
14. A. Amadei, M. E. F. Apol, and H. J. C. Berendsen, J. Chem. Phys. 109, 3004-3016 (1998).
15. A. Amadei, M. E. F. Apol, and H. J. C. Berendsen, J. Chem. Phys. 106, 1893-1912 (1997).
16. W. K. den Otter and W. J. Briels, J. Chem. Phys. 109, 4139-4146 (1998).
17. M. Fixman, Proc. Natl. Acad. Sci. USA 69, 1527 (1974).
18. in.
19. 6 the full mass tensor determinant and hence the Fixman determinant are pure constants.
20. 6 constrain completely the three Eulerian angles when fixed at zero, they cannot properly describe rotational motions as for their nonzero values rigid body rotations and internal deformations are mixed.
21. David van der Spoel, Herman J. C. Berendsen, Aldert R. van Buuren, Emile Apol, Pieter J. Meulenhoff, Alfons L. T. M. Sijbers, and Rudi van Drunen, Gromacs User Manual. Nijenborgh 4, 9747 AG Groningen, The Netherlands. Internet: http://rugmd0.chem.rug.nl/~gmx (1995).
22. M. J. Frisch et al., GAUSSIAN 94 (Gaussian, Inc., Pittsburgh, PA, 1994).