MD simulations with DMol³

Within first principles molecular dynamics (MD) simulations the electronic structure is determined quantum mechanically using, e.g., density functional methods and the atomic forces are the first derivative of the potential energy with respect to the atomic coordinates. The MD implementation of DMol³ does not allow to examine quantum effects of the nuclei, e.g. tunneling of protons, because the nuclei are treated classically.
To control the temperature, i.e. the kinetic energy of the atoms, during the MD simulations, explicit reversible extended-system methods [1] like the Nosé-Hoover (NH) [2,3], Nosé-Hoover chain (NHC) [4] and the generalized Gaussian moment thermostats (GGMT) [5] are implemented. Within the extended-system methods the temperature is driven by the dynamics of fictitious variables that are added to the equations of motion (EOM) of the atoms. The thermostat variables correspond to heat baths to that the atoms are coupled. Explicit reversible means that the extended EOM possess the symmetry of time reversibility. The extended-system methods produce dynamics with well defined conserved quantities. Assuming the dynamics are ergodic, the extended-system methods generate canonical trajectories in the coordinate-momentum phase space, {r,p} = {r₁,...,r_N, p₁,...,p_N}, where r_i are the coordinates and p_ithe corresponding momenta of an N-nuclear system. Ergodicity means, there is at least one trajectory that passes through all points in phase space for which the probability density is non-zero.

DMol³ can be used to perform MD simulations with structural constraints. The examination of slower modes in a system (e.g. torsional conformation interconversion) necessitates a relatively long simulation time because the upper limit of the MD time step is determined by the presence of fast modes (e.g. bond-stretching and bond-angle vibrations). Hence, a large number of short time steps is required. Substantial improvement in the efficiency of MD simulations can be achieved by freezing the fast structural modes by constraining the appropriate degrees of freedom.
Another application of constrained MD simulations is searching for transition states and understanding of chemical reactions. Structural constraints in MD simulations are used to move a system on the potential energy surface "up-hill" towards a transition state. The imposed constraint must resembles the reaction coordinate as closely as possible. While the system moves from the initial configuration across the barrier, all atoms are free to relax under the given constraint. The force to keep the constraint during the MD simulation has a finite value, whose sign indicates on which side of the barrier the system is. A transition state is definitely reached when all forces obtained vanish and that there is exactly one imaginary vibrational frequency.

Further literature:

• Thermostatting in MD simulations ( pdf, 146KB)
• Massive thermostatting in isothermal density functional molecular dynamics simulations ( link to J. Chem. Phys.)
• Reaction Modeling from Molecular Dynamics Simulations ( pdf, 129KB)

References

[1] G. J. Martyna, M. E. Tuckerman, D. J. Tobias, and M. L. Klein, Mol. Phys., 87, 1117 (1996).

[2] W. G. Hoover, Phys. Rev. A, 31, 1695 (1985).

[3] M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys., 97, 1990 (1992).

[4] G. J. Martyna, M.~L. Klein, and M. E. Tuckerman, J. Chem. Phys., 97, 2635 (1992).

[5] Y. Liu and M. E. Tuckerman, J. Chem. Phys., 112, 1685 (2000).