Longitudinal wavevector- and frequency-dependent dielectric constant of the TIP4P water model

A computer adapted theory for self-consistent calculations of the wavevector- and frequency-dependent dielectric constant for interaction site models of polar systems is proposed. A longitudinal component of the dielectric constant is evaluated for the TIP4P water model in a very wide scale of wavenumbers and frequencies using molecular dynamics simulations. It is shown that values for the dielectric permittivity, calculated within the exact interaction site description, differ in a characteristic way from those obtained by the point dipole approximation which is usually used in computer experiment. It is also shown that the libration oscillations, existing in the shape of longitudinal time-dependent polarization fluctuations at small and intermediate wavevector values, vanish however for bigger wavenumbers. A comparison between the wavevector and frequency behaviour of the dielectric constant for the TIP4P water and the Stockmayer model is made. The static screening of external charges and damping of longitudinal electric excitations in water are considered as well. A special investigation is devoted to the time dependence of dielectric quantities in the free motion regime.Comment: 21 pages, 7 figure

On the numerical integration of motion for rigid polyatomics: The modified quaternion approach

A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This allows to resolve the rigidity problem rigorously using constraint forces. It is shown that the procedure for preservation of molecular rigidity can be realized particularly simply within the Verlet algorithm in velocity form. We demonstrate that the presented method leads to an improved numerical stability with respect to the usual quaternion rescaling scheme and it is roughly as good as the cumbersome atomic-constraint technique.Comment: 14 pages, 2 figure

Ewald summation technique for interaction site models of polar fluids

A computer adapted fluctuation formula for the calculation of the wavevector- and frequency-dependent dielectric permittivity for interaction site models of polar fluids within the Ewald summation technique is proposed and applied to molecular dynamics simulations of the TIP4P water. The formula is analyzed and optimal parameters of the Ewald method are identified. A comparison of the obtained results with those evaluated within the reaction field approach is made.Comment: 14 pages, 3 figure

Algorithm for numerical integration of the rigid-body equations of motion

A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in terms of either principal axes or quaternions. Due to specific features of the algorithm, orthonormality and unit norms of the orientational variables are integrals of motion, despite an approximate character of the produced trajectories. It is shown that the method presented appears to be the most efficient among all known algorithms of such a kind.Comment: 4 pages, 1 figur

Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in the literature to further split up the kinetic part of the Hamiltonian, which lowers the accuracy. The goal of this note is to comment on the best combination of optimized splitting and gradient methods that avoids splitting the kinetic energy. These schemes are generally applicable, but the optimal scheme depends on the desired level of accuracy. For simulations of liquid water it is found that the velocity Verlet scheme is only optimal for crude simulations with accuracies larger than 1.5%, while surprisingly a modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for publication in the Journal of Chemical Physic

Processed Splitting Algorithms for Rigid-Body Molecular Dynamics Simulations

A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and orientational coordinates are decoded by processing transformations. This allows to overcome the barrier on the order of precision of the integration at a given number of force-torque evaluations per time step. Testing in dynamics of water versus previous methods shows that the obtained algorithms significantly improve the accuracy of the simulations without extra computational costs.Comment: 6 pages, 2 figures, submitted to Physical Review