arXiv subjects

Igor P. Omelyan

Publications and source records attributed to Igor P. Omelyan.

11 recordsLinked to original sources

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2008

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.

cond-mat.stat-mech↗

arXiv1999

A new approach to the integration of rotational motion in systems with interacting rigid bodies

A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration, whereas orientational positions are expressed in terms of either principal axes or quaternions. As a result, the rigidness of molecules appears to be an integral of motion, despite the atom trajectories are evaluated approximately. The algorithm derived is free of any iterative procedures and it allows to perform both energy- and temperature-conserving simulations. The corresponding integrators are time reversible but the symplectic behaviour is only achieved in mean. Symplectic versions are also described. The provide the conservation of volume in phase space precisely at each time step and, moreover, lead to exact solutions for angular velocities in the inertial-motion regime. It is shown that the algorithm exhibits excellent stability properties and conserves the energy even somewhat better than the atomic-constraint technique.

physics.comp-ph↗

arXiv1999

Transverse wavevector dependent and frequency dependent dielectric function, magnetic permittivity and generalized conductivity of interaction site fluids. MD calculations for the TIP4P water

It is shown that the dielectric properties of interaction site models of polar fluids can be investigated in computer experiment using not only the charge fluctuations but also correlations corresponding to a current of moving charges. This current can be associated with a generalized dynamical polarization or separated into electric and magnetic components. The first approach deals with the dielectric permittivity related to a generalized conductivity, whereas the second one leads to the functions describing polarization and magnetization fluctuations separately. The last way is only the source to calculate the magnetic susceptibility for a system of interaction sites. The transverse wavevector- and frequency-dependent dielectric functions and magnetic susceptibility are evaluated for the TIP4P water model in a very wide scale of wavelengths and frequencies using molecular dynamics simulations. We demonstrate that the transverse part of the dielectric functions may differ drastically from their longitudinal component. A relationship between the two approaches is discussed and the limiting transition to the static dielectric constant in the infinite-wavelength regime is analyzed. The propagation of transverse electromagnetic waves in the TIP4P water is also considered.

physics.chem-ph↗

arXiv1999

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.

physics.chem-ph↗

arXiv1999

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.

physics.comp-ph↗

arXiv1999

On the reaction field for interaction site models of polar systems

It is rigorously shown that the fluctuation formula, which is used in simulations to calculate the dielectric constant of interaction site models, corresponds to the reaction field with an individual site cut-off rather than with the usual molecular center of mass truncation. Within the molecular cut-off scheme, a modified reaction field is proposed. An influence of the truncation effects is discussed and examined by actual Monte Carlo simulations for a MCY water model.

physics.comp-ph↗

arXiv1999

A new leapfrog integrator of rotational motion. The revised angular-momentum approach

A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational positions. Contrary to the standard implicit method by Fincham [Mol. Simul., 8, 165 (1992)], the revised angular momentum approach presented corresponds completely to the leapfrog idea on interpolation of dynamical variables without using any extrapolations. The proposed scheme intrinsically preserves rigid molecular structures and considerably improves stability properties and energy conservation. As is demonstrated on the basis of simulations for water, it allows to reproduce correct results with extra large step sizes of order 5 fs and 10 fs in the cases of energy- and temperature-conserving dynamics, respectively. We show also that iterative solutions can be avoided within our implicit scheme shifting from quaternions to the entire rotation-matrix representation.

physics.comp-ph↗

arXiv1999

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.

physics.comp-ph↗

arXiv1999

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.

physics.comp-ph↗

arXiv1999

Numerical integration of the equations of motion for rigid polyatomics: The matrix method

A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are integrated within the Verlet framework in velocity form. It is shown that, contrary to previous methods, in the approach introduced the rigidity of molecules can be conserved automatically without any additional transformations. A comparison of various techniques with respect to numerical stability is made.

physics.comp-ph↗