Computer simulation long-range forces

Despite all the effort to reduce both the frequency of Coulomb solves (periodic or not) and the computational complexity of each call when required, the long-range force evaluation remains the dominant computational cost of MD simulations. 

Tlierc are two major sources of error associated with the calculation of free energies fi computer simulations. Errors may arise from inaccuracies in the Hamiltonian, be it potential model chosen or its implementation (the treatment of long-range forces, e j lie second source of error arises from an insufficient sampling of phase space. 

A. Barker, in The Problem of Long-Range Forces in the Computer Simulation of Condensed Matter, Ed. by D. Ceperley, Vol. 9, NRCC Workshop toceedings, 1980, p. 45. 

P. J. Steinbach and B. R. Brooks, New Spherical-Cutoff Methods for Long-Range Forces in Macromolecular Simulation, J. Comput. Chem., 15 (1994), 667-683. 

J. P. Valleau, The problem of coulombic forces in computer simulation, in The problem of long-range forces in the computer simulation of condensed matter, ed. D. Ceperley (NRCC Workshop Proceedings, 1980), pp. 3. 

H. E. Alper, D. Bassolino and T. R. Stouch, Computer Simulation of a Phospholipid Monolayer-Water System The Influence of Long Range Forces on Water Structure and Dynamics, 7. Chem. Phys. 98 (1993) 9798. 

Computer simulation of molecular dynamics is concerned with solving numerically the simultaneous equations of motion for a few hundred atoms or molecules that interact via specified potentials. One thus obtains the coordinates and velocities of the ensemble as a function of time that describe the structure and correlations of the sample. If a model of the induced polarizabilities is adopted, the spectral lineshapes can be obtained, often with certain quantum corrections [425,426]. One primary concern is, of course, to account as accurately as possible for the pairwise interactions so that by carefully comparing the calculated with the measured band shapes, new information concerning the effects of irreducible contributions of inter-molecular potential and cluster polarizabilities can be identified eventually. Pioneering work has pointed out significant effects of irreducible long-range forces of the Axilrod-Teller triple-dipole type [10]. Very recently, on the basis of combined computer simulation and experimental CILS studies, claims have been made that irreducible three-body contributions are observable, for example, in dense krypton [221]. 

A quantity which has also attracted a good deal of attention in connection with dipolar and associating fluids is the dielectric constant. In finite samples of volume V (used in computer simulations) the natural quantity to measure is the fluctuation of the total dipole moment of the system, (M2), M = YliLi Mi> where /a., are the dipole moments of the individual molecules. For nonpolarizable molecules in the periodic boundary conditions and with the long-range forces treated by the Ewald summation the dielectric constant, e, is... 

G. N. Patey, in D. Ceperley, Ed., The Problem of Long Range Forces in Computer Simulation of Condensed Media, NRCC Proceedings No. 9, 1980. 

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