Continuum molecular dynamics

Quantitative models of solute-solvent systems are often divided into two broad classes, depending upon whether the solvent is treated as being composed of discrete molecules or as a continuum. Molecular dynamics and Monte Carlo simulations are examples of the former 8"11 the interaction of a solute molecule with each of hundreds or sometimes even thousands of solvent molecules is explicitly taken into account, over a lengthy series of steps. This clearly puts a considerable demand upon computer resources. The different continuum models,11"16 which have evolved from the work of Bom,17 Bell,18 Kirkwood,19 and Onsager20 in the pre-computer era, view the solvent as a continuous, polarizable isotropic medium in which the solute molecule is contained within a cavity. The division into discrete and continuum models is of course not a rigorous one there are many variants that combine elements of both. For example, the solute molecule might be surrounded by a first solvation shell with the constituents of which it interacts explicitly, while beyond this is the continuum solvent.16... 

M. Marchi, D. Borgis, N. Levy, and P. Ballone (2001) A dielectric continuum molecular dynamics method. J. Chem. Phys. 114, p. 4377... 

Balbuena et al. (1998) studied the reorientation times of water molecules over a range of temperatures including supercritical ones, employing semi-continuum molecular dynamics by means of the SPC/E water model (500 water molecules per ion). The reorientation times in bulk water relative to those in the first hydration shell, assuming a coordination number of Nco = 6, are Tiw/Tri = 0.20,0.47,0.65, and 0.90 for Na+, K+, Rb" ", and Cr, respectively, at 25 °C, showing faster reorientation as... 

Simulations of chains grafted to interfaces in vacuum and in liquid solvents have been reviewed[73]. The repulsive force of interaction between surfaces coated with grafted athermal chains (good solvent conditions) has been calculated with lattice MC[74] and continuum molecular dynamics[75] methods. The first simulations of interfaces in supercritical fluids considered the adsorption of pure solvent (no chains) in a flat-wall pore[76]. Near the solvent critical temperature (7 ) a maximum in adsorbed amount was observed at densities slightly below the solvent critical density (pc) The maximum in adsorbed amount was attributed to local density enhancement of solvent in the pore. 

D. D. Humphreys, R. A. Friesner, and B. J. Berne. Simulated annealing of a protein in a continuum solvent by multiple-time-step molecular dynamics. J. Phys. Chem., 99 10674-10685, 1995. 

In this chapter we shall consider four important problems in molecular n iudelling. First, v discuss the problem of calculating free energies. We then consider continuum solve models, which enable the effects of the solvent to be incorporated into a calculation witho requiring the solvent molecules to be represented explicitly. Third, we shall consider the simi lation of chemical reactions, including the important technique of ab initio molecular dynamic Finally, we consider how to study the nature of defects in solid-state materials. 

The concentration of salt in physiological systems is on the order of 150 mM, which corresponds to approximately 350 water molecules for each cation-anion pair. Eor this reason, investigations of salt effects in biological systems using detailed atomic models and molecular dynamic simulations become rapidly prohibitive, and mean-field treatments based on continuum electrostatics are advantageous. Such approximations, which were pioneered by Debye and Huckel [11], are valid at moderately low ionic concentration when core-core interactions between the mobile ions can be neglected. Briefly, the spatial density throughout the solvent is assumed to depend only on the local electrostatic poten-... 

For reasons of space and because of their prime importance, we focus here on free energy calculations based on detailed molecular dynamics (MD) or Monte Carlo (MC) simulations. However, several other computational approaches exist to calculate free energies, including continuum dielectric models and integral equation methods [4,14]. 

The idea of a finite simulation model subsequently transferred into bulk solvent can be applied to a macromolecule, as shown in Figure 5a. The alchemical transformation is introduced with a molecular dynamics or Monte Carlo simulation for the macromolecule, which is solvated by a limited number of explicit water molecules and otherwise surrounded by vacuum. Then the finite model is transferred into a bulk solvent continuum... 

In literature, some researchers regarded that the continuum mechanic ceases to be valid to describe the lubrication behavior when clearance decreases down to such a limit. Reasons cited for the inadequacy of continuum methods applied to the lubrication confined between two solid walls in relative motion are that the problem is so complex that any theoretical approach is doomed to failure, and that the film is so thin, being inherently of molecular scale, that modeling the material as a continuum ceases to be valid. Due to the molecular orientation, the lubricant has an underlying microstructure. They turned to molecular dynamic simulation for help, from which macroscopic flow equations are drawn. This is also validated through molecular dynamic simulation by Hu et al. [6,7] and Mark et al. [8]. To date, experimental research had "got a little too far forward on its skis however, theoretical approaches have not had such rosy prospects as the experimental ones have. Theoretical modeling of the lubrication features associated with TFL is then urgently necessary. 

This section provides an alternative measurement for a material parameter the one in the ensemble averaged sense to pave the way for usage of continuum theory from a hope that useful engineering predictions can be made. More details can be found in Ref. [15]. In fact, macroscopic flow equations developed from molecular dynamics simulations agree well with the continuum mechanics prediction (for instance. Ref. [16]). 

The flat interface model employed by Marcus does not seem to be in agreement with the rough picture obtained from molecular dynamics simulations [19,21,64-66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water-DCE junction [8,19]. It was found that the electric field induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total field as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. 

Nina, M. Beglov, D. Roux, B., Atomic radii for continuum electrostatics calculations based on molecular dynamics free energy simulations, J. Phys. Chem. B 1997, 101, 5239-5248... 

Simonson, T., Electrostatic free energy calculations for macromolecules a hybrid molecular dynamics/continuum electrostatics approach, J. Phys. Chem. B 2000, 104, 6509-6513. 

Archontis, G. Simonson, T. Dielectric relaxation in an enzyme active site molecular dynamics simulations intepreted with a macroscopic continuum model, J. Am. Chem. Soc. 2001,123, 11047-11056. 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

---