Molecular-Continuum Simulation

Hybrid simulation Molecular-continuum simulation Multiscale modeling... 

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-... 

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. 

In this section, we discuss applications of the FEP formalism to two systems and examine the validity of the second-order perturbation approximation in these cases. Although both systems are very simple, they are prototypes for many other systems encountered in chemical and biological applications. Furthermore, the results obtained in these examples provide a connection between molecular-level simulations and approximate theories, especially those based on a dielectric continuum representation of the solvent. 

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. 

This volume of Modem Aspects covers a wide spread of topics presented in an authoritative, informative and instructive manner by some internationally renowned specialists. Professors Politzer and Dr. Murray provide a comprehensive description of the various theoretical treatments of solute-solvent interactions, including ion-solvent interactions. Both continuum and discrete molecular models for the solvent molecules are discussed, including Monte Carlo and molecular dynamics simulations. The advantages and drawbacks of the resulting models and computational approaches are discussed and the impressive progress made in predicting the properties of molecular and ionic solutions is surveyed. 

An interesting combined use of discrete molecular and continuum techniques was demonstrated by Floris et al.181,182 They used the PCM to develop effective pair potentials and then applied these to molecular dynamics simulations of metal ion hydration. Another approach to such systems is to do an ab initio cluster calculation for the first hydration shell, which would typically involve four to eight water molecules, and then to depict the remainder of the solvent as a continuum. This was done by Sanchez Marcos et al. for a group of five cations 183 the continuum model was that developed by Rivail, Rinaldi et al.14,108-112 (Section III.2.ii). Their results are compared in Table 14 with those of Floris et al.,139 who used a similar procedure but PCM-based. In... 

Monte Carlo and Molecular Dynamics simulations of water near hydrophobic surfaces have yielded a wealth of information about the structure, thermodynamics and transport properties of interfacial water. In particular, they have demonstrated the presence of molecular layering and density oscillations which extend many Angstroms away from the surfaces. These oscillations have recently been verified experimentally. Ordered dipolar orientations and reduced dipole relaxation times are observed in most of the simulations, indicating that interfacial water is not a uniform dielectric continuum. Reduced dipole relaxation times near the surfaces indicate that interfacial water experiences hindered rotation. The majority of simulation results indicate that water near hydrophobic surfaces exhibits fewer hydrogen bonds than water near the midplane. 

The complications for fhe fheoretical description of proton fransporf in the interfacial region befween polymer and water are caused by the flexibility of fhe side chains, fheir random distributions at polymeric aggregates, and their partial penetration into the bulk of water-filled pores. The importance of an appropriate flexibilify of hydrated side chains has been explored recently in extensive molecular modeling studies. Continuum dielectric approaches and molecular dynamics simulations have been utilized to explore the effects of sfafic inferfacial charge distributions on proton mobility in single-pore environments of Molecular level simulations were employed... 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular d5mamics simulations of protons and water in single iono-mer pores, as reviewed in Section 6.7.2. The hydrod5mamic contribution to n can be studied, at least qualitatively, using continuum approaches. Solution of the Poisson-Boltzmann (PB) equation. 

TvaroSka, KoS r and Hricovini in this book). One way to account for the effect of solvent on conforxnation might be to represent the molecule without environmental influences, and then explicitly include the solvent or other environmental molecules in the calculation. While avoiding built-in influences of environment is a satisfying concept, it is difficult to obtain by experiment parameters that lack those influences. Several methods have been used to study solvation effects, including continuum descriptions (24) and the explicit treatment of solvent molecules in Monte Carlo and molecular dynamics simulation. 

Fig. 4. Decaniobate Nbi0O286 ion. Symmetrically equivalent oxygen atoms are shown in different colors. The niobium ions are labeled 1,2,3, as shown in the Figure. The oxygen atoms are then labeled with respect to the numbers on the niobium atoms, and whether they are bridging (p) or terminal (r ). Bond lengths are compared for density functional theory in continuum solvent versus model predictions as averaged over a molecular dynamics simulation in water. DFT-calculated bond lengths are above, and model predictions are below, given in angstroms.

The problem of linking atomic scale descriptions to continuum descriptions is also a nontrivial one. We will emphasize here that the problem cannot be solved by heroic extensions of the size of molecular dynamics simulations to millions of particles and that this is actually unnecessary. Here we will describe the use of atomic scale calculations for fixing boundary conditions for continuum descriptions in the context of the modeling of static structure (capacitance) and outer shell electron transfer. Though we believe that more can be done with these approaches, several kinds of electrochemical problems—for example, those associated with corrosion phenomena and both inorganic and biological polymers—will require approaches that take into account further intermediate mesoscopic scales. There is less progress to report here, and our discussion will be brief. 

The COSMO solvent model has been used to simulate the influence of water on the electronic spectrum of A -methylacetamide [81], and the results was compared with the results of molecular dynamics simulations (where the electronic spectrum were calculated as an average over 90 snapshots from MD simulations). Most of the hydration effects were found to come from the first solvation shell hydrogen-bonded water molecules, and the continuum model does not properly account for these effects. The rotatory strengths were not calculated directly in ref. [81]. However, the results were used to model ECD spectra of peptides via the coupled oscillator model, with satisfactory result. 

P. F. B. Gon9alves and H. Stassen, New approach to free energy of solvation applying continuum models to molecular dynamics simulation, J. Comput. Chem., 23 (2002) 706-714. 

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