Multiscale Modeling of Liquids with Molecular Specificity

The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which addresses this problem by keeping the full molecular nature of the system where it is of interest and coarse graining it elsewhere. This is made possible by coupling molecular dynamics with a mesoscopic description of realistic liquids based on Landau’s fluctuating hydrodynamics. We show that our scheme correctly couples hydrodynamics and that fluctuations, at both the molecular and continuum levels, are thermodynamically consistent. Hybrid simulations of sound waves in bulk water and reflected by a lipid monolayer are presented as illustrations of the scheme.

Figure 1

(a) The setup used for our hybrid molecular simulations and (b) a close-up of the hybrid interface. The FH description, resolved by the finite volume method, is coupled to a molecular model (MD) representing a dimyristoylphosphatidylcholine (DMPC) lipid monolayer solvated with water and restrained at the lipid head groups. We indicate by “$P$” and “$C$,” respectively, the particle and continuum cells adjacent to the hybrid interface “$H$.” The buffer region of the MD system “$B$” (overlapping the $C$ cell) is indicated by translucent water molecules, and the water molecule density in the buffer region is shown in (c).

Figure 2

(a) The normalized mean error in mass $E_M(\tau )$ and momentum $E_{P_{\alpha }}(\tau )$ evaluated as $E_A^2(\tau )=⟨[{\int }_{t_0}^{t_0+\tau }\delta A(t)dt/\tau {]}^2{⟩}_{t_0}/⟨M_k{⟩}^2$, with $\delta A=A-⟨A⟩$. The dashed and solid horizontal lines are, respectively, the normalized standard deviation of mass and momentum within one cell ($\sigma [M_k]/⟨M_k⟩$). (b) Density field in a hybrid MD equilibrium simulation of water. The solid circles correspond to MD cells. The error bars are the standard deviation of each cell density. The GC result is $⟨\rho ⟩=0.632(\mathrm{g}/\mathrm{mol})/{\AA }^3$ and $\sigma [\rho ]=0.0045(\mathrm{g}/\mathrm{mol})/{\AA }^3$.

Figure 3

(a) Spatiotemporal diagram along $z$ for the density field of a three-dimensional simulation of two sound waves traveling within a closed box filled with water. The region of width 45 Å around the center of the box is described with MD, while the rest of the domain is solved via FH. (b) The longitudinal velocity arising from the interaction between a sound wave and a grafted lipid layer [setup of Fig. 1a]. We compare hybrid MD (solid line), full MD (circles), and full FH simulation using purely reflecting walls (dashed line). Results are averaged over 15 nm from the monolayer; error bars indicate the standard deviation over 10 runs.