Adaptive resolution scheme for efficient hybrid atomistic-mesoscale molecular dynamics simulations of dense liquids

The adaptive resolution scheme (AdResS) for efficient hybrid particle-based atomistic/mesoscale molecular dynamics (MD) simulations recently introduced by us, [J. Chem. Phys. 123, 224106 (2005)] is extended to high density molecular liquids with spherical boundaries between the atomistic and mesoscale regions. The key feature of this approach is that it allows for a dynamical change of the number of molecular degrees of freedom during the course of a MD simulation by an on-the-fly switching between the atomistic and mesoscopic levels of detail. Pressure and density variations occurring at the atomistic/mesoscale boundary in the original version are considerably reduced employing the improved methodology presented here.

Figure 1

(Color) (a) Schematic representation of the hybrid system with spherically shaped regions modeled with different levels of detail. In the center there is the all-atom regime with the tetrahedral molecules surrounded by the transition regime with the hybrid molecules followed by the mesoscopic regime with one-particle coarse-grained molecules. (b) Cross section of the hybrid system with spherical resolution boundaries at molecular number density $\rho =0.175∕{\sigma }^3\approx 1.0∕{\sigma }_{\mathit{cg}}^3$ and $T=1.0\epsilon ∕k_B$, where ${\sigma }_{\mathit{cg}}$ is the excluded volume diameter of the coarse-grained molecule and $k_B$ the Boltzmann’s constant. For the presentation convenience the transition regime is not shown.

Figure 2

The weighting function $w\left(r\right)∊[0,1]$ defined by Eq. (7). The values $w=1$ and $w=0$ correspond to the atomistic and coarse-grained regions of the hybrid atomistic-mesoscopic system with the box length $a$, respectively, whereas the values $0<w<1$ correspond to the interface layer. Shown is the example where the width $d$ of the interface layer is $a∕10$ and the radius of the atomistic region $r_0$ is $a∕6$. The vertical lines denote the boundaries of the interface layer.

Figure 3

(a) The tabulated effective potential $U_{\mathit{tab}}^{\mathit{cm}}\left(r\right)$ for the $\mathit{cg}$ system at $\rho =0.175$ and $T=1$. Shown is also $U^{\mathit{cm}}\left(r\right)$, which holds for $\rho =0.1$ as given by Eq. (10) for comparison. (b) ${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ of the $\mathit{ex}$ and $\mathit{cg}$ systems at $\rho =0.175$ and $T=1$. The ${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ match to the line-thickness.

Figure 4

Equations of state at $T=1$ for the $\mathit{ex}$ and $\mathit{cg}$ systems using the tabulated effective potential $U_{\mathit{tab}}^{\mathit{cm}}\left(r\right)$. Shown is the pressure $p$ as a function of the number density $\rho$ of the system.

Figure 5

${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ of the $\mathit{ex}$ and $\mathit{ex}\text{−}\mathit{cg}$ systems with $r_0=12.0$ and $d=2.5$ at $\rho =0.1$ and $T=1$.

Figure 6

Time evolution of the number of molecules in the $\mathit{ex}$, $\mathit{cg}$, and interface $\left(\mathit{int}\right)$ regions of the $\mathit{ex}\text{−}\mathit{cg}$ system with $r_0=12.0$ and $d=2.5$ at $\rho =0.1$ and $T=1$. The average numbers of molecules in the $\mathit{ex}$, $\mathit{cg}$, and $\mathit{int}$ regions are $724\pm 35$, $3736\pm 53$, and $539\pm 32$, respectively.

Figure 7

The normalized radial number density profiles of the $\mathit{ex}\text{−}\mathit{cg}$ system at $\rho =0.1$ and $T=1$. (a) $r_0=6.0$. (b) $r_0=12.0$. The vertical lines denote the boundaries of the interface region with $d=2.5$.

Figure 8

${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ of the $\mathit{ex}$ and $\mathit{ex}\text{−}\mathit{cg}$, and systems with $r_0=6.0$ and $d=2.5$ at $\rho =0.175$ and $T=1$.

Figure 9

Time evolution of the number of molecules in different regimes of the $\mathit{ex}\text{−}\mathit{cg}$ system with $r_0=11.0$ and $d=2.5$ at $\rho =0.175$ and $T=1$. The theoretical predictions for the numbers of molecules in different regions of a homogeneous liquid are $n_{\mathit{ex}}=975$, $n_{\mathit{cg}}=3197$, and $n_{\mathit{int}}=828$. The corresponding simulation averages in the $\mathit{ex}$, $\mathit{cg}$, and interface $\left(\mathit{int}\right)$ regions are $979\pm 31$, $3210\pm 33$, and $809\pm 26$, respectively.

Figure 10

The normalized radial number density profiles of the $\mathit{ex}\text{−}\mathit{cg}$ system at $\rho =0.175$ and $T=1$. (a) $r_0=6.0$. (b) $r_0=11.0$. The vertical lines denote the boundaries of the interface region with $d=2.5$.

Figure 11

${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ of the $\mathit{ex}$, $\mathit{ex}\text{−}\mathit{cg}(w=\frac{1}{2})$, and $\mathit{ex}\text{−}\mathit{cg}(w=\frac{1}{2}{)}_{\mathit{ic}})$ systems at $\rho =0.1$ and $T=1$. In the inset the corrected effective pair potential $U_{\mathit{ic}}^{\mathit{cm}}\left(r\right)$ for hybrid molecules as defined by Eq. (17) and the effective pair potential $U^{\mathit{cm}}\left(r\right)$ as defined by Eq. (10) are shown.

Figure 12

The normalized radial number density profile of the $\mathit{ex}\text{−}{\mathit{cg}}_{\mathit{ic}}$ system with $r_0=12.0$ at $\rho =0.1$ and $T=1$. The vertical lines denote the boundaries of the interface region with $d=2.5$.

Figure 13

${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ of the $\mathit{ex}$, $\mathit{ex}\text{−}\mathit{cg}(w=\frac{1}{2})$, and $\mathit{ex}\text{−}\mathit{cg}{(w=\frac{1}{2})}_{\mathit{ic}}$ systems at $\rho =0.175$ and $T=1$. The ${\mathrm{RDF}}_{\mathit{cm}}\mathrm{s}$ of the $\mathit{ex}$ and $\mathit{ex}\text{−}\mathit{cg}{(w=\frac{1}{2})}_{\mathit{ic}}$ systems match within the line thickness. In the inset the corresponding corrected effective pair potential $U_{{\mathit{tab}}_{\mathit{ic}}}^{\mathit{cm}}\left(r\right)$ and the effective pair potential $U_{\mathit{tab}}^{\mathit{cm}}\left(r\right)$ are shown.

Figure 14

The normalized radial number density profile of the $\mathit{ex}\text{−}{\mathit{cg}}_{\mathit{ic}}$ system with $r_0=11.0$ at $\rho =0.175$ and $T=1$. The vertical lines denote the boundaries of the interface region with $d=2.5$.