Adaptive molecular resolution approach in Hamiltonian form: An asymptotic analysis

Adaptive molecular resolution approaches in molecular dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer (transition) region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined, and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size, and thus a Hamiltonian approach such as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes.

Figure 1

Pictorial representation of the adaptive resolution setup.

Figure 2

Intramolecular interactions of the full atomistic model.

Figure 3

Intermolecular interactions of the full atomistic model.

Figure 4

(a) Coarse-grained model and its corresponding numerical potential derived by the IBI procedure. (b) Comparison between the c.m.-c.m. radial distribution function of the full atomistic simulation and the equivalent obtained from the coarse-grained potential of (a) within the IBI procedure.

Figure 5

Temperature as a function of time for system 6. Data are analyzed after 500 ps to allow the system time for basic equilibration in the adaptive setup.

Figure 6

(a) Molecular number density as a function of the position in the simulation box of system 6. The horizontal line corresponds to the uniform target density. The blue vertical lines correspond to the borders between the HY and CG regions, and the vertical green lines correspond instead to the borders between the HY and AT regions. (b) A zoom of the density in the AT region.

Figure 7

Atom-atom radial distribution functions in the AT region compared with the equivalent from the full atomistic simulation of reference.

Figure 8

Temperature as a function of time for system 2. Data are analyzed after 500 ps to allow the system time for basic equilibration in the adaptive setup.

Figure 9

Temperature as a function of time for system 7. Data are analyzed after 500 ps to allow the system time for basic equilibration in the adaptive setup.

Figure 10

Temperature as a function of time for system 6 for 4.0 ns. Data are analyzed after 500 ps to allow the system time for basic equilibration in the adaptive set up. The continuous lines represent the curve of linear regression for, respectively, the adaptive resolution simulation and the corresponding full atomistic simulation.

Figure 11

(a) Molecular number density as a function of the position in the simulation box of system 6 in the time window 1.0–4.0 ns. The horizontal line corresponds to the uniform target density. The blue vertical lines correspond to the borders between the HY and CG regions, and the vertical green lines correspond instead to the borders between the HY and AT regions. (b) A zoom of the density in the AT region.

Figure 12

Atom-atom radial distribution functions in the AT region compared with the equivalent from the full atomistic simulation of reference for system 6. Calculations are performed over the time window 1.0–4.0 ns.