Adaptive molecular resolution via a continuous change of the phase space dimensionality

Abstract

For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being developed for many applications. However in almost all cases, the regions of different resolution are fixed and not in a true equilibrium with each other. We here give the theoretical framework for an efficient and flexible coupling of the different regimes. The approach leads to an analog of a geometry induced phase transition and a counterpart of the equipartition theorem for fractional degrees of freedom. This provides a rather general formal basis for advanced computer simulation methods applying different levels of resolution. A long standing and often most challenging problem in condensed matter physics, up to some simple crystalline materials, is to understand the microscopic origin of macroscopic properties. While in certain cases a microscopic scale can be clearly separated from a macroscopic one, this is not the case for most experimental systems -details of the local interaction and generic/universal aspects are closely related. Already the proper determination of the fracture energy and crack propagation in crystalline materials requires a hierarchical and interrelated description, which links the breaking of the interatomic bonding in the fracture region to the response of the rest of the system on a micron scale [1]. The presence of microscopic chemical impurities in many metals and alloys changes their macroscopic mechanical behavior [2,3]. Even more complicated are synthetic and biological soft matter systems. Whether one is dealing with the morphology, the glass transition of a polymeric system, the function of a molecular assembly, e.g. for electronic applications or studies ligand-protein recognition or protein-protein interaction, in all cases the generic soft matter properties, such as matrix or chain conformation fluctuations, and details of the local chemistry apply to roughly the same length scales. For all these problems, which due to their complexity are heavily studied by computer simulations, there is a common underlying physical scenario: the number of degrees of freedom (DOFs) involved is very large and the exhaustive exploration of the related phase space is prohibitive. For many questions, however, such a deep level of detail in the description is only required locally.Theoretical methods employed to study these systems span from quantum-mechanical to macroscopic statistical approaches. Their efficiency and scope increases significantly if two or more such different approaches are combined into hybrid multiscale schemes. This is the case for the quantum based QM/MM ap- * On leave from the National

Modeling diffusive dynamics in adaptive resolution simulation of liquid water

“…[4][5][6][7][8][9][10][11][12][13][14] In general, to build a multiscale model two main issues need to be addressed. The first issue consists of mapping the system into a robust reduced model while preserving the here relevant physico-chemical properties, i.e., radial distribution functions, pressure, and temperature, of the reference all-atom system.…”

Transport properties controlled by a thermostat: An extended dissipative particle dynamics thermostat

“…However, in typical soft matter systems different time-and length-scales are intrinsically interconnected and a multiscale modeling approach is required to tackle such problems in the most efficient way 9,10,11,12,13,14,15,16 . Recently, we have proposed an adaptive resolution scheme (AdResS) that couples the atomistic and coarsegrained levels of detail 17,18,19,20,21,22 . Due to the reduction in DOFs upon coarse-graining, which eliminates the fluctuating forces associated with those missing molecular DOFs, the coarse-grained molecules typically move faster than the corresponding atomistically resolved ones 23,24 .…”

Multiscale simulations of complex systems: computation meets reality

“…To this end, detailed calculations of the electronic properties of DNA bases need to be carried out, at the level of quantum chemistry, including all the details of the base-pair atomistic structure. Assembling the entire picture in a coherent model is a serious challenge to current computational capabilities and is likely to require profound conceptual and mathematical innovations in the way we handle the phase-space of complex systems [19,20].…”