# C01 - Adaptive coupling of scales in molecular dynamics and beyond to fluid dynamics

**Head(s):** Prof. Dr. Luigi Delle Site (FU Berlin), Prof. Dr. Felix Höfling (FU Berlin), Prof. Dr.-Ing. Rupert Klein (FU Berlin)**Project member(s):** Roya Ebrahimi Viand, Abbas Gholami Poshtehani, Muhittin Cenk Eser, Gottfried Hastermann, Dr. Arthur Straube**Participating institution(s):** FU Berlin

### Project Summary

The project concerns the construction of a well-founded statistical mechanics framework, with a corresponding mathematical formalisation, for the Adaptive Resolution Simulation (AdResS) technique in the field of molecular dynamics (MD) and its generalisation to multi-scale fluid flow modelling. AdResS adaptively couples an atomistically resolved subsystem to an environment that is represented by a coarse-grained (CG) model. Prior to the first funding period, basic work, developed in Berlin, had anticipated the possibility of re-framing the AdResS idea within the principles of the grand-canonical (GC) ensemble. Starting from this point and as an initial step in the first funding period, we reformulated the method first within the frame of the GC ensemble and next in more general terms of systems with open boundaries. Such results go well beyond the specific technical implementation of AdResS and are general enough to be extended to all techniques of MD that treat systems composed by a region of space embedded in a larger reservoir of energy and particles.

In this context, the Bergman–Lebowitz (BL) formalism for systems with open boundaries was used to justify the definition and calculation of observables in AdResS’ atomistic subsystem, such as time correlation functions. Under certain asymptotic conditions concerning length scales, an underlying Hamiltonian structure was found. In conclusion, the computational atomistic/coarsegrained coupling strategy of AdResS, developed earlier following intuitive principles, has been transformed into a theoretically well-founded method for open systems (GC-AdResS) in this project. The potential of the method was demonstrated by calculating the molecular dipole– dipole time correlation function, e.g., in water, which gives access to the spatially local IR spectrum of molecular systems.

For the next funding period, as its ultimate goal, the project foresees the seamless coupling of the particle-based GC-AdResS to a *grid-based finite volume* continuum hydrodynamics solver to make large-scale and non-equilibrium systems accessible to simulations within this framework. One reference application for this technology concerns the physics of colloidal microswimmers. These nanoparticles are set in motion within a fluid at low Reynolds number by the interplay of non-equilibrium molecular surface processes and long-ranged hydrodynamic fields. Another advanced application concerns molecular transport in nano-porous materials, such as metalorganic frameworks (MOFs), within the context of species separation or storage to be investigated in cooperation with Dr. Sebastian Matera’s Junior Research Group at FU Berlin.

The challenge in this development is to build an efficient and well-justified framework that consistently links regions in space with atomistic, coarse-grained, and continuum representations of the pertinent processes through coupling conditions that properly reflect the scale-dependent physics at the respective interfaces. Depending on the application, different scaling regimes must be allowed for. These include molecular subsystems in or close to thermodynamic equilibrium as well as systems in full non-equilibrium, coupled to continuum models for deterministic or fluctuating hydrodynamics.

The project’s central goals for the coming funding period are (i) to extend the technical capabilities of the AdResS scheme to a larger scale range by transferring its successful paradigm also to coarse-grained/continuum interfaces, (ii) to systematically map out the rather rich landscape of different possible scaling regimes as a basis for the judicious choice of atomistic, coarse-grained, and continuum model components for concrete applications, and (iii) to contribute to our understanding of nano-fluidic applications, such as micro-swimmers and flows near nano-porous materials.

### Project publications

- Delle Site, L. and Klein, R. (2020)
*Liouville-type equations for the n-particle distribution functions of an open system.*Journal of Mathematical Physics, 61 (8). - Straube, Arthur V. and Kowalik, Bartosz G. and Netz, Roland R. and Höfling, Felix (2020)
*Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures.*Communications Physics, 3 (126). pp. 1-11. - Delle Site, Luigi and Klein, Rupert and Höfling, Felix and Viand, Roya Ebrahimi (2020)
*Open Systems out of Equilibrium: Theory and Simulation Preprint arXiv:2005.07481.*SFB 1114 Preprint in arXiv . pp. 1-11. (Submitted) - Delle Site, Luigi and Praprotnik, Matej and Bell, John B. and Klein, Rupert (2020)
*Particle–Continuum Coupling and its Scaling Regimes: Theory and Applications.*Advanced Theory and Simulation, 3, 1900232 (2020), 3 (190023). pp. 1-20. - Delle Site, L. and Krekeler, C. and Whittaker, J. and Agarwal, A. and Klein, R. and Höflling, F. (2019)
*Molecular dynamics of open systems: construction of a mean-field particle reservoir.*Adv. Th. Simul, 2 (5). - Ciccotti, G. and Delle Site, L. (2019)
*The physics of open systems for the simulation of complex molecular environments in soft matter.*Soft Matter, 15 (10). pp. 2114-2124. ISSN 1744-683X, ESSN: 1744-6848 - Shadrack Jabes, B. and Delle Site, L. (2018)
*Nanoscale domains in Ionic Liquids: A statistical mechanics definition for molecular dynamics studies.*J. Chem. Phys., 149 (18). p. 184502. ISSN 0021-9606, ESSN: 1089-7690 - Krekeler, C. and Agarwal, A. and Junghans, C. and Praprotnik, M. and Delle Site, L. (2018)
*Adaptive Resolution Molecular Dynamics Technique: Down to the Essential.*J. Chem. Phys., 149 . 024104. ISSN 0021-9606, ESSN: 1089-7690 - Shadrack Jabes, B. and Krekeler, C. and Klein, R. and Delle Site, L. (2018)
*Probing Spatial Locality in Ionic Liquids with the Grand Canonical Adaptive Resolution Molecular Dynamics Technique.*The Journal of Chemical Physics, 148 (19). ISSN online: 1089-7690 - Peters, J.H. and Gräser, C. and Klein, R. (2017)
*Membrane Deformation by N-BAR Proteins: Extraction of membrane geometry and protein diffusion characteristics from MD simulations.*SFB 1114 Preprint in arXiv:1712.02666 . pp. 1-12. (Unpublished) - Delle Site, L. and Ciccotti, G. and Hartmann, C. (2017)
*Partitioning a macroscopic system into independent subsystems.*Journal of Statistical Mechanics: Theory and Experiment, 2017 . pp. 1-13. - Delle Site, L. and Praprotnik, M. (2017)
*Molecular systems with open boundaries: Theory and Simulation.*Physics Reports, 693 . pp. 1-56. ISSN 0370-1573 - Junghans, C. and Agarwal, A. and Delle Site, L. (2017)
*Computational Efficiency and Amdahl's law for the Adaptive Resolution Simulation Technique.*Computer Physics Communications, 215 . pp. 20-25. ISSN 0010-4655 - Seshaditya, A. and Ghiringhelli, L. M. and Delle Site, L. (2017)
*Levy-Lieb-based Monte Carlo study of the dimensionality behaviour of the electronic kinetic functional.*Computationa, 5 (2). pp. 1-10. ISSN 2079-3197 - Agarwal, A. and Clementi, C. and Delle Site, L. (2017)
*Path Integral-GC-AdResS simulation of a large hydrophobic solute in water: A tool to investigate the interplay between local microscopic structures and quantum delocalization of atoms in space.*Physical Chemistry Chemical Physics, 19 . pp. 13030-13037. ISSN 1463-9084 - Winkelmann, S. (2017)
*Markov Control with Rare State Observation: Average Optimality.*Markov Processes and Related Fields, 23 . pp. 1-34. ISSN 1024-2953 - Zhu, J. and Klein, R. and Delle Site, L. (2016)
*Adaptive Molecular Resolution Approach in Hamiltonian Form: An Asymptotic Analysis.*Physical Review E, 94 (043321). - Delle Site, L. (2016)
*Formulation of Liouville's theorem for grand ensemble molecular simulations.*Physical Review E, 93 (022130). - Delle Site, L. and Agarwal, A. (2016)
*Grand-Canonical Adaptive Resolution Centroid Molecular Dynamics: Implementation and Application.*Computer Physics Communications (206). pp. 26-34. - Peters, J.H. and Klein, R. and Delle Site, L. (2016)
*Simulation of macromolecular liquids with the adaptive resolution molecular dynamics technique.*Phys. Rev. E, 94 (2). 023309. - Enciso, M. and Schütte, Ch. and Delle Site, L. (2015)
*Influence of pH and sequence in peptide aggregation via molecular simulation.*Journal of Chemical Physics, 143 (24). p. 243130. ISSN 0021-9606 - Agarwal, A. and Delle Site, L. (2015)
*Path Integral Molecular Dynamics within the Grand Canonical-like Adaptive Resolution Technique: Simulation of Liquid Water.*Journal of Chemical Physics, 143 (9). ISSN 0021-9606 - Hartmann, C. and Delle Site, L. (2015)
*Scale Bridging in Molecular Simulation.*The European Physical Journal Special Topics, 224 (12). pp. 2173-2176. ISSN 1951-6355 - Klein, R. (2015)
*Comments on "Open Boundary Molecular Dynamics " by R. Delgado-Buscalioni, J. Sablic, and M. Praprotnik.*The European Physical Journal, 224 (12). pp. 2509-2510. ISSN Online: 1951-6401 Print: 1951-6355 - Klein, R. (2015)
*Comments on "Advantages and challenges in coupling an ideal gas to atomistic models in adaptive resolution simulations" by K. Kreis, A.C. Fogarty, K. Kremer R. Potestio.*The European Physical Journal, 224 (12). pp. 2503-2504. ISSN Online: 1951-6401 Print: 1951-6355 - Agarwal, A. and Zhu, J. and Wang, H. and Hartmann, C. and Delle Site, L. (2015)
*Molecular dynamics in a Grand Ensemble: Bergmann-Lebowitz model and adaptive resolution simulation.*New Journal of Physics, 17 (083042). ISSN 1367-2630 - Klein, R. (2015)
*Comments on "Adaptive Resolution Simulation in Equilibrium and Beyond" by H. Wang and A. Agarwal.*The European Physical Journal, 224 (12). pp. 2497-2499.