Hybrid molecular-continuum

However, the length and time scales that molecular-based simulations can probe are still very limited (tens of nanosecond and a few nanometers), due to computer memory and CPU power limitations. On the other hand, nanoscale flows are often a part of larger scale devices that could contain both nanochannels and microfluidic domains. The dynamics of these systems depends on the intimate connection of different scales from nanoscale to microscale and beyond. MD simulation cannot simulate the whole systems due to its prohibitive computational cost, whereas continuum Navier-Stokes simulation cannot elucidate the details in the small scales. These limitations and the practical needs arising from the study of multiscale problems have motivated research on multiscale (or hybrid) simulation techniques that bridge a wider range of time and length scales with the minimum loss of information. A hybrid molecular-continuum scheme can make such multiscale computation feasible. A molecular-based method, such as MD for liquid or DSMC for gas, is used to describe the molecular details within the desired, localized subdomain of the large system. A continuum method, such as finite element or finite volume based Navier-Stokes/Stokes simulation, is used to describe the continuum flow in the remainder of the system Such hybrid method can be applied to solve the multiscale phenomena in gas, liquid, or solid. 

Spatial multi-scale methods are based on the paradigm that in many real situations the atomic description is only required within small parts of the simulation domain whereas for the majority the continuum model is still valid. This allows one to apply concurrent continuum and molecular simulations for the respective parts of the simulation domain using a coupling scheme that permits to connect between the two domains. The majority of the spatial domain is calculated by continuum solvers (computational fluid dynamics) which are very fast and only the active part is calculated using molecular simulation methods. In some cases several other coarser-grained (mesoscale) methods than the atomic simulations ones are used as interfaces between the molecular simulation and the continuum domains. Such approaches are called hybrid molecular-continuum methods and allow the simulation of problems that are not accessible either by continuum or by pure molecular simulation methods. 

Simonson, T., Electrostatic free energy calculations for macromolecules a hybrid molecular dynamics/continuum electrostatics approach, J. Phys. Chem. B 2000, 104, 6509-6513. 

Values of AGsolvation and Its Components in Two Different Solvents, in kcal/mol, As Predicted by a Hybrid Discrete Molecular/Continuum Solvent... 

AGhydration For Metal Ions, In Kcal/Mole, Computed By Two Hybrid Discrete Molecular/Continuum Methods... 

In a recent article [5] we have proposed a new hybrid isotherm for adsorption in nonporous materials. The isotherm combines our recent molecular-continuum model for higher pressures, with other widely used models such as the Unilan model for the low-pressure region... 

The hybrid isotherm uses our recent molecular-continuum model for higher pressures [ 18,19],... 

The molecular mechanism of the Hoffmann elimination involving (iV-Cl)-N-methyl-ethanolamine has been theoretically characterized by using DFT at the B3LYP/ 6-31++G computing level.49 The role of water as a solvent has been analysed by using both discrete and hybrid discrete-continuum models. The rearrangement proceeds by a water-assisted asynchronous concerted mechanism. 

T. Vreven, B. Mennucci, C. O. da Silva, K. Morokuma and J. Tomasi, The ONIOM-PCM method Combining the hybrid molecular orbital method and the polarizable continuum model for solvation. Application to the geometry and properties of a merocyanine in solution, J. Chem. Phys., 115 (2001) 62-72. 

Hybrid simulation Molecular-continuum simulation Multiscale modeling... 

It is also possible to treat solvent explicitly, that is, to include one or several solvent molecules in the QM description of the system. As most solvents are fairly small molecules, this might seem like an affordable, desirable, and more accurate approach that could be combined with continuum models in a scheme where the first shell of solvent is described explicitly and the second shell is treated with a continuum. Hybrid techniques in which one part of a system is treated with one level of theory and another part (e.g., the solvent) with another, lower, level of theory such as molecular mechanics (in which case one has a QM/MM method) also seem well suited to describe solutions. Indeed, this type of approach can be very useful in many cases. Treating at least some solvent explicitly is of course necessary when the solvent participates directly in a reaction, by proton transfer or by bonding to a metal, for example. 

This section describes systems which are at the border of what has been defined as being the scope of this review and therefore does not pretend to be comprehensive. Indeed, if there is a wealth of strictly inorganic materials and glasses into which NIR-crnitting lanthanide ions have been incorporated and which are clearly excluded from the review, there also exist a continuum between these materials and molecular entities, for instance coordination polymers and clusters which have been described in the two preceding sections. In continuity with these concepts are micro- and mesoporous materials into which lanthanide salts or complexes can be incorporated or attached. These are essentially zeolites and sol-gel materials, either conventional or the so-called inorganic-organic hybrids, as well as polymers. 

The fourth chapter presents extensions and generalizations of continuum models to classical molecular dynamics simulations, to layered and to hybrid methods as well as to... 

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