Hybrid molecular-continuum modeling

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. 

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. 

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. 

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. 

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... 

An alternative to the continuum model is to model the protein electrostatic field directly. This is normally achieved by carrying out a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment in which the active site model is treated with DFT while the rest of the protein is modelled via classical molecular mechanics (MM) [44]. The MM charges then implicitly define the dielectric inside the protein. In either event, it appears that excessive charges are to be avoided. That is, the quantum mechanical part of the model system will normally not have an overall charge greater in magnitude than one. 

Hybrid simulation Molecular-continuum simulation Multiscale modeling... 

We obtained the atomic structure from molecular dynamics for the CNT molecule (not shown), DNA molecule (not shown) as well as for the hybrid (Fig. 7.4). We performed electronic structure calculations in vacuum as well as in solvent conditions. For the solvent conditions, we also tested an alternative method, the PCM method (Polarizable Continuum Model) [54], which models the solvent as a... 

In essence, CPMD is a fairly typical example of the hierar-chy-of-models approach in which the electrons are treated quantum-mechanically as a massless fluid while nuclei are described as a set of classical particles. A wide scope for the application of hybrid simulations is provided by problems in polymer science. There are hybrid methods coupling a classical molecular-dynamics model with an elastic continuum modd, " RISM theory," " " and so on. The... 

A new molecular simulation technique is developed to solve the perturbation equations for a multicomponent, isothermal stured-tank adsorber under equilibrium controlled conditions. The method is a hybrid between die Gibbs ensemble and Grand Canonical Monte Carlo methods, coupled to macroscopic material balances. The bulk and adsorbed phases are simulated as two separate boxes, but the former is not actually modelled. To the best of our knowledge, this is the first attempt to predict the macroscopic behavior of an adsorption process from knowledge of the intermolecular forces by combining atomistic and continuum modelling into a single computational tool. 

Another class of spatial multi-scale methods concerns the quantum chemistry community where efforts have been focussed on the combination of quantum mechanics (QM) methods with continuum electrostatic theories in order to realistically represent the solvation free energy in a polar environment. These methods have been refined over the years and can now give a reasonable description of solvation properties of an isotropic and homogeneous medium. However, these continuum models are not appropriate to represent the electrostatic and steric interactions of the structured environment with the active site. This is particularly true in the descriptions of complex systems like enzymes or catalysts. An appropriate description of such systems has been developed using a hybrid quantum mechanical/molecular mechanical (QM/MM) approaches where the QM methods are used to describe the active site where chemical reactions or electronic excitations occur, and MM methods are employed to capture the effect of the environment on the active site. 

In the next section we will discuss the approach we have developed for obtaining the molecular Hartree-Fock continuum orbitals. We will discuss how our approach is based on the Schwinger variational method and how in its present form it can be viewed as a hybrid method that uses both the basis-set expansion techniques of quantum chemistry and the numerical single-center expansion techniques of atomic collision physics. We will then discuss the results of applications of this approach to study shape resonances in the photolonlzatlon of several molecules, e.g., N2, CO, CO2, C2H2, and C2N2. These results will also be compared with available experimental data and with the results of studies of these same systems by different methods and models. 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

It is likely, in the interim, while we await models from the molecular modeling perspective for the more difficult complex fluids, that the most success in predicting fluid mechanics results for non-Newtonian fluids will come from a hybrid approach combining some elements of both continuum mechanics and molecular modeling to produce relatively simple empirical models. There is a great deal of current research focused on all aspects of constitutive model development on numerical analysis of flow solutions based on these models and on experimental studies of many flows. There are a number of books and references available, but this is a complicated field that really requires a textbook/class of its own. At this point, it is time to return from our little sojourn into the land of complex fluids and come back to the principle subject of Newtonian fluids. 

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