Cost function hybrid approach

Solvation effects have been incorporated into the calculations of anionic proton transfer potentials in a number of ways. The simplest is the microsolvation model where a few solvent molecules are included to form a supermolecular system that is directly characterized by quantum mechanical calculations. This has the advantage of high accuracy, but is limited to small systems. Moreover, one must assume that a limited number of solvent molecules can adequately model a tme solution. A more realistic approach is to explicitly describe the inner solvation shell with quantum calculations and then treat the outer solvation sphere and bulk solvent as a continuum (infinite polarizable dielectric medium). In this way, the specific interactions can be treated by high-level calculations, but the effect of the bulk solvent and its dielectric is not neglected. An ej tension of this approach is to characterize the reaction partners by quantum mechanics and then treat the solvent with a molecular mechanics approach (hybrid quantum mechanics/molecular mechanics QM/MM). The low-cost of the molecular mechanics treatment allows the solvent to be involved in molecular dynamics simulations and consequently free energies can be calculated. In more recent work, solvent also has been treated with a frozen or constrained density functional theory approach. ... 

In Table 12-5 we compare the binding energies computed using several hybrid functionals and basis sets, attempting to approach the basis set limit for each functional in a systematic (but not necessarily cost effective) way. At first we note the reasonable performance of all functionals. The converged results, however, indicate a slight tendency to underestimate the experimental value by about 1-2 kcal/mol. This trend is slightly more emphasized for... 

A variant of the combined QM/MM approach introduces a hybrid description of the solute. The main motivation for the introduction of this additional approximation lies in computational costs. Combined QM/MM calculations are quite costly, even when all the possible simplifications are introduced in the QM part and in the MM interaction potentials. On the other hand, QM formulation is more reliable than an empirical potential function to describe chemical reactions which involve bond-formation and disruption processes. To temperate contrasting factors, i.e. the need for a QM description and the computational costs, one may resort to the well established fact that, in chemical reactions, the quantum bond-breaking and bond-forming processes are limited to a restricted portion of the molecular system, with the remainder playing an auxiliary role. Hence, it may be convenient to resort to hybrid descriptions, where the active part of the molecule is described at the QM level and the remainder via MM potentials. 

MD simulations require the description of the interactions between the particles (potential function, or a force field) of a molecular system [27]. The potential function can be defined on various levels. The most conunonly adopted potential functions in chemistry and biology are based on molecular mechanics (MM), with a classical treatment of particle-particle interactions. With well-chosen parameter sets, these potential functions can reproduce structural and conformational changes in systems, except chemical reactions. The analytic forms of the potential functions, which involve low computational cost, make it possible for MD simulations to include a huge number of atoms. When potentials based on quantum mechanics (QM) are adopted, MD simulations can give finer levels of detail, such as chemical reactions and electronic structures, but expensive computational costs are involved simultaneously. As a compromise, hybrid QM/MM approaches are... 

It is reported that hybrid systems face stiff competition from direct-compounded, long-fiber polypropylene RPs in semi-structural load-bearing automotive uses. All-plastic RPs have greater potential for weight and cost reduction than do hybrids, while both approaches increase parts consolidation and foster functional integration. 

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