Continuum methods liquids

This mention of a family of solvents with particular physical properties prompt us to remark that there are other solvents with special physical quantities requiring some modifications in the methodological formulation of basic PCM. We cite, among others, liquid crystals in which the electric permittivity has an intrinsic tensorial character, and ionic solutions. Both solvents are included in the IEF formulation of the continuum method [20] which is the standard PCM version. 

E. Cances and B. Mennucci, New applications of integral equations methods for solvation continuum methods Ionic solutions and liquid crystals, J. Mater. Chem., 23 (1998) 309-326. 

The combination of all the points reported above seems to indicate versatile and efficient ab initio procedures as the best choice. However, there are other considerations to be added. Both continuum and discrete approaches suffer from limitations due to the separation of the whole liquid system into two parts, i.e. the primary part, or solute, and the secondary larger part, the solvent. These limitations cannot be eliminated until more holistic methods will be fully developed. We have already discussed some problems related to the shape of the cavity, which is the key point of this separation in continuum methods. We would like to remark that discrete methods suffer from similar problems of definition a tiny change in the non-boded interaction parameters in the solute-solvent interaction potential corresponds to a not so small change in the cavity shape. 

ZoandaAy lubAd.catd.on is a familiar term in the vocabulary of the tribologist. In the general concept of the boundary lubricated condition, the lubricant film between the two surfaces is no longer a liquid layer instead the surfaces are separated by films of only molecular dimensions. Friction is influenced by the nature of the underlying surface and by the chemical constitution of the lubricant films. This view of lubricating action at the solid surface was introduced by Sir W. B. Hardy [1] as an extension of Osborne Reynolds concept that hydrodynamic action within the liquid film is a process treated by continuum methods which are not applicable at the discontinuity or "boundary" between liquid and solid. 

Simulations can give more details than continuum methods, which exploit a simplified and averaged model of the medium. Among the simulation results we quote the recognition that small cations, exhibiting strong interactions with water molecules, tend to keep bound the first solvation layer when forced to pass from water to another solvent. Analogous effects are under examination for neutral polar solutes at water/liquid interfaces in case... 

For the reasons given above, a number of authors [23-28] have applied MD to shock wave studies in an effort to obtain details of the various shock compression processes that are not easily available from the conventional continuum method. We have carried out calculations of the shock compression of one-, two- and three-dimensional systems in both solid and liquid phases [29,30], using essentially the same model as in Fig. 1. Here I shall first summarize the general features of the shock profile from our studies, then I shall discuss one representative case, with special reference to the thermal relaxation problem, as an illustration of some of the general results. 

As a preliminary step, we consider the dynamics of the macromolecular coil moving in the flow of a viscous liquid. The bead-spring model of a macromolecule is usually used to investigate large-scale or low-frequency dynamics of a macromolecular coil, while molecules of solvent are considered to constitute a continuum - viscous liquid. This is a mesoscopic approach to the dynamics of dilute solutions of polymers. There is no intention to collect all the available results and methods concerning the dynamics of a macromolecule in viscous liquid in this section. They can be found elsewhere [9,29]. We need to consider the results for dilute solutions mainly as a background to the discussion of the dynamics of a macromolecule in very concentrated solutions and melts of polymers. 

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. 

The QM/MM method, and the polarizable continuum method as well, are usually considered as prototypical examples of the so-called multi-scale approaches. They combine two different description levels for the chemical system in both cases, a quantum part interacts with a classical part. Indeed, the QM/MM method can easily be extended to multi-scale schemes that include more than two description levels. Examples of three level schemes are the QM/MM/Continuum [47] and QM/QM7 MM approaches [48, 49]. In the later case, the system is divided into two QM parts, which may be described with the same or different methods, and a classical MM part. Dielectric continuum models for liquid interfaces are already available [43,50, 51] and a QM/MM/Continuum partition could be imagined in this case too, for instance to describe a solute-solvent cluster interacting with a polarizable dielectric medium. Here, however, we will focus on the QM/QM /MM partition. There is not a general scheme for this kind of approach and different algorithms can be employed to describe the interaction between subsystems. The main issue is the calculation of the interaction between two quantum subsystems that are described at QM (possibly different) theoretical levels. 

The hybrid methods which combine quantum-mechanical (QM) and classical descriptions are surely one of the mostly well-suited strategies in this context. Two main families of hybrid methods can be defined according to the model used to describe the classical part of the system. Either continuum or atomistic formulations can be introduced where, in the first case, the classical subsystem is described as a dielectric medium while, in the second case, a Molecular Mechanics (MM) formulation is generally adopted. While QM/continuum methods have been largely and successfully applied to molecular solutes in liquid solutions [2-5], QM/MM formulations have been more often used in the field of structured (biological) environments [6-10] even if the study of chemical reaction dynamics in solution represents another important field of applications of the method [11, 12]. 

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

An interesting method for generation of a broad wavelength continuum with a time duration of some picoseconds has been deseribed by Busch et al. I61e) By focussing the intense mode locked laser beam from a frequency-doubled neodynium laser into various liquids (H2O, P2O, etc.) a light continuum can be generated which spans several thousand wave numbers and yet has a picosecond pulse duration. This enables absorption spectroscopy measurements to be made in the picosecond time scale. 

There are the further advantages that rotational lines can be studied and that fluorescent substances can be investigated by the inverse Raman effect. Benzene and other molecular liquids have been studied by this method by McQuillan and Stoicheff 232) jhe required continuum radiation was anti-Stokes emission produced by passing the laser beam in liquid toluene. 

Using as the background continuum the short-lived spontaneous fluorescence of rhodamine B or 6 G, McLaren and Stoicheff 233) developed this method further to obtain inverse Raman spectra over the range of frequency shifts 300-3500 cm" in liquids and solids in a time of 40 nsec The stimulating monochromatic radiation at 6940 A is provided by a giant-pulse ruby laser. A small part of the main laser beam is frequency-doubled in a KDP-crystal and serves to excite the rhodamine fluorescence, thus ensuring simultaneous irradiation of the sample by both beams. 

Much like the RISM method, the LD approach is intermediate between a continuum model and an explicit model. In the limit of an infinite dipole density, the uniform continuum model is recovered, but with a density equivalent to, say, the density of water molecules in liquid water, some character of the explicit solvent is present as well, since the magnitude of the dipoles and their polarizability are chosen to mimic the particular solvent (Papazyan and Warshel 1997). Since the QM/MM interaction in this case is purely electrostatic, other non-bonded interaction terms must be included in order to compute, say, solvation free energies. When the same surface-tension approach as that used in many continuum models is adopted (Section 11.3.2), the resulting solvation free energies are as accurate as those from pure continuum models (Florian and Warshel 1997). Unlike atomistic models, however, the use of a fixed grid does not permit any real information about solvent structure to be obtained, and indeed the fixed grid introduces issues of how best to place the solute into the grid, where to draw the solute boundary, etc. These latter limitations have curtailed the application of the LD model. 

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