Distribution function liquid structure simulation

Other workers have explored the structure in liquid water using approaches based upon more general descriptions such as the spatial or pair distribution functions. In their simulation study Laztiridis and Karplus [12] split the full pair distribution function into radial and angular contributions. They then... 

A very important aspect of both these methods is the means to obtain radial distribution functions. Radial distribution functions are the best description of liquid structure at the molecular level. This is because they reflect the statistical nature of liquids. Radial distribution functions also provide the interface between these simulations and statistical mechanics. 

Once the structures of liquid and amorphous InP have been generated using MD simulations, various properties of these materials can be explored. To give just one example, the structure of disordered materials is often characterized using the radial distribution function ... 

In short, our S-MC/QM methodology uses structures generated by MC simulation to perform QM supermolecular calculations of the solute and all the solvent molecules up to a certain solvation shell. As the wave-function is properly anti-symmetrized over the entire system, CIS calculations include the dispersive interaction[35]. The solvation shells are obtained from the MC simulation using the radial distribution function. This has been used to treat solvatochromic shifts of several systems, such as benzene in CCI4, cyclohexane, water and liquid benzene[29, 37] formaldehyde in water(28, 38] pyrimidine in water and in CCl4(31] acetone in water[39] methyl-acetamide in water[40] etc. 

Considerable evidence exits of the survival of Zintl ions in the liquid alloy. Neutron diffraction measurements [5], as well as molecular dynamics simulations [6, 7], give structure factors and radial distribution functions in agreement with the existence of a superstructure which has many features in common with a disordered network of tetrahedra. Resistivity plots against Pb concentration [8] show sharp maxima at 50% Pb in K-Pb, Rb-Pb and Cs-Pb. However, for Li-Pb and Na-Pb the maximum occurs at 20% Pb, and an additional shoulder appears at 50% Pb for Na-Pb. This means that Zintl ion formation is a well-established process in the K, Rb and Cs cases, whereas in the Li-Pb liquid alloy only Li4Pb units (octet complex) seem to be formed. The Na-Pb alloy is then a transition case, showing coexistence of Na4Pb clusters and (Pb4)4- ions and the predominance of each one of them near the appropiate stoichiometric composition. Measurements of other physical properties like density, specific heat, and thermodynamic stability show similar features (peaks) as a function of composition, and support also the change of stoichiometry from the octet complex to the Zintl clusters between Li-Pb and K-Pb [8]. 

The radial distribution function plays an important role in the study of liquid systems. In the first place, g(r) is a physical quantity that can be determined experimentally by a number of techniques, for instance X-ray and neutron scattering (for atomic and molecular fluids), light scattering and imaging techniques (in the case of colloidal liquids and other complex fluids). Second, g(r) can also be determined from theoretical approximations and from computer simulations if the pair interparticle potential is known. Third, from the knowledge of g(r) and of the interparticle interactions, the thermodynamic properties of the system can be obtained. These three aspects are discussed in more detail in the following sections. In addition, let us mention that the static structure is also important in determining physical quantities such as the dynamic an other transport properties. Some theoretical approaches for those quantities use as an input precisely this structural information of the system [15-17,30,31]. 

Data available from a computer simulation is not similarly limited, as a complete description of the system, the positions and orientations of all its molecules, is immediately available therefore the full molecular pair distribution function should, in principle, be obtainable. Still the practical considerations of accumulating and presenting this 6-dimensional function have made it virtually inaccessible, despite its obvious importance. Computer simulation studies of molecular liquids and solutions have then traditionally relied almost exclusively upon radial distribution functions to provide structural information. 

There are, of course, many different kinds of approximations involved, when deriving explicit expressions from a theoretical model. Many of these are, of course, also required for deriving results from the MD simulation. However, the MD simulations depends only on the most fundamental and highly reliable approximations, which need no examination. The remaining approximations, which the MD simulation can examine, are the ones concerning the structure and dynamics of the liquid. In some sense, these are system specific and therefore very difficult to treat. The approximations involve assumptions of the form of time correlation functions and radial distribution functions, or whether different motions are correlated or not. 

Of course, dielectric properties are also closely related to structural quantities [69-71]. Structure in liquids, namely pair distribution functions, g r) s, have been widely studied in simulations and compared to experimental data, also to validate the description of interaction forces adopted. 

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