Pair-additive potentials, application

The correlation functions provide an alternate route to the equilibrium properties of classical fluids. In particular, the two-particle correlation fimction of a system with a pairwise additive potential detemrines all of its themiodynamic properties. It also detemrines the compressibility of systems witir even more complex tliree-body and higher-order interactions. The pair correlation fiinctions are easier to approximate than the PFs to which they are related they can also be obtained, in principle, from x-ray or neutron diffraction experiments. This provides a useful perspective of fluid stmcture, and enables Hamiltonian models and approximations for the equilibrium stmcture of fluids and solutions to be tested by direct comparison with the experimentally detennined correlation fiinctions. We discuss the basic relations for the correlation fiinctions in the canonical and grand canonical ensembles before considering applications to model systems. 

In the vast majority of MD applications a further simplification is made by using effective pair-wise additive potentials for atomic interactions. In simulations which contain flexible molecules, it is common practice to add terms which represent chemical bonds, bond angles, improper torsions and dihedrals. Interactions between atoms of molecules are represented by effective pair-wise additive potentials. This empirical approach splits the total potential energy of the system into a bonded (inter-molecule) and non-bonded (intra-molecular) part. 

Oxidative additions can occur at all sorts of X-Y bonds, but they are most commonly seen at H-H (also H-Si, H-Sn, or other electropositive elements) and carbon-halogen bonds. In the oxidative addition of H2 to a metal, a d orbital containing a lone pair interacts with the cr orbital of Ik, lengthening and breaking the H-H cr bond. The two pairs of electrons from the metal and the II2 cr bond are used to form two new M-H bonds. C-H bonds can oxidatively add to metals in the same way, and this process, called C H bond activation, is of enormous current interest for its potential applications to petrochemical processing and green chemistry. Si-H, Si-Si, B-B, and other bonds between electropositive elements undergo oxidative addition, too. 

As a second example of the application of the functional derivatives, we show that the pair distribution function can be obtained as a functional derivative of the configurational partition function. For a system of N spherical particles, with pairwise additive potential, we write... 

The first example of the application of atomistic simulation to a materi-als-related area is probably the work of Vineyard and co-workers. They used classical trajectories to model damage induced in a solid by bombardment with ions having hyperthermal kinetic energies. These calculations, which were done at about the same time as Rahman s initial studies on liquids, provided important data related to damage depth as well as new insights into many-body collisions in solids. The potentials used were continuous pair-additive interactions similar to those employed in Rahman s simulations. 

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