Short-range repulsive energies

When two or more molecular species involved in a separation are both adsorbed, selectivity effects become important because of interaction between the 2eobte and the adsorbate molecule. These interaction energies include dispersion and short-range repulsion energies (( ) and ( )j ), polarization energy (( )p), and components attributed to electrostatic interactions. 

Ionic bonds are formed by the transfer of electrons from an electropositive to an electronegative atom. The long-range coulombic attraction of these charged species for each other, together with a short-range repulsive energy component, results in the formation of an ionic bond at an equilibrium interatomic distance. 

In this equation rjkis a nonbonded interatomic distance between atoms j and k, q is the point electrostatic charge on an atom, and Aj Bj and are adjustable parameters that have been obtained from experimental measurements of unit cell dimensions, interatomic distances, and packing arrangements in crystal structures. Ajk represents the coefficient of ffie London dispersion attraction term between atoms j and k, while Bjk and Cjk are short-range repulsive energy terms. The summation is over all interatomic interactions (between all j atoms and all k atoms). For PAHs the terms in Eq. (1) represent forces between pairs of... 

The summations are over all atoms i and / with separations and C,y, and Pij are the adjustable parameters of the model. The interaction energy of the system as a whole is then the sum of the Coulombic energies, short-range repulsive energies, and the weakly attractive energy components for all constituents. As we shall see, the individual components are typically the atomic centers and the points representing the polarization centers of the system. The successes of the simple ionic models introduced by Born and coworkers have been well documented and cover a wide range of applications. 

Short-range repulsion A first improvement is related to the repulsive forces which become effective at short inter-ionic distances. In the original model, steric - or hard-core - repulsive forces prevent two ions i and J from coming closer than the sum of their ionic radii r,- and rj. The short-range repulsion energy is infinite if Rij < r, + ry, and zero otherwise, which may be written in the form ... 

Two additional terms are required to get the total energy E a coulomb repulsion energy between the ionic cores, which is equal to N Nq/R, and a short-range repulsion energy, already discussed in Bom s model. In numerical approaches which account for atomic orbital overlap, this latter... 

The short-range repulsion energy, written in a Lennard-Jones form, reads ... 

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