Jones expression, Lennard

A key to both methods is the force field that is used,65 or more precisely, the inter- and possibly intramolecular potentials, from which can be obtained the forces acting upon the particles and the total energy of the system. An elementary level is to take only solute-solvent intermolecular interactions into account. These are typically viewed as being electrostatic and dispersion/exchange-repulsion (sometimes denoted van der Waals) they are represented by Coulombic and (frequently) Lennard-Jones expressions ... 

The symbols have their usual significan(%. For the sake of (X)mpleteness, the Lennard-Jones expression for the vdW bond foiee (X>nstant will be given ... 

During the simulations, the SBUs are treated as rigid bodies. The rule that controls the possible assembly of D4R units is a force field with some Lennard-Jones expressions that essentially favor the attraction between ligand atoms. In other words, this force field favors the formation of L - L sticky-atom pairs and allows two D4R units to assemble... 

One has to include the repulsive contribution to obtain the interaction potential. In the Lennard-Jones expression, the attractive and repulsive contributions can be described by... 

When one adds the attractive van der Waals potential terms to the repulsive term, one obtains the Lennard-Jones expression for the intermolecular potential energy for a simple fluid such as an inert gas like argon. On the basis of the above, the Lennard-Jones potential function may be written... 

The Lennard-Jones expression may have some weak points in it but it gives good results when compared with the experimental lattice energies of non-polar solids. This may be due to the cancellation of a variety of erroneous factors. 

Water models can be conveniently divided into three types. In the simple interaction-site models each water molecule is maintained in a rigid geometry and the interaction between molecules is described using pairwise Coulombic and Lennard-Jones expressions. Flexible models permit internal changes in conformation of the molecule. Finally, models have been developed that explicitly include the effects of polarisation and many-body effects. 

The resultant of the attractive and repulsive van der Waals (vdW) energies between two atoms has the general shape shown in Figure 7. In the relevant distance regime this curve can be represented by several algebraic expressions the discussion here is in terms of the Lennard-Jones expression (equation 1) for atoms i and j separated by dy... 

The van der Waals energy represents the short-range energy component associated with atomic interactions. Electronic overlap as two atoms approach each other leads to repulsion (positive energy) and is often expressed as a function. An attractive force (negative energy) occurs with the fluctuations in electron density on adjacent atoms. This second contribution is referred to as the London dispersion interaction and is proportional to 1//. The most common function for the combined interactions is provided by the Lennard-Jones expression ... 

The Boltzmann factor depends on the positions of all atoms that interact with the penetrant. For a pairwise additive penetrant polymer force field, such as the Lennard-Jones expression... 

Uo is the energy of adsorption. It can be calculated from the Lennard-Jones expression of the potential energy of interaction of an adsorbate molecule in a pore ... 

The van der Waals Hamiltonian takes into account all non-electrostatic interactions and may be approximated by using Lennard-Jones expressions such as ... 

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