Repulsion-dispersion parameters

Force fields for [BMIM][PF6] that explicitly treat aU hydrogens (all-atom models) were developed soon after this by Margulis et al. [14], and Morrow and Maginn [11], while Stassen and coworkers [83] published a force field for the [EMIM]+ and [BMIM]+ cations paired with tetrachloroaluminate and tetrafluoroborate anions. The force fields aU have similar functional forms, and parameters were again maiiily developed using literature force field parameters for similar compounds and ab initio calculations of single ions or ion pairs. In these and later studies, repulsion-dispersion parameters were generally adapted from those available from one of three popular force field databases (Amber [114], OPLS [118] and CHARMM [119]). For [BMIM][PF6], the added realism of the all-atom model enabled densities to be predicted vyithin 1% of the experimental value [11]. The first indications of restricted dynamics in these systems were also observed [11,14,15]. 

The interaction parameters for the water molecules were taken from nonempirical configuration interaction calculations for water dimers (41) that have been shown to give good agreement between experimental radial distribution functions and simulations at low sorbate densities. The potential terms for the water-ferrierite interaction consisted of repulsion, dispersion, and electrostatic terms. The first two of these terms are the components of the 6-12 Lennard-Jones function, and the electrostatic term accounts for long-range contributions and is evaluated by an Ewald summation. The... 

However, with the exception of these unusually sensitive structures, the accurate electrostatic model does very well in predicting the relative orientation in hydrogen bonding and polar molecules, despite the crudeness of the repulsion-dispersion potential. Attempts to improve the predictions by optimizing the repulsion potential parameters have not yet been successful, as... 

A slightly different empirical scheme has also been used to look at cation locations. The work of No and co-workers has been concerned with setting up a force field based upon electrostatic, repulsion, dispersion, polarisation and harmonic bond stretching energy contributions , which can be used to assess interactions within zeolites. In setting up this force field, the parameters have been optimised for Na-zeolite A, however, this has been extended to in-... 

Electrostatic interactions can be most simply modeled as the Coulomb interaction between partial atomic charges, while the repulsion-dispersion part is usually described by a Lennard-Jones or, more accurately, an exp-6 form, each of which contains parameters that must be fixed. High-quality empirically fitted parameter sets have been developed, where the atom-atom interactions are parameterized to reproduce the structures, sublimation enthalpies and, sometimes, further observable properties of organic molecular crystals [73,74]. Their use has been very effective in CSP. Nonempirical approaches to fitting intermolecular force fields, where the parameters are derived from quantum mechanical calculations, have occasionally been applied for CSP [75-78], but these are currently limited to small molecules, so currently lack relevance for typical pharmaceutical molecules. 

Born-Mayer repulsion. The parameter y was fixed to agree with the findings of Tosi on the alkali halides. The three remaining parameters were adjusted so that theory and experiment would agree for the crystal energy and its first two volume derivatives, at zero temperature and pressure. This model gives a good account of the phonon dispersion curves of bcc sodium, and of the thermodynamic properties of sodium up to room temperature. ... 

Once the models for the charge distributions are in hand, the electrostatic interaction is computed as the interaction between the sets of point charges or distributed nuiltipoles, and added to an atom-atom, exp-6 fonn that represents the repulsion and dispersion interactions. Different exp-6 parameters, often from [140. 

The parameters a and b are characteristic of the substance, and represent corrections to the ideal gas law dne to the attractive (dispersion) interactions between the atoms and the volnme they occupy dne to their repulsive cores. We will discnss van der Waals equation in some detail as a typical example of a mean-field theory. 

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