Crystal classical Coulomb

Many-body problems wnth RT potentials are notoriously difficult. It is well known that the Coulomb potential falls off so slowly with distance that mathematical difficulties can arise. The 4-k dependence of the integration volume element, combined with the RT dependence of the potential, produce ill-defined interaction integrals unless attractive and repulsive mteractions are properly combined. The classical or quantum treatment of ionic melts [17], many-body gravitational dynamics [18] and Madelung sums [19] for ionic crystals are all plagued by such difficulties. 

Classical electrostatic modeling based on the Coulomb equation demonstrated that the model system chosen could account for as much as 85% of the effect of the protein electric field on the reactants. Several preliminary computations were, moreover, required to establish the correct H-bond pattern of the catalytic water molecule (WAT in Fig. 2.6). Actually, in the crystal structure of Cdc42-GAP complex [60] the resolution of 2.10 A did not enable determination of the positions of the hydrogen atoms. Thus, in principle, the catalytic water molecule could establish several different H-bond patterns with the amino acids of the protein-active site. Both classical and quantum mechanical calculations showed that WAT, in its minimum-energy conformation,... 

Present-day diffraction facilities provide easy access to very low-temperature data collection and hence to an accurate determination of electron densities in crystals. Application of standard theorems of classical physics then provides an evaluation of the Coulombic interaction energies in crystal lattices [27]. These calculations are parameter-less and hence are as accurate as the electron density is. Moreover, for highly polar compounds, typically aminoacid zwitterions and the like, a fortunate coincidence cancels out all other attractive and repulsive contributions, and the Coulombic term almost coincides with the total interaction energy. 

The quantum mechanical approach cannot be used for the calculation of complete lattice energies of organic crystals, because of intrinsic limitations in the treatment of correlation energies. The classical approach is widely applicable, but is entirely parametric and does not adequately represent the implied physics. An intermediate approach, which allows a breakdown of the total intermolecular cohesion energy into recognizable coulombic, polarization, dispersion and repulsion contributions, and is based on numerical integrations over molecular electron densities, is called semi-dassical density sums (SCDS) or more briefly Pixel method. [12-14]... 

The absence of crystal field splitting and the shielding of the / orbitals makes classical molecular dynamics (MD) simulations feasible. Hence, for solvents without covalent bonding like water, ion-solvent forces can be well represented by simple Coulomb and van der Waals terms. The polarization of water molecules in the first coordination shell due to the strong electric field of the trivalent ions has... 

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