Chemical long-range contributions

Note that, due to their infinite-range character, pure Coulombic potentials can actually lead to significant bond non-additivity for any proposed separation into bonded and nonbonded units. This reflects the fact that classical electrostatics is oblivious to any perceived separation into chemical units, because all Coulombic pairings (whether in the same or separate units) make long-range contributions to the total interaction energy. 

In infinite periodic systems, an attractive alternative to the use of a cut-off distance is the Ewald sum technique, first described for chemical systems by York, Darden and Pedersen (1993). By using a reciprocal-space technique to evaluate long-range contributions, the total electrostatic interaction can be calculated to a pre-selected level of accuracy (i.e., the Ewald sum limit is exact) witli a scaling that, in tlie most favorable case (called Particle-mesh Ewald , or PME), is AlogA. Prior to the introduction of Ewald sums, the modeling of polyelectrolytes (e.g., DNA) was rarely successful because of the instabilities introduced... 

In infinite periodic systems, an attractive alternative to the use of a cut-off distance is the Ewald sum technique, first described for chemical systems by York, Darden and Pedersen (1993). By using a reciprocal-space technique to evaluate long-range contributions, the total... 

With the ion-dipole asymptotics (4.74) and (4.75), calculation of the solvation chemical potential from expression (4.A.17) requires analytical treatment of the long-range contributions. They appear in the terms (/r (r)) and h r)c (r) but cancel out in c (r) owing to the electroneutrality of the solvent molecule. On separating out the electrostatic terms, the integration can be performed merely over the supercell volume,... 

Because of long-range F—F coupling constants that contribute to the second-order nature of the system, the fluorine signals of 2,3,5,6-tetrafluoroaryl groups generally consist of complex multiplets. The chemical shifts of a few examples of such systems are given in Scheme 6.33. 

It is immediately apparent that because only differences in chemical potential between states can be measured, the intrinsic term will always disappear. It will be further assumed that long-range and short-range contributions to the solvation process may be separated out. Thus... 

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