Long-range energy terms

The nonbonded interactions (long-range energy terms i.(... 

J. Perrin Introduction of the term delayed fluorescence Prediction of long-range energy transfer... 

The long-range energy arises from the first-order term... 

Table 4.4.1 lists typical values of dipole moments and polarizabilities of some simple molecules and the three coefficients of the r 6 term at 300 K. Except for H2O which is small and highly polar, the dispersion term dominates the long-range energy. The induction term is always the least significant. 

Justice and Justice [61] founded their theoretical description of ion-pairing on the Rasaiah and Friedman formulation of the concentration dependence of the activity coefficient. They took into account both a short-range interaction energy and a long-range coulombic term and a many-body interaction was considered. Their final expression is in agreement with that of Bjerrnm, since E = oo for r < fl and E = 0 for r>a, and the result [65] is comparable to Bjerrum s. 

In the simple case of noble gases, for example, dispersion energy will be the (attractive) dominant contribution at medium to long range, with terms that should depend on distance as, r" and see Table 2. Combining these with a repulsive term as above discussed the following form is obtained as appropriate for this kind of systems ... 

TD-DFT can also be used to get better approximations to the ground-state exchange-correlation energy based on frequency dependent response functions. For example, the long-range dispersion term between two well-separated systems can be obtained from the frequency dependent susceptibility of the two systems [228,229]. 

Various attempts have been made to include interactions between adsorbed species. As pointed out by Conway et al. [1984], the correct way to handle interactions is to include the appropriate pairwise or long-range interaction term into the partition function, which allows calculation of the Helmholtz free energy and the chemical potential. These quantities are a function of due to (a) the configurational term, as included in the Langmuir case and (b) the interaction or deviation from ideality. 

Forcefield methods, as noted above, can employ various functional forms to describe the energy of interatomic interactions. One of the most convenient forms IS (hat based on a nonbonded model in which all of the interatomic interactions are incorporated in the long-range eleclrostatics term and short-range van der Waals U lin ... 

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