Bound pairs

While nonbonded atom pairs will typically not come within 1A of each other, it is possible for covalently bound pairs, either directly bounds, as in 1-2 pairs, or at the vertices of an angle, as in 1-3 pairs. Accordingly it may be considered desirable to omit the 1-2 and 1-3 dipole-dipole interactions as is commonly performed on additive force fields for the Coulombic and van der Waals terms. However, it has been shown that inclusion of the 1-2 and 1-3 dipole-dipole interactions is required to achieve anistropic molecular polarizabilites when using isotropic atomic polariz-abilites [50], For example, in a Drude model of benzene in which isotropic polarization was included on the carbons only inclusion of the 1-2 and 1-3 dipole-dipole interactions along with the appropriate damping of those interactions allowed for reproduction of the anisotropic molecular polarizability of the molecule [64], Thus, it may be considered desirable to include these short range interactions in a polarizable force field. 

F(J ) is the pair interaction potential, T the temperature and k the Boltzmann factor. The integral to the right is over the volume v of the container it is often referred to as the configuration integral, Q2(T). For large enough volumes, the integral may be replaced by the volume. With the help of Hill s effective potentials, Eq. 2.28, this expression may be written as a sum of free and bound pair state sums, respectively [183, 184],... 

Hill s effective potentials. The division of phase space into free and bound pairs is possible by introducing Hill s effective potentials [183, 184],... 

This substitution has permitted us to write Z2 as a sum of free and bound pair partition functions, Eq. 2.17. 

Because of the existence of two-particle bound states the three-particle scattering states split into channels that means, we have to take into account scattering processes between free particles and bound pairs. To study the effect of composite particle scattering processes, we pay atten-... 

VK is the interaction in the channel /q, which describes the interaction between the free particle and a bound pair. Thus we have... 

This term describes the inelastic scattering of a bound pair (b2c3) with a free particle ax,... 

This collision integral has the shape of the usual Boltzmann collision integral for the scattering of a bound pair and a free particle and corresponds to the process... 

This equation describes the change of the density na as a result of ionization and recombination of bound pairs, the density of which is denoted by n(12). For this reason we call a the ionization coefficient, given by (na = nb = nc)... 

The quantity (3.115) may be interpreted as effective interaction between the free particle a and the bound pair (be). The expression (3.116) characterizes the static charge distribution in the atom (be). 

The summation over the species in (3.67) yields in the case that only two bound pairs (e, p) are taken into account for the relevant matrix element of the interaction ... 

In Section IV, the correlation function of the fluctuations of the pair density was determined under the assumption of the weakening of the initial correlation between the pairs. This assumption is different from the total weakening of any initial correlation, because, in the bound-state case, we have correlations between the elementary particles of one bound pair. 

Since TEP is a measure of entropy per carrier, the TEP in the two-fluid state can be given by a combination of two contributions from the independent normal carriers (S ) and the bound pairs (Sp) [2] as... 

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