Equation 60 Dipole moment Dissociation

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

In spite of the fact that we have introduced the factor of exp(—) in equation (47), our analytical expression for the dipole moment does not have a qualitatively correct asymptotic behaviour for the bond lengths r,—> 00. The function does not converge to the dipole moment of the NH2 fragment if we remove a hydrogen atom. However, neither does it diverge The calculated dipole moment values at large r, are around 2-3 D depending on which dissociation path we use. Obviously, the asymptotic behaviour of the dipole moment is of no importance for the simulations carried out in the present work we are only concerned with molecular states well below dissociation. 

Table 5.1. Gaseous monomeric alkalimetal halides, MX(g) experimental electric dipole moments, /Tgi electric dipole moments predicted by the spherical ion model, /rel(calc) equihbiium bond distances, Rg vibrational wavenumbers, ox, dissociation energies at zero K, Dq reduced masses, /xm force constants,/r dissociation energies calculated from the spherical ion model according to equation (5.16a), Do(calc).

In principle, each of these can be used to formulate an exact theory of water. The choice of the particular level depends on the questions we want to ask about the system. If we are interested only in explaining some macroscopic thermodynamic properties of pure water, we might be satisfied with the choice of a relatively simple mixture model. If we want to compute the pair correlation function, then a rigid model for water molecules may be used. If we are also interested in the dielectric properties of pure water or the solvation of ions in water, we need to assign an electric dipole moment, or perhaps a quadrupole moment, to our rigid water molecule. If we want to allow for dissociation into ions, then clearly a rigid model for water molecules will not be appropriate, and we need to consider a lower level of treatment such as a collection of and 0 . Finally, if we are interested in the chemical reactivity of water molecules, we must start from the more elementary description of the system in terms of electrons and various nuclei and solve the Schrodinger equation for all the molecules involved in the chemical reaction. 

This equation works also quite well for the aromatics and the halogenated solvents, but it does not hold for the protic solvents. For these, the predicted values of the relative permittivities are orders of magnitude too large, revealing how poorly the associates are dissociated by the macroscopically attainable fields. A correlation similar to [12.1.5] has been proposed between the gas phase dipole moment and ti ... 

---