Charge-permanent dipole

B. Comparison of SACM and VTST for Anisotropic Charge-Permanent Dipole Systems... 

The final result for cap also allows for a rigorous determination of the thermal rigidity factors /ngjd(T). This is particularly illuminating when approximate models such as the pure oscillator model of Eqs. (22)-(24) are compared with the complete result. The charge-permanent dipole capture (i.e., a — -0), for 2, using Eqs. (25) and (26), would be characterized... 

It is easily shown that, in the classical limit, Eqs. (41) and (42) are consistent with the thermal capture rate constants for the oscillator model of charge-permanent dipole capture. The relevant part of the activated complex partition function, instead of Eq. (11), can be written as... 

As a second example we analyze the anisotropic charge-permanent dipole potential where SACM and PST differ from each other. Here, for demonstration, we only consider the low-energy perturbation and the high-energy harmonic oscillator limits. In the former limit, the adiabatic channel potential curve for the lowest channel j = m = 0 has the form... 

Figure 8.1 Plot of charge-induced dipole (solid line) and charge-permanent dipole (dotted line) interaction energy for a polarizability of cm and 1 Debye, respectively.

Coulombic Terms. Coulombie energy of interaetion arises from permanent dipoles within the molecule to be modeled, for example, the partial - - and — charges within a carbonyl group... 

The permanent dipole moment of an isolated molecule depends on the magnitude of the charge and on the distance separating the positive and negative charges. It is defined as... 

Now let us examine the molecular origin of Molecular polarity may be the result of either a permanent dipole moment p or an induced dipole moment ind here the latter arises from the distortion of the charge distribution in a molecule due to an electric field. We saw in Chap. 8 that each of these types of polarity are sources of intermolecular attraction. In the present discussion we assume that no permanent dipoles are present and note that the induced dipole moment is proportional to the net field strength at the molecule ... 

The and Oj terms always contribute, regardless of the specific electric charge distributions ia the adsorbate molecules, which is why they are called nonspecific. The third nonspecific Op term also always contributes, whether or not the adsorbate molecules have permanent dipoles or quadmpoles however, for adsorbent surfaces which are relatively nonpolar, the polarization energy Op is small. 

The dipoles are shown interacting directly as would be expected. Nevertheless, it must be emphasized that behind the dipole-dipole interactions will be dispersive interactions from the random charge fluctuations that continuously take place on both molecules. In the example given above, the net molecular interaction will be a combination of both dispersive interactions from the fluctuating random charges and polar interactions from forces between the two dipoles. Examples of substances that contain permanent dipoles and can exhibit polar interactions with other molecules are alcohols, esters, ethers, amines, amides, nitriles, etc. 

Let us first consider the case where a molecule has no net charge, but the spatial distribution of the positive and negative charges is such that a permanent dipole moment exists. Highly polar molecules such as water, HCI, HF, and NH are examples of such molecules. 

The neutral reactants possess permanent dipoles, the product is ionic, and the transition state must be intermediate in its charge separation, so an increase in solvent polarity should increase the rate. Except for selective solvation effects of the type cited in the preceding section, this qualitative prediction is correct. 

The type of conjugation is also reflected in the frontier orbital profile, the charge distribution, and the permanent dipole moments. The results of semiempirical calculations on l-methylpyridinium-3-olate (16), Malloapeltine (17), Trigollenine (18), and Homarine (19) are presented in Scheme 7. Characteristically for the class of conjugated mesomeric betaines, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are distributed over the entire molecule as examplifled for l-methylpyridinium-3-olate. It was shown that 90% of the... 

The symbols 5+ and 5- indicate polarity of the two ends or poles of the electrically neutral molecule. Such a polar molecule constitutes a permanent dipole, i.e., two equal and opposite charges (e) separated by a distance (d) in space. A quantitative measure of the polarity of a molecule is the dipole moment (p in Debye units), which is defined as the product of the charge (e in electrostatic units) and the distance (d in cm). 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

Dispersive forces are more difficult to describe. Although electric in nature, they result from charge fluctuations rather than permanent electrical charges on the molecule. Examples of purely dispersive interactions are the molecular forces that exist between saturated aliphatic hydrocarbon molecules. Saturated aliphatic hydrocarbons are not ionic, have no permanent dipoles and are not polarizable. Yet molecular forces between hydrocarbons are strong and consequently, n-heptane is not a gas, but a liquid that boils at 100°C. This is a result of the collective effect of all the dispersive interactions that hold the molecules together as a liquid. 

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