Drude molecules

We now introduce a second Drude molecule, identical to the first, with the positive charge also located on the z axis and an oscillating negative charge (Figure 4.33). When the two molecules are infinitely separated, they do not interact and the total ground-state energy of the system is... 

The force constant, k, is related to the polarisability of the molecule, a as follows. Suppose a single Drude molecule is exposed to an external electric field E. In the electric field, a force qE acts on each charge (in opposite directions as the charges are of opposite sign) This force causes the charges to separate and equilibrium is reached when the restoring force due to the stretching of the bond (kz) is equal to the electrostatic force qE = kz. This separation... 

Fig. 4, 33 The Drude model for dispersive interactions. (Figure adapted from Rigby M, E B Smith, W A Wakeham and G C Maitland 1986. The Forces Between Molecules. Oxford, Clarendon Press.)...

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. 

Thole s polarizability parameters were selected to optimize the molecular polarizabilities for a set of 16 molecules. The method was later expanded to fit 52 molecules [146], It must be emphasized that this electric-field damping method is totally independent of the polarization scheme used. For the Drude and fluctuating charge methods only /i(r) is required, whereas for methods based on induced dipoles both /i(r) and /2(r) are necessary. In the context of the induced dipole model other models were proposed since the formula of Thole does not provide enough attenuation. For example, in Ref. [152] the field is evaluated using... 

Drude first proposed that the rotatory power of a dissymmetric substance could be understood if its absorption of light involved the motion of a charged particle along a helical path within the molecule [8]. This type of motion would result in the simultaneous production of an electric dipole from the translatory motion and a magnetic dipole from the rotatory motion. The model requires that the electric and dipole moments have at least some components which are collinear with each other, or else stereospecific interaction with circularly polarized light would not be possible. 

Some applications of the method will be shown for the ternary salt trimethylammonium (TMA)-TCNQ-I. Tanner et al. [43] have obtained a best fit with a Drude-Lorentz dielectric function with a>p = 5290 cm-1, -y = 2560 cm"1, ec = 2.65, , is the frequency and T is the relaxation rate of the second oscillator. The average value of the frequency-dependent conductivity below 200 cm"1 should be 19 IS- cm"1. The energy gap of 0.10 to 0.14 eV, the effective quantity of electrons participating in the electric transport Ncfi = 0.67 per molecule, and the effective mass of the carriers m = 5.2 m were found from the plasma frequency. 

The analysis is carried out using the Drude equations this leads to a combination of the ellipsometric thickness and the refractive index Increment. These characteristics of the adsorbate cannot be unambiguously separated. Conversion of the refractive index increment into the composition of the adsorbate layer is usually done by assuming drt/dx to be the same as in a fluid of composition x for 0 not too high this is usually allowed, but problems may arise when the adsorbate differs substantially from the solution, for Instance because of alignment of adsorbed chain molecules. The result obtained is not unique, in the sense that different profiles may lead to the same pair of ellipsometric parameters. Therefore, normally totally adsorbed amounts are presented. For accurate measurements a good optical contrast between adsorbate and solution is mandatory. 

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