## 1 Introduction  
A simple way to understand the origin of various optical effects in many substances is based on an atom-dipole interaction model. The atoms in a molecule are regarded as isotropic particles, which interact by way of the dipole moments induced in them by an external field. In a diatomic molecule AB whose atoms have isotropic polarizabilities \(\alpha_{\rm A}\) and \(\alpha_{\rm B}\), respectively, the additive model of polarizability allows calculating the isotropic molecular polarizability \(\alpha_{\rm mol}\!=\alpha_{\rm A}+\alpha_{\rm B}\). The diagonal form of \(\alpha_{\rm mol}\) has only one component:  
\[\alpha_{\rm mol}=\!\left[ \begin{array}{cccc}\alpha_{\rm A}+\alpha_{\rm B}&0& 0\\ 0&\alpha_{\rm A}+\alpha_{\rm B}&0\\ 0&0&\alpha_{\rm A}+\alpha_{\rm B}\end{array} \right] \tag{1}\]  
In the interacting induced-dipole polarization model, the molecular polarizability of AB can be placed in a simple and explicit form. The diagonal form of anisotropic \(\alpha_{\rm mol}\) has two distinct components \(\alpha_{\parallel}\) and \(\alpha_{\perp}\), parallel and perpendicular, respectively, to the bond axis. [PERSON]'s equations for this case follow [1, 2, 3]:  
\[\alpha_{\parallel}=\!\frac{\alpha_{\rm A}+\alpha_{\rm B}+4\alpha_{\rm A} \alpha_{\rm B}/r^{3}}{1-4\alpha_{\rm A}\alpha_{\rm B}/r^{6}} \tag{2}\]  
\[\alpha_{\perp}=\frac{\alpha_{\rm A}+\alpha_{\rm B}-2\alpha_{\rm A}\alpha_{\rm B }/r^{3}}{1-\alpha_{\rm A}\alpha_{\rm B}/r^{6}} \tag{3}\]  
\[\alpha_{\rm mol}=\!\left[ \begin{array}{cccc}\alpha_{\perp}&0&0\\ 0&\alpha_{\perp}&0\\ 0&0&\alpha_{\parallel}\end{array} \right] \tag{4}\]  
The mean polarizability \(\overline{\alpha}\) and anisotropy \(\delta\)are defined by:  
\[\overline{\alpha}=\big{(}\alpha_{\parallel}+2\alpha_{\perp}\big{)}3 \tag{5}\]  
\[\delta=\big{(}\alpha_{\parallel}-\alpha_{\perp}\big{)}\overline{\alpha} \tag{6}\]  
As an example of the manner in which the molecular polarizability depends on the atom polarizabilities, the isotropic molecule methane (CH\({}_{4}\)) is considered [4]. Certain features of the dependence are illustrated by the surface in Figure 1. Additivity of atom polarizabilities would require that the surface be a plane, which is approximately true in the vicinity of the origin, where interactions are small. However, the experimental polarizability of CH\({}_{4}\) is 2.62A\({}^{3}\), which is reached in only regions of the surface where the influence of interactions is quite marked. Notice a curve of discontinuity along which the polarizability approaches \(\pm\infty\). The behaviour is seen in the polarizability surfaces of several molecules that have been similarly explored. Its origin for diatomic molecules can be seen in Equations (2) and (3), where the denominators vanish when \(\alpha_{\rm A}\alpha_{\rm B}\) approaches \(r^{6}\)/4 or \(r^{6}\), respectively. For this case the \(\alpha_{\rm A}\) and \(\alpha_{\rm B}\) are inversely related along the curve of discontinuity, which in the \(\alpha_{\rm H}\)-\(\alpha_{\rm C}\) plane follows the relation \(\alpha_{\rm H}\alpha_{\rm C}\!=\!0.193\)A\({}^{6}\), which is of the form expected for diatomic molecules, though the numerical constant is not predictable from Equations (2) or (3). The significance of a polarizability of \(\pm\infty\) is that the molecule is in a state of resonance and absorbs energy from the applied field, which occurs in spite of the fact that any absorption properties of the atoms are not introduced [4]. The behaviour of the model can be understood from its close relation to the classical system of \(N\) coupled oscillators, which likewise shows resonance under conditions other than the resonance conditions of the isolated oscillators [5]. The absorption properties [6-8] of some types of systems can be predicted from the point-dipole interaction approach used in the present report, but it seems doubtful that this could be done reliably for molecules with the model [7]; the neglect of electron exchange between atoms is probably serious.