Complex Refractive Index and a Two-Band Model in the Theory of Hypochromism

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Abstract
A calculation of the complex refractive index of an arbitrary thermally agitated fluid is adumbrated. The theory starts from a 3‐space Dyson‐type equation comparable with a 4‐space equation recently discussed in the literature in the context of the hypochromism of biological materials. It is shown that the refractive index contains a local field “self‐energy” term which involves multiple‐scattering processes of all orders. Poor convergence close to resonance means that the high‐order multiple‐scattering processes are important there. It is shown that the complexity of such processes does not necessarily prevent the proof of a sum rule for oscillator strengths. It is shown also that in the one case of a system of rigid macromolecules at infinite dilution the multiple‐scattering terms can even be explicitly summed to a single‐scattering expression. The implications of this particular expression in the theory of hypochromism (in which it must necessarily have restricted validity) are contrasted with those consequent on the more general multiple‐scattering theory; but here, because of complexity, only the first‐order (single‐scattering) contributions to the general theory can be considered in detail. The contrast is explicitly exhibited in terms of a two‐band model. Although qualitative generalizations to an arbitrary number of bands are then easy, the choice of only two bands means that closed‐form (non‐perturbative) analytical expressions for band shifts, changes of oscillator strength, and other features of their interaction can be given. It is shown that a one‐band model considered previously is valid for small enough shifts or large enough band spacings, that a collective mechanism is possible in principle but scarcely compatible with the small shift and large hypochromism observed in DNA, that the band‐shifting term and therefore the band shifts can be considerably reduced or even eliminated in the single‐scattering model, and that this last contrasts strongly with the consequences of the rigid macromolecule (rodlike) model. It is argued that the single‐scattering model can exhibit features of the more correct multiple‐scattering theory which are eliminated in the rigid macromolecular model. The reduction of the shifting term may therefore be a significant feature of the small shift exhibited by the 2600‐Å band in DNA.

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