Metallic reflection in a crystalline polymethinium dye and in crystalline TCNQ: Theory of the damping

Abstract

Metallic reflection occurs in molecular crystals when a stopping band associated with a strong molecular electronic transition emerges. Variations in reflectivity over the band are studied here theoretically for two cases—1,5-bis (dimethylamino)pentamethinium perchlorate (BDP) and tetracyanoquinodimethane (TCNQ). The variations are described by a frequency dependent damping term Γ (ω) in the expression for the polarizability. For the case of one molecule per unit cell (BDP), the observed reflection band shape can be matched using a theoretical expression iΓ (ω) = (γ2/N) Σk 1/(ω−ωk−Δ), where γ is a molecular vibrational relaxation constant and Δ is the frequency of a single active vibration. The variation of ωk with k is approximated by the long-wave method. For the case of two molecules per unit cell (TCNQ) a more complicated expression is obtained which predicts a reflection spectrum richer in structure than in the case of one molecule per unit cell. The number and location of features in the theoretical spectrum match those in the observed spectrum reasonably well.