Optical oscillator strengths and excitation energies in solids, liquids, and molecules

Abstract

An examination of average dipole coordinate matrix elements and electronic excitation energies in over 140 solids, liquids, and molecules reveals simple trends related to polarity, metallicity, ionicity, anion–anion ’’contact’’, cation core hybridization, and disorder. These results point to the key roles played by metallicity and polarity in crystalline solids as expressed by the empirical relationship ?2=fdZa/30.16, where 30.16 eV Å is a fundamental constant given by e/6ε0, ? is the dimensionless coordinate matrix element introduced by Harrison and Pantelides, d is the bond length in Å, Za is the formal chemical valency of the anion, and f is a coefficient associated with first-neighbor and second-neighbor delocalization, i.e., f=4.8±0.3 eV in ’’covalent’’ crystals, f=3.0±0.2 eV in ’’ionic’’ crystals, and f=3.8±0.2 eV in ’’anion-contact’’ crystals. The latter classification includes a variety of materials with close-spaced anions such as LiF, MgS, several rutile-structure compounds, and CdI2. Wurtzite-structure chalcogenides form a transitional group between large ’’ionic’’ and ’’covalent’’ classes. Direct contributions to ?2 from valencelike d10 and s2 ’’cores’’ are evident in some cases (e.g., CuCl, TlBr, PbTe, BiI3) and can be accounted for simply by including these ’’cores’’ in the valence electron count. Such direct effects are not observed, for example, in the Zn or Cd salts. Metallicity trends (described by d) and polarity trends (described by Za) are absent in liquids and molecules, and oscillator strengths (f) are considerably larger than observed in solids although matrix elements are comparable. The primary excitation energy results relate both to an approximate power law dependence on bond length of the form E0∼d−s, where 2<s<3 and to a substantial reduction in E0 for materials with valencelike d10 or s2 cation ’’cores’’. In most molecules the average excitation energy E0 falls close to the first ionization potential. Finally, the implications of these results on the dielectric models of Phillips and Harrison and on the nature of the chemical bond are discussed.