Calculated forbidden band gap in periodic protein models indicating them to be insulators

Abstract

THE idea of electron and hole transport between distant sites in biological macromolecules, especially in fibrous proteins¹ prompted quantum chemists to calculate the forbidden energy band gap in simple periodic protein models^2–7. Conductivity measurements of several proteins under various conditions indicated a band gap or activation energy (E in the expression for the conductivity σ = σ₀ exp(– E/2kT) as function of the temperature T) of the order of 3 eV (refs 8, 9), a value in agreement with the only theoretical energy band gap available at that time (ref. 2). Therefore, the intrinsic mechanism of semiconduction along hydrogen bridges seemed to be well established in 1960. Later, however, both experimentally^10–13 and theoretically the question arose whether the conduction mechanism is really intrinsic. The more, refined all-valence-electron quantum chemical calculations^5–7 indicated larger gaps (values in the range 6.1–16.7 eV were reported) than obtained in experiments. Most interestingly the calculation of Morokuma⁵ at complete-neglect-of-differential-overlap level showed that in a polyglycine chain the bandgap was not too sensitive to the changes of the chain's conformation: in conformers with appreciable H-bonding the gap found was slightly larger than in the β-sheet conformation. This latter finding pointed out the very small influence of H-bonds on the forbidden gap of periodic protein models. These semi-empirical calculation methods were designed for molecular purposes and there is still little known of their applicability to the calculation of the gap in crystals and polymers^14,19. Thus we describe here use of the more reliable non-empirical (‘ab initio’) crystal orbital method¹⁵ to calculate the band gap in a most simple polypeptide model β-polyglycine.