Semiconductor Band Structure, Symmetry, and Molecular Interface Hybridization for the Chemist

Merging molecular bonding concepts with semiconductor- and materials-based concepts of band structure is challenging due to the mutually exclusive historical development and notations used in those respective fields: symmetry adapted linear combinations (SALCs) and Mulliken terms for molecules, versus k space and Bloch sums for materials. This lack of commonality brings the issue of hybridization (aka electronic coupling) between molecules and materials to the forefront in many aspects of modern chemical research─including nanocrystal properties, solar energy conversion, and molecular computing. It is thus critical to establish a holistic approach to hybridizing orbital (molecule) and plane-wave (semiconductor/material) systems to better describe symmetry-based molecule|material bonding and the corresponding symmetry-adapted molecular orbital (MO) diagrams. Such a unified approach would enable the construction of testable hypotheses about the role of symmetry and electronic structure in determining the extent of electronic coupling between molecular orbitals and semiconductor band structure. This Perspective provides an analysis and compendium of "translations" between the physics and chemistry language of group theory. In this vein, this approach describes the symmetries─and corresponding point groups─that occur in k space along the available descent in symmetry pathways (k space vectors). As a result, chemists may arrive at a more intuitive understanding of the band symmetries of semiconductors, as well as insights into the corresponding algebraic formulations. This analysis can ultimately generate MO diagrams for hybrid molecule|material systems. Lastly, an Outlook provides some context to the application of this analysis to modern problems at the interface of molecular and materials chemistry.