The quantum geometry of the chemical bond

Electronic properties of materials depend both on band energies and quantum geometry of electronic states. We relate bonding indices to the quantum geometric tensor (QGT), showing how chemical bonding dictates the momentum-space texture of bands, bridging chemical and physical descriptions of solids. We show the QGT decomposed into the three center bond index, weighted by their oriented area. Resolving these contributions by orbital pair reveals the donor--acceptor character that distinguish ionic, covalent, hypervalent, and metavalent bonding. We identify the bonding pattern for topology in materials: noncollinear three center bonds, which are the source of Berry curvature in solids. Bond fluctuation can be directly linked to electromagnetic response by resolving their energy spectrum, opening a quantitative route towards the design of physical properties of materials from bonding motifs.