Natural bond orbital (NBO) analysis is a powerful analysis technique capable of generating intuitive chemical representations of otherwise complex quantum mechanical electronic structure results, yielding a localized "Lewis-like" description of bonding and reactivity. We generalize this algorithm to periodic systems, thus expanding the scope of NBO analysis to bulk materials and/or periodic surface models. We employ a projection scheme to further expand the algorithm's applicability to ubiquitous plane-wave density functional theory (PW DFT) calculations. We also present a variety of example applications: examining bulk bonding and surface reconstruction and elucidating fundamental aspects of heterogeneous catalysis-all derived from rigorous underlying PW DFT calculations.

A new tool to elucidate chemical bonding in bulk solids, surfaces and nanostructures has been developed. Solid State Adaptive Natural Density Partitioning (SSAdNDP) is a method to interpret chemical bonding in terms of classical lone pairs and two-center bonds, as well as multi-center delocalized bonds. Here we extend the domain of AdNDP to bulk materials and interfaces, yielding SSAdNDP. We demonstrate the versatility of the method by applying it to several systems featuring both localized and many-center chemical bonding, and varying in structural complexity: boron α-sheet, magnesium diboride and the Na8BaSn6 Zintl phase.

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Plane wave density functional theory (DFT) is a powerful tool for gaining accurate, atomic level insight into bulk and surface structures. Yet, the delocalized nature of the plane wave basis set hinders the application of many powerful post-computation analysis approaches, many of which rely on localized atom-centered basis sets. Traditionally, this gap has been bridged via projection-based techniques from a plane wave to atom-centered basis. We instead propose an alternative projection-free approach utilizing direct calculation of matrix elements of the converged plane wave DFT Hamiltonian in an atom-centered basis. This projection-free approach yields a number of compelling advantages, including strict orthonormality of the resulting bands without artificial band mixing and access to the Hamiltonian matrix elements, while faithfully preserving the underlying DFT band structure. The resulting atomic orbital representation of the Kohn-Sham wavefunction and Hamiltonian provides a gateway to a wide variety of analysis approaches. We demonstrate the utility of the approach for a diverse set of chemical systems and example analysis approaches.