Projection-Based Molecular Quantum Embedding via Singular-Value-Informed Orbital Partitioning

This chapter provides an overview of projection-based quantum embedding, which permits the investigation of a chosen property local to some moiety through a “high-level” quantum mechanical treatment. While this method has been applied to various systems, the efficacy of projection-based embedding depends on a well-defined partitioning of the subspaces. In response to the subjectivity in a choice of cutoff thresholds commonly used in atom-centered partitioning schemes, we present a nearly “black-box” alternative informed by a singular-value decomposition spectrum, denoted as SPADE. Capitalizing on a similar rationale and recognizing the need to reduce the computational expense of many treatments of electron correlation, a singular-value decomposition is also used to systematically construct an effective virtual space and discard the orbitals that have little impact on the desired features. We begin this chapter by providing context for projection-based quantum embedding followed by a detailed overview of the topic. We then justify the need for robust subspace partitioning and offer a step-by-step overview of the SPADE partitioning scheme. Finally, we review the major points of employing concentric localization to truncate the virtual space and make challenging chemical systems more tractable. In this chapter, we provide some examples of projection-based embedding that use the concentric localization and/or SPADE schemes that highlight the robustness of these methods while also emphasizing the accuracy that projection-based embedding can provide relative to the chosen “high-level” method.