Bootstrap Embedding for Molecules

Abstract

Fragment embedding is one way to circumvent the high computational scaling of accurate electron correlation methods. The challenge of applying fragment embedding to molecular systems primarily lies in the strong entanglement and correlation that prevent accurate fragmentation across chemical bonds. Recently, Schmidt decomposition has been shown effective for embedding fragments that are strongly coupled to a bath in several model systems. In this work, we extend a recently developed quantum embedding scheme, bootstrap embedding (BE), to molecular systems. The resulting method utilizes the matching conditions naturally arising from using overlapping fragments to optimize the embedding. Numerical simulation suggests that the accuracy of the embedding improves rapidly with fragment size for small molecules, whereas larger fragments that include orbitals from different atoms may be needed for larger molecules. BE scales linearly with system size (apart from an integral transform) and hence can potentially be useful for large-scale calculations.

Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory

“…It may be possible to further reduce this boundary error using the dynamical cluster approximation formulation of DMET (DCA-DMET) 22 or bootstrap embedding. [75][76][77] We finally consider DMET results obtained using the non-interacting bath (NIB), as also shown in Fig. 2.…”

Field‐Induced Slow Magnetic Relaxation in Mononuclear Tetracoordinate Cobalt(II) Complexes Containing a Neocuproine Ligand

“…Therefore, the overall value is a very delicate balance of the contributions from individual excitations, which mostly compensate one another. [22] Although the spin-orbit coupling constant supports the magnitude of the numerator, the sign is given by the abovementioned integrals. The trend of the excitation energies is difficult to assess as they depend not only upon the crystal-field strengths but also on radial and angular geometry factors.…”

Quantum embedding electronic structure methods

“…MBE is powerful because it can be optimized by exploiting the topology of the system. In this regard, bootstrap embedding [ 34 ] can exploit matching conditions for the density (or DM elements) of the “center” and the “edge” of fragments to, once again, improve convergence of the MBE. The contribution by Ricard et al [ 119 ] exploits topology in a formal way, invoking graph theory within the embedding framework offered by ONIOM.…”

“…This very idea applies well to bulk crystals containing transition metal elements [32] of, even more extremely, lanthanides and actinides. [33] Similar embedding methods requiring the definition of a supersystem Hilbert space are those that reproduce KS-DFT while aiming to reduce the cost, for example, bootstrap embedding [34,35] and the projection-based embedding methods developed initially by the Piela group [36] and F I G U R E 1 Interactions during the Spring 2019 National ACS meeting in Orlando, Fl. A, Crowds in search of a lunch spot.…”