Embedding Methods in Materials Discovery

Abstract

This chapter reviews a class of methods that allow for high accuracy and lift the constraints imposed by the periodic boundary conditions. Known under the generic name of the embedded cluster approach, this group of methods stems from the molecular perspective on matter, i.e., all materials are finite and can be represented using a finite collections of atoms, subjected to the boundary conditions that reproduce the rest of the system that is not necessarily periodic. We then give a few examples of using these methods in materials modeling and offer an outlook for the future.

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

“…Over the years, several embedding strategies have been developed at different levels of complexity, such as: ONIOM 430 , electrostatic embedding 431 , quantum mechanics/molecular mechanics (QM/MM) 432,433 , fragment methods 372 , density-functional-based embedding [434][435][436][437][438] , density embedding (DET) 439 , density matrix embedding (DMET) 440 , projector-based embedding [441][442][443] , embedded mean-field theory 444 , self-energy 445 and Green's function embedding. [446][447][448] For a general overview of embedding approaches we refer the reader to numerous reviews that have been published on the subject.…”

“…[446][447][448] For a general overview of embedding approaches we refer the reader to numerous reviews that have been published on the subject. 372,431,[449][450][451][452][453] All embedding approaches rely on partitioning the full system into subsystems and a definition of the energy. For two subsystems, A embedded in the environment of B, one can, within the language of DFT, write the formal DFT-in-DFT embedding energy expression as 435 ,…”

Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches

“…In this approach, ρ A is represented within the set of basis functions centered on active atoms and ρ B is expressed by the basis functions centered on environment atoms. The first algorithm, "orbital localization", is similar to the above descriptions with total truncation, but the Huzinaga projector is redefined in terms of the separate basis sets, (16) where the superscripts on the Fock and overlap matrices indicate that they have mixed indices over the separated active and environment AOs and γ B is expressed in only the AOs centered on nonactive atoms. The second algorithm, referred to as "iterative freeze-and-thaw", bypasses the need for orbital localization and density partitioning by performing alternating, iterative QM-in-QM calculations on each subsystem in their corresponding restricted basis sets.…”

“…The active subsystem can be tackled with an accurate level of theory that would be prohibitive for the full system, while the environment is treated at a cost efficient level that provides broadly acceptable accuracy on larger systems. Over the years, a variety of schemes have been developed around the concept of embedding subsystems − at different theoretical levels, including quantum mechanics/molecular mechanics (QM/MM), , ONIOM, , DFT embedding, ,, partition DFT, , potential-functional embedding, embedded mean-field theory (EMFT), Green’s function embedding, , self-energy embedding, , density matrix embedding theory (DMET), and stochastic embedding DFT . In this manuscript, we focus on the projector-based embedding approach.…”

Huzinaga Projection Embedding for Efficient and Accurate Energies of Systems with Localized Spin-densities

“…18 Quantum embedding calculations seek to improve upon the small model simulations by including some influence of the full system on the final energy. Quantum embedding methods such as QM/MM, 19 ONIOM, 20 DMET, 21,22 embedded mean-field theory, [23][24][25][26][27] Green's function embedding, 22,[28][29][30] partition DFT, [31][32][33] and DFT embedding 22,[34][35][36][37] among many others [38][39][40][41][42][43] were designed to combine the benefits of high accuracy and systematic improvability from WF theory for a small subsystem, while including effects from the full system at a comparably negligible computational cost. Projection operator based DFT embedding has been developed by many groups with significant success.…”