2018/07/23 by Lin Lin, Lin, Lin, Leonardo Zepeda-Núñez +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Computational Physics (physics.comp-ph) #Computer science #Density functional theory #Density matrix #Discretization #Embedding #FOS: Mathematics #FOS: Physical sciences #Geometry #Hamiltonian (control theory) #Kohn–Sham equations #Linear algebra #Linear subspace #Mathematical analysis #Mathematical optimization #Mathematics #Numerical Analysis (math.NA) #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Projector #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Time-dependent density functional theory
paper · pdf · doi:10.48550/arxiv.1807.08859
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2018/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum embedding theories are playing an increasingly important role in bridging different levels of approximation to the many body Schrödinger equation in physics, chemistry and materials science. In this paper, we present a linear algebra perspective of the recently developed projection based embedding theory (PET) [Manby et al, J. Chem. Theory Comput. 8, 2564, 2012], restricted to the context of Kohn-Sham density functional theory. By partitioning the global degrees of freedom into a `system' part and a `bath' part, and by choosing a proper projector from the bath, PET is an in principle exact formulation to confine the calculation to the system part only, and hence can be carried out with reduced computational cost. Viewed from the perspective of the domain decomposition method, one particularly interesting feature of PET is that it does not enforce a boundary condition explicitly, and remains applicable even when the discretized Hamiltonian matrix is dense, such as in the context of the planewave discretization. In practice, the accuracy of PET depends on the accuracy of the projector for the bath. Based on the linear algebra reformulation, we develop a first order perturbation correction to the projector from the bath to improve its accuracy. Numerical results for real chemical systems indicate that with a proper choice of reference system, the perturbatively corrected PET can be sufficiently accurate even when strong perturbation is applied to very small systems, such as the computation of the ground state energy of a SiH3F molecule, using a SiH4 molecule as the reference system.