Quantum embedding electronic structure methods

Svetlana Sokolova

Garnet Kin‐Lic Chan, Gerald Knizia

Self-consistent quantum embedding forms a route to bridge local descriptions of electronic structure methods and the electronic structure of very large systems and condensed phases. Existing examples of quantum embedding methods include the density functional embedding of Cortona, Wesolowski and Warshel, based on the single-particle density and Carter, and the dynamical mean-field theory, based on the single-particle Greens function. In this talk, however, I will describe a new formalism for quantum embedding that is based on the single-particle density matrix, and which is based on a self-consistent approximation to the exact entanglement embedding of a subsystem in an environment. Unlike density functional embedding, this formalism can practically describe strongly correlated systems, and unlike dynamical mean-field theory, it is easily combined with traditional ground-state electronic structure methods, such as quantum chemical wavefunction methods and projector and variational Monte Carlo approaches. I will demonstrate the performance of the method on the phase diagram of the 1D and 2D Hubbard models and discuss applications to ab-initio systems.

Srinivasan S. Iyengar, Debadrita Saha, Anurag Dwivedi +6 more

Shreya Verma

Strongly correlated electronic systems underpin a wide range of emerging quantum technologies, including solid-state defects for quantum information processing, molecular magnets, spin qubits, and quantum sensing platforms. Predictive computational design of these materials requires electronic structure methods capable of simultaneously describing strong electron correlation, excited-state phenomena, spin-dependent interactions, and environmental effects. While multireference wave function methods provide the necessary accuracy, their computational cost severely limits their application to realistic molecular and condensed-phase systems. This dissertation addresses this challenge through the development and application of quantum embedding and fragmentation methodologies that extend multireference electronic structure theory to increasingly complex quantum materials. The first part of this dissertation develops embedding-based approaches for describing optical properties of strongly correlated defects in extended solids. Complete Active Space Density Matrix Embedding Theory (CAS-DMET) and NEVPT2-DMET are applied to oxygen vacancy defects in magnesium oxide, where a systematic double-extrapolation protocol is introduced to approach both the non-embedding and thermodynamic limits. This framework enables quantitatively reliable calculations of absorption and emission energies while significantly reducing the computational cost of conventional multireference treatments of periodic systems. The second part extends embedding methodologies to the description of spin-dependent electronic structure. Density Matrix Embedding Pair-Density Functional Theory (DME-PDFT) is developed to recover dynamic electron correlation beyond the embedded active space, providing an efficient route for studying transition metal complexes and other strongly correlated molecular systems. Building upon these developments, CAS-DMET is further extended to investigate spin-phonon relaxation in molecular magnets and molecular crystals, demonstrating that quantum embedding can accurately describe spin dynamics and decoherence processes while substantially reducing computational cost. Beyond classical electronic structure calculations, this dissertation explores fragmentation strategies for hybrid quantum-classical algorithms through the development of efficient methodologies within the Localized Active Space Unitary Selective Coupled Cluster (LAS-USCC) framework. These developments improve the scalability of quantum chemistry algorithms for large active spaces and establish connections between embedding concepts and emerging quantum computing approaches. Finally, electronic structure calculations based on time-dependent density functional theory are employed to investigate fluorescent protein chromophores as potential biocompatible quantum sensors. These studies demonstrate how first-principles calculations can provide insight into spin-dependent properties in biologically relevant systems and expand the scope of computational approaches for quantum materials beyond traditional inorganic and molecular platforms. Collectively, the work presented in this dissertation establishes embedding and fragmentation as versatile frameworks for accurately describing the optical and spin properties of strongly correlated quantum systems across multiple length scales. By combining multireference electronic structure methods with physically motivated subsystem decompositions,these approaches bridge the gap between chemical accuracy and computational scalability, providing practical computational tools for the study and design of quantum materials relevant to quantum information science, molecular spintronics, and quantum sensing.

Ilya G. Kaplan, Jacques Soullard

An approach, where the embedded-cluster method (ECM) is applied in the frame of the Gaussian program to calculate the local electronic structure of crystals at the electron correlation level is presented. This approach is applied to a ground-state electronic structure calculation of the pure and Zn-doped Y123 ceramics at the second-order Møller–Plesset (MP2) correlation level (the ECM-MP2 approach). This allows to study the influence of the Zn doping on the charge distribution and the hole symmetry on the Cu and O ions obtained in the natural bond orbital (NBO) population analysis at the MP2 level. The possible mechanisms of the degradation of superconductivity in the Zn-doped Y ceramics are discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 320–326, 2000

Anthony Dean Dutoi