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arXiv:1810.12005 · Physical Review Materials

Quantum embedding theory in the screened Coulomb interaction: Combining configuration interaction with GW/BSE

Marc Dvorak, Dorothea Golze, Patrick Rinke

Published Jul 31, 2019• 23 citations
arXivHTMLPDF

Abstract

We present a quantum embedding theory called dynamical configuration interaction (DCI) that combines wave function and Green's function theories. DCI captures static correlation in a correlated subspace with configuration interaction and couples to high-energy, dynamic correlation outside the subspace with many-body perturbation theory based on Green's functions. DCI takes the strengths of both theories to balance static and dynamic correlation in a single, fully ab initio embedding concept. The theory adds dynamic correlation around a fixed active space of orbitals with efficient $\mathcal{O}({N}^{5})$ scaling, while maintaining a multireference treatment of the active space. We show that treating high-energy correlation up to the $GW$ and Bethe-Salpeter equation level is sufficient even for challenging multireference problems. Our theory treats ground and excited states on equal footing, and we compute the dissociation curve of ${\mathrm{N}}_{2}$, the vertical excitation energies of small molecules, and the ionization spectrum of benzene in excellent agreement with high-level quantum chemistry methods and experiment.

DOI
10.1103/physrevmaterials.3.070801

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Physical Review B•May 30, 2007•17 citations
We present a quantum embedding theory called dynamical configuration interaction (DCI) that combines wave function and Green's function theories. DCI captures static correlation in a correlated subspace with configuration interaction and couples to high-energy, dynamic correlation outside the subspace with many-body perturbation theory based on Green's functions. DCI takes the strengths of both theories to balance static and dynamic correlation in a single, fully ab initio embedding concept. The theory adds dynamic correlation around a fixed active space of orbitals with efficient O(N5)\mathcal{O}({N}^{5})O(N5) scaling, while maintaining a multireference treatment of the active space. We show that treating high-energy correlation up to the GWGWGW and Bethe-Salpeter equation level is sufficient even for challenging multireference problems. Our theory treats ground and excited states on equal footing, and we compute the dissociation curve of N2{\mathrm{N}}_{2}N2​, the vertical excitation energies of small molecules, and the ionization spectrum of benzene in excellent agreement with high-level quantum chemistry methods and experiment.
We present the concept, derivation, and implementation of dynamical configuration interaction, a quantum embedding theory that combines Green's function methodology with the many-body wave function. In a strongly correlated active space, we use full configuration interaction (CI) to describe static correlation exactly. We add energy-dependent corrections to the CI Hamiltonian which, in principle, include all remaining correlations derived from the bath space surrounding the active space. Next, we replace the exact Hamiltonian in the bath with one of excitations defined over a correlated ground state. This transformation is naturally suited to the methodology of many-body Green's functions. In this space, we use a modified GWGWGW/Bethe-Salpeter equation procedure to calculate excitation energies. Combined with an estimate of the ground-state energy in the bath, we can efficiently compute the energy-dependent corrections, which correlate the full set of orbitals, for very low computational cost. We present dimer dissociation curves for H2{\mathrm{H}}_{2}H2​ and N2{\mathrm{N}}_{2}N2​ in good agreement with exact results. Additionally, excited states of N2{\mathrm{N}}_{2}N2​ and C2{\mathrm{C}}_{2}C2​ are in excellent agreement with benchmark theory and experiment. By combining the strengths of two disciplines, we achieve a balanced description of static and dynamic correlation in a fully ab initio, systematically improvable framework.
We present a multilevel embedding framework for quantum chemistry calculations on a quantum computer. In our framework, a quantum algorithm treats the strongly correlated active space, while a high-level wave-function method such as coupled cluster theory or multireference perturbation theory recovers the remaining correlation in the surrounding region. A sampling-based quantum algorithm, quantum-selected configuration interaction, bridges the quantum and classical treatments. The entire calculation is embedded in a low-cost density functional theory description of the surrounding environment using Manby's projection technique. We apply the framework to organic, metal-organic, and metallic systems, computing bond dissociation energies, adsorption energies, and reaction barriers using only the subset of qubits of a 144-qubit superconducting quantum computer at the University of Osaka and achieving $\sim$1 kcal/mol agreement with classical references for a Menshutkin SN2\mathrm{S_N2}SN​2 reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.
The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green's function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.
Quantitative simulation of electronic structure of solids requires treating local and nonlocal electron correlations on an equal footing. We present a new ab initio formulation of Green's function embedding which, unlike dynamical mean-field theory that uses noninteracting bath, derives bath representation with general two-particle interactions in a systematically improvable manner. The resulting interacting-bath dynamical embedding theory (ibDET) utilizes an efficient real-axis coupled-cluster solver to compute the self-energy, approaching the full system limit at much reduced cost. When combined with the GW theory, GW+ibDET achieves good agreement with experimental spectral properties across a range of semiconducting, insulating, and metallic materials. Our approach also enables quantifying the role of nonlocal electron correlation in determining material properties and addressing the long-standing debate on the bandwidth narrowing of metallic sodium.
Entangled atoms, exemplified by the two singlet-coupled atoms in a dissociating nitrogen molecule, are key to the unique properties of qubits, quantum sensors, and other quantum materials. Simulating entangled atoms and strong electron correlation is a prerequisite for modeling quantum materials and remains an outstanding challenge for theory. I introduce a correlated wave function approach capable of simulating strong electron correlation in large active spaces. Projected-interacting full configuration interaction plus density functional theory PiFCI+DFT combines near-exact correlated wave functions of multiple partially interacting model systems, each corrected by a formally exact density functional. This approach can access large active spaces and visualize entanglement and strong correlation while maintaining competitive accuracy for molecular properties. I demonstrate PiFCI+DFT for general main-group chemistry, benchmark dissociation curves, and a model for a large entangled-atom system: the spin-singlet ground state of a square lattice of 100 nitrogen atoms. This system’s 300-electron active space is out of reach for existing ab initio multireference methods. PiFCI+DFT accurately recovers the strongly correlated dissociation limit at a modest computational cost, motivating further development for modeling quantum materials.
In order to properly understand the utility of many-body perturbation theory as applied to finite systems, we use the configuration interaction approach to compute the electronic self-energy. The validity of the commonly used GWGWGW approximation from many-body perturbation theory is tested by comparing the self-energy explicitly computed according to the diagrammatic expansions to that from the inversion of the Dyson equation. It is constructed as a functional of the interacting Green function GGG and screened Coulomb interaction WWW. WWW is explicitly computed through the diagonalization of the many-body Hamiltonian and, thus, takes polarization effects into account beyond the random phase approximation. The Na9+\mathrm{Na}_{9}{}^{+}Na9​+ cluster and the dissociation of the C2{\mathrm{C}}_{2}C2​ molecule are discussed as examples. We find that the GWGWGW approximation yields accurate results for weakly correlated systems with a predominantly single-determinant ground state such as Na9+\mathrm{Na}_{9}{}^{+}Na9​+ clusters. The C2{\mathrm{C}}_{2}C2​ molecule is a pathological system with multideterminantal ground state where the GWGWGW approach ceases to be valid.