The computational design of molecular quantum devices requires methods that capture "the quantum and the chemistry," approaching chemical accuracy for large numbers of entangled and/or strongly correlated electrons. Projected-interacting full configuration interaction (PiFCI) is a candidate for such simulations, providing a formally exact and systematically improvable approximation for correlation in large active spaces. PiFCI extends Kohn-Sham density functional theory by introducing multiple reference systems, each experiencing an electron-electron interaction projected onto one or more one-electron states. Compact CI expansions yield near-exact reference system wavefunctions, and projected exchange-correlation (XC) density functionals enable formally exact combinations of reference system correlation energies. This work presents a general treatment of the projected interactions in PiFCI and introduces regularized second-order many-body perturbation theory (MP2) as an approximate projected XC functional. Numerical results show that PiFCI plus regularized MP2 can accurately treat dynamical and nondynamical correlation in relatively large active spaces, including stacks of entangled singlet-coupled tetrathiafulvalene and phenalenyl organic radicals modeling molecular quantum devices.
The computational design of molecular quantum devices requires methods that capture "the quantum and the chemistry," approaching chemical accuracy for large numbers of entangled and/or strongly correlated electrons. Projected-interacting full configuration interaction (PiFCI) is a candidate for such simulations, providing a formally exact and systematically improvable approximation for correlation in large active spaces. PiFCI extends Kohn-Sham density functional theory by introducing multiple reference systems, each experiencing an electron-electron interaction projected onto one or more one-electron states. Compact CI expansions yield near-exact reference system wavefunctions, and projected exchange-correlation (XC) density functionals enable formally exact combinations of reference system correlation energies. This work presents a general treatment of the projected interactions in PiFCI and introduces regularized second-order many-body perturbation theory (MP2) as an approximate projected XC functional. Numerical results show that PiFCI plus regularized MP2 can accurately treat dynamical and nondynamical correlation in relatively large active spaces, including stacks of entangled singlet-coupled tetrathiafulvalene and phenalenyl organic radicals modeling molecular quantum devices.
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.
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 reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.
Providing sufficient accuracy at low-computational cost, not surprisingly, density-functional theory ( DFT ) is a standard tool in theoretical material science. Similarly, quantum-electrodynamical density-functional theory ( QEDFT ) provides a promising route to describe experiments at the interface of quantum optics and quantum chemistry. Formally, in the Kohn-Sham ( KS ) formulation of DFT and QEDFT the exact many-particle Schrödinger equation is replaced by a set of coupled non-linear one-particle differential equations. The electron-electron, the electron-ion and the electron-photon interactions of the interacting system are mimicked by their corresponding effective KS potential with an, in principle unknown exchange-correlation ( xc ) term. In practice, DFT and QEDFT require approximations for this xc potential. The quality of which fully determines how much the DFT and QEDFT observables deviate from the exact ones. Understanding the shortcomings and improving the quality of approximate functionals makes the study of the exact functional of model systems indispensable. Here, we employ exact diagonalization for the Hamiltonian of different types of real-space lattice models in one spatial dimension to access the ground-state wave function, and thus to explicitly construct the exact functionals of DFT and QEDFT . To study the functional behavior of purely electronic systems, we consider two singlet-state electrons moving in an external potential with two connected atomic wells of variable depth and distance. To study coupled electron-photon systems, we consider the Rabi Hamiltonian with variable electron-photon coupling strength. By varying the model parameters, we systematically construct the functionals for systems from weak to strong coupling between the building blocks of the global system. Using the concept of the effective density-to- potential map, we discuss the intrasystem steepening which is an exact condition on the xc functional that captures the static correlation present in the system and carve out how it relates to the well-known intersystem derivative discontinuity. We further construct arbitrary observables as functionals of the internal variables which are directly affected by such features of the effective density-to-potential map. By constructing the reduced dipole map in the four-particle case of coupled electron-photon system, we show that the density-to-potential map helps to identify and understand recently discovered physical effects in the field of strongly coupled electron-photon systems. This work provides a contribution to the development of approximate function- als required in practical density-functional calculations of arbitrary experimentally accessible observables. Both the intrasystem steepening and the intersystem derivative discontinuity play a crucial role for systems with highly-localized electrons. Including both features in approximate functionals will improve the accu- racy of DFT evaluation of observables for such systems. Those results provide novel insight into the properties of the exact xc potentials in QEDFT . This work opens a new route to construct new functionals using coarse-grained or embed- ding approaches within the general and exact frameworks of DFT and QEDFT.
We establish theoretical foundations for embedding a correlated wavefunction in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation that equates two, in principle, distinct kinetic-energy functionals yields an embedding functional identical to the projection-based wavefunction-in-density functional theory (DFT) formulation of Miller and co-workers. We demonstrate that this functional is inherently nonvariational: its minimum is not guaranteed to coincide with the exact ground-state energy and remains bounded from above by it. Building on this formal framework, we analyze the dominant sources of error in projection-based density matrix renormalization group-in-DFT embedding with approximate exchange-correlation (xc) functionals. Using molecules with dissociating covalent bonds as a diagnostic example, we demonstrate that the primary source of error is the nonadditive exchange-correlation energy describing the nonclassical coupling between the active subsystem and its environment. Eliminating the fractional-spin error by employing a pair-density xc functional (pair-density functional theory) instead of a semilocal generalized gradient approximation (GGA) does not remedy this deficiency, because the inaccuracy stems from self-interaction effects at the subsystem-environment interface.
Facilitated by a rigorous partitioning of a molecular system's orbital basis into two fundamental subspaces-a reference and an expansion space, both with orbitals of unspecified occupancy-we generalize our recently introduced many-body expanded full configuration interaction (MBE-FCI) method to allow for electron-rich model and molecular systems dominated by both weak and strong correlation to be addressed. By employing minimal or even empty reference spaces, we show through calculations on the one-dimensional Hubbard model with up to 46 lattice sites, the chromium dimer, and the benzene molecule how near-exact results may be obtained in an entirely unbiased manner for chemical and physical problems of not only academic but also applied chemical interest. Given the massive parallelism and overall accuracy of the resulting method, we argue that generalized MBE-FCI theory possesses an immense potential to yield near-exact correlation energies for molecular systems of unprecedented size, composition, and complexity in the years to come.
Abstract The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein–Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H 2 S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H 64 square lattice with an active space of (42e, 42o).