© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1911.12449 · Journal of Chemical Theory and Computation

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems

Daniel S. Graham, Xuelan Wen, Dhabih V. Chulhai, Jason D. Goodpaster

Published Feb 27, 2020• 23 citations

Abstract

Abstract Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. This work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

DOI: 10.1021/acs.jctc.9b01185

Related papers

Improved Accuracy and Efficiency in Quantum Embedding through Absolute Localization

Dhabih V. Chulhai, Jason D. Goodpaster

Projection-based quantum embedding methodologies provide a framework for performing wave function-in-density functional theory (WF-in-DFT) calculations. The total WF-in-DFT energy is dependent on the partitioning of the total system and requires similar partitioning in each system for accurate energy differences. To achieve this, we enforce an absolute localization of the WF orbitals to basis functions only associated with the WF subsystem. This absolute localization, followed by iterative optimization of the subsystems' orbitals, provides improved energy differences for WF-in-DFT while simultaneously improving the computational efficiency.

Journal of Chemical Theory and Computation•Mar 6, 2017•69 citations

Quantum computing for accurate large-scale electronic-structure calculations: DFT-embedded, post-processed quantum-selected configuration interaction

Tuan Minh Do, Yuichiro Yoshida, Tomoya Shiota +1 more

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 $\mathrm{S_N2}$ reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.

physics.chem-phCross-listedarXiv:2606.06015•Jun 5, 2026•0 citations

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

Jonathan M. Waldrop, Theresa L. Windus, Niranjan Govind

Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.

The Journal of Physical Chemistry A•Jul 14, 2021•23 citations

Projection-Based DMRG-in-DFT Embedding Corrected by Nonadditive Exchange-Correlation

Enzo Monino, Daria Drwal, Pavel Beran +3 more

The projection-based wave function in density functional theory (WF-in-DFT) embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [ Beran, P. J. Phys. Chem. Lett. 2023, 14, 716–722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H 20 chain and the cleavage of a triple CN bond in propionitrile.

Journal of Chemical Theory and Computation•Feb 9, 2026•3 citations

Projection-based DMRG-in-DFT embedding corrected by non-additive exchange-correlation

Enzo Monino, Daria Drwal, Pavel Beran +3 more

The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. et al. J. Phys. Chem. Lett. 2023, 14, 3, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

arXiv:2511.13346•Nov 17, 2025•0 citations

Fully Quantum Embedding with Density Functional Theory for Full Configuration Interaction Quantum Monte Carlo

Hayley Petras, Daniel S. Graham, Sai Kumar Ramadugu +2 more

We here develop a fully quantum embedded version of initiator full configuration interaction quantum Monte Carlo ( i –FCIQMC) and apply it to study an ionic bond (lithium hydride, LiH) and a covalent bond (hydrogen flouride, HF) physisorbed to a benzene molecule. The embedding is performed using a recently developed Huzinaga projection operator approach, which affords good synergy with i –FCIQMC by minimizing the number of orbitals in the calculation. When considering the dissociation energy of these bonds into closed-shell ionic fragments, we find that i −FCIQMC embedded in density functional theory ( i −FCIQMC-in-DFT) delivers comparable accuracy with coupled cluster singles and doubles with perturbative triples embedded in density functional theory (CCSD(T)-in-DFT). In treating the bond dissociation energy curve of HF, i –FCIQMC-in-DFT has improved accuracy over CCSD(T)-in-DFT due to the presence of strong correlation. We discuss the implications of the new i –FCIQMC-in-DFT method as applied to bond breaking in catalysis.

arXiv:1906.03699•Journal of Chemical Theory and Computation•Aug 26, 2019•15 citations

Abstract Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. This work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

Projection-based quantum embedding methodologies provide a framework for performing wave function-in-density functional theory (WF-in-DFT) calculations. The total WF-in-DFT energy is dependent on the partitioning of the total system and requires similar partitioning in each system for accurate energy differences. To achieve this, we enforce an absolute localization of the WF orbitals to basis functions only associated with the WF subsystem. This absolute localization, followed by iterative optimization of the subsystems' orbitals, provides improved energy differences for WF-in-DFT while simultaneously improving the computational efficiency.

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

\mathrm{S_N2}

reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.

Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.

The projection-based wave function in density functional theory (WF-in-DFT) embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [ Beran, P. J. Phys. Chem. Lett. 2023, 14, 716–722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H 20 chain and the cleavage of a triple CN bond in propionitrile.

The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. et al. J. Phys. Chem. Lett. 2023, 14, 3, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

We here develop a fully quantum embedded version of initiator full configuration interaction quantum Monte Carlo ( i –FCIQMC) and apply it to study an ionic bond (lithium hydride, LiH) and a covalent bond (hydrogen flouride, HF) physisorbed to a benzene molecule. The embedding is performed using a recently developed Huzinaga projection operator approach, which affords good synergy with i –FCIQMC by minimizing the number of orbitals in the calculation. When considering the dissociation energy of these bonds into closed-shell ionic fragments, we find that i −FCIQMC embedded in density functional theory ( i −FCIQMC-in-DFT) delivers comparable accuracy with coupled cluster singles and doubles with perturbative triples embedded in density functional theory (CCSD(T)-in-DFT). In treating the bond dissociation energy curve of HF, i –FCIQMC-in-DFT has improved accuracy over CCSD(T)-in-DFT due to the presence of strong correlation. We discuss the implications of the new i –FCIQMC-in-DFT method as applied to bond breaking in catalysis.