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Aliverti-Piuri D, Chatterjee K, Ding L, Liao K, Liebert J, Schilling C. What can quantum information theory offer to quantum chemistry? Faraday Discuss 2024. [PMID: 39099471 DOI: 10.1039/d4fd00059e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/06/2024]
Abstract
It is the ultimate goal of this work to foster synergy between quantum chemistry and the flourishing field of quantum information theory. For this, we first translate quantum information concepts, such as entanglement and correlation, into the context of quantum chemical systems. In particular, we establish two conceptually distinct perspectives on 'electron correlation', leading to a notion of orbital and particle correlation. We then demonstrate that particle correlation equals total orbital correlation minimized over all orbital bases. Accordingly, particle correlation resembles the minimal, thus intrinsic, complexity of many-electron wave functions, while orbital correlation quantifies their complexity relative to a basis. We illustrate these concepts of intrinsic and extrinsic correlation complexity in molecular systems, which also manifests the crucial link between the two correlation pictures. Our results provide theoretical justification for the long-favored natural orbitals for simplifying electronic structures, and open new pathways for developing more efficient approaches towards the electron correlation problem.
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Affiliation(s)
- Damiano Aliverti-Piuri
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Kaustav Chatterjee
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Lexin Ding
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Ke Liao
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Julia Liebert
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Christian Schilling
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
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Góger S, Karimpour MR, Tkatchenko A. Four-Dimensional Scaling of Dipole Polarizability: From Single-Particle Models to Atoms and Molecules. J Chem Theory Comput 2024. [PMID: 39015013 DOI: 10.1021/acs.jctc.4c00582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/18/2024]
Abstract
Scaling laws enable the determination of physicochemical properties of molecules and materials as a function of their size, density, number of electrons or other easily accessible descriptors. Such relations can be counterintuitive and nonlinear, and ultimately yield much needed insight into quantum mechanics of many-particle systems. In this work, we show on the basis of single-particle models, multielectron atoms and molecules that the dipole polarizability of quantum systems is generally proportional to the fourth power of a characteristic length, computed from the ground-state wave function. This four-dimensional (4D) scaling is independent of the ratio of bound-to-bound and bound-to-continuum electronic transitions and applies to many-electron atoms when a correlated length metric is used. Finally, this scaling law is applied to predict the polarizability of molecules by electrostatically coupled atoms-in-molecules approach, obtaining approximately 8% absolute and relative accuracy with respect to hybrid density functional theory (DFT) on the QM7-X data set of organic molecules, providing an efficient and scalable model for the anisotropic polarizability tensors of extended (bio)molecules.
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Affiliation(s)
- Szabolcs Góger
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Mohammad Reza Karimpour
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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Yu JM, Tsai J, Rajabi A, Rappoport D, Furche F. Natural determinant reference functional theory. J Chem Phys 2024; 160:044102. [PMID: 38252940 DOI: 10.1063/5.0180319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 12/27/2023] [Indexed: 01/24/2024] Open
Abstract
The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an N-electron state of interest. Unlike the Kohn-Sham (KS) determinant, which yields the exact ground-state density, the NDR only yields the best idempotent approximation to the interacting one-particle reduced density matrix, but it is well-defined in common atom-centered basis sets and is representation-invariant. We show that the under-determination problem of prior attempts to define a ground-state energy functional of the NDR is overcome in a grand-canonical ensemble framework at the zero-temperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an "exactification" of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KS-inversion or optimized effective potentials.
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Affiliation(s)
- Jason M Yu
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Jeffrey Tsai
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Ahmadreza Rajabi
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Dmitrij Rappoport
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Filipp Furche
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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Gibney D, Boyn JN, Mazziotti DA. Universal Generalization of Density Functional Theory for Static Correlation. PHYSICAL REVIEW LETTERS 2023; 131:243003. [PMID: 38181140 DOI: 10.1103/physrevlett.131.243003] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 09/27/2023] [Accepted: 11/01/2023] [Indexed: 01/07/2024]
Abstract
A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.
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Affiliation(s)
- Daniel Gibney
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA
| | - Jan-Niklas Boyn
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA
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Jones GM, Li RR, DePrince AE, Vogiatzis KD. Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory. J Phys Chem Lett 2023:6377-6385. [PMID: 37418691 DOI: 10.1021/acs.jpclett.3c01382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/09/2023]
Abstract
The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced-density matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can enable large-scale calculations on such systems, the quality of the solution is limited by the fact that only a subset of known necessary N-representability constraints can be applied to the 2RDM in practical calculations. Here, we demonstrate that violations of partial three-particle (T1 and T2) N-representability conditions, which can be evaluated with knowledge of only the 2RDM, can serve as physics-based features in a machine-learning (ML) protocol for improving energies from v2RDM calculations that consider only two-particle (PQG) conditions. Proof-of-principle calculations demonstrate that the model yields substantially improved energies relative to reference values from configuration-interaction-based calculations.
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Affiliation(s)
- Grier M Jones
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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