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Vladaj M, Marécat Q, Senjean B, Saubanère M. Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain. J Chem Phys 2024; 161:074105. [PMID: 39145549 DOI: 10.1063/5.0219898] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2024] [Accepted: 07/29/2024] [Indexed: 08/16/2024] Open
Abstract
The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of the Kohn-Sham scheme and the complexity of the pure N-representability conditions are still impeding its wild utilization. Fortunately, ensemble N-representability conditions derived in the natural orbital basis are known and trivial such that almost every functional of the 1-RDM is actually natural orbital functional, which does not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble N-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal parts of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws-Pastor functionals, as well as on the dihydrogen molecule using the Müller functional.
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Affiliation(s)
- Matthieu Vladaj
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France
| | - Quentin Marécat
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France
| | - Bruno Senjean
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France
| | - Matthieu Saubanère
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
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2
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Pitts TC, Bousiadi S, Gidopoulos NI, Lathiotakis NN. Effective local potentials for density and density-matrix functional approximations with non-negative screening density. J Chem Phys 2023; 158:2889006. [PMID: 37154280 DOI: 10.1063/5.0143757] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 04/20/2023] [Indexed: 05/10/2023] Open
Abstract
A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. 136, 224109 (2012)]. As illustrated, a convenient variational quantity in that approach is the "screening" or "electron repulsion" density, ρrep, corresponding to the local, KS Hartree, exchange and correlation potential through Poisson's equation. Two constraints, applied to this minimization, largely remove self-interaction errors from the effective potential: (i) ρrep integrates to N - 1, where N is the number of electrons, and (ii) ρrep ≥ 0 everywhere. In this work, we introduce an effective "screening" amplitude, f, as the variational quantity, with the screening density being ρrep = f2. In this way, the positivity condition for ρrep is automatically satisfied, and the minimization problem becomes more efficient and robust. We apply this technique to molecular calculations, employing several approximations in DFT and in reduced density matrix functional theory. We find that the proposed development is an accurate, yet robust, variant of the constrained effective potential method.
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Affiliation(s)
- Thomas C Pitts
- Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Sofia Bousiadi
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11635 Athens, Greece
- Faculty of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 157 84, Greece
| | - Nikitas I Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Nektarios N Lathiotakis
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11635 Athens, Greece
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3
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Bousiadi S, Gidopoulos N, Lathiotakis N. Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT. Phys Chem Chem Phys 2022; 24:19279-19286. [DOI: 10.1039/d2cp01866g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds...
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Seenithurai S, Chai JD. Electronic Properties of Carbon Nanobelts Predicted by Thermally-Assisted-Occupation DFT. NANOMATERIALS (BASEL, SWITZERLAND) 2021; 11:2224. [PMID: 34578540 PMCID: PMC8465987 DOI: 10.3390/nano11092224] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Revised: 08/23/2021] [Accepted: 08/26/2021] [Indexed: 11/16/2022]
Abstract
Accurate prediction of properties of large-scale multi-reference (MR) electronic systems remains difficult for traditional computational methods (e.g., the Hartree-Fock theory and Kohn-Sham density functional theory (DFT)). Recently, thermally-assisted-occupation (TAO)-DFT has been demonstrated to offer reliable description of electronic properties of various large-scale MR electronic systems. Consequently, in this work, TAO-DFT is used to unlock the electronic properties associated with C-Belt[n] (i.e., the carbon nanobelts containing n fused 12-membered carbon rings). Our calculations show that for all the system sizes reported (n = 4-24), C-Belt[n] have singlet ground states. In general, the larger the size of C-Belt[n], the more pronounced the MR character of ground-state C-Belt[n], as evident from the symmetrized von Neumann entropy and the occupation numbers of active TAO-orbitals. Furthermore, the active TAO-orbitals are delocalized along the circumference of C-Belt[n], as evident from the visualization of active TAO-orbitals.
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Affiliation(s)
- Sonai Seenithurai
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan;
| | - Jeng-Da Chai
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan;
- Center for Theoretical Physics and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
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Head-Marsden K, Flick J, Ciccarino CJ, Narang P. Quantum Information and Algorithms for Correlated Quantum Matter. Chem Rev 2020; 121:3061-3120. [PMID: 33326218 DOI: 10.1021/acs.chemrev.0c00620] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.
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Affiliation(s)
- Kade Head-Marsden
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Christopher J Ciccarino
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States.,Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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Ramberger B, Sukurma Z, Schäfer T, Kresse G. RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods. J Chem Phys 2019; 151:214106. [DOI: 10.1063/1.5128415] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Ramberger
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
| | - Zoran Sukurma
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
| | - Tobias Schäfer
- Institute for Theoretical Physics, Technical University of Vienna, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
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7
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Baerends EJ. On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1612955] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Theophilou I, Buchholz F, Eich FG, Ruggenthaler M, Rubio A. Kinetic-Energy Density-Functional Theory on a Lattice. J Chem Theory Comput 2018; 14:4072-4087. [PMID: 29969552 PMCID: PMC6096452 DOI: 10.1021/acs.jctc.8b00292] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We
present a kinetic-energy density-functional theory and the corresponding
kinetic-energy Kohn–Sham (keKS) scheme on a lattice and show
that, by including more observables explicitly in a density-functional
approach, already simple approximation strategies lead to very accurate
results. Here, we promote the kinetic-energy density to a fundamental
variable alongside the density and show for specific cases (analytically
and numerically) that there is a one-to-one correspondence between
the external pair of on-site potential and site-dependent hopping
and the internal pair of density and kinetic-energy density. On the
basis of this mapping, we establish two unknown effective fields,
the mean-field exchange-correlation potential and the mean-field exchange-correlation
hopping, which force the keKS system to generate the same kinetic-energy
density and density as the fully interacting one. We show, by a decomposition
based on the equations of motions for the density and the kinetic-energy
density, that we can construct simple orbital-dependent functionals
that outperform the corresponding exact-exchange Kohn–Sham
(KS) approximation of standard density-functional theory. We do so
by considering the exact KS and keKS systems and comparing the unknown
correlation contributions as well as by comparing self-consistent
calculations based on the mean-field exchange (for the effective potential)
and a uniform (for the effective hopping) approximation for the keKS
and the exact-exchange approximation for the KS system, respectively.
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Affiliation(s)
- Iris Theophilou
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Florian Buchholz
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - F G Eich
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany.,Center for Computational Quantum Physics (CCQ) , Flatiron Institute , New York , New York 10010 , United States
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9
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Tognetti V, Loos PF. Natural occupation numbers in two-electron quantum rings. J Chem Phys 2016; 144:054108. [PMID: 26851909 DOI: 10.1063/1.4940919] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.
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Affiliation(s)
- Vincent Tognetti
- Normandy Univ., COBRA UMR 6014 & FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére, 76821 Mont Saint Aignan, Cedex, France
| | - Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
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