1
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Cernatic F, Fromager E. Extended N-centered ensemble density functional theory of double electronic excitations. J Comput Chem 2024; 45:1945-1962. [PMID: 38700389 DOI: 10.1002/jcc.27387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2024] [Revised: 04/12/2024] [Accepted: 04/19/2024] [Indexed: 05/05/2024]
Abstract
A recent work (arXiv:2401.04685) has merged N-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended N-centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density-functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn-Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two-electron Hubbard dimer model. A thorough comparison of the true physical ground- and excited-state electronic structures with that of the fictitious ensemble density-functional KS system is also presented. Depending on the choice of the density-functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant.
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Affiliation(s)
- Filip Cernatic
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
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2
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Liao K, Ding L, Schilling C. Quantum Information Orbitals (QIO): Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality. J Phys Chem Lett 2024; 15:6782-6790. [PMID: 38913404 DOI: 10.1021/acs.jpclett.4c01105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/25/2024]
Abstract
The simultaneous treatment of static and dynamic correlations in strongly correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wave function is a formidable and longstanding problem. As a contribution toward its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wave function, once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more nontrivial information on the many-body wave function, indicated by the improved wave function and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C2 and Cr2 molecule.
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Affiliation(s)
- Ke Liao
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Lexin Ding
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Christian Schilling
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
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3
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Franco L, Bonfil-Rivera IA, Huan Lew-Yee JF, Piris M, M Del Campo J, Vargas-Hernández RA. Softmax parameterization of the occupation numbers for natural orbital functionals based on electron pairing approaches. J Chem Phys 2024; 160:244107. [PMID: 38920134 DOI: 10.1063/5.0213719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 06/07/2024] [Indexed: 06/27/2024] Open
Abstract
Within the framework of natural orbital functional theory, having a convenient representation of the occupation numbers and orbitals becomes critical for the computational performance of the calculations. Recognizing this, we propose an innovative parametrization of the occupation numbers that takes advantage of the electron-pairing approach used in Piris natural orbital functionals through the adoption of the softmax function, a pivotal component in modern deep-learning models. Our approach not only ensures adherence to the N-representability of the first-order reduced density matrix (1RDM) but also significantly enhances the computational efficiency of 1RDM functional theory calculations. The effectiveness of this alternative parameterization approach was assessed using the W4-17-MR molecular set, which demonstrated faster and more robust convergence compared to previous implementations.
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Affiliation(s)
- Lizeth Franco
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P. 04510, Mexico
| | - Iván A Bonfil-Rivera
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P. 04510, Mexico
| | | | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Spain
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), 20018 Donostia, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P. 04510, Mexico
| | - Rodrigo A Vargas-Hernández
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada
- Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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4
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Giarrusso S, Gori-Giorgi P, Agostini F. Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction. Chemphyschem 2024:e202400127. [PMID: 38837609 DOI: 10.1002/cphc.202400127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 06/01/2024] [Accepted: 06/03/2024] [Indexed: 06/07/2024]
Abstract
We generalize the definitions of local scalar potentials namedυ kin ${\upsilon _{{\rm{kin}}} }$ andυ N - 1 ${\upsilon _{N - 1} }$ , which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.
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Affiliation(s)
- Sara Giarrusso
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France
| | - Paola Gori-Giorgi
- Department of Chemistry & Pharmaceutical Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV, Amsterdam, The Netherlands
- Microsoft Research AI4Science, Evert van de Beekstraat 354, 1118CZ, Schiphol, The Netherlands
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France
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5
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Cartier NG, Giesbertz KJH. Exploiting the Hessian for a Better Convergence of the SCF-RDMFT Procedure. J Chem Theory Comput 2024; 20:3669-3682. [PMID: 38668734 PMCID: PMC11099978 DOI: 10.1021/acs.jctc.4c00118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Revised: 04/03/2024] [Accepted: 04/04/2024] [Indexed: 05/15/2024]
Abstract
One-body reduced density matrix functional theory provides an alternative to density functional theory, which is able to treat static correlation while keeping a relatively low computation scaling. Its disadvantageous cost comes mainly from a slow convergence of the self-consistent energy optimization. To improve on that problem, we propose in this work the use of the Hessian of the energy, including the coupling term. We show that using the exact Hessian is very effective at reducing the number of iterations. However, since the exact Hessian is too expensive to use in practice, we propose an approximation based on an inexpensive exact part and BFGS updates.
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Affiliation(s)
- Nicolas G. Cartier
- Department of Chemistry & Pharmaceutical
Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS),
Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Klaas J. H. Giesbertz
- Department of Chemistry & Pharmaceutical
Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS),
Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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6
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Lew-Yee JFH, Bonfil-Rivera IA, Piris M, M. del Campo J. Excited States by Coupling Piris Natural Orbital Functionals with the Extended Random-Phase Approximation. J Chem Theory Comput 2024; 20:2140-2151. [PMID: 38353418 PMCID: PMC10938499 DOI: 10.1021/acs.jctc.3c01194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Revised: 01/30/2024] [Accepted: 01/31/2024] [Indexed: 03/13/2024]
Abstract
In this work, we explore the use of Piris natural orbital functionals (PNOFs) to calculate excited-state energies by coupling their reconstructed second-order reduced density matrix with the extended random-phase approximation (ERPA). We have named the general method PNOF-ERPA, and specific approaches are referred to as PNOF-ERPA0, PNOF-ERPA1, and PNOF-ERPA2, according to the way the excitation operator is built. The implementation has been tested in the first excited states of H2, HeH+, LiH, Li2, and N2 showing good results compared to the configuration interaction (CI) method. As expected, an increase in accuracy is observed on going from ERPA0 to ERPA1 and ERPA2. We also studied the effect of electron correlation included by PNOF5, PNOF7, and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where GNOF achieves better results. Overall, the extension of PNOF to excited states has been successful, making it a promising method for further applications.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento
de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P.
04510, Mexico
- Donostia
International Physics Center (DIPC), 20018 Donostia, Spain
| | - Iván Alejandro Bonfil-Rivera
- Departamento
de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P.
04510, Mexico
| | - Mario Piris
- Donostia
International Physics Center (DIPC), 20018 Donostia, Spain
- Kimika
Fakultatea, Euskal Herriko Unibertsitatea
(UPV/EHU), 20018 Donostia, Spain
- IKERBASQUE,
Basque Foundation for Science, 48013 Bilbao, Spain
| | - Jorge M. del Campo
- Departamento
de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P.
04510, Mexico
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7
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Rivero Santamaría A, Piris M. Time evolution of natural orbitals in ab initio molecular dynamics. J Chem Phys 2024; 160:071102. [PMID: 38364005 DOI: 10.1063/5.0188491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 01/28/2024] [Indexed: 02/18/2024] Open
Abstract
This work combines for the first time ab initio molecular dynamics (AIMD) within the Born-Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(4S) + H2(1Σ) → NH(3Σ) + H(2S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H2 and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results.
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Affiliation(s)
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain; Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain; and Basque Foundation for Science (IKERBASQUE), 48009 Bilbao, Euskadi, Spain
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8
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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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9
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Giarrusso S, Loos PF. Exact Excited-State Functionals of the Asymmetric Hubbard Dimer. J Phys Chem Lett 2023; 14:8780-8786. [PMID: 37739406 PMCID: PMC10561271 DOI: 10.1021/acs.jpclett.3c02052] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 08/31/2023] [Indexed: 09/24/2023]
Abstract
The exact functionals associated with the (singlet) ground state and the two singlet excited states of the asymmetric Hubbard dimer at half-filling are calculated using both Levy's constrained search and Lieb's convex formulation. While the ground-state functional is, as is commonly known, a convex function with respect to the density, the functional associated with the doubly excited state is found to be concave. Also, because the density-potential mapping associated with the first excited state is noninvertible, its "functional" is a partial, multivalued function composed of one concave and one convex branch that correspond to two separate domains of the external potential. Remarkably, it is found that, although the one-to-one mapping between density and external potential may not apply (as in the case of the first excited state), each state-specific energy and corresponding universal functional are "functions" whose derivatives are each other's inverse, just as in the ground state formalism.
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Affiliation(s)
- Sara Giarrusso
- Laboratoire de Chimie et
Physique Quantiques (UMR 5626), Université
de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et
Physique Quantiques (UMR 5626), Université
de Toulouse, CNRS, UPS, 31062 Toulouse, France
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10
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Mazziotti DA. Quantum Many-Body Theory from a Solution of the N-Representability Problem. PHYSICAL REVIEW LETTERS 2023; 130:153001. [PMID: 37115895 DOI: 10.1103/physrevlett.130.153001] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 02/13/2023] [Accepted: 03/16/2023] [Indexed: 06/19/2023]
Abstract
Here we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H_{8} ring.
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Affiliation(s)
- David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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11
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Huan Lew-Yee JF, Piris M, Del Campo JM. Outstanding improvement in removing the delocalization error by global natural orbital functional. J Chem Phys 2023; 158:084110. [PMID: 36859086 DOI: 10.1063/5.0137378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023] Open
Abstract
This work assesses the performance of the recently proposed global natural orbital functional (GNOF) against the charge delocalization error. GNOF provides a good balance between static and dynamic electronic correlations leading to accurate total energies while preserving spin, even for systems with a highly multi-configurational character. Several analyses were applied to the functional, namely, (i) how the charge is distributed in super-systems of two fragments, (ii) the stability of ionization potentials while increasing the system size, and (iii) potential energy curves of a neutral and charged diatomic system. GNOF was found to practically eliminate the charge delocalization error in many of the studied systems or greatly improve the results obtained previously with PNOF7.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain; Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain; and Basque Foundation for Science (IKERBASQUE), 48009 Bilbao, Euskadi, Spain
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico
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12
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Lew-Yee JFH, Del Campo JM, Piris M. Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations. J Chem Theory Comput 2023; 19:211-220. [PMID: 36579972 PMCID: PMC9996833 DOI: 10.1021/acs.jctc.2c01093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Møller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México CityC.P. 04510, México
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México CityC.P. 04510, México
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080Donostia, Euskadi, Spain.,Donostia International Physics Center (DIPC), 20018Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science, 48013Bilbao, Euskadi, Spain
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13
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Mercero JM, Grande-Aztatzi R, Ugalde JM, Piris M. Natural orbital functional theory studies of all-metal aromaticity: The Al 3−anion. ADVANCES IN QUANTUM CHEMISTRY 2023. [DOI: 10.1016/bs.aiq.2023.02.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/28/2023]
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14
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Benavides-Riveros CL, Chen L, Schilling C, Mantilla S, Pittalis S. Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-Based Approach. PHYSICAL REVIEW LETTERS 2022; 129:066401. [PMID: 36018631 DOI: 10.1103/physrevlett.129.066401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
State-average calculations based on a mixture of states are increasingly being exploited across chemistry and physics as versatile procedures for addressing excitations of quantum many-body systems. If not too many states should need to be addressed, calculations performed on individual states are also a common option. Here we show how the two approaches can be merged into one method, dealing with a generalized yet single pure state. Implications in electronic structure calculations are discussed and for quantum computations are pointed out.
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Affiliation(s)
- Carlos L Benavides-Riveros
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- INO-CNR BEC Center, I-38123 Trento, Italy
| | - Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Christian Schilling
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Sebastián Mantilla
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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15
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Lemke Y, Kussmann J, Ochsenfeld C. Efficient Integral-Direct Methods for Self-Consistent Reduced Density Matrix Functional Theory Calculations on Central and Graphics Processing Units. J Chem Theory Comput 2022; 18:4229-4244. [DOI: 10.1021/acs.jctc.2c00231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Y. Lemke
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
| | - J. Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
| | - C. Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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16
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Boyn JN, Mazziotti DA. Elucidating the molecular orbital dependence of the total electronic energy in multireference problems. J Chem Phys 2022; 156:194104. [PMID: 35597644 DOI: 10.1063/5.0090342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference and dynamic correlation effects. A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an exponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investigated. Recent research has shown the ability of Kohn-Shan density functional theory to provide improved orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations. Here, we extend the search for optimal and more cost effective MOs to post-configuration-interaction [post-(CI)] methods, surveying the ability of the MOs obtained with various density functional theory (DFT) functionals, as well as Hartree-Fock and CC and MP calculations to accurately capture the total electronic correlation energy. Applying the anti-Hermitian contracted Schrödinger equation to the dissociation of N2, the calculation of biradical singlet-triplet gaps, and the transition states of bicylobutane isomerization, we demonstrate that DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for post-CI dynamic correlation calculations.
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Affiliation(s)
- Jan-Niklas Boyn
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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Jara-Cortés J, Matta CF, Hernández-Trujillo J. A fast approximate extension of the interacting quantum atoms energy decomposition to excited states. J Comput Chem 2022; 43:1068-1078. [PMID: 35470908 DOI: 10.1002/jcc.26863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Revised: 02/25/2022] [Accepted: 03/23/2022] [Indexed: 11/11/2022]
Abstract
An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact Vxc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.
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Affiliation(s)
- Jesús Jara-Cortés
- Unidad Académica de Ciencias Básicas e Ingenierías, Universidad Autónoma de Nayarit, Tepic, Mexico
| | - Chérif F Matta
- Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, Nova Scotia, Canada
| | - Jesús Hernández-Trujillo
- Departamento de Física y Química Teórica, Facultad de Química, UNAM. Circuito Escolar, Ciudad Universitaria, Mexico City, Mexico
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Gibney D, Boyn JN, Mazziotti DA. Density Functional Theory Transformed into a One-Electron Reduced-Density-Matrix Functional Theory for the Capture of Static Correlation. J Phys Chem Lett 2022; 13:1382-1388. [PMID: 35113577 DOI: 10.1021/acs.jpclett.2c00083] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Density Functional Theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically transformed into a one-electron reduced-density-matrix (1-RDM) functional theory, which can address the limitations of DFT while retaining favorable computational scaling compared to wave function based approaches. In addition to relaxing the idempotency restriction on the 1-RDM in the kinetic energy term, we add a quadratic 1-RDM-based term to DFT's density-based exchange-correlation functional. Our approach, which we implement by quadratic semidefinite programming at DFT's computational scaling of O(r3), yields substantial improvements over traditional DFT in the description of static correlation in chemical structures and processes such as singlet biradicals and bond dissociations.
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Affiliation(s)
- Daniel Gibney
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jan-Niklas Boyn
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A Mazziotti
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
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Liebert J, Castillo F, Labbé JP, Schilling C. Foundation of One-Particle Reduced Density Matrix Functional Theory for Excited States. J Chem Theory Comput 2021; 18:124-140. [PMID: 34931830 DOI: 10.1021/acs.jctc.1c00561] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In Phys. Rev. Lett. 2021, 127, 023001 a reduced density matrix functional theory (RDMFT) was proposed for calculating energies of selected eigenstates of interacting many-Fermion systems. Here, we develop a solid foundation for this so-called w-RDMFT and present the details of various derivations. First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights w in combination with the constrained search would lead to a universal functional of the one-particle reduced density matrix. To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. This general procedure includes Valone's pioneering work on ground state RDMFT as the special case w = (1,0, ···). Then, we work out in a comprehensive manner a methodology for deriving a compact description of the functional's domain. This leads to a hierarchy of generalized exclusion principle constraints which we illustrate in great detail. By anticipating their future pivotal role in functional theories and to keep our work self-contained, several required concepts from convex analysis are introduced and discussed.
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Affiliation(s)
- 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
| | - Federico Castillo
- Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany
| | - Jean-Philippe Labbé
- 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.,Institut für Mathematik, Freie Universität Berlin, Arnimallee 2, 14195, Berlin, 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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Ensemble Density Functional Theory of Neutral and Charged Excitations : Exact Formulations, Standard Approximations, and Open Questions. Top Curr Chem (Cham) 2021; 380:4. [PMID: 34825294 DOI: 10.1007/s41061-021-00359-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 11/02/2021] [Indexed: 10/19/2022]
Abstract
Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and N-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx) energies is discussed in detail. We show in passing that state-averaging individual exact Hx energies can lead to severe (although solvable) v-representability issues. Finally, we explore the possibility of using the concept of density-driven correlation, which has been introduced recently and does not exist in regular ground-state DFT, for improving state-of-the-art correlation density-functional approximations for ensembles. The present review reflects the efforts of a growing community to turn ensemble DFT into a rigorous and reliable low-cost computational method for excited states. We hope that, in the near future, this contribution will stimulate new formal and practical developments in the field.
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