1
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Constantin LA, Jana S, Śmiga S, Della Sala F. Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas. J Chem Phys 2023; 159:244111. [PMID: 38149733 DOI: 10.1063/5.0178800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 11/27/2023] [Indexed: 12/28/2023] Open
Abstract
The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.
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Affiliation(s)
- Lucian A Constantin
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
| | - Subrata Jana
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudziądzka 5, 87-100 Toruń, Poland
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano (LE), Italy
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2
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Jana S, Śmiga S, Constantin LA, Samal P. Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations. J Phys Chem A 2023; 127:8685-8697. [PMID: 37811903 PMCID: PMC10591512 DOI: 10.1021/acs.jpca.3c03976] [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: 06/12/2023] [Revised: 08/24/2023] [Indexed: 10/10/2023]
Abstract
The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.
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Affiliation(s)
- Subrata Jana
- Department
of Chemistry & Biochemistry, The Ohio
State University, Columbus, Ohio 43210, United States
| | - Szymon Śmiga
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzikadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Istituto
di Nanoscienze, Consiglio Nazionale delle
Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School
of Physical Sciences, National Institute of Science Education and
Research, HBNI, Bhubaneswar 752050, India
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3
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Giarrusso S, Pribram-Jones A. Møller-Plesset and Density-Fixed Adiabatic Connections for a Model Diatomic System at Different Correlation Regimes. J Chem Theory Comput 2023; 19:5835-5850. [PMID: 37642270 DOI: 10.1021/acs.jctc.3c00529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In recent years, adiabatic connection (AC) interpolations developed within density functional theory (DFT) have been found to provide good performances in the calculation of interaction energies when used with Hartree-Fock (HF) ingredients. The physical and mathematical reasons for such unanticipated performance have been clarified, to some extent, by studying the strong-interaction limit of the Møller-Plesset (MP) AC. In this work, we calculate both the MP and the DFT AC integrand for the asymmetric Hubbard dimer, which allows for a systematic investigation of different correlation regimes by varying two simple parameters in the Hamiltonian: the external potential, Δv, and the interaction strength, U. Notably, we find that, while the DFT AC integrand appears to be convex in the full parameter space, the MP integrand may change curvature twice. Furthermore, we discuss different aspects of the second-order expansion of the correlation energy in each AC, and we demonstrate why the derivative of the λ-dependent density in the MP AC at λ = 0 (i.e., at the HF density) is zero in the model. Concerning the strong-interaction limit of both ACs in the Hubbard dimer setting, we show that the asymptotic value of the MP AC, W∞HF, is lower than (or equal to) its DFT analogue, W∞KS, if the two are compared at a given density, just like in real space. However, we also show that this is not always the case if the two quantities are compared at a given external potential.
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Affiliation(s)
- Sara Giarrusso
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Rd., Merced, California 95343, United States
| | - Aurora Pribram-Jones
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Rd., Merced, California 95343, United States
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4
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Śmiga S, Della Sala F, Gori-Giorgi P, Fabiano E. Self-Consistent Implementation of Kohn-Sham Adiabatic Connection Models with Improved Treatment of the Strong-Interaction Limit. J Chem Theory Comput 2022; 18:5936-5947. [PMID: 36094908 PMCID: PMC9558377 DOI: 10.1021/acs.jctc.2c00352] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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Adiabatic connection
models (ACMs), which interpolate between the
limits of weak and strong interaction, are powerful tools to build
accurate exchange–correlation functionals. If the exact weak-interaction
expansion from the second-order perturbation theory is included, a
self-consistent implementation of these functionals is challenging
and still absent in the literature. In this work, we fill this gap
by presenting a fully self-consistent-field (SCF) implementation of
some popular ACM functionals. While using second-order perturbation
theory at weak interactions, we have also introduced new generalized
gradient approximations (GGAs), beyond the usual point-charge-plus-continuum
model, for the first two leading terms at strong interactions, which
are crucial to ensure robustness and reliability. We then assess the
SCF–ACM functionals for molecular systems and for prototypical
strong-correlation problems. We find that they perform well for both
the total energy and the electronic density and that the impact of
SCF orbitals is directly connected to the accuracy of the ACM functional
form. For the H2 dissociation, the SCF–ACM functionals
yield significant improvements with respect to standard functionals
also thanks to the use of the new GGAs for the strong-coupling functionals.
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Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudziądzka 5, 87-100 Toruń, Poland
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Lecce, Via Monteroni 73100, Italy.,Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, Arnesano, Lecce 73010, Italy
| | - 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
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Lecce, Via Monteroni 73100, Italy.,Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, Arnesano, Lecce 73010, Italy
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5
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Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits. COMPUTATION 2022. [DOI: 10.3390/computation10050077] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, we present details of the Sham–Schluter equation approach that we use to obtain, in principle, an exact XC potential from a many-body theory solution for the nonequilibrium electron self-energy. We derive the XC potentials for the one-band Hubbard model in the limits of weak and strong on-site Coulomb repulsion. To test the accuracy of the obtained potentials, we compare the TDDFT results obtained with these potentials with the corresponding nonequilibrium DMFT solution for the one-band Hubbard model and find that the agreement between the solutions is rather good. We also discuss possible directions to obtain a universal XC potential that would be appropriate for the case of intermediate interaction strengths, i.e., a nonadiabatic potential that can be used to perform TDDFT analysis of nonequilibrium phenomena, such as transport and other ultrafast properties of materials with any strength of electron correlation at any value in the applied perturbing field.
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6
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Vacondio S, Varsano D, Ruini A, Ferretti A. Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms. J Chem Theory Comput 2022; 18:3703-3717. [PMID: 35561415 PMCID: PMC9202310 DOI: 10.1021/acs.jctc.2c00048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
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We investigate the
performance of beyond-GW approaches in many-body
perturbation theory by addressing atoms described within the spherical
approximation via a dedicated numerical treatment based on B-splines
and spherical harmonics. We consider the GW, second Born (2B), and
GW + second order screened exchange (GW+SOSEX) self-energies and use
them to obtain ionization potentials from the quasi-particle equation
(QPE) solved perturbatively on top of independent-particle calculations.
We also solve the linearized Sham–Schlüter equation
(LSSE) and compare the resulting xc potentials against exact data.
We find that the LSSE provides consistent starting points for the
QPE but does not present any practical advantage in the present context.
Still, the features of the xc potentials obtained with it shed light
on possible strategies for the inclusion of beyond-GW diagrams in
the many-body self-energy. Our findings show that solving the QPE
with the GW+SOSEX self-energy on top of a PBE or PBE0 solution is
a viable scheme to go beyond GW in finite systems, even in the atomic
limit. However, GW shows a comparable performance if one agrees to
use a hybrid starting point. We also obtain promising results with
the 2B self-energy on top of Hartree–Fock, suggesting that
the full time-dependent Hartree–Fock vertex may be another
viable beyond-GW scheme for finite systems.
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Affiliation(s)
- S Vacondio
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via G. Campi 213/a, Modena 41121, Italy.,Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
| | - D Varsano
- Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
| | - A Ruini
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via G. Campi 213/a, Modena 41121, Italy.,Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
| | - A Ferretti
- Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
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7
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Sim E, Song S, Vuckovic S, Burke K. Improving Results by Improving Densities: Density-Corrected Density Functional Theory. J Am Chem Soc 2022; 144:6625-6639. [PMID: 35380807 DOI: 10.1021/jacs.1c11506] [Citation(s) in RCA: 34] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.
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Affiliation(s)
- Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Stefan Vuckovic
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni,Campus Unisalento, 73100 Lecce, Italy.,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
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
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8
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Daas T, Kooi DP, Grooteman AJAF, Seidl M, Gori-Giorgi P. Gradient Expansions for the Large-Coupling Strength Limit of the Møller-Plesset Adiabatic Connection. J Chem Theory Comput 2022; 18:1584-1594. [PMID: 35179386 PMCID: PMC8908763 DOI: 10.1021/acs.jctc.1c01206] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Indexed: 11/28/2022]
Abstract
The adiabatic connection that has, as weak-interaction expansion, the Møller-Plesset perturbation series has been recently shown to have a large coupling-strength expansion, in terms of functionals of the Hartree-Fock density with a clear physical meaning. In this work, we accurately evaluate these density functionals and we extract second-order gradient coefficients from the data for neutral atoms, following ideas similar to the ones used in the literature for exchange, with some modifications. These new gradient expansions will be the key ingredient for performing interpolations that have already been shown to reduce dramatically MP2 errors for large noncovalent complexes. As a byproduct, our investigation of neutral atoms with large number of electrons N indicates that the second-order gradient expansion for exchange grows as N log(N) rather than as N, as often reported in the literature.
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Affiliation(s)
- Timothy
J. Daas
- 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
| | - Derk P. Kooi
- 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
| | - Arthur J. A. F. Grooteman
- 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
| | - Michael Seidl
- 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
| | - 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
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9
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Siecińska S, Śmiga S, Grabowski I, Della Sala F, Fabiano E. Boosting the OEP2-sc method with spin-component scaling. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2037771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sylwia Siecińska
- Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Toruń, Toruń, Poland
| | - Szymon Śmiga
- Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Toruń, Toruń, Poland
| | - Ireneusz Grabowski
- Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Toruń, Toruń, Poland
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Arnesano, Italy
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Arnesano, Italy
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10
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Jana S, Śmiga S, Constantin LA, Samal P. Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms. J Chem Theory Comput 2020; 16:7413-7430. [PMID: 33205659 PMCID: PMC7735712 DOI: 10.1021/acs.jctc.0c00823] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Indexed: 11/28/2022]
Abstract
Connections between the Görling-Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew-Burke-Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.
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Affiliation(s)
- Subrata Jana
- School
of Physical Sciences, National Institute
of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Szymon Śmiga
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Consiglio
Nazionale delle Ricerche CNR-NANO, Istituto
di Nanoscienze, 41125 Modena, Italy
| | - Prasanjit Samal
- School
of Physical Sciences, National Institute
of Science Education and Research, HBNI, Bhubaneswar 752050, India
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11
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Jana S, Patra A, Śmiga S, Constantin LA, Samal P. Insights from the density functional performance of water and water–solid interactions: SCAN in relation to other meta-GGAs. J Chem Phys 2020; 153:214116. [DOI: 10.1063/5.0028821] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Istituto di Nanoscienze, Consiglio Nazionale delle Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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12
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Patra A, Jana S, Constantin LA, Samal P. Efficient yet accurate dispersion-corrected semilocal exchange–correlation functionals for non-covalent interactions. J Chem Phys 2020; 153:084117. [DOI: 10.1063/5.0011849] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Lucian A. Constantin
- Istituto di Nanoscienze, Consiglio Nazionale delle Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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13
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Grossi J, Musslimani ZH, Seidl M, Gori-Giorgi P. Kohn-Sham equations with functionals from the strictly-correlated regime: investigation with a spectral renormalization method. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:475602. [PMID: 32759484 DOI: 10.1088/1361-648x/abace2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 08/06/2020] [Indexed: 06/11/2023]
Abstract
We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory, with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential.
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Affiliation(s)
- Juri Grossi
- 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
| | - Ziad H Musslimani
- 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
- Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, United States of America
| | - Michael Seidl
- 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
| | - 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
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14
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Śmiga S, Constantin LA. Modified Interaction-Strength Interpolation Method as an Important Step toward Self-Consistent Calculations. J Chem Theory Comput 2020; 16:4983-4992. [PMID: 32559078 PMCID: PMC7588043 DOI: 10.1021/acs.jctc.0c00328] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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The modified point charge plus continuum (mPC) model [ConstantinL. A.; Phys. Rev. B2019, 99, 085117] solves
the important failures of the original counterpart, namely, the divergences
when the reduced gradient of the density is large, such as in the
tail of the density and in quasi-dimensional density regimes. The
mPC allows us to define a modified interaction-strength interpolation
(mISI) method inheriting these good features, which are important
steps toward the full self-consistent treatment. Here, we provide
an assessment of mISI for molecular systems (i.e.,
considering thermochemistry properties, correlation energies, vertical
ionization potentials, and several noncovalent interactions), harmonium
atoms, and functional derivatives in the strong-interaction limit.
For all our tests, mISI provides a systematic improvement over the
original ISI method. Semilocal approximations of the second-order
Görling–Levy (GL2) perturbation theory are also considered
in the mISI method, showing considerable worsening of the results.
Possible further development of mISI is briefly discussed.
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Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Lucian A Constantin
- Consiglio Nazionale delle Ricerche CNR-NANO, Istituto di Nanoscienze, 41125 Modena, Italy
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15
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Śmiga S, Constantin LA. Unveiling the Physics Behind Hybrid Functionals. J Phys Chem A 2020; 124:5606-5614. [PMID: 32551627 PMCID: PMC7590981 DOI: 10.1021/acs.jpca.0c04156] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2020] [Revised: 06/16/2020] [Indexed: 11/30/2022]
Abstract
We show that accurate exchange-correlation hybrid functionals give very physically optimized effective-correlation potentials, capable of correctly describing the quantum oscillations of atoms and molecules. Based on this analysis and on understanding the error cancellation between semilocal exchange and correlation functionals, we propose a very simple, semilocal correlation potential model compatible with the exact exchange of density functional theory, which performs remarkably well for charge densities and orbital energies.
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Affiliation(s)
- Szymon Śmiga
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Center
for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia (IIT), Via Barsanti, 73010 Arnesano (LE), Italy
- Istituto
di Nanoscienze, Consiglio Nazionale delle
Ricerche CNR-NANO, 41125 Modena, Italy
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16
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Śmiga S, Marusiak V, Grabowski I, Fabiano E. The ab initio density functional theory applied for spin-polarized calculations. J Chem Phys 2020; 152:054109. [DOI: 10.1063/1.5128933] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Volodymyr Marusiak
- Department of Theoretical Physics and Astronomy, I. I. Mechnikov Odessa National University, Dvoryanskaya 2, Odessa 65082, Ukraine
| | - Ireneusz Grabowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
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17
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Gerolin A, Grossi J, Gori-Giorgi P. Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem. J Chem Theory Comput 2020; 16:488-498. [PMID: 31855421 PMCID: PMC6964418 DOI: 10.1021/acs.jctc.9b01133] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Indexed: 11/29/2022]
Abstract
In this work, we study the entropic regularization of the strictly correlated electrons formalism, discussing the implications for density functional theory and establishing a link with earlier works on quantum kinetic energy and classical entropy. We carry out a very preliminary investigation (using simplified models) on the use of the solution of the entropic regularized problem to build approximations for the kinetic correlation functional at large coupling strengths. We also analyze lower and upper bounds to the Hohenberg-Kohn functional using the entropic regularized strictly correlated electrons problem.
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Affiliation(s)
- Augusto Gerolin
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Juri Grossi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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18
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Śmiga S, Grabowski I, Witkowski M, Mussard B, Toulouse J. Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method. J Chem Theory Comput 2019; 16:211-223. [DOI: 10.1021/acs.jctc.9b00807] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Ireneusz Grabowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Mateusz Witkowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Bastien Mussard
- Department of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
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19
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Abstract
The attraction density functional theory (DFT) has for electronic structure theory is that it is easier to do computationally than ab initio, correlated wavefunction methods, due to its effective one-particle structure. On the contrary, ab initio theorists insist on the ability to converge to the right answer in appropriate limits, but this requires a treatment of the reduced two-particle density matrix. DFT avoids that by appealing to an "existence" theorem (not a constructive one) that all its effects are subsummed into a DFT functional of the one-particle density. However, the existence of thousands of DFT functionals emphasizes that there is no satisfactory way to systematically improve the Kohn-Sham (KS) version as most changes in parameterization or formulation seldom lead to a new functional that is genuinely better than others. Some researchers in the DFT community try to address this issue by imposing conditions rigorously derived from exact DFT considerations, but to date, no one has shown how this route will ever lead to converged results even for the ground state, much less for all the other electronic states obtained from time-dependent DFT that are critically important for chemistry. On the contrary, coupled-cluster (CC) theory and its equation-of-motion extensions provide rigorous results for both that KS-DFT methods are attempting to emulate. How to use them and their exact formal properties to tie CC theory to an effective one-particle form is the target of this perspective. This route addresses the devil's triangle of KS-DFT problems: the one-particle spectrum, self-interaction, and the integer discontinuity.
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Affiliation(s)
- Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611-8435, USA
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