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Daas K, Klute E, Seidl M, Gori-Giorgi P. Møller-Plesset Adiabatic Connection at Large Coupling Strengths for Open-Shell Systems. J Phys Chem A 2024; 128:4138-4149. [PMID: 38717868 PMCID: PMC11129316 DOI: 10.1021/acs.jpca.4c00788] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 03/29/2024] [Accepted: 04/05/2024] [Indexed: 05/24/2024]
Abstract
We study the adiabatic connection that has as weak-coupling expansion the Møller-Plesset perturbation series, generalizing to the open-shell case previous closed-shell results for the large-coupling limit. We first focus on the hydrogen atom with fractional spins, providing results along the adiabatic connection from small to large coupling strengths. We reveal an intriguing phase diagram and an equation for the large-coupling leading order that has closed-form solutions for specific choices of its relevant quantum numbers. We then show that the hydrogen atom results provide variational estimates for the large-coupling leading terms for the general many-electron open-shell case in terms of functionals of the Hartree-Fock α-spin and β-spin densities.
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Affiliation(s)
- Kimberly
J. Daas
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081 HV, The Netherlands
| | - Eveline Klute
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081 HV, 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, Amsterdam 1081 HV, 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, Amsterdam 1081 HV, The Netherlands
- Microsoft
Research AI for Science, Evert van de Beekstraat 354, Schiphol 1118 CZ, The Netherlands
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2
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Burgess AC, Linscott E, O'Regan DD. The convexity condition of density-functional theory. J Chem Phys 2023; 159:211102. [PMID: 38038199 DOI: 10.1063/5.0174159] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Accepted: 11/08/2023] [Indexed: 12/02/2023] Open
Abstract
It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham bandgap and the exchange-correlation derivative discontinuity of DFT.
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Affiliation(s)
- Andrew C Burgess
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Ireland
| | - Edward Linscott
- Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - David D O'Regan
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Ireland
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Daas KJ, Kooi DP, Peters NC, Fabiano E, Della Sala F, Gori-Giorgi P, Vuckovic S. Regularized and Opposite Spin-Scaled Functionals from Møller-Plesset Adiabatic Connection─Higher Accuracy at Lower Cost. J Phys Chem Lett 2023; 14:8448-8459. [PMID: 37721318 DOI: 10.1021/acs.jpclett.3c01832] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/19/2023]
Abstract
Noncovalent interactions (NCIs) play a crucial role in biology, chemistry, material science, and everything in between. To improve pure quantum-chemical simulations of NCIs, we propose a methodology for constructing approximate correlation energies by combining an interpolation along the Møller-Plesset adiabatic connection (MP AC) with a regularization and spin-scaling strategy applied to MP2 correlation energies. This combination yields cosκos-SPL2, which exhibits superior accuracy for NCIs compared to any of the individual strategies. With the N4 formal scaling, cosκos-SPL2 is competitive or often outperforms more expensive dispersion-corrected double hybrids for NCIs. The accuracy of cosκos-SPL2 particularly shines for anionic halogen bonded complexes, where it surpasses standard dispersion-corrected DFT by a factor of 3 to 5.
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Affiliation(s)
- Kimberly 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
- Microsoft Research AI4Science, Evert van de Beekstraat 354, 1118CZ Schiphol, The Netherlands
| | - Nina C Peters
- 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), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, 73010 Arnesano, Italy
| | - 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, 73010 Arnesano, 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
- Microsoft Research AI4Science, Evert van de Beekstraat 354, 1118CZ Schiphol, The Netherlands
| | - Stefan Vuckovic
- Department of Chemistry, Faculty of Science and Medicine, Université de Fribourg/Universität Freiburg, Chemin du Musée 9, CH-1700 Fribourg, Switzerland
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Coveney CJN, Tew DP. A Regularized Second-Order Correlation Method from Green's Function Theory. J Chem Theory Comput 2023. [PMID: 37367932 DOI: 10.1021/acs.jctc.3c00246] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.
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Affiliation(s)
| | - David P Tew
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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Prokopiou G, Hartstein M, Govind N, Kronik L. Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals. J Chem Theory Comput 2022; 18:2331-2340. [PMID: 35369687 PMCID: PMC9009176 DOI: 10.1021/acs.jctc.2c00082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Indexed: 11/29/2022]
Abstract
We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H2+, and improve the dissociation curves of many-electron molecules such as H2 and Li2, but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.
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Affiliation(s)
- Georgia Prokopiou
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Michal Hartstein
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Niranjan Govind
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Leeor Kronik
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
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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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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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