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Moltved KA, Kepp KP. Using electronegativity and hardness to test density functionals. J Chem Phys 2020; 152:244113. [PMID: 32610960 DOI: 10.1063/5.0006189] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy-density relationship via the chemical potential ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1-36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at ∼0.2 eV-0.3 eV for η. In contrast, variable performance for χ indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional, we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most "universal" among the tested functionals. B98 and B97-1 are accurate for very diverse metal-ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E2/∂N2, via χ and η, is probably a first simple probe of universality.
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Affiliation(s)
- Klaus A Moltved
- Technical University of Denmark, DTU Chemistry, Building 206, 2800 Kgs. Lyngby, Denmark
| | - Kasper P Kepp
- Technical University of Denmark, DTU Chemistry, Building 206, 2800 Kgs. Lyngby, Denmark
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52
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Savarese M, Brémond É, Ciofini I, Adamo C. Electron Spin Densities and Density Functional Approximations: Open-Shell Polycyclic Aromatic Hydrocarbons as Case Study. J Chem Theory Comput 2020; 16:3567-3577. [DOI: 10.1021/acs.jctc.0c00059] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Marika Savarese
- CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa, Italy
| | - Éric Brémond
- ITODYS, UMR CNRS 7086, Université de Paris, 15 rue J.-A. de Baïf, F-75013 Paris, France
| | - Ilaria Ciofini
- Chimie ParisTech, PSL Research University, CNRS, Institute of Chemistry for Health and Life Sciences, F-75005 Paris, France
| | - Carlo Adamo
- Chimie ParisTech, PSL Research University, CNRS, Institute of Chemistry for Health and Life Sciences, F-75005 Paris, France
- France and Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris, France
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53
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How do the Hückel and Baird Rules Fade away in Annulenes? Molecules 2020; 25:molecules25030711. [PMID: 32045990 PMCID: PMC7037833 DOI: 10.3390/molecules25030711] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Revised: 01/27/2020] [Accepted: 01/29/2020] [Indexed: 01/27/2023] Open
Abstract
Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the Hückel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.
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Lonsdale DR, Goerigk L. The one-electron self-interaction error in 74 density functional approximations: a case study on hydrogenic mono- and dinuclear systems. Phys Chem Chem Phys 2020; 22:15805-15830. [PMID: 32458849 DOI: 10.1039/d0cp01275k] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The self-interaction error (SIE), i.e. unphysical interactions of electrons with themselves, has plagued developers and users of Density Functional Approximations (DFAs) since the inception of Density Functional Theory (DFT). Formally, it can be separated into the one-electron and many-electron SIE; herein we present one of the most comprehensive studies of the first. While we focus mostly on the total SIE, we also make use of two different decompositions. The first is a separation into functional and density-driven errors as championed by Sim, Burke and co-workers [J. Phys. Chem. Lett., 2018, 9, 6385-6392]; the second separates the error into exchange, correlation, and one-electron components, with the latter being a density error that has not been discussed in this form before. After investigating the familiar hydrogen atom and dihydrogen cation, we establish a relationship between the SIE and the nuclear charge with the help of a series of heavier hydrogenic analogues. For the mononuclear systems and the diatomics at the dissociation limit, this relationship is linear in nature with prominent exceptions, mostly belonging to the Minnesota and range-separated (double-)hybrid DFAs. For the first time, we also show how the magnitude of the SIE depends on the underlying atomic-orbital basis set and how DFAs that rely on a popular van-der-Waals DFT type London-dispersion term exhibit "self-dispersion". We find that range separation is not a panacea for solving the one-electron SIE. DFAs that have been developed to be one-electron SIE free for one system, such as the hydrogen atom, show larger errors for heavier hydrogenic systems. Often, one-electron SIE-free DFAs rely on fortuitous error cancellation between their exchange and correlation components. An analysis of the most robust methods for general applications to date reveals that they suffer moderately from the one-electron SIE, while DFAs that are nearly SIE-free do not perform well in applications. Implicit in the continued existence of the one-electron SIE is that well-performing DFAs continue to suffer insufficiencies at their fundamental levels that are being compensated for by the SIE. Our analysis includes more than 250 000 datapoints, resulting in multiple insights that may drive future developments of new DFAs or SIE corrections.
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Affiliation(s)
- Dale R Lonsdale
- School of Chemistry, The University of Melbourne, Parkville, Australia.
| | - Lars Goerigk
- School of Chemistry, The University of Melbourne, Parkville, Australia.
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55
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Wodyński A, Kaupp M. Noncollinear Relativistic Two-Component X2C Calculations of Hyperfine Couplings Using Local Hybrid Functionals. Importance of the High-Density Coordinate Scaling Limit. J Chem Theory Comput 2019; 16:314-325. [PMID: 31834796 DOI: 10.1021/acs.jctc.9b00911] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Local hybrid functionals with position-dependent exact-exchange admixture have been implemented in the noncollinear spin form into a two-component X2C code and are evaluated for the hyperfine coupling tensors of a series of 3d, 4d, and 5d transition-metal complexes. One aim is to see if the potential of local hybrid functionals toward an improved balance between core-shell and valence-shell spin polarization, recently identified in nonrelativistic computations on 3d complexes (Schattenberg, C.; Maier, T. M.; Kaupp, M. J. Chem. Theory Comput. 2018, 14, 5653-5672), can be extended to the hyperfine couplings of heavier metal centers. The correctness of the two-component implementation is first established by comparison to previous computations for 3d systems with or without notable spin-orbit contributions to their hyperfine tensors, and the good performance of a standard "t-LMF" local mixing function is confirmed. However, when moving to 4d and 5d metal centers, the performance of such local mixing functions deteriorates. This is likely due to their violation of the homogeneous coordinate scaling condition in the high-density limit, which is particularly important for the core shells of heavier atoms. A local mixing function that respects this high-density limit performs notably better for heavier metal centers. However, it brings in much too high exact-exchange admixtures for the 3d systems and is too inflexible to simultaneously provide reasonable chemical accuracy in other areas. These results point to the ongoing need to develop improved local mixing functions and local hybrid functionals that exhibit favorable properties in different areas of space defined by very high and much lower electron densities.
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Affiliation(s)
- Artur Wodyński
- Technische Universität Berlin , Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry , Secr. C7, Strasse des 17 Juni 135 , D-10623 Berlin , Germany
| | - Martin Kaupp
- Technische Universität Berlin , Institute of Chemistry, Theoretical Chemistry/Quantum Chemistry , Secr. C7, Strasse des 17 Juni 135 , D-10623 Berlin , Germany
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56
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Vuckovic S, Song S, Kozlowski J, Sim E, Burke K. Density Functional Analysis: The Theory of Density-Corrected DFT. J Chem Theory Comput 2019; 15:6636-6646. [DOI: 10.1021/acs.jctc.9b00826] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stefan Vuckovic
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - John Kozlowski
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
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Moltved KA, Kepp KP. The Metal Hydride Problem of Computational Chemistry: Origins and Consequences. J Phys Chem A 2019; 123:2888-2900. [PMID: 30884233 DOI: 10.1021/acs.jpca.9b02367] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Formation and breaking of metal-hydrogen bonds are central to many important catalytic processes such as transition-metal catalyzed ammonia synthesis, hydrogenation reactions, and water splitting, and thus, they require an adequate theoretical description. We studied a data set of all 30 M-H and 30 M+-H bonds of the 3d, 4d, and 5d transition series; 50 of these systems have experimentally known bond dissociation enthalpies (BDE). To probe both the limit of low and high coordination number, we also studied a data set of 19 ML nH complexes. The BDEs were computed using Hartree-Fock (HF), MP2, CCSD, CCSD(T), and 10 diverse density functionals including local, GGA, hybrid GGA, meta hybrid, range-separated, and double hybrids. Our ten most important findings are as follows: (1) HF fails completely to describe the metal hydrogen bond due to its lack of static correlation; (2) this makes post-HF methods such as MP2 and even CCSD(T) perform worse than many density functionals; (3) DFT requires much more HF exchange (∼35% on average) to describe the pure M-H bonds than to describe other metal ligand bonds (0-20%); (4) we design a test to determine if self-interaction error (SIE) is important by correlating DFT errors against a one-electron SIE metric; (5) we show that SIE correlates directly with the DFT errors and thus causes most of the problem; (6) HF-DFT cannot handle these systems because the HF method is too pathological already at the density level; (7) instead, we define and apply a simple metric of electronic abnormality as the difference in PBE energy computed at the self-consistent PBE0 and SVWN densities, and this metric gives appropriate spread and effectively captures density-derived errors; (8) the low electronegativity of the metal enforces a diffuse hydride-like electron density, which make the metal hydrides primary examples of many-electron systems exhibiting SIE already at equilibrium geometries; (9) in the coordinatively saturated ML nH systems, much less HF exchange is required; i.e., the HF exchange requirements vary drastically with coordination number. Accordingly, DFT is unbalanced for any catalytic process involving both M-H and M-L bonds and changing coordination numbers; (10) importantly, the range-separated and double-hybrid functionals CAM-B3LYP and B2PLYP alone perform well for both M-H and M-L systems and in both limits of low and high coordination number, and at least as well as CCSD(T). This lends hope to a balanced treatment of computational chemistry for all types of M-L bonds at variable coordination number, as required for real catalytic reactions.
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Affiliation(s)
- Klaus A Moltved
- DTU Chemistry , Technical University of Denmark , Building 206 , 2800 Kgs . Lyngby , DK , Denmark
| | - Kasper P Kepp
- DTU Chemistry , Technical University of Denmark , Building 206 , 2800 Kgs . Lyngby , DK , Denmark
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58
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Kim Y, Song S, Sim E, Burke K. Halogen and Chalcogen Binding Dominated by Density-Driven Errors. J Phys Chem Lett 2019; 10:295-301. [PMID: 30562033 DOI: 10.1021/acs.jpclett.8b03745] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Dispersion corrections of various kinds usually improve DFT energetics of weak noncovalent interactions. However, in some cases involving molecules or halides, especially those with σ-hole interactions, the density-driven errors of uncorrected DFT are larger than the dispersion corrections. In these abnormal situations, HF-DFT (using Hartree-Fock densities instead of self-consistent densities) greatly improves bond energies, while dispersion corrections can even worsen the results. On the other hand, pnictogen bonds and the S22 data set are normal and are not improved by this procedure. Such effects should be accounted for when parametrizing dispersion interactions.
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Affiliation(s)
- Yeil Kim
- 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
| | - Eunji Sim
- Department of Chemistry , Yonsei University , 50 Yonsei-ro , Seodaemun-gu, Seoul 03722 , Korea
| | - Kieron Burke
- Department of Chemistry , and Department of Physics , University of California , Irvine , California 92697 , United States
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59
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Mostafanejad M, Haney J, DePrince AE. Kinetic-energy-based error quantification in Kohn–Sham density functional theory. Phys Chem Chem Phys 2019; 21:26492-26501. [DOI: 10.1039/c9cp04595c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a basis-independent metric to assess the quality of the electron density obtained from Kohn–Sham (KS) density functional theory (DFT).
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Affiliation(s)
| | - Jessica Haney
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
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60
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Seidl M, Giarrusso S, Vuckovic S, Fabiano E, Gori-Giorgi P. Communication: Strong-interaction limit of an adiabatic connection in Hartree-Fock theory. J Chem Phys 2018; 149:241101. [DOI: 10.1063/1.5078565] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael Seidl
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - 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
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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