1
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Macke E, Timrov I, Marzari N, Ciacchi LC. Orbital-Resolved DFT +U for Molecules and Solids. J Chem Theory Comput 2024; 20:4824-4843. [PMID: 38820347 PMCID: PMC11171274 DOI: 10.1021/acs.jctc.3c01403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Revised: 03/25/2024] [Accepted: 05/02/2024] [Indexed: 06/02/2024]
Abstract
We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS2) and pyrolusite (β-MnO2), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+U beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.
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Affiliation(s)
- Eric Macke
- Faculty
of Production Engineering, Bremen Center
for Computational Materials Science and MAPEX Center for Materials
and Processes, Hybrid Materials Interfaces Group, University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
| | - Iurii Timrov
- Theory
and Simulation of Materials (THEOS) and National Centre for Computational
Design and Discovery of Novel Materials (MARVEL), École Polytechnique
Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Nicola Marzari
- Theory
and Simulation of Materials (THEOS) and National Centre for Computational
Design and Discovery of Novel Materials (MARVEL), École Polytechnique
Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- University
of Bremen Excellence Chair, Bremen Center
for Computational Materials Science, Am Fallturm 1, 28359 Bremen, Germany
| | - Lucio Colombi Ciacchi
- Faculty
of Production Engineering, Bremen Center
for Computational Materials Science and MAPEX Center for Materials
and Processes, Hybrid Materials Interfaces Group, University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
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2
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Chen X, Cifuentes-Lopez A, Shao X, Lin L, Prokopchuk D, Pavanello M. Unraveling the Hydration Shell Structure and Dynamics of Group 10 Aqua Ions. J Phys Chem Lett 2024; 15:5517-5528. [PMID: 38749061 DOI: 10.1021/acs.jpclett.4c00464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/24/2024]
Abstract
We present ab initio simulations based on subsystem DFT of group 10 aqua ions accurately compared against experimental data on hydration structure. Our simulations provide insights into the molecular structures and dynamics of hydration shells, offering recalibrated interpretations of experimental results. We observe a soft, but distinct second hydration shell in Palladium (Pd) due to a balance between thermal fluctuations, metal-water interactions, and hydrogen bonding. Nickel (Ni) and platinum (Pt) exhibit more rigid hydration shells. Notably, our simulations align with experimental findings for Pd, showing axial hydration marked by a broad peak at about 3 Å in the Pd-O radial distribution function, revising the previously sharp "mesoshell" prediction. We introduce the "hydrogen bond dome" concept to describe a resilient network of hydrogen-bonded water molecules around the metal, which plays a critical role in the axial hydration dynamics.
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Affiliation(s)
- Xin Chen
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | | | - Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Lirong Lin
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Demyan Prokopchuk
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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3
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Cho Y, Kulik HJ. Improving gas adsorption modeling for MOFs by local calibration of Hubbard U parameters. J Chem Phys 2024; 160:154101. [PMID: 38624114 DOI: 10.1063/5.0201934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 03/31/2024] [Indexed: 04/17/2024] Open
Abstract
While computational screening with density functional theory (DFT) is frequently employed for the screening of metal-organic frameworks (MOFs) for gas separation and storage, commonly applied generalized gradient approximations (GGAs) exhibit self-interaction errors, which hinder the predictions of adsorption energies. We investigate the Hubbard U parameter to augment DFT calculations for full periodic MOFs, targeting a more precise modeling of gas molecule-MOF interactions, specifically for N2, CO2, and O2. We introduce a calibration scheme for the U parameter, which is tailored for each MOF, by leveraging higher-level calculations on the secondary building unit (SBU) of the MOF. When applied to the full periodic MOF, the U parameter calibrated against hybrid HSE06 calculations of SBUs successfully reproduces hybrid-quality calculations of the adsorption energy of the periodic MOF. The mean absolute deviation of adsorption energies reduces from 0.13 eV for a standard GGA treatment to 0.06 eV with the calibrated U, demonstrating the utility of the calibration procedure when applied to the full MOF structure. Furthermore, attempting to use coupled cluster singles and doubles with perturbative triples calculations of isolated SBUs for this calibration procedure shows varying degrees of success in predicting the experimental heat of adsorption. It improves accuracy for N2 adsorption for cases of overbinding, whereas its impact on CO2 is minimal, and ambiguities in spin state assignment hinder consistent improvements of O2 adsorption. Our findings emphasize the limitations of cluster models and advocate the use of full periodic MOF systems with a calibrated U parameter, providing a more comprehensive understanding of gas adsorption in MOFs.
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Affiliation(s)
- Yeongsu Cho
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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4
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Gallagher C, Siddiqui W, Arnold T, Cheng C, Su E, Zhao Q. Benchmarking a Molecular Flake Model on the Road to Programmable Graphene-Based Single-Atom Catalysts. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2024; 128:2876-2883. [PMID: 38414836 PMCID: PMC10895666 DOI: 10.1021/acs.jpcc.3c07681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Revised: 01/19/2024] [Accepted: 01/30/2024] [Indexed: 02/29/2024]
Abstract
Single-atom catalysts (SACs) of embedding an active metal in nitrogen-doped graphene are emergent catalytic materials in various applications. The rational design of efficient SACs necessitates an electronic and mechanistic understanding of those materials with reliable quantum mechanical simulations. Conventional computational methods of modeling SACs involve using an infinite slab model with periodic boundary condition, limiting to the selection of generalized gradient approximations as the exchange correlation (XC) functional within density functional theory (DFT). However, these DFT approximations suffer from electron self-interaction error and delocalization error, leading to errors in predicted charge-transfer energetics. An alternative strategy is using a molecular flake model, which carved out the important catalytic center by cleaving C-C bonds and employing a hydrogen capping scheme to saturate the innocent dangling bonds at the molecular boundary. By doing so, we can afford more accurate hybrid XC functionals, or even high-level correlated wavefunction theory, to study those materials. In this work, we compared the structural, electronic, and catalytic properties of SACs simulated using molecular flake models and periodic slab models with first-row transition metals as the active sites. Molecular flake models successfully reproduced structural properties, including both global distortion and local metal-coordination environment, as well as electronic properties, including spin magnetic moments and metal partial charges, for all transition metals studied. In addition, we calculated CO binding strength as a descriptor for electrochemical CO2 reduction reactivity and noted qualitatively similar trends between two models. Using the computationally efficient molecular flake models, we investigated the effect of tuning Hartree-Fock exchange in a global hybrid functional on the CO binding strength and observed system-dependent sensitivities. Overall, our calculations provide valuable insights into the development of accurate and efficient computational tools to simulate SACs.
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Affiliation(s)
- Colin Gallagher
- Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Wali Siddiqui
- Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Tyler Arnold
- Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Carmen Cheng
- Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Eric Su
- Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Qing Zhao
- Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
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5
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Cytter Y, Nandy A, Duan C, Kulik HJ. Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models. Phys Chem Chem Phys 2023; 25:8103-8116. [PMID: 36876903 DOI: 10.1039/d3cp00258f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Abstract
Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.
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Affiliation(s)
- Yael Cytter
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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6
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Janesko BG. Unification of Perdew-Zunger self-interaction correction, DFT+U, and Rung 3.5 density functionals. J Chem Phys 2022; 157:151101. [PMID: 36272781 DOI: 10.1063/5.0109338] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This Communication presents a unified derivation of three different approximations used in density functional theory (DFT): the Perdew-Zunger self-interaction correction (PZSIC), the Hubbard correction DFT+U, and the Rung 3.5 density functionals. All three approximations can be derived by introducing electron self-interaction into the Kohn-Sham (KS) reference system of noninteracting electrons. The derivation uses the Adiabatic Projection formalism: one projects the electron-electron interaction operator onto certain states, introduces the projected operator into the reference system, and defines a density functional for the remainder. Projecting onto individual localized KS orbitals recovers our previous derivation of the PZSIC [B. G. Janesko, J. Phys. Chem. Lett. 13, 5698-5702 (2022)]. Projecting onto localized atom-centered orbitals recovers a variant of DFT+U. Projecting onto localized states at each point in space recovers Rung 3.5 approaches. New results include an "atomic state PZSIC" that does not require localizing the KS orbitals, a demonstration that typical Hubbard U parameters reproduce a scaled-down PZSIC, and a Rung 3.5 variant of DFT+U that does not require choosing atom-dependent states.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76109, USA
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7
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Cytter Y, Nandy A, Bajaj A, Kulik HJ. Ligand Additivity and Divergent Trends in Two Types of Delocalization Errors from Approximate Density Functional Theory. J Phys Chem Lett 2022; 13:4549-4555. [PMID: 35579948 DOI: 10.1021/acs.jpclett.2c01026] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The predictive accuracy of density functional theory (DFT) is hampered by delocalization errors, especially for correlated systems such as transition-metal complexes. Two complementary strategies have been developed to reduce delocalization error: eliminating the global curvature with change in charge, and applying a linear response Hubbard U as a measure of local curvature at a metal center at fixed charge in a DFT+U framework. We investigate the relationship between the two delocalization error measures as the ligand field strength is varied with the number of strong-field ligands in a series of heteroleptic complexes or by geometrically constraining the metal-ligand bond length in homoleptic octahedral complexes. We show that across these sets of complexes an inverse relationship generally exists between global and local curvatures. We find that effects of ligand substitution on both measures of delocalization are typically additive, but the quantities seldom coincide.
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Affiliation(s)
- Yael Cytter
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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8
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Bajaj A, Duan C, Nandy A, Taylor MG, Kulik HJ. Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry. J Chem Phys 2022; 156:184112. [DOI: 10.1063/5.0089460] [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
Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.
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Affiliation(s)
- Akash Bajaj
- Massachusetts Institute of Technology, United States of America
| | - Chenru Duan
- Massachusetts Institute of Technology, United States of America
| | - Aditya Nandy
- Massachusetts Institute of Technology, United States of America
| | | | - Heather J. Kulik
- Dept of Chemical Engineering, Massachusetts Institute of Technology, United States of America
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9
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Bajaj A, Kulik HJ. Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U. J Chem Theory Comput 2022; 18:1142-1155. [PMID: 35081711 DOI: 10.1021/acs.jctc.1c01178] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO2) and late (i.e., PtO2) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO2(110) and PtO2(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.,Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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10
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Nandy A, Duan C, Taylor MG, Liu F, Steeves AH, Kulik HJ. Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning. Chem Rev 2021; 121:9927-10000. [PMID: 34260198 DOI: 10.1021/acs.chemrev.1c00347] [Citation(s) in RCA: 70] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.
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Affiliation(s)
- Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Michael G Taylor
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Fang Liu
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Adam H Steeves
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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11
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Janesko BG. Replacing hybrid density functional theory: motivation and recent advances. Chem Soc Rev 2021; 50:8470-8495. [PMID: 34060549 DOI: 10.1039/d0cs01074j] [Citation(s) in RCA: 55] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Dr, Fort Worth, TX 76129, USA.
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12
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Mariano LA, Vlaisavljevich B, Poloni R. Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density. J Chem Theory Comput 2021; 17:2807-2816. [PMID: 33831303 DOI: 10.1021/acs.jctc.1c00034] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.
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Affiliation(s)
- Lorenzo A Mariano
- University Grenoble Alpes, CNRS, Grenoble-INP, SIMaP, F-38042 Grenoble, France
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Roberta Poloni
- University Grenoble Alpes, CNRS, Grenoble-INP, SIMaP, F-38042 Grenoble, France
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13
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Bajaj A, Kulik HJ. Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error. J Phys Chem Lett 2021; 12:3633-3640. [PMID: 33826346 DOI: 10.1021/acs.jpclett.1c00796] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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14
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Affiliation(s)
- Heather J. Kulik
- Department of Chemical Engineering Massachusetts Institute of Technology 77 Massachusetts Ave Rm 66–464 Cambridge MA 02139 USA
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15
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Fransson T, Brumboiu IE, Vidal ML, Norman P, Coriani S, Dreuw A. XABOOM: An X-ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s → π* Transitions. J Chem Theory Comput 2021; 17:1618-1637. [PMID: 33544612 PMCID: PMC8023667 DOI: 10.1021/acs.jctc.0c01082] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Indexed: 01/05/2023]
Abstract
The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precision rather than on accuracy of transition energies and intensities-in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange-correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2-0.3 eV and ∼10%, respectively, as compared to 0.3-0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initio calculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.
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Affiliation(s)
- Thomas Fransson
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls
University, Im Neuenheimer
Feld 205, 69120 Heidelberg, Germany
- Fysikum, Stockholm University, Albanova, 10691 Stockholm, Sweden
| | - Iulia E. Brumboiu
- Department
of Theoretical Chemistry and Biology, KTH
Royal Institute of Technology, 10691 Stockholm, Sweden
- Department
of Chemistry, Korea Advanced Institute of
Science and Technology, 34141 Daejeon, Korea
| | - Marta L. Vidal
- DTU
Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
| | - Patrick Norman
- Department
of Theoretical Chemistry and Biology, KTH
Royal Institute of Technology, 10691 Stockholm, Sweden
| | - Sonia Coriani
- DTU
Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
- Department
of Chemistry, NTNU-Norwegian University
of Science and Technology, N-7991 Trondheim, Norway
| | - Andreas Dreuw
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls
University, Im Neuenheimer
Feld 205, 69120 Heidelberg, Germany
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16
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Mariano LA, Vlaisavljevich B, Poloni R. Biased Spin-State Energetics of Fe(II) Molecular Complexes within Density-Functional Theory and the Linear-Response Hubbard U Correction. J Chem Theory Comput 2020; 16:6755-6762. [DOI: 10.1021/acs.jctc.0c00628] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Lorenzo A. Mariano
- Grenoble-INP, SIMaP, University of Grenoble-Alpes, CNRS, F-38042 Grenoble, France
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Roberta Poloni
- Grenoble-INP, SIMaP, University of Grenoble-Alpes, CNRS, F-38042 Grenoble, France
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17
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Duan C, Liu F, Nandy A, Kulik HJ. Data-Driven Approaches Can Overcome the Cost-Accuracy Trade-Off in Multireference Diagnostics. J Chem Theory Comput 2020; 16:4373-4387. [PMID: 32536161 DOI: 10.1021/acs.jctc.0c00358] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
High-throughput computational screening typically employs methods (i.e., density functional theory or DFT) that can fail to describe challenging molecules, such as those with strongly correlated electronic structure. In such cases, multireference (MR) correlated wavefunction theory (WFT) would be the appropriate choice but remains more challenging to carry out and automate than single-reference (SR) WFT or DFT. Numerous diagnostics have been proposed for identifying when MR character is likely to have an effect on the predictive power of SR calculations, but conflicting conclusions about diagnostic performance have been reached on small data sets. We compute 15 MR diagnostics, ranging from affordable DFT-based to more costly MR-WFT-based diagnostics, on a set of 3165 equilibrium and distorted small organic molecules containing up to six heavy atoms. Conflicting MR character assignments and low pairwise linear correlations among diagnostics are also observed over this set. We evaluate the ability of existing diagnostics to predict the percent recovery of the correlation energy, %Ecorr. None of the DFT-based diagnostics are nearly as predictive of %Ecorr as the best WFT-based diagnostics. To overcome the limitation of this cost-accuracy trade-off, we develop machine learning (ML, i.e., kernel ridge regression) models to predict WFT-based diagnostics from a combination of DFT-based diagnostics and a new, size-independent 3D geometric representation. The ML-predicted diagnostics correlate as well with MR effects as their computed (i.e., with WFT) values, significantly improving over the DFT-based diagnostics on which the models were trained. These ML models thus provide a promising approach to improve upon DFT-based diagnostic accuracy while remaining suitably low cost for high-throughput screening.
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Affiliation(s)
- Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Fang Liu
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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18
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Fabrizio A, Meyer B, Corminboeuf C. Machine learning models of the energy curvature vs particle number for optimal tuning of long-range corrected functionals. J Chem Phys 2020; 152:154103. [DOI: 10.1063/5.0005039] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Alberto Fabrizio
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Benjamin Meyer
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Clemence Corminboeuf
- Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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19
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Hait D, Head-Gordon M. Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory. J Chem Theory Comput 2020; 16:1699-1710. [PMID: 32017554 DOI: 10.1021/acs.jctc.9b01127] [Citation(s) in RCA: 99] [Impact Index Per Article: 24.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.
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Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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20
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Liu F, Kulik HJ. Impact of Approximate DFT Density Delocalization Error on Potential Energy Surfaces in Transition Metal Chemistry. J Chem Theory Comput 2019; 16:264-277. [DOI: 10.1021/acs.jctc.9b00842] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Affiliation(s)
- Fang Liu
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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21
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Zhao Q, Kulik HJ. Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry? J Phys Chem Lett 2019; 10:5090-5098. [PMID: 31411023 PMCID: PMC6748670 DOI: 10.1021/acs.jpclett.9b01650] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Accepted: 08/14/2019] [Indexed: 05/25/2023]
Abstract
Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree-Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.
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Affiliation(s)
- Qing Zhao
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Mechanical Engineering, Massachusetts
Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
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22
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Shishkin M, Sato H. DFT+U in Dudarev's formulation with corrected interactions between the electrons with opposite spins: The form of Hamiltonian, calculation of forces, and bandgap adjustments. J Chem Phys 2019; 151:024102. [PMID: 31301721 DOI: 10.1063/1.5090445] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Hubbard corrected density functional theory (DFT) methods, such as the DFT+U approach in Dudarev's approximation, are widely used for the description of energetics and electronic structure of strongly correlated materials, providing higher level of accuracy than local DFT calculations (e.g., local density approximation or generalized gradient approximation). However, the DFT+U method in Dudarev's formulation limits the introduced corrections to interactions between the electrons within the same spin channel, whereas interactions between the electrons with opposite spins are still treated using local DFT functional (e.g., Perdew-Burke-Ernzerhof). In recent years, the need for correction of these interactions between the electrons with opposite spins has been recognized and additional terms have been added to the Hubbard term to reflect it. Although such extended DFT+U functionals have been proposed, the form of respective Hamiltonian operator, defined as a total energy derivative over density with appropriate treatment of double counting corrections due to additional Hubbard terms, has not been explicitly presented. In this work, we provide an expression for such a type of Hamiltonian, which contains the respective double counting correction contributions. This formulation also allows evaluation of atomic forces, using computational settings discussed herein. In addition, we also introduce adjustments for too narrow theoretical bandgaps, using scissor operator technique. This allows for a greater level of corrections of energetics and magnetic properties of studied transition metal compounds, avoiding possible unphysical overlap between occupied and unoccupied electronic bands.
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Affiliation(s)
- M Shishkin
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Nishikyo-ku, Kyoto 615-8520, Japan
| | - H Sato
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Nishikyo-ku, Kyoto 615-8520, Japan
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23
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Bajaj A, Liu F, Kulik HJ. Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT. J Chem Phys 2019; 150:154115. [PMID: 31005112 DOI: 10.1063/1.5091563] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Fang Liu
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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24
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Brumboiu IE, Haldar S, Lüder J, Eriksson O, Herper HC, Brena B, Sanyal B. Ligand Effects on the Linear Response Hubbard U: The Case of Transition Metal Phthalocyanines. J Phys Chem A 2019; 123:3214-3222. [DOI: 10.1021/acs.jpca.8b11940] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Iulia Emilia Brumboiu
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, 10691 Stockholm, Sweden
- Department of Chemistry, Korea Advanced Institute of Science and Technology, 34141 Daejeon, Korea
| | - Soumyajyoti Haldar
- Institute of Theoretical Physics and Astrophysics, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - Johann Lüder
- Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan
| | - Olle Eriksson
- Department of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden
| | - Heike C. Herper
- Department of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden
| | - Barbara Brena
- Department of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden
| | - Biplab Sanyal
- Department of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden
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25
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Hait D, Head-Gordon M. Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number. J Phys Chem Lett 2018; 9:6280-6288. [PMID: 30339010 DOI: 10.1021/acs.jpclett.8b02417] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. We present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C12H14 polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.
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Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States
- Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
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26
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Bajaj A, Janet JP, Kulik HJ. Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost. J Chem Phys 2018; 147:191101. [PMID: 29166114 DOI: 10.1063/1.5008981] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree-Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane and we find this shape to be remarkably consistent across ions and molecules. We introduce the judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. We select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jon Paul Janet
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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27
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Zhao Q, Kulik HJ. Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U. J Chem Theory Comput 2018; 14:670-683. [PMID: 29298057 DOI: 10.1021/acs.jctc.7b01061] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Approximate density functional theory (DFT) is widely used in chemistry and physics, despite delocalization errors that affect energetic and density properties. DFT+U (i.e., semilocal DFT augmented with a Hubbard U correction) and global hybrid functionals are two commonly employed practical methods to address delocalization error. Recent work demonstrated that in transition-metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity. In this work, we compare density localization trends with DFT+U and global hybrids on a diverse set of 34 transition-metal-containing solids with varying magnetic state, electron configuration and valence shell, and coordinating-atom orbital diffuseness (i.e., O, S, Se). We also study open-framework solids in which the metal is coordinated by molecular ligands, i.e., MCO3, M(OH)2, M(NCNH)2, K3M(CN)6 (M = V-Ni). As in transition-metal complexes, incorporation of Hartree-Fock exchange consistently localizes density away from the metal, but DFT+U exhibits diverging behavior, localizing density (i) onto the metal in low-spin and late transition metals and (ii) away from the metal in other cases in agreement with hybrids. To isolate the effect of the crystal environment, we extract molecular analogues from open-framework transition-metal solids and observe consistent localization of the density away from the metal in all cases with both DFT+U and hybrid exchange. These observations highlight the limited applicability of trends established for functional tuning on transition-metal complexes even to equivalent coordination environments in the solid state.
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Affiliation(s)
- Qing Zhao
- Department of Chemical Engineering and ‡Department of Mechanical Engineering, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering and ‡Department of Mechanical Engineering, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
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28
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Gani TZH, Kulik HJ. Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics. J Chem Theory Comput 2017; 13:5443-5457. [DOI: 10.1021/acs.jctc.7b00848] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Terry Z. H. Gani
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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29
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Li X, Parrish RM, Liu F, Kokkila Schumacher SIL, Martínez TJ. An Ab Initio Exciton Model Including Charge-Transfer Excited States. J Chem Theory Comput 2017; 13:3493-3504. [PMID: 28617595 DOI: 10.1021/acs.jctc.7b00171] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The Frenkel exciton model is a useful tool for theoretical studies of multichromophore systems. We recently showed that the exciton model could be used to coarse-grain electronic structure in multichromophoric systems, focusing on singly excited exciton states [ Acc. Chem. Res. 2014 , 47 , 2857 - 2866 ]. However, our previous implementation excluded charge-transfer excited states, which can play an important role in light-harvesting systems and near-infrared optoelectronic materials. Recent studies have also emphasized the significance of charge-transfer in singlet fission, which mediates the coupling between the locally excited states and the multiexcitonic states. In this work, we report on an ab initio exciton model that incorporates charge-transfer excited states and demonstrate that the model provides correct charge-transfer excitation energies and asymptotic behavior. Comparison with TDDFT and EOM-CC2 calculations shows that our exciton model is robust with respect to system size, screening parameter, and different density functionals. Inclusion of charge-transfer excited states makes the exciton model more useful for studies of singly excited states and provides a starting point for future construction of a model that also includes double-exciton states.
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Affiliation(s)
- Xin Li
- Department of Chemistry and the PULSE Institute, Stanford University , Stanford, California 94305, United States.,SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Robert M Parrish
- Department of Chemistry and the PULSE Institute, Stanford University , Stanford, California 94305, United States.,SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Fang Liu
- Department of Chemistry and the PULSE Institute, Stanford University , Stanford, California 94305, United States.,SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Sara I L Kokkila Schumacher
- Department of Chemistry and the PULSE Institute, Stanford University , Stanford, California 94305, United States.,SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University , Stanford, California 94305, United States.,SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
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30
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Ioannidis EI, Kulik HJ. Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering. J Phys Chem A 2017; 121:874-884. [DOI: 10.1021/acs.jpca.6b11930] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Efthymios I. Ioannidis
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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31
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Abstract
PBE calculations, performed non-self-consistently on densities evaluated with Rung 3.5 density functionals, give improved performance for hydrogen transfer reaction barriers.
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Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry & Biochemistry
- Texas Christian University
- 2800 S. University Dr
- Fort Worth
- USA
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32
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Janet JP, Zhao Q, Ioannidis EI, Kulik HJ. Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example. MOLECULAR SIMULATION 2016. [DOI: 10.1080/08927022.2016.1258465] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Jon Paul Janet
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Qing Zhao
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Efthymios I. Ioannidis
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Heather J. Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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33
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Gani TZH, Kulik HJ. Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U. J Chem Theory Comput 2016; 12:5931-5945. [DOI: 10.1021/acs.jctc.6b00937] [Citation(s) in RCA: 53] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Terry Z. H. Gani
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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