1
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Burgess AC, Linscott E, O'Regan DD. Tilted-Plane Structure of the Energy of Finite Quantum Systems. PHYSICAL REVIEW LETTERS 2024; 133:026404. [PMID: 39073931 DOI: 10.1103/physrevlett.133.026404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2023] [Revised: 04/18/2024] [Accepted: 05/17/2024] [Indexed: 07/31/2024]
Abstract
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived. Moving to fractional electron count, the tilted-plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat-plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat-plane structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at noninteger values. A diverse set of tilted-plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.
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2
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Janesko BG. Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian. J Phys Chem A 2024; 128:5077-5087. [PMID: 38878060 DOI: 10.1021/acs.jpca.4c02326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2024]
Abstract
This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas 76129, United States
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3
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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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4
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Liu Y, Sulaiman HF, Johnson BR, Ma R, Gao Y, Fernando H, Amarasekara A, Ashley-Oyewole A, Fan H, Ingram HN, Briggs JM. QM/MM study of N501 involved intermolecular interaction between SARS-CoV-2 receptor binding domain and antibody of human origin. Comput Biol Chem 2023; 102:107810. [PMID: 36610304 PMCID: PMC9811887 DOI: 10.1016/j.compbiolchem.2023.107810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Revised: 01/02/2023] [Accepted: 01/03/2023] [Indexed: 01/06/2023]
Abstract
Intermolecular interaction between key residue N501 of the epitope on SARS-CoV-2 RBD and screening antibody B38 was studied using the QM/MM and QM approach. The QM/MM optimized geometry shows that angle X-H---Y is 165° for O-H---O between mAb light chain S30 and RBD N501. High level MP2 calculations indicated the interaction between RBD N501 and S30 of B38 Fab light chain provide a relatively strong attractive force of - 3.32 kcal/mol, whereas the hydrogen bond between RBD Q498 and S30 was quantified as 0.10 kcal/mol. The decrease in ESP partial charge on hydrogen atom of hydroxyl group on S30 drops from 0.38 a.u. to 0.31 a.u., exhibiting the sharing of 0.07 a.u. from the lone pair electron oxygen of N501 due to hydrogen bond formation. The NBO occupancy of hydrogen atom also decreases from 25.79 % to 22.93 % in the hydroxyl H-O NBO bond of S30. However, the minor change of NBO hybridization of hydroxyl oxygen of S30 from sp3.00 to sp3.05 implies the rigidity of hydrogen bond tetrahedral geometry in the relative dynamic protein complex. The O-H---O angle is 165° which is close but not exactly linear. The structural requirement for sp3 hybridization of oxygen for hydroxyl group on S30 and dimension of protein likely prevent O-H---O from adopting linear geometry. The hydrogen bond strengths were also calculated using a variety of DFT methods, and the result of - 3.33 kcal/mol from the M06L method is the closest to that of the MP2 calculation. Results of this work may aid in the COVID-19 vaccine and drug screening.
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Affiliation(s)
- Yuemin Liu
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America,Department of Chemistry, Rice University, Houston, TX 77005, the United States of America,Corresponding author at: Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - Hana F. Sulaiman
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - Bruce R. Johnson
- Department of Chemistry, Rice University, Houston, TX 77005, the United States of America
| | - Rulong Ma
- Department of Biology and Biochemistry, University of Houston, Houston, TX 77004, the United States of America
| | - Yunxiang Gao
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - Harshica Fernando
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - Ananda Amarasekara
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - Andrea Ashley-Oyewole
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - Huajun Fan
- College of Chemical Engineering, Sichuan University Science and Engineering, Zigong, Sichuan 643000, PR China
| | - Heaven N. Ingram
- Department of Chemistry, Prairie View A&M University, Prairie View, TX 77446, the United States of America
| | - James M. Briggs
- Department of Biology and Biochemistry, University of Houston, Houston, TX 77004, the United States of America
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5
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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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6
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Mahler A, Williams J, Su NQ, Yang W. Localized orbital scaling correction for periodic systems. PHYSICAL REVIEW. B 2022; 106:035147. [PMID: 37727592 PMCID: PMC10508887 DOI: 10.1103/physrevb.106.035147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/21/2023]
Abstract
Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band gaps of finite and bulk systems, energy level alignments, and electron distributions at interfaces. The localized orbital scaling correction (LOSC) was developed to correct delocalization error by using orbitals localized in space and energy. These localized orbitals span both the occupied and unoccupied spaces and can have fractional occupations in order to correct both the total energy and the one-electron energy eigenvalues. We extend the LOSC method to periodic systems, in which the localized orbitals employed are dually localized Wannier functions. In light of the effect of the bulk environment on the electrostatic interaction between localized orbitals, we modify the LOSC energy correction to include a screened Coulomb kernel. For a test set of semiconductors and large-gap insulators, we show that the screened LOSC method consistently improves the band gap compared to the parent density functional approximation.
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Affiliation(s)
- Aaron Mahler
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Jacob Williams
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Neil Qiang Su
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education) and Renewable Energy Conversion and Storage Center (RECAST), Nankai University, Tianjin 300071, China
| | - Weitao Yang
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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7
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Ariyarathna IR, Duan C, Kulik HJ. Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations. J Chem Phys 2022; 156:184113. [PMID: 35568536 DOI: 10.1063/5.0090128] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf-O or Hf-B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X4Σ-) and HfO(X1Σ+) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (De) from HfO to HfPo and the singlet-triplet energy gap (ΔES-T) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange-correlation functionals spanning multiple rungs of "Jacob's ladder." When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.
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Affiliation(s)
- Isuru R Ariyarathna
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Chenru Duan
- 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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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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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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10
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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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11
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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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12
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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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13
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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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