1
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Xu X, Soriano-Agueda L, López X, Ramos-Cordoba E, Matito E. All-Purpose Measure of Electron Correlation for Multireference Diagnostics. J Chem Theory Comput 2024; 20:721-727. [PMID: 38157841 PMCID: PMC10809408 DOI: 10.1021/acs.jctc.3c01073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Revised: 11/24/2023] [Accepted: 11/27/2023] [Indexed: 01/03/2024]
Abstract
We present an analytical relationship between two natural orbital occupancy-based indices, I N D ¯ and INDmax, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0, and the D2 diagnostic. Numerical validation revealed that I N D ¯ and INDmax can effectively substitute for c0 and D2, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for INDmax, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.
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Affiliation(s)
- Xiang Xu
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Luis Soriano-Agueda
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Xabier López
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Eloy Ramos-Cordoba
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
- Ikerbasque
Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
| | - Eduard Matito
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Ikerbasque
Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
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2
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Šulka M, Šulková K, Jurečka P, Dubecký M. Dynamic and Nondynamic Electron Correlation Energy Decomposition Based on the Node of the Hartree-Fock Slater Determinant. J Chem Theory Comput 2023; 19:8147-8155. [PMID: 37942987 DOI: 10.1021/acs.jctc.3c00828] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. It can be challenging to make a clear distinction between the two types of correlation energy or to determine their actual contributions in specific cases using wave function theory. This is because both single-reference and multireference methods cover both types of correlation energy to some extent. Fixed-node diffusion quantum Monte Carlo (FNDMC) accurately covers dynamic correlations, but it is limited in overall accuracy by the node of the trial wave function. We introduce a methodology for partitioning an exact electron correlation energy into its dynamic and nondynamic components. This is accomplished by restricting a ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. The FNDMC method is used as a tool to conveniently project out a lowest-energy state obeying such a boundary condition. The proposed approach provides an unambiguous and useful procedure for separating electron correlation energy, as demonstrated on multiple systems, including the He atom, bond breaking of H2, the parametric H2-H2 system, the Be-Ne atomic series with low- and high-spin states for C, N, and O atoms, and small molecules such as BH, HF, and CO at both equilibrium and elongated configurations, respectively.
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Affiliation(s)
- Martin Šulka
- Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, Trnava 917 24, Slovakia
| | - Katarína Šulková
- Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, Trnava 917 24, Slovakia
| | - Petr Jurečka
- Department of Physical Chemistry, Faculty of Science, Palacky University Olomouc, 17. listopadu 12, Olomouc 779 00, Czech Republic
| | - Matúš Dubecký
- Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, Trnava 917 24, Slovakia
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, Ostrava 701 03, Czech Republic
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3
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Hostaš J, Pérez-Becerra KO, Calaminici P, Barrios-Herrera L, Lourenço MP, Tchagang A, Salahub DR, Köster AM. How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2. J Chem Phys 2023; 159:184301. [PMID: 37947508 DOI: 10.1063/5.0169409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023] Open
Abstract
Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.
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Affiliation(s)
- Jiří Hostaš
- Department of Chemistry, CMS - Centre for Molecular Simulation, IQST - Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Kevin O Pérez-Becerra
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
| | - Patrizia Calaminici
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
| | - Lizandra Barrios-Herrera
- Department of Chemistry, CMS - Centre for Molecular Simulation, IQST - Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Maicon Pierre Lourenço
- Departamento de Química e Física - Centro de Ciências Exatas, Naturais e da Saúde - CCENS - Universidade Federal do Espírito Santo, 29500-000 Alegre, Espírito Santo, Brazil
| | - Alain Tchagang
- Digital Technologies Research Centre, National Research Council of Canada, 1200 Montréal Road, Ottawa, Ontario K1A 0R6, Canada
| | - Dennis R Salahub
- Department of Chemistry, CMS - Centre for Molecular Simulation, IQST - Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Andreas M Köster
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
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4
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Neugebauer H, Vuong HT, Weber JL, Friesner RA, Shee J, Hansen A. Toward Benchmark-Quality Ab Initio Predictions for 3d Transition Metal Electrocatalysts: A Comparison of CCSD(T) and ph-AFQMC. J Chem Theory Comput 2023; 19:6208-6225. [PMID: 37655473 DOI: 10.1021/acs.jctc.3c00617] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Generating accurate ab initio ionization energies for transition metal complexes is an important step toward the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and developing new ones but is complicated to obtain for many transition metal compounds due to the potential presence of both strong dynamical and static electron correlation. In this regime, it is questionable whether the so-called gold standard, coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), provides the desired level of accuracy─roughly 1-3 kcal/mol. In this work, we compiled a test set of 28 3d metal-containing molecules relevant to homogeneous electrocatalysis (termed 3dTMV) and computed their vertical ionization energies (ionization potentials) with CCSD(T) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) in the def2-SVP basis set. A substantial effort has been made to converge away the phaseless bias in the ph-AFQMC reference values. We assess a wide variety of multireference diagnostics and find that spin-symmetry breaking of the CCSD wave function and the PBE0 density functional correlate well with our analysis of multiconfigurational wave functions. We propose quantitative criteria based on symmetry breaking to delineate correlation regimes inside of which appropriately performed CCSD(T) can produce mean absolute deviations from the ph-AFQMC reference values of roughly 2 kcal/mol or less and outside of which CCSD(T) is expected to fail. We also present a preliminary assessment of density functional theory (DFT) functionals on the 3dTMV set.
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Affiliation(s)
- Hagen Neugebauer
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, D-53115 Bonn, Germany
| | - Hung T Vuong
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - James Shee
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, D-53115 Bonn, Germany
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5
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Abstract
Heteroatom-centered diradical(oid)s have been in the focus of molecular main group chemistry for nearly 30 years. During this time, the diradical concept has evolved and the focus has shifted to the rational design of diradical(oid)s for specific applications. This review article begins with some important theoretical considerations of the diradical and tetraradical concept. Based on these theoretical considerations, the design of diradical(oid)s in terms of ligand choice, steric, symmetry, electronic situation, element choice, and reactivity is highlighted with examples. In particular, heteroatom-centered diradical reactions are discussed and compared with closed-shell reactions such as pericyclic additions. The comparison between closed-shell reactivity, which proceeds in a concerted manner, and open-shell reactivity, which proceeds in a stepwise fashion, along with considerations of diradical(oid) design, provides a rational understanding of this interesting and unusual class of compounds. The application of diradical(oid)s, for example in small molecule activation or as molecular switches, is also highlighted. The final part of this review begins with application-related details of the spectroscopy of diradical(oid)s, followed by an update of the heteroatom-centered diradical(oid)s and tetraradical(oid)s published in the last 10 years since 2013.
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Affiliation(s)
- Alexander Hinz
- Institut für Anorganische Chemie (AOC), Karlsruher Institut für Technologie (KIT), Engesserstrasse 15, 76131 Karlsruhe, Germany
| | - Jonas Bresien
- Institut für Chemie, Universität Rostock, Albert-Einstein-Strasse 3a, 18059 Rostock, Germany
| | - Frank Breher
- Institut für Anorganische Chemie (AOC), Karlsruher Institut für Technologie (KIT), Engesserstrasse 15, 76131 Karlsruhe, Germany
| | - Axel Schulz
- Institut für Chemie, Universität Rostock, Albert-Einstein-Strasse 3a, 18059 Rostock, Germany
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6
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Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
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Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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7
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Naim C, Besalú-Sala P, Zaleśny R, Luis JM, Castet F, Matito E. Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties? J Chem Theory Comput 2023; 19:1753-1764. [PMID: 36862983 DOI: 10.1021/acs.jctc.2c01212] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/04/2023]
Abstract
Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.
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Affiliation(s)
- Carmelo Naim
- Donostia International Physics Center (DIPC), Manuel Lardizabal Ibilbidea 4, 20018 Donostia, Euskadi, Spain.,Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France.,Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, 20080 Donostia, Euskadi, Spain
| | - Pau Besalú-Sala
- Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, 17003 Girona, Catalonia, Spain
| | - Robert Zaleśny
- Faculty of Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, PL-50370 Wrocław, Poland
| | - Josep M Luis
- Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, 17003 Girona, Catalonia, Spain
| | - Frédéric Castet
- Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France
| | - Eduard Matito
- Donostia International Physics Center (DIPC), Manuel Lardizabal Ibilbidea 4, 20018 Donostia, Euskadi, Spain.,Ikerbasque Foundation for Science, 48011 Bilbao, Euskadi, Spain
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8
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Duan C, Nandy A, Terrones GG, Kastner DW, Kulik HJ. Active Learning Exploration of Transition-Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores. JACS AU 2023; 3:391-401. [PMID: 36873700 PMCID: PMC9976347 DOI: 10.1021/jacsau.2c00547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 11/15/2022] [Accepted: 11/16/2022] [Indexed: 06/18/2023]
Abstract
Transition-metal chromophores with earth-abundant transition metals are an important design target for their applications in lighting and nontoxic bioimaging, but their design is challenged by the scarcity of complexes that simultaneously have well-defined ground states and optimal target absorption energies in the visible region. Machine learning (ML) accelerated discovery could overcome such challenges by enabling the screening of a larger space but is limited by the fidelity of the data used in ML model training, which is typically from a single approximate density functional. To address this limitation, we search for consensus in predictions among 23 density functional approximations across multiple rungs of "Jacob's ladder". To accelerate the discovery of complexes with absorption energies in the visible region while minimizing the effect of low-lying excited states, we use two-dimensional (2D)efficient global optimization to sample candidate low-spin chromophores from multimillion complex spaces. Despite the scarcity (i.e., ∼0.01%) of potential chromophores in this large chemical space, we identify candidates with high likelihood (i.e., >10%) of computational validation as the ML models improve during active learning, representing a 1000-fold acceleration in discovery. Absorption spectra of promising chromophores from time-dependent density functional theory verify that 2/3 of candidates have the desired excited-state properties. The observation that constituent ligands from our leads have demonstrated interesting optical properties in the literature exemplifies the effectiveness of our construction of a realistic design space and active learning approach.
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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
| | - 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
| | - Gianmarco G. Terrones
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - David W. Kastner
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Biological 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
- Department
of Chemistry, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, United States
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9
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Cho Y, Nandy A, Duan C, Kulik HJ. DFT-Based Multireference Diagnostics in the Solid State: Application to Metal-Organic Frameworks. J Chem Theory Comput 2023; 19:190-197. [PMID: 36548116 DOI: 10.1021/acs.jctc.2c01033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
When a many-body wave function of a system cannot be captured by a single determinant, high-level multireference (MR) methods are required to properly explain its electronic structure. MR diagnostics to estimate the magnitude of such static correlation have been primarily developed for molecular systems and range from low in computational cost to as costly as the full MR calculation itself. We report the first application of low-cost MR diagnostics based on the fractional occupation number calculated with finite-temperature DFT to solid-state systems. To compare the behavior of the diagnostics on solids and molecules, we select metal-organic frameworks (MOFs) as model materials because their reticular nature provides an intuitive way to identify molecular derivatives. On a series of closed-shell MOFs, we demonstrate that the DFT-based MR diagnostics are equally applicable to solids as to their molecular derivatives. The magnitude and spatial distribution of the MR character of a MOF are found to have a good correlation with those of its molecular derivatives, which can be calculated much more affordably in comparison to those of the full MOF. The additivity of MR character discussed here suggests the set of molecular derivatives to be a good representation of a MOF for both MR detection and ultimately for MR corrections, facilitating accurate and efficient high-throughput screening of MOFs and other porous solids.
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Affiliation(s)
- Yeongsu Cho
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
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10
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Casademont‐Reig I, Soriano‐Agueda L, Ramos‐Cordoba E, Torrent‐Sucarrat M, Matito E. Reply to the Correspondence on “How Aromatic Are Molecular Nanorings? The Case of a Six‐Porphyrin Nanoring”**. Angew Chem Int Ed Engl 2022; 61:e202206836. [DOI: 10.1002/anie.202206836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Indexed: 11/08/2022]
Affiliation(s)
- Irene Casademont‐Reig
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Department of General Chemistry (ALGC) Vrije Universiteit Brussel (VUB) Pleinlaan 2 1050 Brussels Belgium
| | | | - Eloy Ramos‐Cordoba
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia Kimika Fakultatea Euskal Herriko Unibertsitatea UPV/EHU P.K. 1072 20080 Donostia Euskadi Spain
| | - Miquel Torrent‐Sucarrat
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Ikerbasque, Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Euskadi Spain
- Department of Organic Chemistry I Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) 20018 Donostia Euskadi Spain
| | - Eduard Matito
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Ikerbasque, Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Euskadi Spain
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11
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Duan C, Ladera AJ, Liu JCL, Taylor MG, Ariyarathna IR, Kulik HJ. Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands. J Chem Theory Comput 2022; 18:4836-4845. [PMID: 35834742 DOI: 10.1021/acs.jctc.2c00468] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.
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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
| | - Adriana J Ladera
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Julian C-L Liu
- Department of Chemical Engineering, 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
| | - Isuru R Ariyarathna
- 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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12
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Casademont‐Reig I, Soriano‐Agueda L, Ramos‐Cordoba E, Torrent‐Sucarrat M, Matito E. Reply to the Correspondence on “How Aromatic Are Molecular Nanorings? The Case of a Six‐Porphyrin Nanoring”**. Angew Chem Int Ed Engl 2022. [DOI: 10.1002/ange.202206836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Irene Casademont‐Reig
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Department of General Chemistry (ALGC) Vrije Universiteit Brussel (VUB) Pleinlaan 2 1050 Brussels Belgium
| | | | - Eloy Ramos‐Cordoba
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia Kimika Fakultatea Euskal Herriko Unibertsitatea UPV/EHU P.K. 1072 20080 Donostia Euskadi Spain
| | - Miquel Torrent‐Sucarrat
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Ikerbasque, Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Euskadi Spain
- Department of Organic Chemistry I Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) 20018 Donostia Euskadi Spain
| | - Eduard Matito
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
- Ikerbasque, Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Euskadi Spain
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13
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Rosenboom J, Chojetzki L, Suhrbier T, Rabeah J, Villinger A, Wustrack R, Bresien J, Schulz A. Radical Reactivity of the Biradical [⋅P(μ-NTer) 2 P⋅] and Isolation of a Persistent Phosphorus-Cantered Monoradical [⋅P(μ-NTer) 2 P-Et]. Chemistry 2022; 28:e202200624. [PMID: 35445770 PMCID: PMC9322606 DOI: 10.1002/chem.202200624] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Indexed: 11/06/2022]
Abstract
The activation of C-Br bonds in various bromoalkanes by the biradical [⋅P(μ-NTer)2 P⋅] (1) (Ter=2,6-bis-(2,4,6-trimethylphenyl)-phenyl) is reported, yielding trans-addition products of the type [Br-P(μ-NTer)2 P-R] (2), so-called 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes. This addition reaction, which represents a new easy approach to asymmetrically substituted cyclo-1,3-diphospha-2,4-diazanes, was investigated mechanistically by different spectroscopic methods (NMR, EPR, IR, Raman); the results suggested a stepwise radical reaction mechanism, as evidenced by the in-situ detection of the phosphorus-centered monoradical [⋅P(μ-NTer)2 P-R].< To provide further evidence for the radical mechanism, [⋅P(μ-NTer)2 P-Et] (3Et⋅) was synthesized directly by reduction of the bromoethane addition product [Br-P(μ-NTer)2 P-Et] (2 a) with magnesium, resulting in the formation of the persistent phosphorus-centered monoradical [⋅P(μ-NTer)2 P-Et], which could be isolated and fully characterized, including single-crystal X-ray diffraction. Comparison of the EPR spectrum of the radical intermediate in the addition reaction with that of the synthesized new [⋅P(μ-NTer)2 P-Et] radical clearly proves the existence of radicals over the course of the reaction of biradical [⋅P(μ-NTer)2 P⋅] (1) with bromoethane. Extensive DFT and coupled cluster calculations corroborate the experimental data for a radical mechanism in the reaction of biradical [⋅P(μ-NTer)2 P⋅] with EtBr. In the field of hetero-cyclobutane-1,3-diyls, the demonstration of a stepwise radical reaction represents a new aspect and closes the gap between P-centered biradicals and P-centered monoradicals in terms of radical reactivity.
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Affiliation(s)
- Jan Rosenboom
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany
| | - Lukas Chojetzki
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany
| | - Tim Suhrbier
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany
| | - Jabor Rabeah
- Leibniz-Institut für Katalyse e.V., Albert-Einstein-Straße 29a, 18059, Rostock, Germany
| | - Alexander Villinger
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany
| | - Ronald Wustrack
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany
| | - Jonas Bresien
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany
| | - Axel Schulz
- Institut für Chemie, Universität, Albert-Einstein-Straße 3a, 18059, Rostock, Germany.,Leibniz-Institut für Katalyse e.V., Albert-Einstein-Straße 29a, 18059, Rostock, Germany
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14
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Xu LT, Dunning TH. Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B-F). J Chem Phys 2022; 157:014107. [DOI: 10.1063/5.0093414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. The present study focused on the effect of dynamical electron correlation on the spectroscopic constants, ( Re , ωe , De ) and potential energy curves, Δ E( R), of the covalently-bound AH and AF molecules, A = B-F. The changes in the spectroscopic constants, (Δ Re , Δωe , Δ De ) caused by dynamical correlation are erratic and, at times, even surprising. These changes could be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ EDEC( R). At large R, the magnitude of Δ EDEC( R) increases nearly exponentially with decreasing R, but this increase slows as R continues to decrease and, in many cases, even reverses at very short R. The changes in Δ EDEC( R) in the region around Re were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ EDEC( R) for the most polar molecules. The variations in Δ EDEC( R) for R ≲ Re are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the SCGVB wave function. The results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on the chemical bond and molecular properties and processes.
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Affiliation(s)
- Lu T. Xu
- University of Washington, United States of America
| | - Thom H. Dunning
- Department of Chemistry, University of Washington, United States of America
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15
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Huang D, Ying F, Chen S, Zhou C, Su P, Wu W. Metal-Ligand Bonds in Rare Earth Metal-Biphenyl Complexes. Inorg Chem 2022; 61:8135-8143. [PMID: 35588219 DOI: 10.1021/acs.inorgchem.2c00144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A series of theoretical methods, including density functional theory, multiconfiguration molecular orbital theory, and ab initio valence bond theory, are devoted to understanding the metal-ligand bonds in M-BP (BP = biphenyl; M = Sc, Y, or La) complexes. Different from most transition metal-BP complexes, the most stable metal-biphenyl conformers are not half-sandwich but clamshell. Energy decomposition analysis results reveal that the M-BP bonds in the clamshell conformers possess extra-large orbital relaxation. According to the wave function analysis, 2-fold donations and 2-fold back-donations exist in the clamshell M-BP bonds. The back-donations from M to BP are quite strong, while donations from BP to M are quite weak. Our work improves our understanding of the metal-ligand bonds, which can be considered as the "reversed" Dewar-Chatt-Duncanson model.
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Affiliation(s)
- Dajiang Huang
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Fuming Ying
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Sifeng Chen
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Chen Zhou
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Peifeng Su
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, iChEM, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
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16
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Via-Nadal M, Rodríguez Mayorga MA, Ramos Cordoba E, Matito E. Natural Range Separation of the Coulomb Hole. J Chem Phys 2022; 156:184106. [DOI: 10.1063/5.0085284] [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
A natural range separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations (hcI ) and the other at short distances (hcII ), is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that hcI, which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how hcI can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how hcII helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold out the promise to aid in developing new electronic structure methods that efficiently capture electron correlation.
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Affiliation(s)
| | | | - Eloy Ramos Cordoba
- Theoretical Chemistry Group, Donostia International Physics Center, Spain
| | - Eduard Matito
- Donostia International Physics Center, Donostia International Physics Center, Spain
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17
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Analyzing cases of significant nondynamic correlation with DFT using the atomic populations of effectively localized electrons. Theor Chem Acc 2022. [DOI: 10.1007/s00214-022-02871-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Duan C, Nandy A, Kulik HJ. Machine Learning for the Discovery, Design, and Engineering of Materials. Annu Rev Chem Biomol Eng 2022; 13:405-429. [PMID: 35320698 DOI: 10.1146/annurev-chembioeng-092320-120230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Machine learning (ML) has become a part of the fabric of high-throughput screening and computational discovery of materials. Despite its increasingly central role, challenges remain in fully realizing the promise of ML. This is especially true for the practical acceleration of the engineering of robust materials and the development of design strategies that surpass trial and error or high-throughput screening alone. Depending on the quantity being predicted and the experimental data available, ML can either outperform physics-based modes, be used to accelerate such models, or be integrated with them to improve their performance. We cover recent advances in algorithms and in their application that are starting to make inroads toward (a) the discovery of new materials through large-scale enumerative screening, (b) the design of materials through identification of rules and principles that govern materials properties, and (c) the engineering of practical materials by satisfying multiple objectives. We conclude with opportunities for further advancement to realize ML as a widespread tool for practical computational materials design. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA; , , .,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA; , , .,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA; , ,
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19
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Semidalas E, Martin JM. The MOBH35 Metal–Organic Barrier Heights Reconsidered: Performance of Local-Orbital Coupled Cluster Approaches in Different Static Correlation Regimes. J Chem Theory Comput 2022; 18:883-898. [PMID: 35045709 PMCID: PMC8830049 DOI: 10.1021/acs.jctc.1c01126] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Abstract
![]()
We have revisited
the MOBH35 (Metal–Organic Barrier Heights,
35 reactions) benchmark [Iron, Janes, , 2019, 123 ( (17), ), 3761−378130973722; ibid. 2019, 123, 6379–6380] for realistic organometallic catalytic reactions, using both canonical
CCSD(T) and localized orbital approximations to it. For low levels
of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T)
perform well; for moderately strong levels of static correlation,
DLPNO-CCSD(T) and (T1) may break down catastrophically,
and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges
smoothly to the canonical CCSD(T) answer with increasingly tight convergence
settings. The only two reactions for which our revised MOBH35 reference
values differ substantially from the original ones are reaction 9
and to a lesser extent 8, both involving iron. For the purpose of
evaluating density functional theory (DFT) methods for MOBH35, it
would be best to remove reaction 9 entirely as its severe level of
static correlation makes it just too demanding for a test. The magnitude
of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T1) is a reasonably good predictor for errors in DLPNO-CCSD(T1) compared to canonical CCSD(T); otherwise, monitoring all of T1, D1, max|tiA|, and 1/(εLUMO – εHOMO) should provide adequate warning
for potential problems. Our conclusions are not specific to the def2-SVP
basis set but are largely conserved for the larger def2-TZVPP, as
they are for the smaller def2-SV(P): the latter may be an economical
choice for calibrating against canonical CCSD(T). Finally, diagnostics
for static correlation are statistically clustered into groups corresponding
to (1) importance of single excitations in the wavefunction; (2a)
the small band gap, weakly separated from (2b) correlation entropy;
and (3) thermochemical importance of correlation energy, as well as
the slope of the DFT reaction energy with respect to the percentage
of HF exchange. Finally, a variable reduction analysis reveals that
much information on the multireference character is provided by T1, IND/Itot, and the exchange-based diagnostic A100[TPSS].
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Affiliation(s)
- Emmanouil Semidalas
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot 7610001, Israel
| | - Jan M.L. Martin
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot 7610001, Israel
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20
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Duan C, Chu DBK, Nandy A, Kulik HJ. Detection of multi-reference character imbalances enables a transfer learning approach for virtual high throughput screening with coupled cluster accuracy at DFT cost. Chem Sci 2022; 13:4962-4971. [PMID: 35655882 PMCID: PMC9067623 DOI: 10.1039/d2sc00393g] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 04/04/2022] [Indexed: 01/08/2023] Open
Abstract
Appropriately identifying and treating molecules and materials with significant multi-reference (MR) character is crucial for achieving high data fidelity in virtual high-throughput screening (VHTS). Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates the MR effect on a chemical property prediction is not well established. We evaluate MR diagnostics for over 10 000 transition-metal complexes (TMCs) and compare to those for organic molecules. We observe that only some MR diagnostics are transferable from one chemical space to another. By studying the influence of MR character on chemical properties (i.e., MR effect) that involve multiple potential energy surfaces (i.e., adiabatic spin splitting, ΔEH–L, and ionization potential, IP), we show that differences in MR character are more important than the cumulative degree of MR character in predicting the magnitude of an MR effect. Motivated by this observation, we build transfer learning models to predict CCSD(T)-level adiabatic ΔEH–L and IP from lower levels of theory. By combining these models with uncertainty quantification and multi-level modeling, we introduce a multi-pronged strategy that accelerates data acquisition by at least a factor of three while achieving coupled cluster accuracy (i.e., to within 1 kcal mol−1 MAE) for robust VHTS. We demonstrate that cancellation in multi-reference effect outweighs accumulation in evaluating chemical properties. We combine transfer learning and uncertainty quantification for accelerated data acquisition with chemical accuracy.![]()
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Affiliation(s)
- 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
| | - Daniel B. K. Chu
- 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
| | - Heather J. Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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21
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Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation. COMPUTATION 2021. [DOI: 10.3390/computation9120135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.
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22
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Naim C, Castet F, Matito E. Impact of van der Waals interactions on the structural and nonlinear optical properties of azobenzene switches. Phys Chem Chem Phys 2021; 23:21227-21239. [PMID: 34542144 DOI: 10.1039/d1cp02500g] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in the meta-position with functional groups of different bulkiness are investigated using various ab initio and density functional approximations. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that London dispersion interactions existing between bulky meta-substituents stabilize the Z conformer. The ωB97X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of the molecules. We show that density functional approximations should include no less than 50% of Hartree-Fock exchange to provide accurate hyperpolarizabilities. A property-structure analysis of the azobenzene derivatives reveals that the main contribution to the first hyperpolarizability comes from the azo bond, but phenyl meso-substituents can enhance it.
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Affiliation(s)
- Carmelo Naim
- Donostia International Physics Center (DIPC), Manuel Lardizabal Ibilbidea 4, 20018 Donostia, Euskadi, Spain.,Institut des Sciences Moléculaires (ISM, UMR CNRS 5255), University of Bordeaux, 351 Cours de la Libération, 33405 Talence, France.
| | - Frédéric Castet
- Institut des Sciences Moléculaires (ISM, UMR CNRS 5255), University of Bordeaux, 351 Cours de la Libération, 33405 Talence, France.
| | - Eduard Matito
- Donostia International Physics Center (DIPC), Manuel Lardizabal Ibilbidea 4, 20018 Donostia, Euskadi, Spain.,Ikerbasque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Euskadi, Spain.
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23
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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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24
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Sitkiewicz SP, Ramos-Cordoba E, Luis JM, Matito E. How Many Electrons Does a Molecular Electride Hold? J Phys Chem A 2021; 125:4819-4835. [PMID: 34038110 DOI: 10.1021/acs.jpca.1c02760] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often form channels or surfaces, furnishing electrides with many traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides to determine the number of isolated electrons held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in designing new electrides.
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Affiliation(s)
- Sebastian P Sitkiewicz
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain.,Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Eloy Ramos-Cordoba
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain.,Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Josep M Luis
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, Universitat de Girona, 17003 Girona, Catalonia, Spain
| | - Eduard Matito
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain.,Ikerbasque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Euskadi, Spain
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25
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Shee J, Loipersberger M, Hait D, Lee J, Head-Gordon M. Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition. J Chem Phys 2021; 154:194109. [PMID: 34240907 DOI: 10.1063/5.0047386] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.
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Affiliation(s)
- James Shee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Matthias Loipersberger
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
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26
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Duan C, Liu F, Nandy A, Kulik HJ. Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery. J Phys Chem Lett 2021; 12:4628-4637. [PMID: 33973793 DOI: 10.1021/acs.jpclett.1c00631] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the biases of training data derived from density functional theory (DFT) and leads to many attempted calculations that are doomed to fail. Many compelling functional materials and catalytic processes involve strained chemical bonds, open-shell radicals and diradicals, or metal-organic bonds to open-shell transition-metal centers. Although promising targets, these materials present unique challenges for electronic structure methods and combinatorial challenges for their discovery. In this Perspective, we describe the advances needed in accuracy, efficiency, and approach beyond what is typical in conventional DFT-based ML workflows. These challenges have begun to be addressed through ML models trained to predict the results of multiple methods or the differences between them, enabling quantitative sensitivity analysis. For DFT to be trusted for a given data point in a high-throughput screen, it must pass a series of tests. ML models that predict the likelihood of calculation success and detect the presence of strong correlation will enable rapid diagnoses and adaptation strategies. These "decision engines" represent the first steps toward autonomous workflows that avoid the need for expert determination of the robustness of DFT-based materials discoveries.
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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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27
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Han R, Rodríguez-Mayorga M, Luber S. A Machine Learning Approach for MP2 Correlation Energies and Its Application to Organic Compounds. J Chem Theory Comput 2021; 17:777-790. [DOI: 10.1021/acs.jctc.0c00898] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ruocheng Han
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | | | - Sandra Luber
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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28
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Alipour M, Khorrami M. Pauli energy and information-theoretic approach for evaluating dynamic and nondynamic electron correlation. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-02689-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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29
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DiRisio RJ, Jones CM, Ma H, Rousseau BJG. Viewpoints on the 2020 Virtual Conference on Theoretical Chemistry. J Phys Chem A 2020; 124:8875-8883. [PMID: 33054223 DOI: 10.1021/acs.jpca.0c08955] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Ryan J DiRisio
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Chey M Jones
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - He Ma
- Institute for Molecular engineering, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, United States
| | - Benjamin J G Rousseau
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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30
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Liu F, Duan C, Kulik HJ. Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening. J Phys Chem Lett 2020; 11:8067-8076. [PMID: 32864977 DOI: 10.1021/acs.jpclett.0c02288] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Despite its widespread use in chemical discovery, approximate density functional theory (DFT) is poorly suited to many targets, such as those containing open-shell, 3d transition metals that can be expected to have strong multireference (MR) character. For discovery workflows to be predictive, we need automated, low-cost methods that can distinguish the regions of chemical space where DFT should be applied from those where it should not. We curate more than 4800 open-shell transition-metal complexes up to hundreds of atoms in size from prior high-throughput DFT studies and evaluate affordable, finite-temperature DFT fractional occupation number (FON)-based MR diagnostics. We show that intuitive measures of strong correlation (i.e., the HOMO-LUMO gap) are not predictive of MR character as judged by FON-based diagnostics. Analysis of independently trained machine learning (ML) models to predict HOMO-LUMO gaps and FON-based diagnostics reveals differences in the metal and ligand sensitivity of the two quantities. We use our trained ML models to rapidly evaluate MR character over a space of ∼187000 theoretical complexes, identifying large-scale trends in spin-state-dependent MR character and finding small HOMO-LUMO gap complexes while ensuring low MR character.
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Affiliation(s)
- Fang Liu
- Department of Chemical Engineering, 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
| | - 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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Duan C, Liu F, Nandy A, Kulik HJ. Semi-supervised Machine Learning Enables the Robust Detection of Multireference Character at Low Cost. J Phys Chem Lett 2020; 11:6640-6648. [PMID: 32692570 DOI: 10.1021/acs.jpclett.0c02018] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multireference (MR) diagnostics are common tools for identifying strongly correlated electronic structure that makes single-reference (SR) methods (e.g., density functional theory or DFT) insufficient for accurate property prediction. However, MR diagnostics typically require computationally demanding correlated wave function theory (WFT) calculations, and diagnostics often disagree or fail to predict MR effects on properties. To overcome these challenges, we introduce a semi-supervised machine learning (ML) approach with virtual adversarial training (VAT) of an MR classifier using 15 WFT and DFT MR diagnostics as inputs. In semi-supervised learning, only the most extreme SR or MR points are labeled, and the remaining point labels are learned. The resulting VAT model outperforms the alternatives, as quantified by the distinct property distributions of SR- and MR-classified molecules. To reduce the cost of generating inputs to the VAT model, we leverage the VAT model's robustness to noisy inputs by replacing WFT MR diagnostics with regression predictions in an MR decision engine workflow that preserves excellent performance. We demonstrate the transferability of our approach to larger molecules and those with distinct chemical composition from the training set. This MR decision engine demonstrates promise as a low-cost, high-accuracy approach to the automatic detection of strong correlation for predictive 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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32
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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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33
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Vu N, Mitxelena I, DePrince AE. An adiabatic connection for doubly-occupied configuration interaction wave functions. J Chem Phys 2019; 151:244121. [PMID: 31893894 DOI: 10.1063/1.5130660] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
An adiabatic connection (AC) is developed as an electron correlation correction for doubly occupied configuration interaction (DOCI) wave functions. Following the work of Pernal [Phys. Rev. Lett. 120, 013001 (2018)], the working equations of the approach, termed AC-DOCI, are rooted in the extended random phase approximation (ERPA) and require knowledge of only the ground-state two-electron reduced density matrix (2RDM) from the DOCI. As such, the AC is naturally suited to modeling electron correlation in variational 2RDM (v2RDM)-based approximations to the DOCI. The v2RDM-driven AC-DOCI is applied to the dissociation of molecular nitrogen and the double dissociation of water; the approach yields energies that are similar in quality to those from second-order multireference perturbation theory near equilibrium, but the quality of the AC-DOCI energy degrades at stretched geometries. The exact adiabatic connection path suggests the assumption that the one-electron reduced-density matrix is constant along the AC path is invalid at stretched geometries, but this deficiency alone cannot explain the observed behavior. Rather, it appears that the ERPA's single-particle-transition ansatz cannot, in general, provide good approximations to the 2RDM along the AC path. The AC-DOCI is also applied to a set of 45 reaction energies; for these systems, the approach has an average accuracy that is comparable to that of single-reference second-order many-body perturbation theory.
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Affiliation(s)
- Nam Vu
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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34
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Via-Nadal M, Rodríguez-Mayorga M, Ramos-Cordoba E, Matito E. Singling Out Dynamic and Nondynamic Correlation. J Phys Chem Lett 2019; 10:4032-4037. [PMID: 31276421 DOI: 10.1021/acs.jpclett.9b01376] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The correlation part of the pair density is separated into two components, one of them being predominant at short electronic ranges and the other at long ranges. The analysis of the intracular part of these components permits to classify molecular systems according to the prevailing correlation: dynamic or nondynamic. The study of the long-range asymptotics reveals the key component of the pair density that is responsible for the description of London dispersion forces and a universal decay with the interelectronic distance. The natural range-separation, the identification of the dispersion forces, and the kind of predominant correlation type that arise from this analysis are expected to be important assets in the development of new electronic structure methods in wave function, density, and reduced density-matrix functional theories.
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Affiliation(s)
- Mireia Via-Nadal
- Donostia International Physics Center (DIPC) , 20018 Donostia , Euskadi , Spain
- Kimika Fakultatea , Euskal Herriko Unibertsitatea (UPV/EHU) , Donostia , Euskadi , Spain
| | - Mauricio Rodríguez-Mayorga
- Donostia International Physics Center (DIPC) , 20018 Donostia , Euskadi , Spain
- Kimika Fakultatea , Euskal Herriko Unibertsitatea (UPV/EHU) , Donostia , Euskadi , Spain
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química , Universitat de Girona , C/Maria Aurèlia Capmany, 69 , 17003 Girona , Catalonia , Spain
| | - Eloy Ramos-Cordoba
- Donostia International Physics Center (DIPC) , 20018 Donostia , Euskadi , Spain
- Kimika Fakultatea , Euskal Herriko Unibertsitatea (UPV/EHU) , Donostia , Euskadi , Spain
| | - Eduard Matito
- Donostia International Physics Center (DIPC) , 20018 Donostia , Euskadi , Spain
- IKERBASQUE , Basque Foundation for Science , 48013 Bilbao , Euskadi , Spain
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35
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Ying F, Zhou C, Zheng P, Luan J, Su P, Wu W. λ-Density Functional Valence Bond: A Valence Bond-Based Multiconfigurational Density Functional Theory With a Single Variable Hybrid Parameter. Front Chem 2019; 7:225. [PMID: 31041304 PMCID: PMC6476929 DOI: 10.3389/fchem.2019.00225] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Accepted: 03/22/2019] [Indexed: 11/13/2022] Open
Abstract
A new valence bond (VB)-based multireference density functional theory (MRDFT) method, named λ-DFVB, is presented in this paper. The method follows the idea of the hybrid multireference density functional method theory proposed by Sharkas et al. (2012). λ-DFVB combines the valence bond self-consistent field (VBSCF) method with Kohn–Sham density functional theory (KS-DFT) by decomposing the electron–electron interactions with a hybrid parameter λ. Different from the Toulouse's scheme, the hybrid parameter λ in λ-DFVB is variable, defined as a function of a multireference character of a molecular system. Furthermore, the EC correlation energy of a leading determinant is introduced to ensure size consistency at the dissociation limit. Satisfactory results of test calculations, including potential energy surfaces, bond dissociation energies, reaction barriers, and singlet–triplet energy gaps, show the potential capability of λ-DFVB for molecular systems with strong correlation.
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Affiliation(s)
- Fuming Ying
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China.,The State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, China.,College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China
| | - Chen Zhou
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China.,The State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, China.,College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China
| | - Peikun Zheng
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China.,The State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, China.,College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China
| | - Jiamin Luan
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China.,The State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, China.,College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China
| | - Peifeng Su
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China.,The State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, China.,College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China
| | - Wei Wu
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China.,The State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, China.,College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China
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36
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Rodríguez-Mayorga M, Ramos-Cordoba E, Lopez X, Solà M, Ugalde JM, Matito E. The Coulomb Hole of the Ne Atom. ChemistryOpen 2019; 8:411-417. [PMID: 30976484 PMCID: PMC6442706 DOI: 10.1002/open.201800235] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Revised: 12/20/2018] [Indexed: 11/10/2022] Open
Abstract
We analyze the Coulomb hole of Ne from highly-accurate CISD wave functions obtained from optimized even-tempered basis sets. Using a two-fold extrapolation procedure we obtain highly accurate results that recover 97 % of the correlation energy. We confirm the existence of a shoulder in the short-range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the K-shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second-row atoms, thus confirming that it is due to K-shell correlation effects.
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Affiliation(s)
- Mauricio Rodríguez-Mayorga
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com.,Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química University of Girona C/ Maria Aurèlia Capmany, 69 17003 Girona Catalonia Spain
| | - Eloy Ramos-Cordoba
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com
| | - Xabier Lopez
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com
| | - Miquel Solà
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química University of Girona C/ Maria Aurèlia Capmany, 69 17003 Girona Catalonia Spain
| | - Jesus M Ugalde
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com
| | - Eduard Matito
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com.,IKERBASQUE, Basque Foundation for Science 48011 Bilbao, Euskadi Spain
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37
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Sitkiewicz SP, Rodríguez-Mayorga M, Luis JM, Matito E. Partition of optical properties into orbital contributions. Phys Chem Chem Phys 2019; 21:15380-15391. [DOI: 10.1039/c9cp02662b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
A new tool to analyze the response property through the partition of nonlinear optical properties in terms of orbital contributions (PNOC), valuable in the assessment of the electronic structure methods in the NLOPs computations, is presented.
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Affiliation(s)
- Sebastian P. Sitkiewicz
- Kimika Fakultatea
- Euskal Herriko Unibertsitatea (UPV/EHU)
- 20080 Donostia
- Spain
- Donostia International Physics Center (DIPC)
| | - Mauricio Rodríguez-Mayorga
- Kimika Fakultatea
- Euskal Herriko Unibertsitatea (UPV/EHU)
- 20080 Donostia
- Spain
- Donostia International Physics Center (DIPC)
| | - Josep M. Luis
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química
- Universitat de Girona
- C/Maria Aurèlia Capmany, 69
- 17003 Girona
- Spain
| | - Eduard Matito
- Donostia International Physics Center (DIPC)
- Donostia
- Spain
- Ikerbasque Foundation for Science
- 48011 Bilbao
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38
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Alipour M, Badooei Z. Toward Electron Correlation and Electronic Properties from the Perspective of Information Functional Theory. J Phys Chem A 2018; 122:6424-6437. [DOI: 10.1021/acs.jpca.8b05703] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Mojtaba Alipour
- Department of Chemistry, College of Sciences, Shiraz University, Shiraz 71946-84795, Iran
| | - Zeinab Badooei
- Department of Chemistry, College of Sciences, Shiraz University, Shiraz 71946-84795, Iran
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39
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Casanova D. Short-range density functional correlation within the restricted active space CI method. J Chem Phys 2018; 148:124118. [DOI: 10.1063/1.5018895] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- David Casanova
- Kimika Fakultatea, Euskal Herria Unibersitatea (UPV/EHU), Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Euskadi, Spain
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40
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Rodríguez-Mayorga M, Via-Nadal M, Solà M, Ugalde JM, Lopez X, Matito E. Electron-Pair Distribution in Chemical Bond Formation. J Phys Chem A 2018; 122:1916-1923. [PMID: 29381071 DOI: 10.1021/acs.jpca.7b12556] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The chemical formation process has been studied from relaxation holes, Δh(u), resulting from the difference between the radial intracule density and the nonrelaxed counterpart, which is obtained from atomic radial intracule densities and the pair density constructed from the overlap of the atomic densities. Δh(u) plots show that the internal reorganization of electron pairs prior to bond formation and the covalent bond formation from electrons in separate atoms are completely recognizable processes from the shape of the relaxation hole, Δh(u). The magnitude of Δh(u), the shape of Δh(u) ∀ u < Req, and the distance between the minimum and the maximum in Δh(u) provide further information about the nature of the chemical bond formed. A computational affordable approach to calculate the radial intracule density from approximate pair densities has been also suggested, paving the way to study electron-pair distributions in larger systems.
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Affiliation(s)
- M Rodríguez-Mayorga
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain.,Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona , C/ Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
| | - M Via-Nadal
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain
| | - M Solà
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona , C/ Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
| | - J M Ugalde
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain
| | - X Lopez
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain
| | - E Matito
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science , 48013 Bilbao, Euskadi, Spain
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41
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Rodríguez-Mayorga M, Ramos-Cordoba E, Via-Nadal M, Piris M, Matito E. Comprehensive benchmarking of density matrix functional approximations. Phys Chem Chem Phys 2018; 19:24029-24041. [PMID: 28832052 DOI: 10.1039/c7cp03349d] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The energy usually serves as a yardstick in assessing the performance of approximate methods in computational chemistry. After all, these methods are mostly used for the calculation of the electronic energy of chemical systems. However, computational methods should be also aimed at reproducing other properties, such strategy leading to more robust approximations with a wider range of applicability. In this study, we suggest a battery of ten tests with the aim to analyze density matrix functional approximations (DMFAs), including several properties that the exact functional should satisfy. The tests are performed on a model system with varying electron correlation, carrying a very small computational effort. Our results not only put forward a complete and exhaustive benchmark test for DMFAs, currently lacking, but also reveal serious deficiencies of existing approximations that lead to important clues in the construction of more robust DMFAs.
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Affiliation(s)
- Mauricio Rodríguez-Mayorga
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain.
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42
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Pérez-Guardiola A, Sandoval-Salinas ME, Casanova D, San-Fabián E, Pérez-Jiménez AJ, Sancho-García JC. The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers. Phys Chem Chem Phys 2018; 20:7112-7124. [DOI: 10.1039/c8cp00135a] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We discuss the nature of electron-correlation effects in carbon nanorings and nanobelts by a combined approach based on FT-DFT and RAS-SF methods.
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Affiliation(s)
- A. Pérez-Guardiola
- Department of Physical Chemistry
- University of Alicante
- E-03080 Alicante
- Spain
| | - M. E. Sandoval-Salinas
- Departament de Ciéncia de Materials i Química Física
- Institut de Química Teòrica i Computacional (IQTCUB)
- Universitat de Barcelona
- E-08028 Barcelona
- Spain
| | - D. Casanova
- Kimika Fakultatea
- Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC)
- E-20018 Donostia
- Spain
- IKERBASQUE
| | - E. San-Fabián
- Department of Physical Chemistry
- University of Alicante
- E-03080 Alicante
- Spain
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