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Ju CW, Shen Y, French EJ, Yi J, Bi H, Tian A, Lin Z. Accurate Electronic and Optical Properties of Organic Doublet Radicals Using Machine Learned Range-Separated Functionals. J Phys Chem A 2024. [PMID: 38382058 DOI: 10.1021/acs.jpca.3c07437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2024]
Abstract
Luminescent organic semiconducting doublet-spin radicals are unique and emergent optical materials because their fluorescent quantum yields (Φfl) are not compromised by the spin-flipping intersystem crossing (ISC) into a dark high-spin state. The multiconfigurational nature of these radicals challenges their electronic structure calculations in the framework of single-reference density functional theory (DFT) and introduces room for method improvement. In the present study, we extended our earlier development of ML-ωPBE [J. Phys. Chem. Lett., 2021, 12, 9516-9524], a range-separated hybrid (RSH) exchange-correlation (XC) functional constructed using the stacked ensemble machine learning (SEML) algorithm, from closed-shell organic semiconducting molecules to doublet-spin organic semiconducting radicals. We assessed its performance for a new test set of 64 doublet-spin radicals from five categories while placing all previously compiled 3926 closed-shell molecules in the new training set. Interestingly, ML-ωPBE agrees with the nonempirical OT-ωPBE functional regarding the prediction of the molecule-dependent range-separation parameter (ω), with a small mean absolute error (MAE) of 0.0197 a0-1, but saves the computational cost by 2.46 orders of magnitude. This result demonstrates an outstanding domain adaptation capacity of ML-ωPBE for diverse organic semiconducting species. To further assess the predictive power of ML-ωPBE in experimental observables, we also applied it to evaluate absorption and fluorescence energies (Eabs and Efl) using linear-response time-dependent DFT (TDDFT), and we compared its behavior with nine popular XC functionals. For most radicals, ML-ωPBE reproduces experimental measurements of Eabs and Efl with small MAEs of 0.299 and 0.254 eV, only marginally different from those of OT-ωPBE. Our work illustrates a successful extension of the SEML framework from closed-shell molecules to doublet-spin radicals and will open the venue for calculating optical properties for organic semiconductors using single-reference TDDFT.
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Affiliation(s)
- Cheng-Wei Ju
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, United States
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - Yili Shen
- Manning College of Information and Computer Sciences, University of Massachusetts, Amherst, Massachusetts 01003, United States
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States
| | - Ethan J French
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, United States
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, United States
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Charlestown, Massachusetts 02129, United States
| | - Jun Yi
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, United States
- Department of Chemistry, Wake Forest University, Winston-Salem, North Carolina 27109, United States
| | - Hongshan Bi
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, United States
| | - Aaron Tian
- Manning College of Information and Computer Sciences, University of Massachusetts, Amherst, Massachusetts 01003, United States
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, United States
| | - Zhou Lin
- Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003, United States
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2
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Wu X, Cao C, Zhou C, Wu W. Hybrid Density Functional Valence Bond Method with Multistate Treatment. J Chem Theory Comput 2024. [PMID: 38279919 DOI: 10.1021/acs.jctc.3c01170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2024]
Abstract
Recently, a hybrid density functional valence bond (VB) method, λ-DFVB(U), has been proposed and shown to give accuracy that is comparable to that of CASPT2 in calculations of atomization energies, atomic excitation energies, and reaction barriers, while its computational cost is approximately the same as the valence bond self-consistent-field (VBSCF) method. However, the interaction between electronic states is not included in λ-DFVB(U) since the last step of λ-DFVB(U) is not a diagonalization of the Hamiltonian matrix on the electronic state basis. Therefore, λ-DFVB(U) gives the wrong topology of the potential energy surfaces (PESs) near the conical intersection region. In the present paper, we propose a novel hybrid density functional VB method with multistate treatment, named λ-DFVB(MS), in which an effective Hamiltonian matrix is constructed on the basis of the diabatic states obtained by the valence-bond-based compression approach for the diabatization scheme, and the interaction between electronic states can be included through the diagonalization of the effective Hamiltonian matrix. Test calculations show that λ-DFVB(MS) gives the correct topology of the PESs near the conical intersection region. We also show that the VBSCF wave function with selected VB structures can be applied as a reference in λ-DFVB(MS).
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Affiliation(s)
- Xun Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Chan Cao
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Chen Zhou
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
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3
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Rodríguez-Jiménez JA, Carreras A, Casanova D. Small-Occupation Density Functional Correlation Energy Correction to Wave Function Approximations. J Chem Theory Comput 2024. [PMID: 38227943 DOI: 10.1021/acs.jctc.3c01067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024]
Abstract
In this work, we introduce a novel hybrid approach, termed WFT-soDFT, designed to seamlessly incorporate DFT correlation into wave function ansatzes. This is achieved through a partitioning of the orbital space, distinguishing between large and small natural occupation numbers associated with wave function theory (WFT) and DFT correlation, respectively. The method uses a novel criterion for partitioning the orbital space and mapping the electron density in natural orbitals with a small occupation with the correlation energy of fast electrons within the homogeneous electron gas. Central to our approach is the introduction of a separation parameter ν, the choice of the WFT approach, and the correlation functional. Here, we combine the RASCI wave function with hole and particle truncation with a local density correlation functional to only account for small-occupation correlation energy. We investigate the performance of the method in the study of small but challenging chemical systems, for which WFT-soDFT demonstrates notable improvements over pristine wave function calculations. These findings collectively highlight the potential of the WFT-soDFT approach as a computationally affordable strategy to improve the accuracy of WFT electronic structure calculations.
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Affiliation(s)
- José Aarón Rodríguez-Jiménez
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), 20018 Donostia, Euskadi, Spain
| | - Abel Carreras
- Multiverse Computing, 20008 Donostia, Euskadi, Spain
| | - David Casanova
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Euskadi, Spain
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4
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Zhu H, Zhao R, Lu Y, Liu M, Zhang J, Gao J. Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory. J Phys Chem A 2023; 127:8473-8485. [PMID: 37768927 DOI: 10.1021/acs.jpca.3c04799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/30/2023]
Abstract
The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.
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Affiliation(s)
- Hong Zhu
- School of Chemical Biology & Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Ruoqi Zhao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Yangyi Lu
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Meiyi Liu
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Jun Zhang
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Jiali Gao
- School of Chemical Biology & Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong 518055, China
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
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5
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Hettich C, Zhang X, Kemper D, Zhao R, Zhou S, Lu Y, Gao J, Zhang J, Liu M. Multistate Energy Decomposition Analysis of Molecular Excited States. JACS AU 2023; 3:1800-1819. [PMID: 37502166 PMCID: PMC10369419 DOI: 10.1021/jacsau.3c00186] [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: 04/13/2023] [Revised: 05/15/2023] [Accepted: 05/16/2023] [Indexed: 07/29/2023]
Abstract
A multistate energy decomposition analysis (MS-EDA) method is described to dissect the energy components in molecular complexes in excited states. In MS-EDA, the total binding energy of an excimer or an exciplex is partitioned into a ground-state term, called local interaction energy, and excited-state contributions that include exciton excitation energy, superexchange stabilization, and orbital and configuration-state delocalization. An important feature of MS-EDA is that key intermediate states associated with different energy terms can be variationally optimized, providing quantitative insights into widely used physical concepts such as exciton delocalization and superexchange charge-transfer effects in excited states. By introducing structure-weighted adiabatic excitation energy as the minimum photoexcitation energy needed to produce an excited-state complex, the binding energy of an exciplex and excimer can be defined. On the basis of the nature of intermolecular forces through MS-EDA analysis, it was found that molecular complexes in the excited states can be classified into three main categories, including (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. The illustrative examples in this Perspective highlight the interplay of local excitation polarization, exciton resonance, and superexchange effects in molecular excited states. It is hoped that MS-EDA can be a useful tool for understanding photochemical and photobiological processes.
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Affiliation(s)
- Christian
P. Hettich
- Department
of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Xiaoyong Zhang
- School
of Chemical Biology & Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - David Kemper
- Department
of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Ruoqi Zhao
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Shaoyuan Zhou
- School
of Chemical Biology & Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Yangyi Lu
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Jiali Gao
- Department
of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
- School
of Chemical Biology & Biotechnology, Peking University Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Jun Zhang
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
| | - Meiyi Liu
- Institute
of Systems and Physical Biology, Shenzhen
Bay Laboratory, Shenzhen, Guangdong 518055, China
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6
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Cheng L, Chen H, Ren Y, Cheng Z, Fan M, Liu Y, Shen Z, Yuan T. Study on enhancement of hemoglobin antitoxic ability modified with chromium and ruthenium. Int J Biol Macromol 2023; 242:124756. [PMID: 37178891 DOI: 10.1016/j.ijbiomac.2023.124756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 04/17/2023] [Accepted: 05/02/2023] [Indexed: 05/15/2023]
Abstract
Hemoglobin is essential for carrying oxygen (O2) in the blood. However, its ability to bind excessively to carbon monoxide (CO) makes it susceptible to CO poisoning. To reduce the risk of CO poisoning, Cr-based heme and Ru-based heme were selected from among many transition metal-based hemes based on their characteristics of adsorption conformation, binding intensity, spin multiplicity, and electronic properties. The results showed that hemoglobin modified by Cr-based heme and Ru-based heme had strong anti-CO poisoning abilities. The Cr-based heme and Ru-based heme exhibited much stronger affinity for O2 (-190.67 kJ/mol and -143.18 kJ/mol, respectively) than Fe-based heme (-44.60 kJ/mol). Moreover, Cr-based heme and Ru-based heme exhibited much weaker affinity for CO (-121.50 kJ/mol and -120.88 kJ/mol, respectively) than their affinity for O2, suggesting that they were less likely to cause CO poisoning. The electronic structure analysis also supported this conclusion. Additionally, molecular dynamics analysis showed that hemoglobin modified by Cr-based heme and Ru-based heme was stable. Our findings offer a novel and effective strategy for enhancing the reconstructed hemoglobin's ability to bind O2 and reduce its potential for CO poisoning.
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Affiliation(s)
- Luwei Cheng
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Hongjiang Chen
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Yuanyang Ren
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Zhiwen Cheng
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China; State Environmental Protection Key Laboratory of Environmental Health Impact Assessment of Emerging Contaminants, Shanghai Academy of Environment Sciences, Shanghai 200233, PR China
| | - Maohong Fan
- College of Engineering & Applied Science, University of Wyoming, Laramie 82070, WY, USA
| | - Yawei Liu
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Zhemin Shen
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China; State Environmental Protection Key Laboratory of Environmental Health Impact Assessment of Emerging Contaminants, Shanghai 200233, PR China; Shanghai Engineering Research Center of Solid Waste Treatment and Resource Recovery, Shanghai 200240, China.
| | - Tao Yuan
- School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China; State Environmental Protection Key Laboratory of Environmental Health Impact Assessment of Emerging Contaminants, Shanghai 200233, PR China; Shanghai Engineering Research Center of Solid Waste Treatment and Resource Recovery, Shanghai 200240, China
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7
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Rizo L, Janesko BG. Reimagining the Wave Function in Density Functional Theory: Exploring Strongly Correlated States in Pancake-Bonded Radical Dimers. J Phys Chem A 2023; 127:3684-3691. [PMID: 37053451 DOI: 10.1021/acs.jpca.2c08616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Pancake bonding between π-conjugated radicals challenges conventional electronic structure approximations, due to the presence of both dispersion (van der Waals) interactions and "strong" electron correlation. Here we use a reimagined wave function-in-density functional theory (DFT) approach to model pancake bonds. Our generalized self-interaction correction extends DFT's reference system of noninteracting electrons, by introducing electron-electron interactions within an active space. We show that a small variation on our previous derivation recovers a DFT-corrected complete active space method proposed by Pijeau and Hohenstein. Comparison of the two approaches shows that the latter provides reasonable dissociation curves for single bonds and pancake bonds, including excited states inaccessible to conventional linear response time-dependent DFT. The results motivate broader adoption of wavefunction-in-DFT approaches for modeling pancake bonds.
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Affiliation(s)
- Luis Rizo
- Intense Laser Physics Theory Unit, Illinois State University, Normal, Illinois 61790, United States
| | - Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Drive, Fort Worth, Texas 75039, United States
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8
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Janesko BG. Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory. J Phys Chem Lett 2022; 13:5698-5702. [PMID: 35709503 DOI: 10.1021/acs.jpclett.2c01359] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Perdew-Zunger self-interaction correction (PZSIC) reintroduces an exact constraint to approximate density functional theory (DFT). However, PZSIC can paradoxically degrade performance, and standard DFT approximations (with or without PZSIC) are not systematically improvable. We use the adiabatic projection formalism (Janesko, B. G. J. Chem. Phys. 2022, 156, 014111, https://doi.org/10.1063/5.0076144) to derive PZSIC in terms of a reference system experiencing only electron self-interaction. Generalization to a "self-and-some-others" interaction introduces correlation into the reference system, systematically bridging from PZSIC to exact wave function theory without the double counting of correlation. Minimal active spaces accurately treat nearly one electron, near-equilibrium, and strongly correlated model systems at modest computational expense.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Drive, Fort Worth, Texas 76129, United States
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9
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Zheng P, Gan Z, Zhou C, Su P, Wu W. λ-DFVB(U): A hybrid density functional valence bond method based on unpaired electron density. J Chem Phys 2022; 156:204103. [DOI: 10.1063/5.0091592] [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
In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn–Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron–electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF.
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Affiliation(s)
- Peikun Zheng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Zixi Gan
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Chen Zhou
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Peifeng Su
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Wei Wu
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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10
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Schmerwitz YLA, Ivanov AV, Jónsson EÖ, Jónsson H, Levi G. Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting. J Phys Chem Lett 2022; 13:3990-3999. [PMID: 35481754 DOI: 10.1021/acs.jpclett.2c00741] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.
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Affiliation(s)
| | - Aleksei V Ivanov
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Elvar Ö Jónsson
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Hannes Jónsson
- Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
- Department of Applied Physics, Aalto University, FI-00076 Espoo, Finland
| | - Gianluca Levi
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
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11
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Athavale V, Teh HH, Subotnik JE. On the inclusion of one double within CIS and TDDFT. J Chem Phys 2021; 155:154105. [PMID: 34686061 DOI: 10.1063/5.0064269] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.
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Affiliation(s)
- Vishikh Athavale
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19 104-6323, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19 104-6323, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19 104-6323, USA
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12
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Casanova D. Restricted active space configuration interaction methods for strong correlation: Recent developments. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1561] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- David Casanova
- Donostia International Physics Center (DIPC) Donostia Spain
- Ikerbasque Basque Foundation for Science Bilbao Spain
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13
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Abstract
Kohn-Sham density functional theory with the available exchange-correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated systems, and available functionals of the spin densities do not accurately predict energies for many strongly correlated systems when one uses multiconfigurational wave functions with spin symmetry. Furthermore, adding a correlation functional to a multiconfigurational reference energy can lead to double counting of electron correlation. Multiconfiguration pair-density functional theory (MC-PDFT) overcomes both obstacles, the second by calculating the quantum mechanical part of the electronic energy entirely by a functional, and the first by using a functional of the total density and the on-top pair density rather than the spin densities. This allows one to calculate the energy of strongly correlated systems efficiently with a pair-density functional and a suitable multiconfigurational reference function. This article reviews MC-PDFT and related background information.
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Affiliation(s)
- Prachi Sharma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA;
| | - Jie J Bao
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA;
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA;
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, USA;
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14
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Meitei OR, Mayhall NJ. Spin-Flip Pair-Density Functional Theory: A Practical Approach To Treat Static and Dynamical Correlations in Large Molecules. J Chem Theory Comput 2021; 17:2906-2916. [PMID: 33861603 DOI: 10.1021/acs.jctc.1c00121] [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
We present a practical approach to treat static and dynamical correlation accurately in large multiconfigurational systems. The static correlation is taken into account by using the spin-flip approach, which is well-known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (J. Comput. Theor. Chem., 2014, 10, 3669). External relaxations are performed in the spin-flip calculations through a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals, and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.
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Affiliation(s)
- Oinam Romesh Meitei
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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15
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Zheng P, Ji C, Ying F, Su P, Wu W. A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited. Molecules 2021; 26:521. [PMID: 33498268 PMCID: PMC7863953 DOI: 10.3390/molecules26030521] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Revised: 01/17/2021] [Accepted: 01/18/2021] [Indexed: 11/29/2022] Open
Abstract
A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.
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Affiliation(s)
| | | | | | - Peifeng Su
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, The State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China; (P.Z.); (C.J.); (F.Y.)
| | - Wei Wu
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, The State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China; (P.Z.); (C.J.); (F.Y.)
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16
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Peters LDM, Kussmann J, Ochsenfeld C. A Fermi smearing variant of the Tamm–Dancoff approximation for nonadiabatic dynamics involving S 1–S 0 transitions: Validation and application to azobenzene. J Chem Phys 2020; 153:094104. [DOI: 10.1063/5.0016487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Laurens D. M. Peters
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Jörg Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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17
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Hapka M, Pernal K, Gritsenko OV. Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density. J Phys Chem Lett 2020; 11:5883-5889. [PMID: 32589027 PMCID: PMC7467739 DOI: 10.1021/acs.jpclett.0c01616] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.
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Affiliation(s)
- Michał Hapka
- Institute
of Physics, Lodz University of Technology, PL-90-924 Lodz, Poland
- Faculty
of Chemistry, University of Warsaw, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Oleg V. Gritsenko
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Section
Theoretical Chemistry, VU University, NL-1081 HV Amsterdam, The Netherlands
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18
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Giner E, Scemama A, Loos PF, Toulouse J. A basis-set error correction based on density-functional theory for strongly correlated molecular systems. J Chem Phys 2020; 152:174104. [DOI: 10.1063/5.0002892] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emmanuel Giner
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut Universitaire de France, Paris, France
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19
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Mostafanejad M, Liebenthal MD, DePrince AE. Global Hybrid Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2020; 16:2274-2283. [PMID: 32101416 DOI: 10.1021/acs.jctc.9b01178] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A global hybrid extension of multiconfiguration pair-density functional theory (MC-PDFT) is developed. Using a linear decomposition of the electron-electron repulsion term, a fraction λ of the nonlocal exchange interaction, obtained from variational two-electron reduced-density matrix (v2RDM)-driven complete active-space self-consistent field (CASSCF) theory, is combined with its local counterpart, obtained from an on-top pair-density functional. The resulting scheme (called λ-MC-PDFT) inherits the benefits of MC-PDFT (e.g., its simplicity and the resolution of the symmetry dilemma) and, when combined with the v2RDM approach to CASSCF, requires only polynomially scaling computational effort. As a result, λ-MC-PDFT can efficiently describe static and dynamical correlation effects in strongly correlated systems. The efficacy of the approach is assessed for several challenging multiconfigurational problems, including the dissociation of molecular nitrogen, the double dissociation of a water molecule, and the 1,3-dipolar cycloadditions of ozone to ethylene and ozone to acetylene in the O3ADD6 benchmark set.
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Affiliation(s)
- Mohammad Mostafanejad
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Marcus Dante Liebenthal
- Department of Chemistry and Biochemistry, Ithaca College, Ithaca, New York 14850, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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20
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Hapka M, Pastorczak E, Krzemińska A, Pernal K. Long-range-corrected multiconfiguration density functional with the on-top pair density. J Chem Phys 2020; 152:094102. [DOI: 10.1063/1.5138980] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Agnieszka Krzemińska
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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21
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Chattopadhyay S. Investigation of Multiple-Bond Dissociation Using Brillouin–Wigner Perturbation with Improved Virtual Orbitals. J Phys Chem A 2020; 124:1444-1463. [DOI: 10.1021/acs.jpca.9b11522] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
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22
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Jin Z, Dou W, Subotnik JE. Configuration interaction approaches for solving quantum impurity models. J Chem Phys 2020; 152:064105. [PMID: 32061216 DOI: 10.1063/1.5131624] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop several configuration interaction approaches for characterizing the electronic structure of an adsorbate on a metal surface (at least in model form). When one can separate the adsorbate from the substrate, these methods can achieve a reasonable description of adsorbate on-site electron-electron correlation in the presence of a continuum of states. While the present paper is restricted to the Anderson impurity model, there is hope that these methods can be extended to ab initio Hamiltonians and provide insight into the structure and dynamics of molecule-metal surface interactions.
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Affiliation(s)
- Zuxin Jin
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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23
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Scaling exchange and correlation in the on-top density functional of multiconfiguration pair-density functional theory: effect on electronic excitation energies and bond energies. Theor Chem Acc 2020. [DOI: 10.1007/s00214-019-2539-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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24
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Pernal K, Gritsenko OV. Embracing local suppression and enhancement of dynamic correlation effects in a CASΠDFT method for efficient description of excited states. Faraday Discuss 2020; 224:333-347. [DOI: 10.1039/d0fd00050g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
In this work we show that the presence of covalent and ionic configurations in a wavefunction gives rise to spatial regions where the effects of suppression and enhancement of correlation energy, respectively, dominate.
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Affiliation(s)
- Katarzyna Pernal
- Institute of Physics
- Lodz University of Technology
- PL-90-924 Lodz
- Poland
| | - Oleg V. Gritsenko
- Institute of Physics
- Lodz University of Technology
- PL-90-924 Lodz
- Poland
- Section Theoretical Chemistry
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25
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Pernal K, Gritsenko OV, van Meer R. Reproducing benchmark potential energy curves of molecular bond dissociation with small complete active space aided with density and density-matrix functional corrections. J Chem Phys 2019; 151:164122. [PMID: 31675879 DOI: 10.1063/1.5124948] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Various effects of electron correlation accompany molecular bond dissociation, which makes the efficient calculation of potential energy curves a notoriously difficult problem. In an attempt to reliably reproduce both absolute energies and shapes of the benchmark dissociation curves, calculations with the combined CASΠDFT method are carried out for the prototype molecules H2, BH, F2, and N2. The complete active space (CAS) part of CASΠDFT accounts for long-range nondynamic correlation, while short-range dynamic correlation is accounted for with the corrected Lee-Yang-Parr correlation functional of density functional theory (DFT). The correction represents the suppression of dynamic correlation with nondynamic correlation, and it is a function of the ratio x(r) between the conditional and conventional densities obtained with the CAS on-top pair density Π(r). For the single-bonded molecules H2, BH, and F2, CASΠDFT succeeds in reproducing the shapes and absolute energies (for H2 and BH) of the benchmark curves, while for the triple-bonded N2 molecule, the addition to CASΠDFT of a multibond correction is required. It accounts for the middle-range dynamic correlation of the same-spin electrons in the (symmetrized) high-spin atomic electron configurations of the dissociating N2.
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Affiliation(s)
- Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, PL-90-924 Lodz, Poland
| | - Oleg V Gritsenko
- Institute of Physics, Lodz University of Technology, PL-90-924 Lodz, Poland
| | - Robert van Meer
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
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26
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Adeyiga O, Suleiman O, Dandu NK, Odoh SO. Ground-state actinide chemistry with scalar-relativistic multiconfiguration pair-density functional theory. J Chem Phys 2019; 151:134102. [DOI: 10.1063/1.5099373] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Olajumoke Adeyiga
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, USA
| | - Olabisi Suleiman
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, USA
| | - Naveen K. Dandu
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, USA
| | - Samuel O. Odoh
- Department of Chemistry, University of Nevada Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, USA
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27
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Teh HH, Subotnik JE. The Simplest Possible Approach for Simulating S 0- S 1 Conical Intersections with DFT/TDDFT: Adding One Doubly Excited Configuration. J Phys Chem Lett 2019; 10:3426-3432. [PMID: 31135162 DOI: 10.1021/acs.jpclett.9b00981] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A simple combination of density functional theory/time-dependent density functional theory (DFT/TDDFT) and configuration interaction is presented to fix the incorrect topology of the S0- S1 conical intersection (CI) and allow a description of bond making and bond breaking in photoinduced dynamics. The proposed TDDFT-1D method includes one lone optimized doubly excited configuration in addition to the DFT/TDDFT singly excited states within the context of a large configuration interaction Hamiltonian. Results for ethylene and stilbene are provided to demonstrate that this ansatz can yield physically meaningful potential energy surfaces near S0- S1 avoided crossings without changing the vertical excitation energies far from the relevant crossings. We also investigate the famous linear water example to show that the algorithm calculates the correct topology of the S0- S1 CI and yields the correct geometric phase.
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Affiliation(s)
- Hung-Hsuan Teh
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104-6323 , United States
| | - Joseph E Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104-6323 , United States
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28
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Chen L, Janssens TVW, Grönbeck H. A comparative test of different density functionals for calculations of NH 3-SCR over Cu-Chabazite. Phys Chem Chem Phys 2019; 21:10923-10930. [PMID: 31089628 DOI: 10.1039/c9cp01576k] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
A general challenge in density functional theory calculations is to simultaneously account for different types of bonds. One such example is reactions in zeolites where both van der Waals and chemical bonds should be described accurately. Here, we use different exchange-correlation functionals to explore O2 dissociation over pairs of Cu(NH3)2+ complexes in Cu-Chabazite. This is an important part of selective catalytic reduction of NOx using NH3 as a reducing agent. The investigated functionals are PBE, PBE+U, PBE+D, PBE+U+D, PBE-cx, BEEF and HSE06+D. We find that the potential energy landscape for O2 activation and dissociation depends critically on the choice of functional. However, the van der Waals contributions are similarly described by the functionals accounting for this interaction. The discrepancies in the potential energy surface are instead related to different descriptions of the Cu-O chemical bond. By investigating the electronic, structural and energetic properties of reference systems including bulk copper oxides and (Cu2O2)2+ enzymatic crystals, we find that the PBE+U approach together with van der Waals corrections provides a reasonable simultaneous accuracy of the different bonds in the systems.
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Affiliation(s)
- Lin Chen
- Department of Physics and Competence Centre for Catalysis, Chalmers University of Technology, SE-412 96 Göteborg, Sweden.
| | - Ton V W Janssens
- Umicore Denmark ApS, Nøjsomhedsvej 20, DK-2800 Kgs. Lyngby, Denmark
| | - Henrik Grönbeck
- Department of Physics and Competence Centre for Catalysis, Chalmers University of Technology, SE-412 96 Göteborg, Sweden.
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29
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Gomez JA, Molla M, Garza AJ, Henderson TM, Scuseria GE. Assessing combinations of singlet-paired coupled cluster and density functional theory for treating electron correlation in closed and open shells. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1615144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- John A. Gomez
- Department of Chemistry, Rice University, Houston, TX, USA
- Applied Physics Graduate Program, Rice University, Houston, TX, USA
| | - Mahlet Molla
- Department of Chemistry, Rice University, Houston, TX, USA
| | | | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
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30
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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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31
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Ferté A, Giner E, Toulouse J. Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density. J Chem Phys 2019; 150:084103. [DOI: 10.1063/1.5082638] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anthony Ferté
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
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32
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Mostafanejad M, DePrince AE. Combining Pair-Density Functional Theory and Variational Two-Electron Reduced-Density Matrix Methods. J Chem Theory Comput 2018; 15:290-302. [DOI: 10.1021/acs.jctc.8b00988] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mohammad Mostafanejad
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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33
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Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 128] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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34
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Lischka H, Nachtigallová D, Aquino AJA, Szalay PG, Plasser F, Machado FBC, Barbatti M. Multireference Approaches for Excited States of Molecules. Chem Rev 2018; 118:7293-7361. [DOI: 10.1021/acs.chemrev.8b00244] [Citation(s) in RCA: 197] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Hans Lischka
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
- Regional Centre of Advanced Technologies and Materials, Palacký University, 78371 Olomouc, Czech Republic
| | - Adélia J. A. Aquino
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Felix Plasser
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
- Department of Chemistry, Loughborough University, Leicestershire LE11 3TU, United Kingdom
| | - Francisco B. C. Machado
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
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35
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Crespo-Otero R, Barbatti M. Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics. Chem Rev 2018; 118:7026-7068. [DOI: 10.1021/acs.chemrev.7b00577] [Citation(s) in RCA: 301] [Impact Index Per Article: 50.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Rachel Crespo-Otero
- School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
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36
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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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37
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Guo X, Qu Z, Gao J. The charger transfer electronic coupling in diabatic perspective: A multi-state density functional theory study. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2017.10.061] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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38
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Bao JL, Wang Y, He X, Gagliardi L, Truhlar DG. Multiconfiguration Pair-Density Functional Theory Is Free From Delocalization Error. J Phys Chem Lett 2017; 8:5616-5620. [PMID: 29090926 DOI: 10.1021/acs.jpclett.7b02705] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Delocalization error has been singled out by Yang and co-workers as the dominant error in Kohn-Sham density functional theory (KS-DFT) with conventional approximate functionals. In this Letter, by computing the vertical first ionization energy for well separated He clusters, we show that multiconfiguration pair-density functional theory (MC-PDFT) is free from delocalization error. To put MC-PDFT in perspective, we also compare it with some Kohn-Sham density functionals, including both traditional and modern functionals. Whereas large delocalization errors are almost universal in KS-DFT (the only exception being the very recent corrected functionals of Yang and co-workers), delocalization error is removed by MC-PDFT, which bodes well for its future as a step forward from KS-DFT.
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Affiliation(s)
- Junwei Lucas Bao
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - Ying Wang
- School of Chemistry and Molecular Engineering, State Key Laboratory of Precision Spectroscopy, East China Normal University , Shanghai 200062, China
| | - Xiao He
- School of Chemistry and Molecular Engineering, State Key Laboratory of Precision Spectroscopy, East China Normal University , Shanghai 200062, China
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
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39
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Grofe A, Chen X, Liu W, Gao J. Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory. J Phys Chem Lett 2017; 8:4838-4845. [PMID: 28914545 PMCID: PMC5792056 DOI: 10.1021/acs.jpclett.7b02202] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.
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Affiliation(s)
- Adam Grofe
- Theoretical Chemistry Institute, Jilin University , Changchun, Jilin Province 130023, People's Republic of China
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Xin Chen
- Theoretical Chemistry Institute, Jilin University , Changchun, Jilin Province 130023, People's Republic of China
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences and College of Chemistry and Molecular Engineering , Beijing 100871, People's Republic of China
| | - Jiali Gao
- Theoretical Chemistry Institute, Jilin University , Changchun, Jilin Province 130023, People's Republic of China
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
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40
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Shu Y, Fales BS, Peng WT, Levine BG. Understanding Nonradiative Recombination through Defect-Induced Conical Intersections. J Phys Chem Lett 2017; 8:4091-4099. [PMID: 28799771 DOI: 10.1021/acs.jpclett.7b01707] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Defects are known to introduce pathways for the nonradiative recombination of electronic excitations in semiconductors, but implicating a specific defect as a nonradiative center remains challenging for both experiment and theory. In this Perspective, we present recent progress toward this goal involving the identification and characterization of defect-induced conical intersections (DICIs), points of degeneracy between the ground and first excited electronic states of semiconductor materials that arise from the deformation of specific defects. Analysis of DICIs does not require the assumption of weak correlation between the electron and hole nor of stationary nuclei. It is demonstrated that in some cases an energetically accessible DICI is present even when no midgap state is predicted by single-particle theories (e.g., density functional theory). We review recent theoretical and computational developments that enable the location of DICIs in semiconductor nanomaterials and present insights into the photoluminescence of silicon nanocrystals gleaned from DICIs.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - B Scott Fales
- Department of Chemistry and the PULSE Institute, Stanford University , Stanford, California 94305, United States
- SLAC National Accelerator Laboratory , Menlo Park, California 94025, United States
| | - Wei-Tao Peng
- Department of Chemistry, Michigan State University , East Lansing, Michigan 48824, United States
| | - Benjamin G Levine
- Department of Chemistry, Michigan State University , East Lansing, Michigan 48824, United States
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41
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Pijeau S, Hohenstein EG. Improved Complete Active Space Configuration Interaction Energies with a Simple Correction from Density Functional Theory. J Chem Theory Comput 2017; 13:1130-1146. [DOI: 10.1021/acs.jctc.6b00893] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Shiela Pijeau
- Department
of Chemistry and Biochemistry, The City College of New York, New York, New York 10031, United States
| | - Edward G. Hohenstein
- Department
of Chemistry and Biochemistry, The City College of New York, New York, New York 10031, United States
- Ph.D.
Program in Chemistry, The City University of New York, New York, New York 10016, United States
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42
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Zhou C, Zhang Y, Gong X, Ying F, Su P, Wu W. Hamiltonian Matrix Correction Based Density Functional Valence Bond Method. J Chem Theory Comput 2017; 13:627-634. [PMID: 27992721 DOI: 10.1021/acs.jctc.6b01144] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this work, a valence bond type multireference density functional theory (MRDFT) method, called the Hamiltonian matrix correction based density functional valence bond method (hc-DFVB), is presented. In hc-DFVB, the static electronic correlation is considered by the valence bond self-consistent field (VBSCF) strategy, while the dynamic correlation energy is taken into account by Kohn-Sham density functional theory (KS-DFT). Different from our previous version of DFVB (J. Chem. Theory Comput. 2012, 8, 1608), hc-DFVB corrects the dynamic correlation energy with a Hamiltonian correction matrix, improving the functional adaptability and computational accuracy. The method was tested for various physical and chemical properties, including spectroscopic constants, bond dissociation energies, reaction barriers, and singlet-triplet gaps. The accuracy of hc-DFVB matches that of KS-DFT and high level molecular orbital (MO) methods quite well. Furthermore, hc-DFVB keeps the advantages of VB methods, which are able to provide clear interpretations and chemical insights with compact wave functions.
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Affiliation(s)
- Chen Zhou
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Yang Zhang
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Xiping Gong
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry 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, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry 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, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry 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, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
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43
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Yu HS, Li SL, Truhlar DG. Perspective: Kohn-Sham density functional theory descending a staircase. J Chem Phys 2016; 145:130901. [DOI: 10.1063/1.4963168] [Citation(s) in RCA: 204] [Impact Index Per Article: 25.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Haoyu S. Yu
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Shaohong L. Li
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
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44
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Nguyen Lan T, Kananenka AA, Zgid D. Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green’s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy. J Chem Theory Comput 2016; 12:4856-4870. [DOI: 10.1021/acs.jctc.6b00638] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tran Nguyen Lan
- Department of Chemistry and ‡Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Alexei A. Kananenka
- Department of Chemistry and ‡Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry and ‡Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
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45
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Filatov M, Martínez TJ, Kim KS. Using the GVB Ansatz to develop ensemble DFT method for describing multiple strongly correlated electron pairs. Phys Chem Chem Phys 2016; 18:21040-50. [PMID: 26947515 DOI: 10.1039/c6cp00236f] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Korea.
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46
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Odoh SO, Manni GL, Carlson RK, Truhlar DG, Gagliardi L. Separated-pair approximation and separated-pair pair-density functional theory. Chem Sci 2016; 7:2399-2413. [PMID: 29997782 PMCID: PMC6003605 DOI: 10.1039/c5sc03321g] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Accepted: 12/11/2015] [Indexed: 11/23/2022] Open
Abstract
Multi-configuration pair-density functional theory (MC-PDFT) has proved to be a powerful way to combine the capabilities of multi-configuration self-consistent-field theory to represent the an electronic wave function with a highly efficient way to include dynamic correlation energy by density functional theory. All applications reported previously involved complete active space self-consistent-field (CASSCF) theory for the reference wave function. For treating large systems efficiently, it is necessary to ask whether good accuracy is retained when using less complete configuration interaction spaces. To answer this question, we present here calculations employing MC-PDFT with the separated pair (SP) approximation, which is a special case (defined in this article) of generalized active space self-consistent-field (GASSCF) theory in which no more than two orbitals are included in any GAS subspace and in which inter-subspace excitations are excluded. This special case of MC-PDFT will be called SP-PDFT. In SP-PDFT, the electronic kinetic energy and the classical Coulomb energy, the electronic density and its gradient, and the on-top pair density and its gradient are obtained from an SP approximation wave function; the electronic energy is then calculated from the first two of these quantities and an on-top density functional of the last four. The accuracy of the SP-PDFT method for predicting the structural properties and bond dissociation energies of twelve diatomic molecules and two triatomic molecules is compared to the SP approximation itself and to CASSCF, MC-PDFT based on CASSCF, CASSCF followed by second order perturbation theory (CASPT2), and Kohn-Sham density functional theory with the PBE exchange-correlation potential. We show that SP-PDFT reproduces the accuracy of MC-PDFT based on the corresponding CASSCF wave function for predicting C-H bond dissociation energies, the reaction barriers of pericyclic reactions and the properties of open-shell singlet systems, all at only a small fraction of the computational cost.
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Affiliation(s)
- Samuel O Odoh
- Department of Chemistry , Chemical Theory Center , Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , MN 55455-0431 , USA . ;
| | - Giovanni Li Manni
- Department of Chemistry , Chemical Theory Center , Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , MN 55455-0431 , USA . ;
- Max-Planck Institut für Festkörperforshung , Heisenbergstraße 1 , 70569 Stuttgart , Germany
| | - Rebecca K Carlson
- Department of Chemistry , Chemical Theory Center , Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , MN 55455-0431 , USA . ;
| | - Donald G Truhlar
- Department of Chemistry , Chemical Theory Center , Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , MN 55455-0431 , USA . ;
| | - Laura Gagliardi
- Department of Chemistry , Chemical Theory Center , Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , MN 55455-0431 , USA . ;
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47
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Carlson RK, Li Manni G, Sonnenberger AL, Truhlar DG, Gagliardi L. Multiconfiguration pair-density functional theory: barrier heights and main group and transition metal energetics. J Chem Theory Comput 2016; 11:82-90. [PMID: 26574206 DOI: 10.1021/ct5008235] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.
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Affiliation(s)
- Rebecca K Carlson
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Giovanni Li Manni
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Andrew L Sonnenberger
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States
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48
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Zou W, Sexton T, Kraka E, Freindorf M, Cremer D. A New Method for Describing the Mechanism of a Chemical Reaction Based on the Unified Reaction Valley Approach. J Chem Theory Comput 2016; 12:650-63. [DOI: 10.1021/acs.jctc.5b01098] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wenli Zou
- Computational and Theoretical
Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Ave, Dallas, Texas 75275-0314, United States
| | - Thomas Sexton
- Computational and Theoretical
Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Ave, Dallas, Texas 75275-0314, United States
| | - Elfi Kraka
- Computational and Theoretical
Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Ave, Dallas, Texas 75275-0314, United States
| | - Marek Freindorf
- Computational and Theoretical
Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Ave, Dallas, Texas 75275-0314, United States
| | - Dieter Cremer
- Computational and Theoretical
Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Ave, Dallas, Texas 75275-0314, United States
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49
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Lan TN, Kananenka AA, Zgid D. Communication: Towards ab initio self-energy embedding theory in quantum chemistry. J Chem Phys 2015; 143:241102. [DOI: 10.1063/1.4938562] [Citation(s) in RCA: 67] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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50
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Li Manni G, Carlson RK, Luo S, Ma D, Olsen J, Truhlar DG, Gagliardi L. Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2015; 10:3669-80. [PMID: 26588512 DOI: 10.1021/ct500483t] [Citation(s) in RCA: 299] [Impact Index Per Article: 33.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.
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Affiliation(s)
- Giovanni Li Manni
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Rebecca K Carlson
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Sijie Luo
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Dongxia Ma
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University , Langelandsgade 140, DK-8000, Aarhus C, Denmark
| | - Donald G Truhlar
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
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