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Hirao K, Ahn DH, Song JW, Chan B, Nakajima T. Validation of Long-Range-Corrected LC2gau Functional for Koopmans' Prediction of Core and Valence Ionization Energies with Diverse Data. J Phys Chem A 2025; 129:4115-4122. [PMID: 40299754 DOI: 10.1021/acs.jpca.5c01769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/01/2025]
Abstract
Koopmans' theorem, based on Kohn-Sham (KS) orbital energies of current approximate functionals, does not predict well the ionization energies of 1s, 2s, and 2p core electrons in third-period elements due to the self-interaction errors (SIEs). To address this limitation, the LC2gau functional is developed, which we have validated in the present study. With a fixed range-separation parameter (μ) of 0.35 bohr-1, it yields a mean absolute deviation (MAD) of 0.37 eV for 401 valence ionization energies from the Chong-Gritsenko-Baerends (CGB) set and an MAD of 0.20 eV for the highest occupied molecular orbital (HOMO) ionization energies of 34 molecules containing third-period elements. It is less accurate in predicting core electron binding energies (CEBEs) of third-period elements. With μ = 0.35 bohr-1, the MAD of CEBEs is 1.30 eV. We observed that the CEBE increases linearly with μ and tuned it for each element. For 2s and 2p electrons in third-period elements, the optimal μ values are approximately 0.35 and 0.30 bohr-1, respectively. For the corresponding 1s electrons, the optimal μ varies across elements, gradually decreasing from 0.40 bohr-1 for Si to 0.12 bohr-1 for Cl. With the optimized μ, a smaller MAD of 0.64 eV is obtained for CEBEs of the third-period elements.
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Affiliation(s)
- Kimihiko Hirao
- Fukui Institute for Fundamental Chemistry, Kyoto University, Takano, Nishihiraki-cho 34-4, Sakyo-ku, Kyoto 606-8103, Japan
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan
| | - Dae-Hwan Ahn
- Department of Chemistry Education, Daegu University, Gyeongsan 113-8656, Korea
| | - Jong-Won Song
- Department of Chemistry Education, Daegu University, Gyeongsan 113-8656, Korea
| | - Bun Chan
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan
- Graduate School of Engineering, Nagasaki University, Bunkyo 1-14, Nagasaki 852-8521, Japan
| | - Takahito Nakajima
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan
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Hirao K, Nakajima T, Chan B. Exploiting the Correlation between the 1s, 2s, and 2p Energies for the Prediction of Core-Level Binding Energies of Si, P, S, and Cl species. J Phys Chem A 2024; 128:6879-6897. [PMID: 39120958 DOI: 10.1021/acs.jpca.4c03252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/11/2024]
Abstract
The binding energies (BEs) of the 1s, 2s, and 2p core electrons of third-period elements (Si, P, S, Cl) were calculated using Hartree-Fock (HF) and B3LYP, BH&HLYP, and LC-BOP ΔSCF, and the shifted KS ΔSCF methods. Linear relationships between two BEs were derived and compared with the Auger parameter. The derived lines are essentially parallel, with only the intercepts differing. The difference in intercepts is due to the lack of electron correlation effects in HF and the self-interaction errors (SIEs) of the functional. The slope is the slope of the linear relationship between the chemical shifts. The straight lines between the 2s and 2p BEs also coincided with the Auger parameter lines, which have a slope of 1 by definition and an intercept being the difference between the 2s and 2p BEs. The shifted KS ΔSCF scheme compensates for SIEs, yielding equations that are approximately invariant. The calculated average gaps for the 2s and 2p BEs are 51.21 eV for Si, 57.48 eV for P, 63.85 eV for S, and 70.48 eV for Cl. The straight lines representing the relationships between the BEs of the 1s and 2s and 1s and 2p electrons are also parallel to each other in ΔSCF and converge into a single line in the shifted ΔSCF scheme. However, these lines are steeper than the Auger parameter line. The derived relationships can be used to predict unknown BEs, which we have applied to many molecules. The results are highly accurate, with mean absolute errors (MAEs) of less than 0.2 eV compared to experimental values.
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Affiliation(s)
- Kimihiko Hirao
- Fukui Institute for Fundamental Chemistry, Kyoto University, Takano, Nishihiraki-cho 34-4, Sakyo-ku, Kyoto 606-8103, Japan
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan
| | - Takahito Nakajima
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan
| | - Bun Chan
- RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan
- Graduate School of Engineering, Nagasaki University, Bunkyo 1-14, Nagasaki 852-8521, Japan
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Ahn DH, Nakajima T, Hirao K, Song JW. Long-range Corrected Density Functional Theory Including a Two-Gaussian Hartree-Fock Operator for High Accuracy Core-excitation Energy Calculations of Both the Second- and Third-Row Atoms (LC2gau-core-BOP). J Chem Theory Comput 2024. [PMID: 39106473 DOI: 10.1021/acs.jctc.4c00651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/09/2024]
Abstract
In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree-Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.
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Affiliation(s)
- Dae-Hwan Ahn
- Department of Chemistry Education, Daegu University, Gyeongsan-si 113-8656, Korea
| | | | - Kimihiko Hirao
- RIKEN Center for Computational Science, Kobe 650-0047, Japan
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8501, Japan
| | - Jong-Won Song
- Department of Chemistry Education, Daegu University, Gyeongsan-si 113-8656, Korea
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Liu L, Xu Q, dos Anjos Cunha L, Xin H, Head-Gordon M, Qian J. Real-Space Pseudopotential Method for the Calculation of Third-Row Elements X-ray Photoelectron Spectroscopic Signatures. J Chem Theory Comput 2024; 20:6134-6143. [PMID: 38970155 PMCID: PMC11270745 DOI: 10.1021/acs.jctc.4c00535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2024] [Revised: 06/18/2024] [Accepted: 06/20/2024] [Indexed: 07/08/2024]
Abstract
X-ray photoelectron spectroscopy (XPS) is a powerful characterization technique that unveils subtle chemical environment differences via core-electron binding energy (CEBE) analysis. We extend the development of real-space pseudopotential methods to calculating 1s, 2s, and 2p3/2 CEBEs of third-row elements (S, P, and Si) within the framework of Kohn-Sham density-functional theory (KS-DFT). The new approach systematically prevents variational collapse and simplifies core-excited orbital selection within dense energy level distributions. However, careful error cancellation analysis is required to achieve accuracy comparable to all-electron methods and experiments. Combined with real-space KS-DFT implementation, this development enables large-scale simulations with both Dirichlet boundary conditions and periodic boundary conditions.
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Affiliation(s)
- Liping Liu
- Department
of Chemical Engineering, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia 24060, United States
| | - Qiang Xu
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Leonardo dos Anjos Cunha
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Department
of Chemistry, University of California,
Berkeley, Berkeley, California 94720, United States
| | - Hongliang Xin
- Department
of Chemical Engineering, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia 24060, United States
| | - Martin Head-Gordon
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Department
of Chemistry, University of California,
Berkeley, Berkeley, California 94720, United States
| | - Jin Qian
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
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Janesko BG. Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations. J Chem Theory Comput 2023. [PMID: 37437304 DOI: 10.1021/acs.jctc.3c00312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/14/2023]
Abstract
Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837-847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C-F and third-period elements Si-Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT's limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT's limitations for Rydberg and charge-transfer excitations.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas 76129, United States
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Janesko BG. Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization. J Chem Theory Comput 2023; 19:837-847. [PMID: 36656811 DOI: 10.1021/acs.jctc.2c01023] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron-electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn-Sham reference system, and employs a formally exact density functional to model the remaining electron-electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew-Burke-Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core-electron binding energies of second-period elements Li-Ne and third-period elements Na-Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas76129, United States
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Fouda AEA, Koulentianos D, Young L, Doumy G, Ho PJ. Resonant double-core excitations with ultrafast, intense X-ray pulses. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2133749] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Affiliation(s)
- Adam E. A. Fouda
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
| | - Dimitris Koulentianos
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
| | - Linda Young
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
- Department of Physics and James Franck Institute, The University of Chicago, Chicago, IL, USA
| | - Gilles Doumy
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
| | - Phay J. Ho
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL, USA
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Zamani AY, Hratchian HP. Assessing the performance of ΔSCF and the diagonal second-order self-energy approximation for calculating vertical core excitation energies. J Chem Phys 2022; 157:084115. [DOI: 10.1063/5.0100638] [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
Vertical core excitation energies are obtained using a combination of the ΔSCF method and the diagonal second-order (D2) self-energy approximation. These methods are applied to a set of neutral molecules and their anionic forms. An assessment of the results with the inclusion of relativistic effects is presented. For core excitations involving delocalized symmetry orbitals, the applied composite method improves upon the overestimation of ΔSCF by providing approximate values close to experimental K-shell transition energies. The importance of both correlation and relaxation contributions to the vertical core-excited state energies, the concept of local and non-local core orbitals, and the consequences of breaking symmetry are discussed.
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Affiliation(s)
| | - Hrant Patrick Hratchian
- Department of Chemistry & Biochemistry, University of California Merced, United States of America
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Jenkins AJ, Hu H, Lu L, Frisch MJ, Li X. Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra. J Chem Theory Comput 2021; 18:141-150. [PMID: 34908414 DOI: 10.1021/acs.jctc.1c00564] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.
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Affiliation(s)
- Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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