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Franzke YJ, Holzer C. Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin-orbit coupling. J Chem Phys 2023; 159:184102. [PMID: 37937936 DOI: 10.1063/5.0171509] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 09/04/2023] [Indexed: 11/09/2023] Open
Abstract
We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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Peluzo BMTC, Makoś MZ, Moura RT, Freindorf M, Kraka E. Linear versus Bent Uranium(II) Metallocenes─A Local Vibrational Mode Study. Inorg Chem 2023. [PMID: 37478353 DOI: 10.1021/acs.inorgchem.3c01761] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/23/2023]
Abstract
Uranium metallocenes have recently attracted attention driven by their use as catalysts in organometallic synthesis. In addition to bent U(IV) and U(III), an U(II) metallocene [(η5-C5i Pr5)2U] was synthesized with an unusual linear Cp-U-Cp angle. In this work, we investigated 22 U(II) metallocenes, (i) assessing the intrinsic strength of the U-ring interactions in these complexes with a novel bond strength measure based on our local vibrational mode analysis and (ii) systematically exploring what makes these U(II) metallocenes bent. We included relativistic effects through the NESCau Hamiltonian and complemented the local mode analysis with natural bonding orbital (NBO) and quantum theory of atoms in molecules (QTAIM) data. Our study led to the following results: (i) reduction of bulky U-ring ligand substituents does not lead to bent complexes for alkyl substituents (iPr and iBu) in contrast to SiMe3 ring substituents, which are all bent. (ii) The most bent complexes are [(η5-C5H4SiMe3)2U] (130°) and [η5-P5H5)2U] (143°). (iii) Linear complexes showed one hybridized NBO with s/d character, while bent structures were characterized by s/d/f mixing. (iv) We did not observe a correlation between the strength of the U-ring interaction and the amount of the ring-U-ring bend; the strongest interaction was found for [η5-Cp)2U] and the weakest for [η5-P5H5)2U]. In conclusion, our results provide a foundation for the design of U(II) metallocenes with specific physicochemical properties and increased reactivity.
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Affiliation(s)
- Bárbara M T C Peluzo
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States
| | - Małgorzata Z Makoś
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States
- Chemical Sciences Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, Tennessee 37830, United States
| | - Renaldo T Moura
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States
- Department of Chemistry and Physics, Center of Agrarian Sciences, Federal University of Paraíba, Areia 58397-000, Paraíba, Brazil
| | - Marek Freindorf
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States
| | - Elfi Kraka
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States
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Costa Peluzo BMT, Kraka E. Uranium: The Nuclear Fuel Cycle and Beyond. Int J Mol Sci 2022; 23:ijms23094655. [PMID: 35563047 PMCID: PMC9101921 DOI: 10.3390/ijms23094655] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2022] [Revised: 04/13/2022] [Accepted: 04/18/2022] [Indexed: 01/01/2023] Open
Abstract
This review summarizes the recent developments regarding the use of uranium as nuclear fuel, including recycling and health aspects, elucidated from a chemical point of view, i.e., emphasizing the rich uranium coordination chemistry, which has also raised interest in using uranium compounds in synthesis and catalysis. A number of novel uranium coordination features are addressed, such the emerging number of U(II) complexes and uranium nitride complexes as a promising class of materials for more efficient and safer nuclear fuels. The current discussion about uranium triple bonds is addressed by quantum chemical investigations using local vibrational mode force constants as quantitative bond strength descriptors based on vibrational spectroscopy. The local mode analysis of selected uranium nitrides, N≡U≡N, U≡N, N≡U=NH and N≡U=O, could confirm and quantify, for the first time, that these molecules exhibit a UN triple bond as hypothesized in the literature. We hope that this review will inspire the community interested in uranium chemistry and will serve as an incubator for fruitful collaborations between theory and experimentation in exploring the wealth of uranium chemistry.
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Franzke YJ, Yu JM. Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance. J Chem Theory Comput 2022; 18:2246-2266. [PMID: 35354319 DOI: 10.1021/acs.jctc.1c01175] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C5Me5)2Y(μ-S)2Mo(μ-S)2Y(C5Me5)2]-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C6Cl5)4]- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Jason M Yu
- Department of Chemistry, University of California─Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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Franzke YJ, Mack F, Weigend F. NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework. J Chem Theory Comput 2021; 17:3974-3994. [PMID: 34151571 DOI: 10.1021/acs.jctc.1c00167] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 1019 T J-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the 1J(119Sn, 31P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany.,Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
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Makoś MZ, Zou W, Freindorf M, Kraka E. Metal–ring interactions in actinide sandwich compounds: A combined normalized elimination of the small component and local vibrational mode study. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1768314] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Małgorzata Z. Makoś
- Computational and Theoretical Chemistry Group (CATCO), Southern Methodist University, Dallas, TX, USA
| | - Wenli Zou
- Institute of Modern Physics, Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an, Shaanxi, People's Republic of China
| | - Marek Freindorf
- Computational and Theoretical Chemistry Group (CATCO), Southern Methodist University, Dallas, TX, USA
| | - Elfi Kraka
- Computational and Theoretical Chemistry Group (CATCO), Southern Methodist University, Dallas, TX, USA
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Zou W, Guo G, Suo B, Liu W. Analytic Energy Gradients and Hessians of Exact Two-Component Relativistic Methods: Efficient Implementation and Extensive Applications. J Chem Theory Comput 2020; 16:1541-1554. [DOI: 10.1021/acs.jctc.9b01120] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Wenli Zou
- Shaanxi Key Laboratory for Theoretical Physics Frontiers and Institute of Modern Physics, Northwest University, Xi’an 710127, Shaanxi, P. R. China
| | - Guina Guo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers and Institute of Modern Physics, Northwest University, Xi’an 710127, Shaanxi, P. R. China
| | - Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers and Institute of Modern Physics, Northwest University, Xi’an 710127, Shaanxi, P. R. China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao 266237, Shandong, P. R. China
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Zhu H, Gao C, Filatov M, Zou W. Mössbauer isomer shifts and effective contact densities obtained by the exact two-component (X2C) relativistic method and its local variants. Phys Chem Chem Phys 2020; 22:26776-26786. [DOI: 10.1039/d0cp04549g] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
A standalone program to calculate scalar relativistic effective contact densities.
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Affiliation(s)
- Hong Zhu
- Institute of Modern Physics
- Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers
- Xi'an
- P. R. China
| | - Chun Gao
- Institute of Modern Physics
- Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers
- Xi'an
- P. R. China
| | - Michael Filatov
- Department of Chemistry
- Kyungpook National University
- Daegu 702-701
- South Korea
| | - Wenli Zou
- Institute of Modern Physics
- Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers
- Xi'an
- P. R. China
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