1
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Peluzo BMTC, Moura RT, Kraka E. Conformation and Bonding of Lanthanide(III) Trihalides LnX 3 (Ln = La-Lu; X = F, Cl, Br): A Relativistic Local Vibrational Mode Study. Inorg Chem 2024; 63:22445-22463. [PMID: 39531452 DOI: 10.1021/acs.inorgchem.4c03348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2024]
Abstract
This study employed relativistic methods to investigate the connection between the conformation and bonding properties of 45 lanthanide trihalides LnX3 (Ln: La-Lu; X:F, Cl, Br). Our findings reveal several insights. The proper symmetry exhibited by open-shell LnX3 requires the inclusion of spin-orbit coupling, achieved with 2-component relativistic Hamiltonians. Fluorines (LnF3) primarily exhibit pyramidal structures, while chlorides and bromides tend to yield planar conformations. For a given halide, the strength of Ln-X bonds increases across the lanthanide series, another outcome of the lanthanide contraction. Both strength and covalency of Ln-X bonds decrease upon the halide, i.e., LnF3 > LnCl3 > LnBr3. We introduced a novel parameter, the local force constant associated with the dihedral β(X-Ln-X-X), ka(β), which quantifies the resistance of these molecules to conformational changes. We observed a correlation between ka(β) and the covalency of the Ln-X bond, with higher ka(β) values indicating a stronger covalent character. Finally, the degree of pyramidalization in the LnX3 structures is connected to (i) the extent of charge donation within the molecule and (ii) the greater covalency of the Ln-X bond. These findings provide valuable insights into the interplay between the electronic structure and molecular geometry in LnX3.
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Affiliation(s)
- Barbara M T C Peluzo
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, United States
| | - Renaldo T Moura
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, United States
- Department of Chemistry and Physics, Center of Agrarian Sciences, Federal University of Paraiba, 58397-000 Areia, Paraiba, Brazil
| | - Elfi Kraka
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, United States
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2
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Li W, Filatov M, Zou W. Calculation of electric field gradients with the exact two-component (X2C) quasi-relativistic method and its local approximations. Phys Chem Chem Phys 2024; 26:18333-18342. [PMID: 38912554 DOI: 10.1039/d4cp01567c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/25/2024]
Abstract
When calculating electric field gradients (EFGs), relativistic and electron correlation effects are crucial for obtaining accurate results, and the commonly used density functional methods produce unsatisfactory results, especially for heavy elements and/or strongly correlated systems. In this work, a stand-alone program is presented, which enables calculation of EFGs from the molecular orbitals supplied by an external high accuracy quantum chemical calculation and includes relativistic effects through the exact two-component (X2C) formalism and efficient local approximations to it. Application to BiN and BiP molecules shows that a high precision can be achieved in the calculation of nuclear quadrupole coupling constants of 209Bi by combining advanced ab initio methods with the X2C approach. For seventeen iron compounds, the Mössbauer nuclear quadrupole splittings (NQS) of 57Fe calculated using a double-hybrid functional method are in very good agreement with the experimental values. It is shown that, for strongly correlated molecules, the double-hybrid functionals are much more accurate than the commonly used hybrid functionals. The computer program developed in this study furnishes a useful utility for obtaining EFGs and related nuclear properties with high accuracy.
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Affiliation(s)
- Wenxin Li
- Institute of Modern Physics, Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an, Shaanxi 710127, P. R. China.
| | - Michael Filatov
- Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), Ulsan, 44919, Republic of Korea.
| | - Wenli Zou
- Institute of Modern Physics, Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an, Shaanxi 710127, P. R. China.
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3
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Peluzo BMTC, Moura RT, Kraka E. Extraction of uranyl from spent nuclear fuel wastewater via complexation-a local vibrational mode study. J Mol Model 2024; 30:216. [PMID: 38888814 PMCID: PMC11614994 DOI: 10.1007/s00894-024-06000-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2024] [Accepted: 05/30/2024] [Indexed: 06/20/2024]
Abstract
CONTEXT The efficient extraction of uranyl from spent nuclear fuel wastewater for subsequent reprocessing and reuse is an essential effort toward minimization of long-lived radioactive waste. N-substituted amides and Schiff base ligands are propitious candidates, where extraction occurs via complexation with the uranyl moiety. In this study, we extensively probed chemical bonding in various uranyl complexes, utilizing the local vibrational modes theory alongside QTAIM and NBO analyses. We focused on (i) the assessment of the equatorial O-U and N-U bonding, including the question of chelation, and (ii) how the strength of the axial U = O bonds of the uranyl moiety changes upon complexation. Our results reveal that the strength of the equatorial uranium-ligand interactions correlates with their covalent character and with charge donation from O and N lone pairs into the vacant uranium orbitals. We also found an inverse relationship between the covalent character of the equatorial ligand bonds and the strength of the axial uranium-oxygen bond. In summary, our study provides valuable data for a strategic modulation of N-substituted amide and Schiff base ligands towards the maximization of uranyl extraction. METHOD Quantum chemistry calculations were performed under the PBE0 level of theory, paired with the relativistic NESCau Hamiltonian, currently implemented in Cologne2020 (interfaced with Gaussian16). Wave functions were expanded in the cc-pwCVTZ-X2C basis set for uranium and Dunning's cc-pVTZ for the remaining atoms. For the bonding properties, we utilized the package LModeA in the local modes analyses, AIMALL in the QTAIM calculations, and NBO 7.0 for the NBO analyses.
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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, TX, 75275-0314, USA
| | - Renaldo T Moura
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, TX, 75275-0314, USA
- Department of Chemistry and Physics, Center of Agrarian Sciences, Federal University of Paraíba, Areia, 58397-000, Paraíba, Brazil
| | - Elfi Kraka
- Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, TX, 75275-0314, USA.
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4
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Xu X, Jiang H, Wu K. Uranyl Affinity between Uranyl Cation and Different Kinds of Monovalent Anions: Density Functional Theory and Quantitative Structure-Property Relationship Model. J Phys Chem A 2024; 128:2960-2970. [PMID: 38576211 DOI: 10.1021/acs.jpca.4c00068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/06/2024]
Abstract
In order to design effective extractants for uranium extraction from seawater, it is imperative to acquire a more comprehensive understanding of the bonding properties between the uranyl cation (UO22+) and various ligands. Therefore, we employed density functional theory to investigate the complexation reactions of UO22+ with 29 different monovalent anions (L-1), exploring both mono- and bidentate coordination. We proposed a novel concept called "uranyl affinity" (Eua) to facilitate the establishment of a standardized scale for assessing the ease or difficulty of coordination bond formation between UO22+ and diverse ligands. Furthermore, we conducted an in-depth investigation into the underlying mechanisms involved. During the process of uranyl complex [(UO2L)+] formation, lone pair electrons from the coordinating atom in L- are transferred to either the lowest unoccupied molecular degenerate orbitals 1ϕu or 1δu of the uranyl ion, which originate from the uranium atom's 5f unoccupied orbitals. In light of discussion concerning the mechanisms of coordination bond formation, quantitative structure-property relationship analyses were conducted to investigate the correlation between Eua and various structural descriptors associated with the 29 ligands under investigation. This analysis revealed distinct patterns in Eua values while identifying key influencing factors among the different ligands.
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Affiliation(s)
- Xiang Xu
- College of Chemistry and Pharmaceutical Sciences, Qingdao Agricultural University, Qingdao 266109, China
| | - Haiyan Jiang
- College of Chemistry and Pharmaceutical Sciences, Qingdao Agricultural University, Qingdao 266109, China
| | - Kechen Wu
- Fujian Key Laboratory of Functional Marine Sensing Materials, Minjiang University, Fuzhou 350108, China
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5
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Ehrman J, Shumilov K, Jenkins AJ, Kasper JM, Vitova T, Batista ER, Yang P, Li X. Unveiling Hidden Shake-Up Features in the Uranyl M 4-Edge Spectrum. JACS AU 2024; 4:1134-1141. [PMID: 38559711 PMCID: PMC10976573 DOI: 10.1021/jacsau.3c00838] [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: 12/28/2023] [Revised: 02/14/2024] [Accepted: 02/15/2024] [Indexed: 04/04/2024]
Abstract
The M4,5-edge high energy resolution X-ray absorption near-edge structure (HR-XANES) spectra of actinyls offer valuable insights into the electronic structure and bonding properties of heavy-element complexes. To conduct a comprehensive spectral analysis, it is essential to employ computational methods that accurately account for relativistic effects and electron correlation. In this work, we utilize variational relativistic multireference configurational interaction methods to compute and analyze the X-ray M4-edge absorption spectrum of uranyl. By employing these advanced computational techniques, we achieve excellent agreement between the calculated spectral features and experimental observations. Moreover, the calculations unveil significant shake-up features, which arise from the intricate interplay between strongly correlated 3d core-electron and ligand excitations. This research provides important theoretical insights into the spectral characteristics of heavy-element complexes. Furthermore, it establishes the foundation for utilizing M4,5-edge spectroscopy as a means to investigate the chemical activities of such complexes. By leveraging this technique, we can gain a deeper understanding of the bonding behavior and reactivity of heavy-element compounds.
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Affiliation(s)
- Jordan
N. Ehrman
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Kirill Shumilov
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J. Jenkins
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joseph M. Kasper
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Tonya Vitova
- Institute
for Nuclear Waste Disposal (INE), Karlsruhe
Institute of Technology, P.O. Box 3640, Karlsruhe D-76021, Germany
| | - Enrique R. Batista
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ping Yang
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
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6
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Liu W. Unified construction of relativistic Hamiltonians. J Chem Phys 2024; 160:084111. [PMID: 38415836 DOI: 10.1063/5.0188794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Accepted: 02/09/2024] [Indexed: 02/29/2024] Open
Abstract
It is shown that the four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock equations can be implemented in a unified manner by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A "one-center small-component" approximation can then be invoked in the evaluation of relativistic integrals, that is, all atom-centered small-component basis functions are regarded as extremely localized near the position of the atom to which they belong such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are, hence, safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell variants are formulated for "high-spin" open-shell systems.
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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7
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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: 8] [Impact Index Per Article: 4.0] [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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8
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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: 2.5] [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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9
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Zhao L, Zou W. A general method for locating stationary points on the mixed-spin surface of spin-forbidden reaction with multiple spin states. J Chem Phys 2023; 158:2895244. [PMID: 37290081 DOI: 10.1063/5.0151630] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 05/25/2023] [Indexed: 06/10/2023] Open
Abstract
Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin-orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129-4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions.
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Affiliation(s)
- Long Zhao
- Institute of Modern Physics, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an, Shaanxi 710127, People's Republic of China
| | - Wenli Zou
- Institute of Modern Physics, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an, Shaanxi 710127, People's Republic of China
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10
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Liu W. Perspective: Simultaneous treatment of relativity, correlation, and
QED. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science Shandong University Qingdao Shandong China
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11
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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: 6.7] [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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12
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Abstract
Intersystem crossing (ISC), a vital component of the electronic and nuclear transitions that compose photophysics, has been successfully simulated in light elements and transition metal complexes. Derived from the Z-dependent spin-orbit coupling (SOC), ISC is expected to be of greater importance in heavier elements, but few attempts have been made at the simulation of ISC in lanthanides or actinides. In this work, we explore several of the challenges that will need to be overcome in order to treat ISC in late-row elements, including the loss of spin as a good quantum number, the need to include SOC variationally via two- or four-component electronic structure, and the high density of states present in late-row complexes. Density functional theory (DFT) calculations are used to illustrate several of these effects, while a model Hamiltonian is used to illustrate the importance of momentum rescaling in surface hopping simulations of strongly coupled states.
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Affiliation(s)
- Andrew J S Valentine
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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13
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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: 4.0] [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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14
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Zheng X, Zhang C, Liu J, Cheng L. Geometry Optimizations with Spinor-Based Relativistic Coupled-Cluster Theory. J Chem Phys 2022; 156:151101. [DOI: 10.1063/5.0086281] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Development of analytic gradients for relativistic coupled-cluster singles and doubles augmented with a non-iterative triples [CCSD(T)] method using an all-electron exact two-component Hamiltonian with atomic mean-field spin-orbit integrals (X2CAMF) is reported. This enables efficient CC geometry optimizations with spin-orbit coupling included in orbitals. The applicability of the implementation is demonstrated using benchmark X2CAMF-CCSD(T) calculations of equilibrium structures and harmonic vibrational frequencies for methyl halides, CH3X, X=Br, I, At, as well as calculations of rotational constants and infrared spectrum for RaSH+, a radioactive molecular ion of interest to spectroscopic study.
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Affiliation(s)
- Xuechen Zheng
- Johns Hopkins University Department of Chemistry, United States of America
| | - Chaoqun Zhang
- Johns Hopkins University Department of Chemistry, United States of America
| | - Junzi Liu
- Chemistry, Johns Hopkins University Department of Chemistry, United States of America
| | - Lan Cheng
- Chemistry, Johns Hopkins University Department of Chemistry, United States of America
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15
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Hu SX, Zou W. Stable copernicium hexafluoride (CnF 6) with an oxidation state of VI. Phys Chem Chem Phys 2021; 24:321-325. [PMID: 34889909 DOI: 10.1039/d1cp04360a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
As the heaviest group 12 element known currently, copernicium (Cn) often presents the oxidation states of I+, II+, and rarely IV+ as in its homologue mercury. In this work we systematically studied the stability of some oxides, fluorides, and oxyfluorides of Cn by two-component relativistic calculations and found that the CnF6 molecule with an oxidation state of VI+ has an extraordinary stability. CnF6 may decompose into CnF4 by conquering an energy barrier of about 34 kcal mol-1 without markedly releasing heat. Our results indicate that CnF6 may exist under some special conditions.
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Affiliation(s)
- Shu-Xian Hu
- Department of Physics, University of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Wenli Zou
- Institute of Modern Physics, Northwest University, and Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an, Shaanxi 710127, P. R. China.
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16
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Takashima C, Seino J, Nakai H. Database-assisted local unitary transformation method for two-electron integrals in two-component relativistic calculations. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.138691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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17
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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: 5.3] [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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18
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Nakai H. Development of Linear-Scaling Relativistic Quantum Chemistry Covering the Periodic Table. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2021. [DOI: 10.1246/bcsj.20210091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering (WISE), Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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19
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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: 1.0] [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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20
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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21
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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: 1.2] [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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22
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Zhang T, Kasper JM, Li X. Localized relativistic two-component methods for ground and excited state calculations. ACTA ACUST UNITED AC 2020. [DOI: 10.1016/bs.arcc.2020.07.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
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