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Kumar S, Maurer LR, Schnakenburg G, Das U, Filippou AC. NHC-Supported 2-Sila and 2-Germavinylidenes: Synthesis, Dynamics, First Reactivity and Theoretical Studies. Angew Chem Int Ed Engl 2024; 63:e202400227. [PMID: 38317632 DOI: 10.1002/anie.202400227] [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: 01/04/2024] [Revised: 02/03/2024] [Accepted: 02/05/2024] [Indexed: 02/07/2024]
Abstract
2-tetrelavinylidenes (C=EH2; E=Si, Ge) are according to quantum chemical studies the least stable isomers on the [E,C,2H] potential energy hypersurface isomerizing easily via the trans-bent tetrelaacetylenes HE≡CH to the thermodynamically most stable 1-tetrelavinylidenes (E=CH2). Consequently, experimental studies on 2-tetrelavinylidenes (C=ER2) and their derivatives are lacking. Herein we report experimental and theoretical studies of the first N-heterocyclic carbene (NHC) supported 2-silavinylidene (NHC)C=SiBr(Tbb) (1-Si: NHC=C[N(Dipp)CH]2, Dipp=2,6-diisopropylphenyl, Tbb=2,6-bis[bis(trimethylsilyl)methyl]-4-tert-butylphenyl) and the isovalent 2-germavinylidenes (NHC)C=GeBr(R) (1-Ge, 1-GeMind: R=Tbb, Mind (1,1,3,3,5,5,7,7-octamethyl-s-hydrindacene-4-yl)). The NHC-supported 2-tetrelavinylidenes were obtained selectively from the 1,2-dibromoditetrelenes (E)-(R)BrE=EBr(R) using the diazoolefin (NHC)CN2 as vinylidene transfer reagent. 1-E (E=Si, Ge) have a planar vinylidene core, a bent-dicoordinated vinylidene carbon atom (CVNL), a very short E=CVNL bond and an almost orthogonal orientation of the NHC five-membered ring to the vinylidene core. Quantum chemical analysis of the electronic structures of 1-E suggest a significantly bent 1-tetrelaallene and tetrelyne character. NMR studies shed light into the dynamics of 1-E involving NHC-rotation around the CVNL-CNHC bond with a low activation barrier. Furthermore, the synthetic potential of 1-E is demonstrated by the synthesis and full characterization of the unprecedented NHC-supported bromogermynes BrGe=C(EBr2Tbb)(NHC) (2-SiGe: E=Si; 2-GeGe: E=Ge).
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Affiliation(s)
- Sandeep Kumar
- Institut für Anorganische Chemie, Universität Bonn, Gerhard-Domagk-Str. 1, 53121, Bonn, Germany
| | - Leonard R Maurer
- Institut für Anorganische Chemie, Universität Bonn, Gerhard-Domagk-Str. 1, 53121, Bonn, Germany
| | - Gregor Schnakenburg
- Institut für Anorganische Chemie, Universität Bonn, Gerhard-Domagk-Str. 1, 53121, Bonn, Germany
| | - Ujjal Das
- Institut für Anorganische Chemie, Universität Bonn, Gerhard-Domagk-Str. 1, 53121, Bonn, Germany
| | - Alexander C Filippou
- Institut für Anorganische Chemie, Universität Bonn, Gerhard-Domagk-Str. 1, 53121, Bonn, Germany
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2
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Wang Y, Robinson GH. Counterintuitive Chemistry: Carbene Stabilization of Zero-Oxidation State Main Group Species. J Am Chem Soc 2023; 145:5592-5612. [PMID: 36876997 DOI: 10.1021/jacs.2c13574] [Citation(s) in RCA: 28] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/07/2023]
Abstract
Carbenes have evolved from transient laboratory curiosities to a robust, diverse, and surprisingly impactful ligand class. A variety of different carbenes have significantly contributed to the development of low-oxidation state main group chemistry. This Perspective focuses upon advances in the chemistry of carbene complexes containing main group element cores in the formal oxidation state of zero, including their diverse synthetic strategies, unusual bonding and structural motifs, and utility in transition metal coordination chemistry and activation of small molecules.
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Affiliation(s)
- Yuzhong Wang
- Department of Chemistry, The University of Georgia, Athens, Georgia 30602-2556, United States
| | - Gregory H Robinson
- Department of Chemistry, The University of Georgia, Athens, Georgia 30602-2556, United States
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3
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Kehl A, Hiller M, Hecker F, Tkach I, Dechert S, Bennati M, Meyer A. Resolution of chemical shift anisotropy in 19F ENDOR spectroscopy at 263 GHz/9.4 T. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 333:107091. [PMID: 34749036 DOI: 10.1016/j.jmr.2021.107091] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 10/14/2021] [Accepted: 10/15/2021] [Indexed: 06/13/2023]
Abstract
Pulsed 19F ENDOR spectroscopy provides a selective method for measuring angstrom to nanometer distances in structural biology. Here, the performance of 19F ENDOR at fields of 3.4 T and 9.4 T is compared using model compounds containing one to three 19F atoms. CF3 groups are included in two compounds, for which the possible occurrence of uniaxial rotation might affect the distance distribution. At 9.4 T, pronounced asymmetric features are observed in many of the presented 19F ENDOR spectra. Data analysis by spectral simulations shows that these features arise from the chemical shift anisotropy (CSA) of the 19F nuclei. This asymmetry is also observed at 3.4 T, albeit to a much smaller extent, confirming the physical origin of the effect. The CSA parameters are well consistent with DFT predicted values and can be extracted from simulation of the experimental data in favourable cases, thereby providing additional information about the geometrical and electronic structure of the spin system. The feasibility of resolving the CSA at 9.4 T provides important information for the interpretation of line broadening in ENDOR spectra also at lower fields, which is relevant for developing methods to extract distance distributions from 19F ENDOR spectra.
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Affiliation(s)
- Annemarie Kehl
- Research Group EPR Spectroscopy, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Markus Hiller
- Research Group EPR Spectroscopy, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Fabian Hecker
- Research Group EPR Spectroscopy, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Igor Tkach
- Research Group EPR Spectroscopy, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Sebastian Dechert
- Department of Chemistry, Georg August University of Göttingen, Tammannstr. 4, Göttingen, Germany
| | - Marina Bennati
- Research Group EPR Spectroscopy, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany; Department of Chemistry, Georg August University of Göttingen, Tammannstr. 4, Göttingen, Germany.
| | - Andreas Meyer
- Research Group EPR Spectroscopy, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany.
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Karwasara S, Maurer LR, Peerless B, Schnakenburg G, Das U, Filippou AC. (NHC)Si═C═N-R: A Two-Coordinated Si 0-Isocyanide Compound as Si(NHC) Transfer Reagent. J Am Chem Soc 2021; 143:14780-14794. [PMID: 34469138 DOI: 10.1021/jacs.1c06628] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Experimental and theoretical studies are reported of the first two-coordinated Si0-isocyanide compound (SIDipp)Si═C═N-ArMes (1: SIDipp (NHC) = C[N(Dipp)CH2]2, ArMes = 2,6-dimesitylphenyl), supported by an N-heterocyclic carbene (NHC). A Si atom economic two-step synthesis of 1 involves a 2e reduction of the isocyanide-stabilized silyliumylidene salt [SiBr(CNArMes)(SIDipp)][B(ArF)4] (2[B(ArF)4], ArF = B(C6H3-3,5-(CF3)2)4) with KC8. 2[B(ArF)4] was obtained from SiBr2(SIDipp) after bromide abstraction with an equimolar mixture of Na[B(ArF)4] and ArMesNC. Exact adherence to the stoichiometry is crucial in the latter reaction, since 2[B(ArF)4] reacts with SiBr2(SIDipp) via isocyanide exchange to afford the disilicon(II) salt [Si2Br3(SIDipp)2)][B(ArF)4] (3[B(ArF)4]), the reaction leading to an equilibrium that favors 3[B(ArF)4] (Keq(298 K) = 10.6, ΔH° = -10.6 kJ mol-1; ΔS° = -16.0 J mol-1 K-1). 3[B(ArF)4] was obtained selectively from the 2:1 reaction of SiBr2(SIDipp) with Na[B(ArF)4] and fully characterized. Detailed studies of 1 reveal an intriguing structure featuring a planar CNHC-Si-C-N skeleton with a V-shaped geometry at the dicoordinated Si0 center, a slightly bent Si═C═N core, a CNHC-Si-CCNR 3c-2e out of plane π-bond (HOMO), and an anticlinal conformation of the SIDipp and ArMes substituents leading to axial chirality and the presence of two enantiomers, (Ra)-1 and (Sa)-1. Compound 1 displays structural dynamics in solution, rapidly interconverting the enantiomers. The silacumulene 1 is a potent Si(SIDipp) transfer agent as demonstrated by the synthesis and full characterization of the NHC-supported germasilyne (Z)-(SIDipp)(Cl)Si═GeArMes (4) from 1 and Ge(ArMes)Cl.
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Affiliation(s)
- Surendar Karwasara
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany
| | - Leonard R Maurer
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany
| | - Benjamin Peerless
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany
| | - Gregor Schnakenburg
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany
| | - Ujjal Das
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany
| | - Alexander C Filippou
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße 1, D-53121 Bonn, Germany
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5
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Maiti A, Mandal D, Omlor I, Dhara D, Klemmer L, Huch V, Zimmer M, Scheschkewitz D, Jana A. Equilibrium Coordination of NHCs to Si(IV) Species and Donor Exchange in Donor-Acceptor Stabilized Si(II) and Ge(II) Compounds. Inorg Chem 2019; 58:4071-4075. [PMID: 30860359 DOI: 10.1021/acs.inorgchem.9b00246] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
We report the reversible coordination of the N-heterocyclic carbene (NHC), NHC iPr2Me2 (NHC iPr2Me2 = 1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene), to silicon(IV)-halides, SiCl4, MeSiCl3, Me2SiCl2, and Me3SiCl. Predicted as well as experimentally determined thermodynamic parameters of these equilibria confirm that the complexation constant increases with the Lewis acidity of the silicon halides. In contrast, the more σ-donating N-heterocyclic carbene, NHCMe4 (NHCMe4 = 1,3,4,5-tetramethylimidazol-2-ylidene), does not show any signs of dissociation from the corresponding SiCl4 and Me2SiCl2 adducts even at higher temperatures. As a consequence, NHC iPr2Me2 in donor-acceptor stabilized Si(II)- and Ge(II)-dimethyl complexes, NHC iPr2Me2·GeMe2·Fe(CO)4 and NHC iPr2Me2·SiMe2·Fe(CO)4, is readily replaced by NHCMe4.
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Affiliation(s)
- Avijit Maiti
- Tata Institute of Fundamental Research Hyderabad , Gopanpally , Hyderabad - 500107 , India
| | - Debdeep Mandal
- Tata Institute of Fundamental Research Hyderabad , Gopanpally , Hyderabad - 500107 , India
| | - Isabell Omlor
- Krupp-Chair of General and Inorganic Chemistry , Saarland University , 66123 Saarbrücken , Germany
| | - Debabrata Dhara
- Tata Institute of Fundamental Research Hyderabad , Gopanpally , Hyderabad - 500107 , India
| | - Lukas Klemmer
- Krupp-Chair of General and Inorganic Chemistry , Saarland University , 66123 Saarbrücken , Germany
| | - Volker Huch
- Krupp-Chair of General and Inorganic Chemistry , Saarland University , 66123 Saarbrücken , Germany
| | - Michael Zimmer
- Krupp-Chair of General and Inorganic Chemistry , Saarland University , 66123 Saarbrücken , Germany
| | - David Scheschkewitz
- Krupp-Chair of General and Inorganic Chemistry , Saarland University , 66123 Saarbrücken , Germany
| | - Anukul Jana
- Tata Institute of Fundamental Research Hyderabad , Gopanpally , Hyderabad - 500107 , India
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6
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Nesterov V, Reiter D, Bag P, Frisch P, Holzner R, Porzelt A, Inoue S. NHCs in Main Group Chemistry. Chem Rev 2018; 118:9678-9842. [PMID: 29969239 DOI: 10.1021/acs.chemrev.8b00079] [Citation(s) in RCA: 547] [Impact Index Per Article: 78.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Since the discovery of the first stable N-heterocyclic carbene (NHC) in the beginning of the 1990s, these divalent carbon species have become a common and available class of compounds, which have found numerous applications in academic and industrial research. Their important role as two-electron donor ligands, especially in transition metal chemistry and catalysis, is difficult to overestimate. In the past decade, there has been tremendous research attention given to the chemistry of low-coordinate main group element compounds. Significant progress has been achieved in stabilization and isolation of such species as Lewis acid/base adducts with highly tunable NHC ligands. This has allowed investigation of numerous novel types of compounds with unique electronic structures and opened new opportunities in the rational design of novel organic catalysts and materials. This Review gives a general overview of this research, basic synthetic approaches, key features of NHC-main group element adducts, and might be useful for the broad research community.
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Affiliation(s)
- Vitaly Nesterov
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
| | - Dominik Reiter
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
| | - Prasenjit Bag
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
| | - Philipp Frisch
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
| | - Richard Holzner
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
| | - Amelie Porzelt
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
| | - Shigeyoshi Inoue
- Department of Chemistry, WACKER-Institute of Silicon Chemistry and Catalysis Research Center , Technische Universität München , Lichtenbergstrasse 4 , Garching bei München 85748 , Germany
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7
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Zhang SH, Carter E, Xi HW, Li Y, Lim KH, So CW. Delocalized Hypervalent Silyl Radical Supported by Amidinate and Imino Substituents. Inorg Chem 2017; 56:701-704. [PMID: 28009159 DOI: 10.1021/acs.inorgchem.6b02427] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The reaction of the amidinato silylsilylene with a functionalized diaminochlorosilyl substituent, [LSiSi(Cl){(NtBu)2C(H)Ph}] (1; L = PhC(NtBu)2), with ArN═C═NAr (Ar = 2,6-iPr2C6H3) in toluene afforded the delocalized hypervalent silyl radical [LSi•(μ-CNAr)2Si{(NtBu)2C(H)Ph}] (2). It possesses a hypervalent silyl radical that delocalizes throughout the Si2C2 ring.
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Affiliation(s)
- Shu-Hua Zhang
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, Singapore
| | - Emma Carter
- School of Chemistry, Cardiff University , Main Building, Park Place, Cardiff CF10 3AT, U.K
| | - Hong-Wei Xi
- Singapore Institute of Technology , Singapore 138683, Singapore
| | - Yongxin Li
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, Singapore
| | - Kok Hwa Lim
- Singapore Institute of Technology , Singapore 138683, Singapore
| | - Cheuk-Wai So
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore 637371, Singapore
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Morosaki T, Fujii T. Recent Advances in Heteroatom-Stabilized Carbones and Their Metal Complexes. ADVANCES IN ORGANOMETALLIC CHEMISTRY 2017. [DOI: 10.1016/bs.adomc.2017.08.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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9
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Arz MI, Schnakenburg G, Meyer A, Schiemann O, Filippou AC. The Si 2H radical supported by two N-heterocyclic carbenes. Chem Sci 2016; 7:4973-4979. [PMID: 30155147 PMCID: PMC6018643 DOI: 10.1039/c6sc01569g] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2016] [Accepted: 04/29/2016] [Indexed: 12/16/2022] Open
Abstract
Cyclic voltammetric studies of the hydridodisilicon(0,II) borate [(Idipp)(H)SiII[double bond, length as m-dash]Si0(Idipp)][B(ArF)4] (1H[B(ArF)4], Idipp = C[N(C6H3-2,6-iPr2)CH]2, ArF = C6H3-3,5-(CF3)2) reveal a reversible one-electron reduction at a low redox potential (E 1/2 = -2.15 V vs. Fc+/Fc). Chemical reduction of 1H[B(ArF)4] with KC8 affords selectively the green, room-temperature stable mixed-valent disilicon(0,I) hydride Si2(H)(Idipp)2 (1H), in which the highly reactive Si2H molecule is trapped between two N-heterocyclic carbenes (NHCs). The molecular and electronic structure of 1H was investigated by a combination of experimental and theoretical methods and reveals the presence of a π-type radical featuring a terminal bonded H atom at a flattened trigonal pyramidal coordinated Si center, that is connected via a Si-Si bond to a bent two-coordinated Si center carrying a lone pair of electrons. The unpaired electron occupies the Si[double bond, length as m-dash]Si π* orbital leading to a formal Si-Si bond order of 1.5. Extensive delocalization of the spin density occurs via conjugation with the coplanar arranged NHC rings with the higher spin density lying on the site of the two-coordinated silicon atom.
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Affiliation(s)
- Marius I Arz
- Institute of Inorganic Chemistry , University of Bonn , Gerhard-Domagk-Str. 1 , D-53121 , Bonn , Germany .
| | - Gregor Schnakenburg
- Institute of Inorganic Chemistry , University of Bonn , Gerhard-Domagk-Str. 1 , D-53121 , Bonn , Germany .
| | - Andreas Meyer
- Institute of Physical and Theoretical Chemistry , University of Bonn , Wegelerstr. 12 , D-53115 , Bonn , Germany
| | - Olav Schiemann
- Institute of Physical and Theoretical Chemistry , University of Bonn , Wegelerstr. 12 , D-53115 , Bonn , Germany
| | - Alexander C Filippou
- Institute of Inorganic Chemistry , University of Bonn , Gerhard-Domagk-Str. 1 , D-53121 , Bonn , Germany .
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10
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Arz MI, Straßmann M, Geiß D, Schnakenburg G, Filippou AC. Addition of Small Electrophiles to N-Heterocyclic-Carbene-Stabilized Disilicon(0): A Revisit of the Isolobal Concept in Low-Valent Silicon Chemistry. J Am Chem Soc 2016; 138:4589-600. [DOI: 10.1021/jacs.6b01018] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Marius I. Arz
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße
1, D-53121 Bonn, Germany
| | - Martin Straßmann
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße
1, D-53121 Bonn, Germany
| | - Daniel Geiß
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße
1, D-53121 Bonn, Germany
| | - Gregor Schnakenburg
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße
1, D-53121 Bonn, Germany
| | - Alexander C. Filippou
- Institute of Inorganic Chemistry, University of Bonn, Gerhard-Domagk-Straße
1, D-53121 Bonn, Germany
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Würtemberger-Pietsch S, Radius U, Marder TB. 25 years of N-heterocyclic carbenes: activation of both main-group element-element bonds and NHCs themselves. Dalton Trans 2015; 45:5880-95. [PMID: 26675582 DOI: 10.1039/c5dt04106f] [Citation(s) in RCA: 129] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
N-Heterocyclic carbenes (NHCs) are widely used ligands and reagents in modern inorganic synthesis as well as in homogeneous catalysis and organocatalysis. However, NHCs are not always innocent bystanders. In the last few years, more and more examples were reported of reactions of NHCs with main-group elements which resulted in modification of the NHC. Many of these reactions lead to ring expansion and the formation of six-membered heterocyclic rings involving insertion of the heteroatom into the C-N bond and migration of hydrides, phenyl groups or boron-containing fragments. Furthermore, a few related NHC rearrangements were observed some decades ago. In this Perspective, we summarise the history of NHC ring expansion reactions from the 1960s till the present.
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Affiliation(s)
- Sabrina Würtemberger-Pietsch
- Institut für Anorganische Chemie, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany. u.radius@uni-wuerzburg
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