Our topic is fundamental research in the field of magnetic resonance.

Research interests

We use predominantly spin resonance of nuclei or electrons to study a wide variety of problems in physics and chemistry. 

With nuclear magnetic resonance (NMR) the emphasis is on the chemical and electronic properties of quantum solids, such as high-temperature superconductors or topological insulators. Spins are powerful quantum sensors of their environment and carry detailed information about the chemical and electronic structure, including dynamics, which is important for theories of materials. 

For example, based on simple NMR data we can predict the highest possible temperature for superconductivity of superconducting cuprates which is set by the degree of chemical  covalency of the copper-oxygen bonds. This could be a game-changing ansatz for new theories. For topological insulators we found that even weak magnetic fields can change  the local charge distribution, which leads to NMR behavior not encountered before, and that NMR can determine the band inversion necessary for topological behavior. 

We also develop sophisticated spin resonance techniques like NMR on the fly in world record high pulsed magnetic fields (up to 60 Tesla), or NMR with microcoils and Giga-Pascal pressure cells, e.g. to measure single crystal’s orientational electronic response over wide ranges of temperature.

 

Our EPR research interests are largely devoted to the study of the structure and electronic properties of paramagnetic centers on surfaces of microporous solids (porous coordination polymers - MOFs, zeolites). We are specifically interested in the interaction between the guest molecules adsorbed in porous materials and these surface centers. These interactions decisively determine the adsorptive and catalytic properties of the porous solids. Furthermore, we investigate paramagnetic defects and impurities in semiconducting metal oxides, silicon carbide and diamond.

In our work we use electron paramagnetic resonance (EPR) spectroscopy in the X (9.5 GHz) and Q (34 GHz) bands. In addition to the classical cw EPR methods, special emphasis in our research is being given to the use of the pulse EPR methods of hyperfine spectroscopy: electron spin-echo modulation (ESEEM) and electron nuclear double resonance (ENDOR)., diese Themen in die Lehre zu überführen.

Publications

The WEB of Science contains the following contributions by our group members in the years

M. Avramovska, C. Chmelik, A. Derkowski, A. Fantalkin, D. Freude, J. Haase, V. Hare, J. Kärger, A. Kuligiewicz, M. Moinester, Searching for the fundamentals of rehydroxylation dating of archaeological ceramics via NMR and IR microscopy, Journal of the American Ceramic Society 104 (2021) 5328—5340.

M. Avramovska, D. Freude, W. Schwieger, C. Song, J. Kärger, J. Haase, NMR Studies of the Dehydroxylation and Rehydroxylation (RHX) of Clays with Respect to the RHX Dating of Ceramic Materials, The Journal of Physical Chemistry C 125 (2021) 26274—26283.

P.C. Bruzzese, E. Salvadori, S. Jäger, M. Hartmann, B. Civalleri, A. Pöppl, M. Chiesa, 17O-EPR determination of the structure and dynamics of copper single-metal sites in zeolites, Nature Communications 12 (2021) 1—13.

C. Chmelik, R. Gläser, J. Haase, S. Hwang, J. Kärger, Application of microimaging to diffusion studies in nanoporous materials, Adsorption 27 (2021) 819—840.

R. Finger, M. Widenmeyer, T.C. Hansen, D. Wallacher, S. Savvin, M. Bertmer, A. Weidenkaff, H. Kohlmann, Effects of Cr Doping and Water Content on the Crystal Structure Transitions of Ba2In2O5, Crystals 11 (2021) 1548.

A.A. Gabrienko, Z.N. Lashchinskaya, S.S. Arzumanov, A.V. Toktarev, D. Freude, J. Haase, A.G. Stepanov, 1H MAS NMR in situ reaction monitoring reveals the particular effects of Zn2+ and ZnO species on the kinetics of isobutane transformation on Zn-modified zeolites, The Journal of Physical Chemistry C 125 (2021) 21471—21480.

A.A. Gabrienko, Z.N. Lashchinskaya, S.S. Arzumanov, A.V. Toktarev, D. Freude, J. Haase, A.G. Stepanov, Isobutene Transformation to Aromatics on Zn-Modified Zeolite: Particular Effects of Zn2+ and ZnO Species on the Reaction Occurrence Revealed with Solid-State NMR and FTIR Spectroscopy, The Journal of Physical Chemistry C 125 (2021) 15343—15353.

C. Grengg, G.J. Gluth, F. Mittermayr, N. Ukrainczyk, M. Bertmer, A.G. Buzanich, M. Radtke, A. Leis, M. Dietzel, Deterioration mechanism of alkali-activated materials in sulfuric acid and the influence of Cu: A micro-to-nano structural, elemental and stable isotopic multi-proxy study, Cement and Concrete Research 142 (2021) 106373.

R. Guehne, G.V.M. Williams, S.V. Chong, J. Haase, Unusual Quadrupole NMR of Topological Insulator Bi2Te3, The Journal of Physical Chemistry C 125 (2021) 6743—6748.

S. Henfling, A. Kultaeva, A. Pöppl, J. Klose, B. Kersting, K.V. Domasevitch, H. Krautscheid, Proton and Electron Transfer in the Formation of a Copper Dithiolene-Based Coordination Polymer, Inorganic Chemistry 60 (2021) 9008—9018.

S. Hwang, J. Haase, E. Miersemann, J. Kärger, Diffusion Analysis in Pore Hierarchies by the Two‐Region Model, Advanced Materials Interfaces 8 (2021) 2000749.

M. Jabłońska, K. Góra-Marek, M. Grilc, P.C. Bruzzese, D. Poppitz, K. Pyra, M. Liebau, A. Pöppl, B. Likozar, R. Gläser, Effect of Textural Properties and Presence of Co-Cation on NH3-SCR Activity of Cu-Exchanged ZSM-5, Catalysts 11 (2021) 843.

J. Kärger, M. Avramovska, D. Freude, J. Haase, S. Hwang, R. Valiullin, Pulsed field gradient NMR diffusion measurement in nanoporous materials, Adsorption 27 (2021) 453—484.

C. Kattinger, R. Guehne, S. Tsankov, M. Jurkutat, A. Erb, J. Haase, Moissanite anvil cell single crystal NMR at pressures of up to 4.4 GPa, Review of Scientific Instruments 92 (2021) 113901.

Y.-K. Liao, P.C. Bruzzese, M. Hartmann, A. Pöppl, M. Chiesa, Chromium Environment within Cr-Doped Silico-Aluminophosphate Molecular Sieves from Spin Density Studies, The Journal of Physical Chemistry C 125 (2021) 8116—8124.

M. Mendt, M. Maliuta, S. Ehrling, F. Schwotzer, I. Senkovska, S. Kaskel, A. Pöppl, Mixed-Metal Ni2+–Mn2+ Paddle Wheels in the Metal–Organic Framework DUT-8 (Ni1–x Mn x) as Electron Paramagnetic Resonance Probes for Monitoring the Structural Phase Transition, The Journal of Physical Chemistry C 126 (2021) 625—633.

A. Mutschke, G.M. Bernard, M. Bertmer, A.J. Karttunen, C. Ritter, V.K. Michaelis, N. Kunkel, Na3SO4H—The First Representative of the Material Class of Sulfate Hydrides, Angewandte Chemie International Edition 60 (2021) 5683—5687.

A. Mutschke, G.M. Bernard, M. Bertmer, A.J. Karttunen, C. Ritter, V.K. Michaelis, N. Kunkel, Na3SO4H–ein erster Vertreter der Materialklasse der Sulfathydride, Angewandte Chemie 133 (2021) 5747—5751.

S. Schmorl, S. Naumov, B. Abel, M. Börner, A. Pöppl, B. Kersting, Metalloligands based on Robson-type amino-thiophenolato macrocycles for assembly of heterotrimetallic complexes, Dalton Transactions 50 (2021) 5784—5788.

A. Setzer, P.D. Esquinazi, O. Daikos, T. Scherzer, A. Pöppl, R. Staacke, T. Lühmann, S. Pezzagna, W. Knolle, S. Buga, Weak Electron Irradiation Suppresses the Anomalous Magnetization of N‐Doped Diamond Crystals, physica status solidi (b) 258 (2021) 2100395.

S. Weber, S. Schäfer, M. Saccoccio, N. Ortner, M. Bertmer, K. Seidel, S. Berendts, M. Lerch, R. Gläser, H. Kohlmann, Mayenite-Based Electride C12A7e−: A Reactivity and Stability Study, Catalysts 11 (2021) 334.

R. Wunderlich, R. Staacke, W. Knolle, B. Abel, J. Haase, J. Meijer, Robust nuclear hyperpolarization driven by strongly coupled nitrogen vacancy centers, Journal of Applied Physics 130 (2021) 104301.

M. Šimėnas, D. Klose, M. Ptak, K. Aidas, M. Mączka, J. Banys, A. Pöppl, G. Jeschke, Magnetic excitation and readout of methyl group tunnel coherence, Science advances 6 (2020) eaba1517.

D. Pavićević, M. Avramovska, J. Haase, Unconventional 17O and 63Cu NMR shift components in cuprate superconductors, Modern Physics Letters B 34 (2020) 2040047.

A. Palčić, P.C. Bruzzese, K. Pyra, M. Bertmer, K. Góra-Marek, D. Poppitz, A. Pöppl, R. Gläser, M. Jabłońska, Nanosized Cu-SSZ-13 and Its Application in NH3-SCR, Catalysts 10 (2020) 506.

M. Navickas, L. Giriūnas, V. Kalendra, T. Biktagirov, U. Gerstmann, W.G. Schmidt, M. Mączka, A. Pöppl, J. Banys, M. Šimėnas, Electron paramagnetic resonance study of ferroelectric phase transition and dynamic effects in a Mn 2+ doped [NH 4][Zn (HCOO) 3] hybrid formate framework, Physical Chemistry Chemical Physics 22 (2020) 8513—8521.

J. Nachtigal, M. Avramovska, A. Erb, D. Pavićević, R. Guehne, J. Haase, Temperature-Independent Cuprate Pseudogap from Planar Oxygen NMR, Condensed Matter 5 (2020) 66.

M. Mączka, M. Ptak, D.L.M.o. Vasconcelos, L. Giriunas, P.T.C. Freire, M. Bertmer, J. Banys, M. Simenas, NMR and Raman Scattering Studies of Temperature-and Pressure-Driven Phase Transitions in CH3NH2NH2PbCl3 Perovskite, The Journal of Physical Chemistry C 124 (2020) 26999—27008.

Z.N. Lashchinskaya, A.A. Gabrienko, S.S. Arzumanov, A.A. Kolganov, A.V. Toktarev, D. Freude, J.r. Haase, A.G. Stepanov, Which Species, Zn2+ Cations or ZnO Clusters, Are More Efficient for Olefin Aromatization? 13C Solid-State NMR Investigation of n-But-1-ene Transformation on Zn-Modified Zeolite, ACS Catalysis 10 (2020) 14224—14233.

U. Gerstmann, W.G. Schmidt, M. Maczka, A. Pöppl, Electron paramagnetic resonance study of ferroelectric phase transition and dynamic effects in a Mn 2 doped [NH4][Zn (HCOO) 3] hybrid formate framework1, Phys. Chem. Chem. Phys 22 (2020) 8513—8521.

A.A. Gabrienko, S.S. Arzumanov, Z.N. Lashchinskaya, A.V. Toktarev, D. Freude, J. Haase, A.G. Stepanov, n-Butane transformation on Zn/H-BEA. The effect of different Zn species (Zn2+ and ZnO) on the reaction performance, Journal of Catalysis 391 (2020) 69—79.

S. Ehrling, M. Mendt, I. Senkovska, J.D. Evans, V. Bon, P. Petkov, C. Ehrling, F. Walenszus, A. Pöppl, S. Kaskel, Tailoring the Adsorption-Induced Flexibility of a Pillared Layer Metal–Organic Framework DUT-8 (Ni) by Cobalt Substitution, Chemistry of Materials 32 (2020) 5670—5681.

V. Bon, E. Brunner, A. Pöppl, S. Kaskel, Unraveling structure and dynamics in porous frameworks via advanced in situ characterization techniques, Advanced Functional Materials 30 (2020) 1907847.

J. Bitzer, S. Otterbach, K. Thangavel, A. Kultaeva, R. Schmid, A. Pöppl, W. Kleist, Experimental Evidence for the Incorporation of Two Metals at Equivalent Lattice Positions in Mixed‐Metal Metal–Organic Frameworks, Chemistry (Weinheim an der Bergstrasse, Germany) 26 (2020) 5667.

M. Bertmer, Solid-state NMR of small molecule adsorption in metal–organic frameworks (MOFs), Annual Reports on NMR Spectroscopy 101 (2020) 1—64.

M. Avramovska, D. Pavićević, J. Haase, NMR shift and relaxation and the electronic spin of superconducting cuprates, Journal of Superconductivity and Novel Magnetism 33 (2020) 2621—2628.

D. Freude, J. Haase: Quadrupole Effects in Solid-state NMR, Basic Principles and Experimental Techniques for Nuclei with Half-integer Spins, www.quad-nmr.de (2013–2019)

M.A. Zaheer, D. Poppitz, K. Feyzullayeva, M. Wenzel, J. Matysik, R. Ljupkovic, A. Zarubica, A.A. Karavaev, A. Pöppl, R. Gläser, Synthesis of highly active ETS-10-based titanosilicate for heterogeneously catalyzed transesterification of triglycerides, Beilstein journal of nanotechnology 10 (2019) 2039-2061.

A. Werwein, C. Benndorf, M. Bertmer, A. Franz, O. Oeckler, H. Kohlmann, Hydrogenation Properties of LnAl2 (Ln= La, Eu, Yb), LaGa2, LaSi2 and the Crystal Structure of LaGa2H0. 71 (2), Crystals 9 (2019) 193.

C. Schneider, M. Mendt, A. Poppl, V. Crocella, R.A. Fischer, Scrutinizing the Pore Chemistry and the Importance of Cu (I) Defects in TCNQ-Loaded Cu3 (BTC) 2 by a Multitechnique Spectroscopic Approach, ACS applied materials & interfaces 12 (2019) 1024-1035.

D. Michel, M. Bertmer, EPR and NMR study of nitric oxide-an interesting molecule for bio-medical applications, Magnetic Resonance and its Applications (2019) 46-46.

M. Mendt, P. Vervoorts, A. Schneemann, R.A. Fischer, A. Pöppl, Probing Local Structural Changes at Cu2+ in a Flexible Mixed-Metal Metal-Organic Framework by in Situ Electron Paramagnetic Resonance during CO2 Ad-and Desorption, The Journal of Physical Chemistry C 123 (2019) 2940-2952.

M. Mendt, S. Ehrling, I. Senkovska, S. Kaskel, A. Pöppl, Synthesis and Characterization of Cu–Ni Mixed Metal Paddlewheels Occurring in the Metal–Organic Framework DUT-8 (Ni0. 98Cu0. 02) for Monitoring Open-Closed-Pore Phase Transitions by X-Band Continuous Wave Electron Paramagnetic Resonance Spectroscopy, Inorganic chemistry 58 (2019) 4561-4573.

A. Kultaeva, W. Böhlmann, M. Hartmann, T. Biktagirov, A. Pöppl, Selective Gas Adsorption of Alkane/Alkene in a Single-Crystal and Powder Bimetallic Metal–Organic Framework Compound Cu2. 97Zn0. 03 (btc) 2 Studied by Electron Paramagnetic Resonance, The Journal of Physical Chemistry C 123 (2019) 26877-26887.

A.H. Khan, K. Peikert, F. Hoffmann, M. Fröba, M. Bertmer, Nitric Oxide Adsorption in Cu3btc2-Type MOFs—Physisorption and Chemisorption as NONOates, The Journal of Physical Chemistry C 123 (2019) 4299-4307.

A.H. Khan, D. Michel, M. Bertmer, Temperature dependent 15N NMR study of nitric oxide, Solid state nuclear magnetic resonance 101 (2019) 38-43.

M. Jurkutat, A. Erb, J. Haase, Tc and other cuprate properties in relation to planar charges as measured by NMR, Condensed Matter 4 (2019) 67.

M. Jurkutat, M. Avramovska, G.V. Williams, D. Dernbach, D. Pavićević, J. Haase, Phenomenology of 63 Cu Nuclear Relaxation in Cuprate Superconductors, Journal of Superconductivity and Novel Magnetism 32 (2019) 3369-3376.

R. Guehne, V. Chlan, G.V. Williams, S.V. Chong, K. Kadowaki, A. Pöppl, J. Haase, Unusual 209Bi NMR quadrupole effects in topological insulator Bi2Se3, Journal of Magnetic Resonance 302 (2019) 34-42.

R. Guehne, H. Auer, H. Kohlmann, J. Haase, M. Bertmer, Determination of element–deuterium bond lengths in Zintl phase deuterides by 2 H-NMR, Physical Chemistry Chemical Physics 21 (2019) 10594-10602.

A.A. Gabrienko, S.S. Arzumanov, A.V. Toktarev, D. Freude, J.r. Haase, A.G. Stepanov, Propylene Transformation on Zn-Modified Zeolite: Is There Any Difference in the Effect of Zn2+ Cations or ZnO Species on the Reaction Occurrence?, The Journal of Physical Chemistry C 123 (2019) 27573-27583.

D. Freude, N. Dvoyashkina, S.S. Arzumanov, D.I. Kolokolov, A.G. Stepanov, C. Chmelik, H. Jin, Y. Li, J. Kärger, J. Haase, NMR Study of the Host Structure and Guest Dynamics Investigated with Alkane/Alkene Mixtures in Metal Organic Frameworks ZIF-8, The Journal of Physical Chemistry C 123 (2019) 1904-1912.

J. Dietel, J. Gröger-Trampe, M. Bertmer, S. Kaufhold, K. Ufer, R. Dohrmann, Crystal structure model development for soil clay minerals–I. Hydroxy-interlayered smectite (HIS) synthesized from bentonite. A multi-analytical study, Geoderma 347 (2019) 135-149.

M. Bahadori, S. Tangestaninejad, M. Bertmer, M. Moghadam, V. Mirkhani, I. Mohammadpoor− Baltork, R. Kardanpour, F. Zadehahmadi, Task-specific ionic liquid functionalized–MIL–101 (Cr) as a heterogeneous and efficient catalyst for the cycloaddition of CO2 with epoxides under solvent free conditions, ACS Sustainable Chemistry & Engineering 7 (2019) 3962-3973.

M. Avramovska, D. Pavićević, J. Haase, Properties of the electronic fluid of superconducting cuprates from 63 Cu NMR shift and relaxation, Journal of Superconductivity and Novel Magnetism 32 (2019) 3761-3771.

S.S. Arzumanov, A.A. Gabrienko, A.V. Toktarev, Z.N. Lashchinskaya, D. Freude, J.r. Haase, A.G. Stepanov, Propane Transformation on Zn-Modified Zeolite. Effect of the Nature of Zn Species on Alkane Aromatization and Hydrogenolysis, The Journal of Physical Chemistry C 123 (2019) 30473-30485.

S.S. Arzumanov, A.A. Gabrienko, A.V. Toktarev, D. Freude, J. Haase, A.G. Stepanov, Propane activation on Zn-modified zeolite. The effect of the nature of Zn-species on the mechanism of H/D hydrogen exchange of the alkane with Brønsted acid sites, Journal of Catalysis 378 (2019) 341-352.

R. Wunderlich, J. Kohlrautz, B. Abel, J. Haase, J. Meijer, Investigation of room temperature multispin-assisted bulk diamond 13C hyperpolarization at low magnetic fields, Journal of Physics: Condensed Matter 30 (2018) 305803.

M. Šimėnas, M. Ptak, A.H. Khan, L. Dagys, V. Balevičius, M. Bertmer, G. Völkel, M. Ma̧czka, A. Pöppl, J.r. Banys, Spectroscopic study of [(CH3) 2NH2][Zn (HCOO) 3] hybrid perovskite containing different nitrogen isotopes, The Journal of Physical Chemistry C 122 (2018) 10284-10292.

M. Šimėnas, A. Ciupa, G. Usevičius, K. Aidas, D. Klose, G. Jeschke, M. Mączka, G. Völkel, A. Pöppl, J. Banys, Electron paramagnetic resonance of a copper doped [(CH 3) 2 NH 2][Zn (HCOO) 3] hybrid perovskite framework, Physical Chemistry Chemical Physics 20 (2018) 12097-12105.

D. Savchenko, A. Pöppl, A.H. Kassiba, CW and Pulse EPR Study of Paramagnetic Centers in Silicon Carbide Nanomaterials, Electron Paramagnetic Resonance in Modern Carbon-Based Nanomaterials 1 (2018) 225-242.

S. Reichardt, M. Jurkutat, R. Guehne, J. Kohlrautz, A. Erb, J. Haase, Bulk Charge Ordering in the CuO2 Plane of the Cuprate Superconductor YBa2Cu3O6. 9 by High-Pressure NMR, Condensed Matter 3 (2018) 23.

R. Pickenhain, M. Schmidt, H. von Wenckstern, G. Benndorf, A. Pöppl, R. Böttcher, M. Grundmann, Negative‐U Properties of the Deep Level E3 in ZnO, physica status solidi (b) 255 (2018) 1700670.

D. Michel, J. Haase, Solid State NMR in nanosized systems: MAS NMR studies in combination with pulsed field gradient techniques, Magnetic resonance and its applications. Spinus-2018 (2018) 45-45.

A. Kultaeva, V. Bon, M.S. Weiss, A. Pöppl, S. Kaskel, Elucidating the formation and transformation mechanisms of the switchable metal–organic framework ELM-11 by powder and single-crystal EPR study, Inorganic chemistry 57 (2018) 11920-11929.

A. Kultaeva, T. Biktagirov, P. Neugebauer, H. Bamberger, J. Bergmann, J. van Slageren, H. Krautscheid, A. Pöppl, Multifrequency EPR, SQUID, and DFT Study of Cupric Ions and Their Magnetic Coupling in the Metal–Organic Framework Compound∞ 3 [Cu (prz–trz–ia)], The Journal of Physical Chemistry C 122 (2018) 26642-26651.

A.H. Khan, B. Barth, M. Hartmann, J.r. Haase, M. Bertmer, Nitric oxide adsorption in MIL-100 (Al) MOF studied by solid-state NMR, The Journal of Physical Chemistry C 122 (2018) 12723-12730.

J. Kärger, D. Freude, J. Haase, Diffusion in nanoporous materials: novel insights by combining MAS and PFG NMR, Processes 6 (2018) 147.

S. Hwang, R. Semino, B. Seoane, M. Zahan, C. Chmelik, R. Valiullin, M. Bertmer, J. Haase, F. Kapteijn, J. Gascon, Revealing the Transient Concentration of CO2 in a Mixed‐Matrix Membrane by IR Microimaging and Molecular Modeling, Angewandte Chemie International Edition 57 (2018) 5156-5160.

N. Dvoyashkina, C.F. Seidler, M. Wark, D. Freude, J. Haase, Proton mobility in sulfonic acid functionalized mesoporous materials studied by MAS PFG NMR diffusometry and impedance spectroscopy, Microporous and Mesoporous Materials 255 (2018) 140-147.

N. Dvoyashkina, D. Freude, A.G. Stepanov, W. Böhlmann, R. Krishna, J. Kärger, J. Haase, Alkane/alkene mixture diffusion in silicalite-1 studied by MAS PFG NMR, Microporous and Mesoporous Materials 257 (2018) 128-134.

M. Dvoyashkin, N. Wilde, J. Haase, R. Gläser, Diffusion of methyl oleate in hierarchical micro-/mesoporous TS-1-based catalysts probed by PFG NMR spectroscopy, RSC advances 8 (2018) 38941-38944.

C. Chmelik, J. Caro, D. Freude, J. Haase, R. Valiullin, J. Kärger, Diffusive spreading of molecules in nanoporous materials, in:  Diffusive spreading in nature, technology and society, Vol., Springer, 2018, pp. 171-202.

Spectrometer

The Departments MQF and AMR use the following solid-state NMR spectrometer with super-conducting wide-bore magnets:

  • AVANCE 750 (Bruker Biospin)
  • AVANCE 500 HD with ASCEND magnet (Bruker Biospin)
  • AVANCE 500 HD with Oxford-Magnet (Bruker Biospin)
  • Apollo 300 (Tecmag, magnet: Bruker Biospin)
  • Apollo 400 (Tecmag, magnet: Bruker Biospin)
  • AVANCE 400 (Bruker Biospin)
  • PFG NMR spectr. FEGRIS 100 (home madeu, magnet: Bruker Biospin)

For EPR spektroskopy (EPR = Electron Paramagnetic Resonance) the following spectrometer with iron magnets are used:

  • Q-Band EPR spectrometer EMX 10-40 (Bruker Biospin)
  • X-Band EPR spectrometer EMX micro (Bruker Biospin)
  • X-Band pulse EPR spectrometer ELEXYS E580 (Bruker Biospin)