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1.
Chemphyschem ; : e202400280, 2024 Jun 18.
Article En | MEDLINE | ID: mdl-38887965

Coordination complexes of rare-earth ions (REI) show optical transitions with narrow linewidths enabling the creation of coherent light-matter interfaces for quantum information processing (QIP) applications. Among the REI-based complexes, Eu(III) complexes showing the 5D0 → 7F0 transition are of interest for QIP applications due to the narrow linewidths associated with the transition. Herein, we report on the synthesis, structure, and optical properties of a novel Eu(III) complex and its Gd(III) analogue composed of 2,9-bis(pyrazol-1-yl)-1,10-phenanthroline (dpphen) and three nitrate (NO3) ligands. The Eu(III) complex-[Eu(dpphen)(NO3)3]-showed sensitized metal-centred emission (5D0 → 7FJ; J = 0,1,2,3, 4, 5, or 6) in the visible region, upon irradiation of the ligand-centered band at 369 nm, with the 5D0 → 7F0 transition centred at 580.9 nm. Spectral hole-burning (SHB) studies of the complex with stoichiometric Eu(III) concentration revealed a narrow homogeneous linewidth (Γh) of 1.55 MHz corresponding to a 0.205 µs long optical coherence lifetime (T2opt). Remarkably, long nuclear spin lifetimes (T1spin) of up to 41 s have been observed for the complex. The narrow optical linewidths and long T1spin lifetimes obtained for the Eu(III) complex showcase the utility of Eu(III) complexes as tunable, following molecular engineering principles, coherent light-matter interfaces for QIP applications.

2.
Chem Asian J ; : e202400574, 2024 Jun 13.
Article En | MEDLINE | ID: mdl-38870468

A new Co(II) complex, [Co(NCS)2(L)2] (1) has been synthesized based on levamisole (L) as a new ligand. Single-crystal X-ray diffraction analyses confirm that the Co(II) ion is having a distorted tetrahedral coordination geometry in the complex. Notably strong intramolecular S∙∙∙S and S∙∙∙N interactions has been confirmed by employing Quantum Theory of Atoms in Molecules (QTAIM). These intramolecular interactions occur among the sulfur and nitrogen atoms of the levamisole ligands and also the nitrogen atoms of the thiocyanate. Direct current (dc) magnetic analyses reveal presence of zero field splitting (ZFS) and large magnetic anisotropy on Co(II). Detailed ab initio ligand field theory calculations quantitatively predicted the magnitude of ZFS. Prominent field-induced single-ion magnet (SIM) behavior was observed for 1 from dynamic magnetization measurements. Slow magnetic relaxation follows an Orbach mechanism with the effective energy barrier Ueff = 29.6 (7) K and relaxation time to = 1.4 (4) × 10-9 s.

3.
Dalton Trans ; 2024 Jun 03.
Article En | MEDLINE | ID: mdl-38826041

Spin-state switching in iron(II) complexes composed of ligands featuring moderate ligand-field strength-for example, 2,6-bi(1H-pyrazol-1-yl)pyridine (BPP)-is dependent on many factors. Herein, we show that spin-state switching in isomeric iron(II) complexes composed of BPP-based ligands-ethyl 2,6-bis(1H-pyrazol-1-yl)isonicotinate (BPP-COOEt, L1) and (2,6-di(1H-pyrazol-1-yl)pyridin-4-yl)methylacetate (BPP-CH2OCOMe, L2)-is dependent on the nature of the substituent at the BPP skeleton. Bi-stable spin-state switching-with a thermal hysteresis width (ΔT1/2) of 44 K and switching temperature (T1/2) = 298 K in the first cycle-is observed for complex 1·CH3CN composed of L1 and BF4- counter anions. Conversely, the solvent-free isomeric counterpart of 1·CH3CN-complex 2a, composed of L2 and BF4- counter anions-was trapped in the high-spin (HS) state. For one of the polymorphs of complex 2b·CH3CN-2b·CH3CN-Y, Y denotes yellow colour of the crystals-composed of L2 and ClO4- counter anions, a gradual and non-hysteretic SCO is observed with T1/2 = 234 K. Complexes 1·CH3CN and 2b·CH3CN-Y also underwent light-induced spin-state switching at 5 K due to the light-induced excited spin-state trapping (LIESST) effect. Structures of the low-spin (LS) and HS forms of complex 1·CH3CN revealed that spin-state switching goes hand-in-hand with pronounced distortion of the trans-N{pyridyl}-Fe-N{pyridyl} angle (ϕ), whereas such distortion is not observed for 2b·CH3CN-Y. This observation points that distortion is one of the factors making the spin-state switching of 1·CH3CN hysteretic in the solid state. The observation of bi-stable spin-state switching with T1/2 centred at room temperature for 1·CH3CN indicates that technologically relevant spin-state switching profiles based on mononuclear iron(II) complexes can be obtained.

4.
Adv Mater ; : e2405178, 2024 May 19.
Article En | MEDLINE | ID: mdl-38762788

Graphyne (GY) and graphdiyne (GDY)-based monolayers represent the next generation 2D carbon-rich materials with tunable structures and properties surpassing those of graphene. However, the detection of band formation in atomically thin GY/GDY analogues has been challenging, as both long-range order and atomic precision have to be fulfilled in the system. The present work reports direct evidence of band formation in on-surface synthesized metallated Ag-GDY sheets with mesoscopic (≈1 µm) regularity. Employing scanning tunneling and angle-resolved photoemission spectroscopies, energy-dependent transitions of real-space electronic states above the Fermi level and formation of the valence band are respectively observed. Furthermore, density functional theory (DFT) calculations corroborate the observations and reveal that doubly degenerate frontier molecular orbitals on a honeycomb lattice give rise to flat, Dirac and Kagome bands close to the Fermi level. DFT modeling also indicates an intrinsic band gap for the pristine sheet material, which is retained for a bilayer with h-BN, whereas adsorption-induced in-gap electronic states evolve at the synthesis platform with Ag-GDY decorating the (111) facet of silver. These results illustrate the tremendous potential for engineering novel band structures via molecular orbital and lattice symmetries in atomically precise 2D carbon materials.

5.
J Am Chem Soc ; 146(20): 13760-13769, 2024 May 22.
Article En | MEDLINE | ID: mdl-38718186

The first structurally characterized organometallic multidecker sandwich complexes featuring a cycloheptatrienyl ring (Cht, C7H73-) in the coordination sphere are presented. The synthesis of inverse sandwich complexes of the rare earth elements YIII and ErIII with a bridging cycloheptatrienyl ligand of the type [(thf)(BH4)2LnIII(µ-η7:η7-Cht)LnIII(BH4)(thf)2] is described first. The subsequent introduction of the CotTIPS ligand (CotTIPS = 1,4-(iPr3Si)2C8H62-) into the coordination sphere of the rare earth cations resulted in the isolation of unprecedented triple-decker compounds with the formula [(thf)3K{(η8-CotTIPS)LnIII}2(µ-η7:η7-Cht)], bearing a seven-membered aromatic carbon ring as a middle deck. These compounds are also the first examples of rare earth triple-decker complexes not bridged by a Cot derivative, based on purely carbon-based ligands. The magnetic properties of the respective ErIII congeners were investigated in detail, leading to the observation of antiferromagnetic coupling of the ErIII cations and a blocking temperature of 13.5 K. The conversion of the YIII compound [(thf)3K{(η8-CotTIPS)YIII}2(µ-η7:η7-Cht)] with [YIII(Cot)I(thf)2] resulted in ligand rearrangement and the selective formation of the first triple-decker complex ([(η8-CotTIPSYIII)2(µ-η8:η8-Cot)]) featuring two Cot ligands with different substituents in its coordination sphere.

6.
J Am Chem Soc ; 146(19): 13083-13092, 2024 May 15.
Article En | MEDLINE | ID: mdl-38701172

Lanthanide metal clusters excel in combining molecular and material chemistry properties. Here, we report an efficient cooperative sensitization UC phenomenon of a Eu3+/Yb3+ nonanuclear lanthanide cluster in CD3OD. The synthesis and characterization of the heteronuclear cluster in the solid state and solution are described together with the UC phenomenon showing Eu3+ luminescence in the visible region upon 980 nm NIR excitation of Yb3+ at concentrations as low as 100 nM. Alongside being the Eu/Yb cluster to display UC (with a quantum yield value of 4.88 × 10-8 upon 1.13 W cm-2 excitation at 980 nm), the cluster exhibits downshifted light emission of Yb3+ in the NIR region upon 578 nm visible excitation of Eu3+, which is ascribed to sensitization pathways for Yb through the 5D0 energy levels of Eu3+. Additionally, a faint emission is also observed at ca. 500 nm upon 980 nm excitation, originating from the cooperative luminescence of Yb3+. The [Eu8Yb(BA)16(OH)10]Cl cluster (BA = benzoylacetonate) is also a field-induced single-molecular magnet (SMM) under 4K with a modest Ueff/kB of 8.48 K, thereby joining the coveted list of Yb-SMMs and emerging as a prototype system for next-generation devices, combining luminescence with single-molecular magnetism in a molecular cluster.

7.
Dalton Trans ; 53(23): 10019, 2024 Jun 10.
Article En | MEDLINE | ID: mdl-38812409

Correction for 'Computational demonstration of isomer- and spin-state-dependent charge transport in molecular junctions composed of charge-neutral iron(II) spin-crossover complexes' by Nicolás Montenegro-Pohlhammer, et al., Dalton Trans., 2023, 52, 1229-1240, https://doi.org/10.1039/D2DT02598A.

8.
Chemistry ; : e202400420, 2024 Apr 02.
Article En | MEDLINE | ID: mdl-38563635

A diradical with engineered g-asymmetry was synthesized by grafting a nitroxide radical onto the [Y(Pc)2]⋅ radical platform. Various spectroscopic techniques and computational studies revealed that the electronic structures of the two spin systems remained minimally affected within the diradical system. Fluid-solution Electron Paramagnetic Resonance (EPR) experiments revealed a weak exchange coupling with |J| ~ 0.014 cm-1, subsequently rationalized by CAS-SCF calculations. Frozen solution continuous-wave (CW) EPR experiments showed a complicated and power-dependent spectrum that eluded analysis using the point-dipole model. Pulse EPR manipulations with varying microwave powers, or under varying magnetic fields, demonstrated that different resonances could be selectively enhanced or suppressed, based on their different tipping angles. In particular, Field-Swept Echo-Detected (FSED) spectra revealed absorptions of MW power-dependent intensities, while Field-Swept Spin Nutation (FSSN) experiments revealed two distinct Rabi frequencies. This study introduces a methodology to synthesize and characterize g-asymmetric two-spin systems, of interest in the implementation of spin-based CNOT gates.

9.
Angew Chem Int Ed Engl ; 63(17): e202401372, 2024 Apr 22.
Article En | MEDLINE | ID: mdl-38390783

Herein, we present the first report on the synthesis of rare-earth complexes featuring a 9,10-diborataanthracene ligand. This 14-π-electron ligand is highly reductive and was previously used in small-molecule activation. Salt elimination reactions between dipotassium 9,10-diethyl-9,10-diborataanthracene [K2(DEDBA)] and [LnIII(η8-CotTIPS)(BH4)(thf)x] (CotTIPS=1,4-(iPr3Si)2C8H6) in a 1 : 1 ratio yielded heteroleptic sandwich complexes [K(η8-CotTIPS)LnIII(η6-DEDBA)] (Ln=Y, Dy, Er). These compounds form Lewis-base-free one-dimensional coordination polymers when crystallised from toluene. In contrast, reaction of [K2(DEDBA)] and [LnIII(η8-CotTIPS)(BH4)(thf)x] in a 1 : 2 ratio led to the formation of heteroleptic triple-decker complexes [(η8-CotTIPS)LnIII(µ-η6:η6-DEDBA)LnIII(η8-CotTIPS)] (Ln=Y, Dy, Er). Notably, these are not only the first lanthanide triple-decker compounds featuring a six-membered ring as a deck but also the first trivalent lanthanide triple-decker featuring a heterocycle in the coordination sphere. Magnetic investigations reveal that [K(η8-CotTIPS)LnIII(η6-DEDBA)] (Ln=Dy, Er) and [(η8-CotTIPS)ErIII(µ-η6:η6-DEDBA)ErIII(η8-CotTIPS)] exhibit Single-Molecule Magnet (SMM) behaviour. In the case of [(η8-CotTIPS)LnIII(µ-η6:η6-DEDBA)LnIII(η8-CotTIPS)] (Ln=Dy, Er), the introduction of a second near lanthanide ion results in strong antiferromagnetic interactions, allowing the enhancement of the magnetic characteristic of the system, compared to the quasi isolated counterpart. This research renews the overlooked coordination chemistry of the DBA ligand and expands it to encompass rare-earth elements.

10.
Phys Chem Chem Phys ; 26(10): 8043-8050, 2024 Mar 06.
Article En | MEDLINE | ID: mdl-38385559

Molecular triangles with competing Heisenberg interactions and significant Dzyaloshinskii-Moriya interactions (DMI) exhibit high environmental sensitivity, making them potential candidates for active elements for quantum sensing. Additionally, these triangles exhibit magnetoelectric coupling, allowing their properties to be controlled using electric fields. However, the manipulation and deposition of such complexes pose significant challenges. This work explores a solution by embedding iron-based molecular triangles in a polymer matrix, a strategy that offers various deposition methods. We investigate how the host matrix alters the magnetic properties of the molecular triangle, with specific focus on the magnetic anisotropy, aiming to advance its practical applications as quantum sensors.

11.
J Am Chem Soc ; 146(9): 5901-5907, 2024 Mar 06.
Article En | MEDLINE | ID: mdl-38408315

Manipulating the chirality of the spin-polarized electronic state is pivotal for understanding many unusual quantum spin phenomena, but it has not been achieved at the single-molecule level. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we successfully manipulate the chirality of spin distribution in a triple-decker single-molecule magnet tris(phthalocyaninato)bis(terbium(III)) (Tb2Pc3), which is evaporated on a Pb(111) substrate via molecular beam epitaxy. The otherwise achiral Tb2Pc3 becomes chiral after being embedded into the self-assembled monolayer films of bis(phthalocyaninato)terbium(III) (TbPc2). The chirality of the spin distribution in Tb2Pc3 is manifested via the spatial mapping of its Kondo resonance state from its ligand orbital. Our first-principles calculations revealed that the spin and molecular chirality are associated with a small rotation followed by a structural distortion of the top Pc, consistent with the experimental observation. By constructing tailored molecular clusters with the STM tip, a single Tb2Pc3 molecule can be manipulated among achiral and differently handed chiral configurations of spin distributions reversibly. This paves the way for designing chiral spin enantiomers for fundamental studies and developing functional spintronic devices.

12.
ChemSusChem ; 17(10): e202301903, 2024 May 21.
Article En | MEDLINE | ID: mdl-38266158

The versatile properties of bipolar organic electrode materials have attracted considerable attention in the field of electrochemical energy storage (EES). However, their practical application is hindered by their inherent limitations including low intrinsic electrical conductivity, low specific capacity, and high solubility. Herein, a bipolar organic molecule combining both porphyrin and ferrocene moieties (CuDEFcP) [5,15-bis(ethynyl)-10,20-di ferrocenyl porphinato]copper(II)) has been developed. It is proposed as a new organic electrode material with multifunctional application for rechargeable organic lithium-based batteries (ROLBs) and dual-ion organic symmetric batteries (SDIBs). Superior performance was delivered as cathode material in lithium based dual-ion batteries (LDIBs), with a high initial discharge capacity of 300 mAh. g-1 at 0.2 A. g-1 and a reversible capacity of 58 mAh. g-1 after 5000 cycles at 1 A. g-1. However, employing it as an anode material in lithium-ion batteries (LIBs), a reversible capacity of 295 mAh. g-1 at 0.2 A. g-1 was delivered. In SDIBs, in which CuDEFcP is used as both anode and cathode, an average discharge voltage of 2.4 V and an energy density of 261 Wh.kg-1 were achieved.

13.
Inorg Chem ; 63(21): 9520-9526, 2024 May 27.
Article En | MEDLINE | ID: mdl-38241036

A series of trivalent lanthanide sandwich complexes [(η5-C4R4As)Ln(η8-C8H8)] using three different arsolyl ligands are reported. The complexes were obtained via salt elimination reactions between potassium arsolyl salts and lanthanide precursors [LnI(COT)(THF)2] (Ln = Sm, Dy, Er; COT = η8-C8H8). The resulting compounds exhibit classical sandwich complex structures with one notable exception. Characterization was conducted in both the solid state using single-crystal X-ray diffraction and in solution for the Sm compounds using NMR spectroscopy. Furthermore, the magnetic properties of an Er complex were investigated, revealing distinctive single-molecule-magnet behavior characterized by an energy barrier of Ueff = 323.3 K. Theoretical calculations were employed to support and interpret the experimental findings, with a comparative analysis performed against previously reported complexes.

14.
Chem Sci ; 15(4): 1338-1347, 2024 Jan 24.
Article En | MEDLINE | ID: mdl-38274072

Synthesis and characterization of Lewis base free coordination polymers of selected lanthanides are presented. For this purpose, the substituted CotTIPS ligand (CotTIPS = 1,4-bis-triisopropylsilyl-cyclo-octatetraendiide) was used to synthesize homoleptic, anionic multidecker compounds of the type [K{LnIII(ɳ8-CotTIPS)2}]n. Depending on the solvent used for crystallization and the ionic radii of the lanthanide cations, three different categories of one-dimensional heterobimetallic coordination polymers were obtained in the solid state. For the early lanthanides La and Ce a unique helical conformation was obtained by crystallization from toluene, while the ionic radius of Pr seems to be a turning point towards the crystallization of zigzag polymers. For Er a third structural motif, a trapezoidal wave polymer was observed. Additionally, the zigzag polymer for all compounds could be obtained by changing the solvent from toluene to Et2O, reavealing a correlation between solid-state structure and ionic radii as well as solvent. While photoluminescence (PL) properties of Cot-lanthanide compounds are scarce, the La complexes show ligand centered green luminescence, whereas the Ce complexes reveal deep red emission origin from d-f transitions. The Er-compounds are single-molecule magnets, in which the magnetic relaxation of each Er ion occurs isolated from its neighbors at temperatures above 10 K, while below 9 K a strong antiferromagnetic coupling between the Er ions was seen.

15.
Inorg Chem ; 62(37): 15148-15156, 2023 Sep 18.
Article En | MEDLINE | ID: mdl-37655998

Single-molecule magnets are molecular complexes proposed to be useful for information storage and quantum information processing applications. In the quest for multilevel systems that can act as Qudits, two dysprosium-based isotopologues were synthesized and characterized. The isotopologues are [164Dy2(tmhd)6(tape)] (1(I=0)) and [163Dy2(tmhd)6(tape)] (2(I=5/2)), where tmhd = 2,2,6,6-tetramethylheptandionate and tape = 1,6,7,12-tetraazaperylene. Both complexes showed slow relaxation at a zero applied magnetic field with dominant Orbach and Raman relaxation mechanisms. µSQUID studies at milli-Kelvin temperatures reveal quasi-single ion loops, in contrast with the expected S-shape (near zero field) butterfly loops, characteristic of antiferromagnetically coupled dimeric complexes. Through analysis of the low-temperature data, we find that the interaction operating between Dy(III) is small, leading to a small exchange biasing from the zero-field transition. The resulting indirectly coupled nuclear states are degenerate or possess a small energy difference between them. We, therefore, conclude that for the creation of Qudits with enlarged Hilbert spaces, shorter Dy(III)···Dy(III) distances are deemed essential.

16.
Nat Chem ; 15(12): 1765-1772, 2023 Dec.
Article En | MEDLINE | ID: mdl-37723257

Aromaticity is an established and widely used concept for the prediction of the reactivity of organic molecules. However, its role remains largely unexplored in on-surface chemistry, where the interaction with the substrate can alter the electronic and geometric structure of the adsorbates. Here we investigate how aromaticity affects the reactivity of alkyne-substituted porphyrin molecules in cyclization and coupling reactions on a Au(111) surface. We examine and quantify the regioselectivity in the reactions by scanning tunnelling microscopy and bond-resolved atomic force microscopy at the single-molecule level. Our experiments show a substantially lower reactivity of carbon atoms that are stabilized by the aromatic diaza[18]annulene pathway of free-base porphyrins. The results are corroborated by density functional theory calculations, which show a direct correlation between aromaticity and thermodynamic stability of the reaction products. These insights are helpful to understand, and in turn design, reactions with aromatic species in on-surface chemistry and heterogeneous catalysis.

17.
Nanomaterials (Basel) ; 13(15)2023 Aug 01.
Article En | MEDLINE | ID: mdl-37570550

Nanostructures, fabricated by locating molecular building blocks in well-defined positions, for example, on a lattice, are ideal platforms for studying atomic-scale quantum effects. In this context, STM data obtained from self-assembled Bis(phthalocyaninato) Terbium (III) (TbPc2) single-molecule magnets on various substrates have raised questions about the conformation of the TbPc2 molecules within the lattice. In order to address this issue, molecular dynamics simulations were carried out on a 2D assembly of TbPc2 molecules. The calculations are in excellent agreement with the experiment, and thus improve our understanding of the self-assembly process. In particular, the calculated electron density of the molecular assembly compares well with STM contrast of self-assembled TbPc2 on Au(111), simultaneously providing the conformation of the two Pc ligands of the individual double-decker molecule. This approach proves valuable in the identification of the STM contrast of LnPc2 layers and could be used in similar cases where it is difficult to interpret the STM images of an assembly of molecular complexes.

18.
ChemSusChem ; 16(21): e202300932, 2023 Nov 08.
Article En | MEDLINE | ID: mdl-37526569

Calcium (Ca) batteries are attractive post-lithium battery technologies, due to their potential to provide high-voltage and high-energy systems in a sustainable manner. We investigated herein 1,5-poly(anthraquinonylsulfide) (PAQS) for Ca-ion storage with calcium tetrakis(hexafluoroisopropyloxy)borate Ca[B(hfip)4 ]2 [hfip=OCH(CF3 )2 ] electrolytes. It is demonstrated that PAQS could be synthesized in a cost-effective approach and be processed environmentally friendly into the electrodes. The PAQS cathodes could provide 94 mAh g-1 capacity at 2.2 V vs. Ca at 0.5C (1C=225 mAh g-1 ). However, cycling of the cells was severely hindered due to the fast degradation of the metal anode. Replacing the Ca metal anode with a calcium-tin (Ca-Sn) alloy anode, the PAQS cathodes exhibited long cycling performance (45 mAh g-1 at 0.5C after 1000 cycles) and superior rate capability (52 mAh g-1 at 5C). This is mainly ascribed to the flexible structure of PAQS and good compatibility of the alloy anodes with the electrolyte solutions, which allow reversible quinone carbonyl redox chemistry in the Ca battery systems. The promising properties of PAQS indicate that further exploration of the organic cathode materials could be a feasible direction towards green Ca batteries.

19.
Nat Commun ; 14(1): 3361, 2023 Jun 08.
Article En | MEDLINE | ID: mdl-37291099

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et4N[GdPc2], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.


Quantum Theory , Ligands , Electron Spin Resonance Spectroscopy
20.
Inorg Chem ; 62(22): 8598-8604, 2023 Jun 05.
Article En | MEDLINE | ID: mdl-37220076

Single-molecule magnets (SMMs) distinguish themselves in the field of quantum magnetism through the ability to combine fundamental research with promising applications. The evolution of quantum spintronics in the last decade exemplifies the potential held by molecular-based quantum devices. Notably, the readout and manipulation of the nuclear spin states embedded in a lanthanide-based SMM hybrid device were employed in proof of principle studies of quantum computation at the single-molecule level. In the quest for further understanding of the relaxation behavior in SMMs for their integration in novel applications, herein, we study the relaxation dynamics of the 159Tb nuclear spins in a diluted molecular crystal employing the recently acquired understanding of the nonadiabatic dynamics of TbPc2 molecules. Through numerical simulation, we find that phonon-modulated hyperfine interaction opens a direct relaxation channel between the nuclear spins and the phonon bath. The mechanism is of potential importance for the theory of spin bath and the relaxation dynamics of the molecular spins.

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