Determining relative f and d orbital contributions to M-Cl covalency in MCl6(2-) (M = Ti, Zr, Hf, U) and UOCl5(-) using Cl K-edge X-ray absorption spectroscopy and time-dependent density functional theory

Magnetic circular dichroism of UCl6− in the ligand-to-metal charge-transfer spectral region

We present a combined ab initio theoretical and experimental study of the magnetic circular dichroism (MCD) spectrum of the octahedral UCl₆⁻ complex ion in the UV-Vis spectral region.

Computational study of An–X bonding (An = Th, U; X = p-block-based ligands) in pyrrolic macrocycle-supported complexes from the quantum theory of atoms in molecules and bond energy decomposition analysis

Good correlations are found between QTAIM BCP and EDA data for a range of Th(iv)- and Th(iii)-p element bonds.

Actinide covalency measured by pulsed electron paramagnetic resonance spectroscopy

Our knowledge of actinide chemical bonds lags far behind our understanding of the bonding regimes of any other series of elements. This is a major issue given the technological as well as fundamental importance of f-block elements. Some key chemical differences between actinides and lanthanides-and between different actinides-can be ascribed to minor differences in covalency, that is, the degree to which electrons are shared between the f-block element and coordinated ligands. Yet there are almost no direct measures of such covalency for actinides. Here we report the first pulsed electron paramagnetic resonance spectra of actinide compounds. We apply the hyperfine sublevel correlation technique to quantify the electron-spin density at ligand nuclei (via the weak hyperfine interactions) in molecular thorium(III) and uranium(III) species and therefore the extent of covalency. Such information will be important in developing our understanding of the chemical bonding, and therefore the reactivity, of actinides.

Molecular and electronic structure of terminal and alkali metal-capped uranium(V) nitride complexes

Determining the electronic structure of actinide complexes is intrinsically challenging because inter-electronic repulsion, crystal field, and spin-orbit coupling effects can be of similar magnitude. Moreover, such efforts have been hampered by the lack of structurally analogous families of complexes to study. Here we report an improved method to U≡N triple bonds, and assemble a family of uranium(V) nitrides. Along with an isoelectronic oxo, we quantify the electronic structure of this 5f1 family by magnetometry, optical and electron paramagnetic resonance (EPR) spectroscopies and modelling. Thus, we define the relative importance of the spin-orbit and crystal field interactions, and explain the experimentally observed different ground states. We find optical absorption linewidths give a potential tool to identify spin-orbit coupled states, and show measurement of UV···UV super-exchange coupling in dimers by EPR. We show that observed slow magnetic relaxation occurs via two-phonon processes, with no obvious correlation to the crystal field.

Thorium-phosphorus triamidoamine complexes containing Th-P single- and multiple-bond interactions

Despite the burgeoning field of uranium-ligand multiple bonds, analogous complexes involving other actinides remain scarce. For thorium, under ambient conditions only a few multiple bonds to carbon, nitrogen, oxygen, sulfur, selenium and tellurium are reported, and no multiple bonds to phosphorus are known, reflecting a general paucity of synthetic methodologies and also problems associated with stabilising these linkages at the large thorium ion. Here we report structurally authenticated examples of a parent thorium(IV)-phosphanide (Th-PH₂), a terminal thorium(IV)-phosphinidene (Th=PH), a parent dithorium(IV)-phosphinidiide (Th-P(H)-Th) and a discrete actinide-phosphido complex under ambient conditions (Th=P=Th). Although thorium is traditionally considered to have dominant 6d-orbital contributions to its bonding, contrasting to majority 5f-orbital character for uranium, computational analyses suggests that the bonding of thorium can be more nuanced, in terms of 5f- versus 6d-orbital composition and also significant involvement of the 7s-orbital and how this affects the balance of 5f- versus 6d-orbital bonding character.

The nature of chemical bonding in actinide and lanthanide ferrocyanides determined by X-ray absorption spectroscopy and density functional theory

The electronic properties of actinide cations are of fundamental interest to describe intramolecular interactions and chemical bonding in the context of nuclear waste reprocessing or direct storage. The 5f and 6d orbitals are the first partially or totally vacant states in these elements, and the nature of the actinide ligand bonds is related to their ability to overlap with ligand orbitals. Because of its chemical and orbital selectivities, X-ray absorption spectroscopy (XAS) is an effective probe of actinide species frontier orbitals and for understanding actinide cation reactivity toward chelating ligands. The soft X-ray probes of the light elements provide better resolution than actinide L3-edges to obtain electronic information from the ligand. Thus coupling simulations to experimental soft X-ray spectral measurements and complementary quantum chemical calculations yields quantitative information on chemical bonding. In this study, soft X-ray XAS at the K-edges of C and N, and the L2,3-edges of Fe was used to investigate the electronic structures of the well-known ferrocyanide complexes K4Fe(II)(CN)6, thorium hexacyanoferrate Th(IV)Fe(II)(CN)6, and neodymium hexacyanoferrate KNd(III)Fe(II)(CN)6. The soft X-ray spectra were simulated based on quantum chemical calculations. Our results highlight the orbital overlapping effects and atomic effective charges in the Fe(II)(CN)6 building block. In addition to providing a detailed description of the electronic structure of the ferrocyanide complex (K4Fe(II)(CN)6), the results strongly contribute to confirming the actinide 5f and 6d orbital oddity in comparison to lanthanide 4f and 5d.

The roles of 4f- and 5f-orbitals in bonding: a magnetochemical, crystal field, density functional theory, and multi-reference wavefunction study

The electronic structures of 4f(3)/5f(3) Cp''3M and Cp''3M·alkylisocyanide complexes, where Cp'' is 1,3-bis-(trimethylsilyl)cyclopentadienyl, are explored with a focus on the splitting of the f-orbitals, which provides information about the strengths of the metal-ligand interactions. While the f-orbital splitting in many lanthanide complexes has been reported in detail, experimental determination of the f-orbital splitting in actinide complexes remains rare in systems other than halide and oxide compounds, since the experimental approach, crystal field analysis, is generally significantly more difficult for actinide complexes than for lanthanide complexes. In this study, a set of analogous neodymium(iii) and uranium(iii) tris-cyclopentadienyl complexes and their isocyanide adducts was characterized by electron paramagnetic resonance (EPR) spectroscopy and magnetic susceptibility. The crystal field model was parameterized by combined fitting of EPR and susceptibility data, yielding an accurate description of f-orbital splitting. The isocyanide derivatives were also studied using density functional theory, resulting in f-orbital splitting that is consistent with crystal field fitting, and by multi-reference wavefunction calculations that support the electronic structure analysis derived from the crystal-field calculations. The results highlight that the 5f-orbitals, but not the 4f-orbitals, are significantly involved in bonding to the isocyanide ligands. The main interaction between isocyanide ligand and the metal center is a σ-bond, with additional 5f to π* donation for the uranium complexes. While interaction with the isocyanide π*-orbitals lowers the energies of the 5fxz(2) and 5fyz(2)-orbitals, spin-orbit coupling greatly reduces the population of 5fxz(2) and 5fyz(2) in the ground state.

Emergence of comparable covalency in isostructural cerium(iv)- and uranium(iv)-carbon multiple bonds

We report comparable levels of covalency in cerium- and uranium-carbon multiple bonds in the iso-structural carbene complexes [M(BIPMTMS)(ODipp)2] [M = Ce (1), U (2), Th (3); BIPMTMS = C(PPh2NSiMe3)2; Dipp = C6H3-2,6-iPr2] whereas for M = Th the M[double bond, length as m-dash]C bond interaction is much more ionic. On the basis of single crystal X-ray diffraction, NMR, IR, EPR, and XANES spectroscopies, and SQUID magnetometry complexes 1-3 are confirmed formally as bona fide metal(iv) complexes. In order to avoid the deficiencies of orbital-based theoretical analysis approaches we probed the bonding of 1-3 via analysis of RASSCF- and CASSCF-derived densities that explicitly treats the orbital energy near-degeneracy and overlap contributions to covalency. For these complexes similar levels of covalency are found for cerium(iv) and uranium(iv), whereas thorium(iv) is found to be more ionic, and this trend is independently found in all computational methods employed. The computationally determined trends in covalency of these systems of Ce ∼ U > Th are also reproduced in experimental exchange reactions of 1-3 with MCl4 salts where 1 and 2 do not exchange with ThCl4, but 3 does exchange with MCl4 (M = Ce, U) and 1 and 2 react with UCl4 and CeCl4, respectively, to establish equilibria. This study therefore provides complementary theoretical and experimental evidence that contrasts to the accepted description that generally lanthanide-ligand bonding in non-zero oxidation state complexes is overwhelmingly ionic but that of uranium is more covalent.

Oxidation of phenyl and hydride ligands of bis(pentamethylcyclopentadienyl)hafnium derivatives by nitrous oxide via selective oxygen atom transfer reactions: insights from quantum chemistry calculations

The mechanisms for the oxidation of phenyl and hydride ligands of bis(pentamethylcyclopentadienyl)hafnium derivatives (Cp* = η(5)-C5Me5) by nitrous oxide via selective oxygen atom transfer reactions have been systematically studied by means of density functional theory (DFT) calculations. On the basis of the calculations, we investigated the original mechanism proposed by Hillhouse and co-workers for the activation of N2O. The calculations showed that the complex with an initial O-coordination of N2O to the coordinatively unsaturated Hf center is not a local minimum. Then we proposed a new reaction mechanism to investigate how N2O is activated and why N2O selectively oxidize phenyl and hydride ligands of . Frontier molecular orbital theory analysis indicates that N2O is activated by nucleophilic attack by the phenyl or hydride ligand. Present calculations provide new insights into the activation of N2O involving the direct oxygen atom transfer from nitrous oxide to metal-ligand bonds instead of the generally observed oxygen abstraction reaction to generate metal-oxo species.

Ligand K-edge XAS, DFT, and TDDFT analysis of pincer linker variations in Rh(i) PNP complexes: reactivity insights from electronic structure

Ligand K-edge XAS and DFT studies of ligand variations in Rh(i) pincer complexes and correlations to small molecule reactivity.

Evidence for 5d-σ and 5d-π covalency in lanthanide sesquioxides from oxygen K-edge X-ray absorption spectroscopy

The electronic structure in the complete series of stable lanthanide sesquioxides, Ln₂O₃ (Ln = La to Lu, except radioactive Pm), has been evaluated using oxygen K-edge X-ray absorption spectroscopy with a scanning transmission X-ray microscope (STXM).

Highly Dense Isolated Metal Atom Catalytic Sites: Dynamic Formation and In Situ Observations

Atomically dispersed noble-metal catalysts with highly dense active sites are promising materials with which to maximise metal efficiency and to enhance catalytic performance; however, their fabrication remains challenging because metal atoms are prone to sintering, especially at a high metal loading. A dynamic process of formation of isolated metal atom catalytic sites on the surface of the support, which was achieved starting from silver nanoparticles by using a thermal surface-mediated diffusion method, was observed directly by using in situ electron microscopy and in situ synchrotron X-ray diffraction. A combination of electron microscopy images with X-ray absorption spectra demonstrated that the silver atoms were anchored on five-fold oxygen-terminated cavities on the surface of the support to form highly dense isolated metal active sites, leading to excellent reactivity in catalytic oxidation at low temperature. This work provides a general strategy for designing atomically dispersed noble-metal catalysts with highly dense active sites.

Stabilization of MIV = Ti, Zr, Hf, Ce, and Th using a selenium bis(phenolate) ligand

We report M(iv) M = Ti, Zr, Hf, Ce, and Th, complexes of a selenium bis(phenolate) ligand, 2,2'-selenobis(4,6-di-tert-butylphenol), (H(2)(Ar)OSeO), 1. Reaction of Ti(NEt(2))(4) with two equivalents of affords Ti((Ar)OSeO)(2), 2. Salt metathesis of ZrCl(4) and HfCl(4) with two equivalents of Na(2)(Ar)OSeO produces Zr((Ar)OSeO)(2)(THF), 3, and Hf((Ar)OSeO)(2)(THF), 4, respectively. Protonolysis of ThCl[N(SiMe(3))(2)](3) with two equivalents of yields Th((Ar)OSeO)(2)(THF)(2), 5. Salt metathesis of Ce(OTf)(3) and two equivalents of Na(2)(Ar)OSeO produces [Na(THF)(3)][Ce((Ar)OSeO)(2)], which was oxidized in situ using 0.5 equivalents of I(2) to yield the diamagnetic Ce(iv) product, Ce((Ar)OSeO)(2)(THF)(2), 6. Addition of 2,2'-bipyridyl to forms Ce((Ar)OSeO)(2)(bipy), 6a. Each diamagnetic complex was characterized using (1)H, (13)C, and (77)Se NMR and IR spectroscopy and the structures of 2-6a were established with X-ray crystallography. Electrochemical measurements using cyclic voltammetry on complexes 2, 5, and 6a re also reported.

Using solution- and solid-state S K-edge X-ray absorption spectroscopy with density functional theory to evaluate M-S bonding for MS4(2-) (M = Cr, Mo, W) dianions

Herein, we have evaluated relative changes in M-S electronic structure and orbital mixing in Group 6 MS4(2-) dianions using solid- and solution-phase S K-edge X-ray absorption spectroscopy (XAS; M = Mo, W), as well as density functional theory (DFT; M = Cr, Mo, W) and time-dependent density functional theory (TDDFT) calculations. To facilitate comparison with solution measurements (conducted in acetonitrile), theoretical models included gas-phase calculations as well as those that incorporated an acetonitrile dielectric, the latter of which provided better agreement with experiment. Two pre-edge features arising from S 1s → e* and t electron excitations were observed in the S K-edge XAS spectra and were reasonably assigned as (1)A1 → (1)T2 transitions. For MoS4(2-), both solution-phase pre-edge peak intensities were consistent with results from the solid-state spectra. For WS4(2-), solution- and solid-state pre-edge peak intensities for transitions involving e* were equivalent, while transitions involving the t orbitals were less intense in solution. Experimental and computational results have been presented in comparison to recent analyses of MO4(2-) dianions, which allowed M-S and M-O orbital mixing to be evaluated as the principle quantum number (n) for the metal valence d orbitals increased (3d, 4d, 5d). Overall, the M-E (E = O, S) analyses revealed distinct trends in orbital mixing. For example, as the Group 6 triad was descended, e* (π*) orbital mixing remained constant in the M-S bonds, but increased appreciably for M-O interactions. For the t orbitals (σ* + π*), mixing decreased slightly for M-S bonding and increased only slightly for the M-O interactions. These results suggested that the metal and ligand valence orbital energies and radial extensions delicately influenced the orbital compositions for isoelectronic ME4(2-) (E = O, S) dianions.

The Renaissance of Non-Aqueous Uranium Chemistry

Prior to the year 2000, non-aqueous uranium chemistry mainly involved metallocene and classical alkyl, amide, or alkoxide compounds as well as established carbene, imido, and oxo derivatives. Since then, there has been a resurgence of the area, and dramatic developments of supporting ligands and multiply bonded ligand types, small-molecule activation, and magnetism have been reported. This Review 1) introduces the reader to some of the specialist theories of the area, 2) covers all-important starting materials, 3) surveys contemporary ligand classes installed at uranium, including alkyl, aryl, arene, carbene, amide, imide, nitride, alkoxide, aryloxide, and oxo compounds, 4) describes advances in the area of single-molecule magnetism, and 5) summarizes the coordination and activation of small molecules, including carbon monoxide, carbon dioxide, nitric oxide, dinitrogen, white phosphorus, and alkanes.

Triamidoamine uranium(IV)-arsenic complexes containing one-, two- and threefold U-As bonding interactions

To further our fundamental understanding of the nature and extent of covalency in uranium-ligand bonding, and the benefits that this may have for the design of new ligands for nuclear waste separation, there is burgeoning interest in the nature of uranium complexes with soft- and multiple-bond-donor ligands. Despite this, there have so far been no examples of structurally authenticated molecular uranium-arsenic bonds under ambient conditions. Here, we report molecular uranium(IV)-arsenic complexes featuring formal single, double and triple U-As bonding interactions. Compound formulations are supported by a range of characterization techniques, and theoretical calculations suggest the presence of polarized covalent one-, two- and threefold bonding interactions between uranium and arsenic in parent arsenide [U-AsH2], terminal arsinidene [U=AsH] and arsenido [U≡AsK2] complexes, respectively. These studies inform our understanding of the bonding of actinides with soft donor ligands and may be of use in future ligand design in this area.

Impact of Coordination Geometry, Bite Angle, and Trans Influence on Metal-Ligand Covalency in Phenyl-Substituted Phosphine Complexes of Ni and Pd

Despite the long-standing use of phosphine and diphosphine ligands in coordination chemistry and catalysis, questions remain as to their effects on metal-ligand bonding in transition metal complexes. Here we report ligand K-edge XAS, DFT, and TDDFT studies aimed at quantifying the impact of coordination geometry, diphosphine bite angle, and phosphine trans influence on covalency in M-P and M-Cl bonds. A series of four-coordinate NiCl2 and PdCl2 complexes containing PPh3 or Ph2P(CH2)nPPh2, where n = 1 (dppm), 2 (dppe), 3 (dppp), and 4 (dppb), was analyzed. The XAS data revealed that changing the coordination geometry from tetrahedral in Ni(PPh3)2Cl2 (1) to square planar in Ni(dppe)Cl2 (2) more than doubles the intensity of pre-edge features assigned to Ni-P and Ni-Cl 1s → σ* transitions. By way of comparison, varying the diphosphine in Pd(dppm)Cl2 (4), Pd(dppp)Cl2 (6), and Pd(dppb)Cl2 (7) yielded Pd-P 1s → σ* transitions with identical intensities, but a 10% increase was observed in the P K-edge XAS spectrum of Pd(dppe)Cl2 (5). A similar observation was made when comparing Ni(dppe)Cl2 (2) to Ni(dppp)Cl2 (3), and DFT and TDDFT calculations corroborated XAS results obtained for both series. Comparison of the spectroscopic and theoretical results to the diphosphine structures revealed that changes in M-P covalency were not correlated to changes in bite angles or coordination geometry. As a final measure, P and Cl K-edge XAS data were collected on trans-Pd(PPh3)2Cl2 (8) for comparison to the cis diphosphine complex Pd(dppe)Cl2 (5). Consistent with phosphine's stronger trans influence compared to chloride, a 35% decrease in the intensity of the Pd-P 1s → σ* pre-edge feature and a complementary 34% increase in Pd-Cl 1s → σ* feature was observed for 8 (trans) compared to 5 (cis). Overall, the results reveal how coordination geometry, ligand arrangement, and diphosphine structure affect covalent metal-phosphorus and metal-chloride bonding in these late transition metal complexes.

A computational study on the complexation of Np(V) with N,N,N',N'-tetramethyl-3-oxa-glutaramide (TMOGA) and its carboxylate analogs

Density functional theory has been used to study the geometries and relative stabilities of the complexes of NpO2(+) with the title compounds (L), including TMOGA, deprotonated N,N'-dimethyl-3-oxa-glutaramic acid (DMOGA) and their deprotonated oxydiacetic analog (ODA). Our calculations suggest that the complexes where the ligands appear as tridentate chelators are more stable than as bidentate ones, and the substitution of the amide group by carboxylate favors the formation of the complexes. Thermodynamically the 1 : 2 complex (Np-L2) is more favorable than the 1 : 1 complex (Np-L) in the cases of TMOGA and DMOGA, but not for the ODA anion. Taking into account the solvation effect of water, the 1 : 2 complex is more favorable than the 1 : 1 complex for all of the three ligands, though the reaction enthalpy decreases compared to that in the gas phase, and the formation of Np-(TMOGA)2 from Np-TMOGA is roughly a thermal neutral process. The strength of the Np=O bond is weakened upon the coordination of ligands to Np(V) and the increase of the negative charge on the ligand (-1e for deprotonated DMOGA and -2e for deprotonated ODA). The Quantum Theory of Atoms-in-Molecules (QTAIM) was used here to analyze the bonding mode of NpO2(+)-Lx (x = 1, 2) and to compare the bond order data.

Hydroxypyridinonate complex stability of group (IV) metals and tetravalent f-block elements: the key to the next generation of chelating agents for radiopharmaceuticals

The solution thermodynamics of the water-soluble complexes formed between 3,4,3-LI(1,2-HOPO) and Zr(IV) or Pu(IV) were investigated to establish the metal coordination properties of this octadentate chelating agent. Stability constants log β110 = 43.1 ± 0.6 and 43.5 ± 0.7 were determined for [Zr(IV)(3,4,3-LI(1,2-HOPO))] and [Pu(IV)(3,4,3-LI(1,2-HOPO))], respectively, by spectrophotometric competition titrations against Ce(IV). Such high thermodynamic stabilities not only confirm the unparalleled Pu(IV) affinity of 3,4,3-LI(1,2-HOPO) as a decorporation agent but also corroborate the great potential of hydroxypyridinonate ligands as new (89)Zr-chelating platforms for immuno-PET applications. These experimental values are in excellent agreement with previous estimates and are discussed with respect to ionic radius and electronic configuration, in comparison with those of Ce(IV) and Th(IV). Furthermore, a liquid chromatography assay combined with mass spectrometric detection was developed to probe the separation of the neutral [M(IV)(3,4,3-LI(1,2-HOPO))] complex species (M = Zr, Ce, Th, and Pu), providing additional insight into the coordination differences between group IV and tetravalent f-block metals and on the role of d and f orbitals in bonding interactions.

Theoretical modeling of the uranium 4f XPS for U(VI) and U(IV) oxides

A rigorous study is presented of the physical processes related to X-Ray photoelectron spectroscopy, XPS, in the 4f level of U oxides, which, as well as being of physical interest in themselves, are representative of XPS in heavy metal oxides. In particular, we present compelling evidence for a new view of the screening of core-holes that extends prior understandings. Our analysis of the screening focuses on the covalent mixing of high lying U and O orbitals as opposed to the, more common, use of orbitals that are nominally pure U or pure O. It is shown that this covalent mixing is quite different for the initial and final, core-hole, configurations and that this difference is directly related to the XPS satellite intensity. Furthermore, we show that the high-lying U d orbitals as well as the U(5f) orbital may both contribute to the core-hole screening, in contrast with previous work that has only considered screening through the U(5f) shell. The role of modifying the U-O interaction by changing the U-O distance has been investigated and an unexpected correlation between U-O distance and XPS satellite intensity has been discovered. The role of flourite and octahedral crystal structures for U(IV) oxides has been examined and relationships established between XPS features and the covalent interactions in the different structures. The physical views of XPS satellites as arising from shake processes or as arising from ligand to metal charge transfers are contrasted; our analysis provides strong support that shake processes give a more fundamental physical understanding than charge transfer. Our theoretical studies are based on rigorous, strictly ab initio determinations of the electronic structure of embedded cluster models of U oxides with formal U(VI) and U(IV) oxidation states. Our results provide a foundation that makes it possible to establish quantitative relationships between features of the XPS spectra and materials properties.

High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory

X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively probing the local structure around an absorbing atomic species in molecules and materials. When applied to heavy elements, however, the quantitative interpretation can be challenging due to the intrinsic spectral broadening arising from the decrease in the core-hole lifetime. In this work we have used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second order Douglas-Kroll-Hess (DKH2) scalar relativistic approximations. We have found that both the predicted energies and intensities are in excellent agreement with experiment, independent of the functional used. The model chosen to account for relativistic effects also has little impact on the calculated spectra. This study provides an important calibration set for future applications of molybdenum HERFD-XAS to complex catalytic systems.

Magnetic properties and chiral states of a trimetallic uranium complex

The magnetic properties of the triangular molecular nanomagnet [UO2L]3 (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) have been investigated through electron paramagnetic resonance spectroscopy, high-field magnetization and susceptibility measurements. The experimental findings are well reproduced by a microscopic model including exchange interactions and local crystal fields. These results show that [UO2L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. The non-axial character of single-ion crystal fields leads to quantum tunneling of the noncollinear magnetization in the presence of a magnetic field applied perpendicularly to the triangle plane.