DyIII Complexes Research Articles

A Dinuclear Dysprosium Complex as an Air-Stable and Recyclable Catalyst: Applications in the Deacetylation of Carbohydrate, Aliphatic, and Aromatic Molecules.

Two dinuclear DyIII complexes, [Dy2 (hmb)2 (OTf)2 (H2 O)4 ]⋅HOTf⋅2 THF (A⋅HOTf⋅2 THF) and [Dy2 (hmi)3 (H2 O)2 ]⋅2 HOTf (B⋅2 HOTf), have been synthesized by the reaction of Dy(OTf)3 and the Schiff-base ligands H2 hmb (N'-(2-hydroxy-3-methoxybenzylidene)benzohydrazide) or H2 hmi ((2-hydroxy-3-methoxyphenyl)methylene isonicotinohydrazine). Disarmed glycosyl trichloroacetimidates can be activated by complex A in the synthesis of 1,2-trans-glycosides with primary and secondary acceptors. This method offers an efficient route to selectively deacetylated monosaccharides and disaccharides in high yields and a green catalyst that can be easily recycled and reused.

A series of CuII–LnIII complexes of an N2O3 donor asymmetric ligand and a possible CuII–TbIII SMM candidate in no bias field

Among four isostructural heterometallic CuII–LnIII complexes (Ln = Tb, Dy, Ho or Er) of an N2O3 donor asymmetric ligand, only the CuII–TbIII complex shows SMM behavior at zero bias field but at applied bias field both the CuII–TbIII and CuII–DyIII complexes show SMM behavior.

Slow magnetic relaxation in Dy2 and Dy4 complexes of a versatile, trifunctional polydentate N,O-ligand.

A tridentate ligand LH3 (C11H13N3O4) comprising o-vanillin, hydrazone and oxime donor groups has been employed to prepare a new class of di- and tetranuclear LnIII complexes. The reaction of LH3 with Ln(NO3)3·xH2O in the presence of a suitable base yields the dinuclear DyIII complex [Dy2(LH2)4(CH3OH)][NO3]2 (1) and the tetranuclear complexes [Dy4(LH)4(LH2)2(OH)2]·2H2O (2) and [Gd4(LH)4(LH2)2(OMe)2]·nH2O, (3). In these complexes, LH3 is either monodeprotonated (1) or a mixture of mono- and doubly-deprotonated ligands (2 and 3) binding lanthanide ions via Ndiazine, Ohydrazone, and Ovanillin donors, while the remaining vacant coordination sites are occupied by OMeOH (1), Ohydroxide (2) and methoxides (3). DC magnetic susceptibility studies on the isotropic tetranuclear GdIII complex (3) reveal weak antiferromagnetic exchange interactions between the LnIII ions. AC studies reveal that the dinuclear complex (1) exhibits field-induced slow relaxation of magnetization with Ueff = 43.4 K, whereas 2 is a single molecule magnet, exhibiting slow relaxation of magnetization under zero field below 18 K, which is modelled using a combination of Orbach (Ueff/kB = 26.7 K) and Raman relaxation processes.

Fine-tuning the type of equatorial donor atom in pentagonal bipyramidal Dy(iii) complexes to enhance single-molecule magnet properties.

A family of new structurally manipulable pentagonal-bipyramidal (PBP) DyIII SMMs, with formulas [Dy(Hbpen)(Cl)3] (1), [Dy(Hbpen)Cl(OPhBr2NO2)2] (2), [Dy(Hbpen)(OPhCl2NO2)3] (3) and [Dy(Mbpen)(Cl)3] (1CH3), were controllably prepared based on a H-substituted amine-based ligand N,N'-bis(2-pyridylmethyl)-ethylenediamine (Hbpen) or a CH3-substituted amine-based ligand N,N'-dimethyl-N,N'-bis(2-pyridylmethyl)-ethylenediamine (Mbpen) and are compared with the reported imine-based DyIII analogues (1'-3'). Upon fine-modulating the type of nitrogen donor on the pentagon plane, the electronic effect is efficiently implemented to significantly modify the magnetic anisotropy and SMM behavior of PBP complexes. Notably, the amine-based 2 shows a three-fold improved energy barrier and an observable hysteresis opening up to 3 K. 1 and 1CH3 exhibit slower relaxation and enhanced anisotropy compared to the imine-based analogue, accompanied by the reorientation of magnetic easy axes. Conversely, poor magnetic properties are observed in 3 after the reduction of imine. The changes in SMM behavior and uniaxial anisotropies are rationalized by both experimental and theoretical studies. The H-substituted amine has formally a larger magnitude of negative charge than imine due to the polarized N-H σ bond. However the repulsion generated by the sp3 N of amine towards the DyIII ion is also affected by the orientation of lone pair electrons. The present work provides a feasible way to rationally optimize the SMM performance of DyIII complexes, highlighting the importance of the electronic properties of an equatorial donor in controlling the quantum tunneling and the magnetic relaxation of PBP DyIII-SMMs.

Mononuclear Dysprosium(III) Complexes with Triphenylphosphine Oxide Ligands: Controlling the Coordination Environment and Magnetic Anisotropy

We report the synthesis, structural and magnetic characterization of five mononuclear DyIII ion complexes using triphenylphosphine oxide as a monodentate ligand. They have formulae [DyIII(OPPh3)3(NO3)3] (1), [DyIII(OPPh3)4(NO3)2](NO3) (2), [DyIII(OPPh3)3Cl3] (3), [DyIII(OPPh3)4Cl2]Cl (4) and [DyIII(OPPh3)4Cl2](FeCl4) (5). These complexes are characterized using single crystal X-ray diffraction, which revealed that each complex has a unique coordination environment around the DyIII ion, which results in varying dynamic magnetic behavior. Ab initio calculations are performed to rationalize the observed magnetic behavior and to understand the effect that the ligand and coordination geometry around the DyIII ion has on the single-molecule magnet (SMM) behavior. In recent years, seven coordinate DyIII complexes possessing pseudo ~D5h symmetry are found to yield attractive blocking temperatures for the development of new SMM complexes. However, here we show that the strength of the donor ligand plays a critical role in determining the effective energy barrier and is not simply dependent on the geometry and the symmetry around the DyIII ion. Seven coordinate molecules possessing pseudo D5h symmetry with strong equatorial ligation and weak axial ligation are found to be inferior, exhibiting no SMM characteristics under zero-field conditions. Thus, this comprehensive study offers insight on improving the blocking temperature of mononuclear SMMs.

Exploring Tuning of Structural and Magnetic Properties by Modification of Ancillary β-Diketonate Co-ligands in a Family of Near-Linear Tetranuclear DyIII Complexes

Three tetranuclear DyIII complexes, [Dy4(LH)2(CH3OH)4(acac)6] (1), [Dy4(LH)2(CH3OH)4(hmacac)6]·2CH3OH (2), and [Dy4(LH)2(CH3OH)4(dpacac)6]·2CHCl3·2CH3OH·2H2O (3), have been synthesized and characterized [LH4 = (2E,N′E)-N′-(2,3-dihydroxybenzylidene)-2-(hydroxyimino)propanehydrazide; acacH = acetylacetone; hmacacH = 2,2,6,6-tetramethyl-3,5-heptanedione; dpacacH = dibenzoylmethane]. The structural elucidation of these complexes reveals two types of DyIII centers in terms of the number of ancillary β-diketonate co-ligands coordinated to the metal centers. Detailed magnetic studies have been carried out on 1–3 which reveal a slow relaxation of magnetization at low temperatures. The relaxation of complexes 2 and 3 is distributed in three temperature ranges: lower temperature process, transition range, and higher temperature process. In the higher temperature range, the best fitting of the data for 2 yields τ0 = (6.3 ± 3.6) × 10–6 s and Ueff = (23.8 ± 4.0) K, and for 3, τ0 = (9.4 ± 5.9) × 10–6 s, Ueff = (29.0 ± ...

Manipulating the Relaxation of Quasi- D4 d Dysprosium Compounds through Alternation of the O-Donor Ligands.

Three mononuclear DyIII complexes with the same auxiliary ligand Lz (2,4-diamino-6-pyridyl-1,3,5-triazine), [Dy(TTA)3Lz] (1Dy) (TTA = 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedionate), [Dy(acac)3Lz]·CH3OH·0.5H2O (2Dy) (acac = acetylacetonate), and [Dy(MQ)2Lz2]Br·CH3OH (3Dy) (HMQ = 2-methyl-8-quinolinol), have been synthesized through alteration of the ligands containing O donors. In all three complexes, the DyIII ions are eight-coordinate and submitted to pseudo- D4 d symmetry in the first coordination sphere. It is noteworthy that the TTA ligands in 1Dy are easily substituted by other bidentate capping ligands with O donors, leading to distinct magnetic properties, which were studied experimentally and via ab initio calculations. All three complexes were found to exhibit single-molecule magnet behavior with Ueff of 22 cm-1 (1Dy), 112 cm-1 (2Dy), and 56 cm-1 (3Dy) under zero applied dc field. Complex 1Dy demonstrates inferior SIM properties compared with 2Dy and 3Dy, which can be attributed to the strong electron-withdrawing effects of TTA ligands, as confirmed by theoretical calculations. However, butterfly-shaped magnetic hysteresis in 1Dy and 3Dy was observed at 1.9 K, while not in 2Dy.

Structure and magnetism of two chair-shaped hexanuclear dysprosium(iii) complexes exhibiting slow magnetic relaxation.

Two novel hexanuclear DyIII complexes with polyhydroxy Schiff-base ligands, [Dy6(L1)4(μ3-OH)4(MeOH)4]Cl2·2MeOH·2MeCN (1) and [Dy6(HL2)2(μ3-OH)2(μ3-OCH3)2(piv)10(MeOH)2] (2) (H3L1 = N,N′-bis(3-methoxysalicylidene)(propylene-2-ol)-1,3-diamine, H3L2 = 2,3-dihydroxypropylimino)methyl)-6-methoxyphenol, piv = pivalate), have been prepared under solvothermal conditions and structurally characterized by single-crystal X-ray diffraction, elemental analyses, thermal analyses, and IR spectroscopy. Each of the hexanuclear complexes is constructed with Dy3 triangular motifs as building blocks, and the six DyIII ions are arranged in a chair-shaped conformation. Variable-temperature magnetic susceptibility measurements in the temperature range of 2–300 K indicate dominant ferromagnetic exchange interactions between the DyIII ions in the complexes. Both complexes exhibit slow magnetic relaxation behavior.

Slow Magnetic Relaxation and Single-Molecule Toroidal Behaviour in a Family of Heptanuclear {CrIII LnIII6 } (Ln=Tb, Ho, Er) Complexes.

The synthesis, magnetic properties, and theoretical studies of three heterometallic {CrIII LnIII6 } (Ln=Tb, Ho, Er) complexes, each containing a metal topology consisting of two Ln3 triangles connected via a CrIII linker, are reported. The {CrTb6 } and {CrEr6 } analogues display slow relaxation of magnetization in a 3000 Oe static magnetic field. Single-crystal measurements reveal opening up of the hysteresis loop for {CrTb6 } and {CrHo6 } molecules at low temperatures. Ab initio calculations predict toroidal magnetic moments in the two Ln3 triangles, which are found to couple, stabilizing a con-rotating ferrotoroidal ground state in Tb and Ho examples and extend the possibility of observing toroidal behaviour in non DyIII complexes for the first time.

Slow Magnetic Relaxation and Single‐Molecule Toroidal Behaviour in a Family of Heptanuclear {CrIIILnIII6} (Ln=Tb, Ho, Er) Complexes

AbstractThe synthesis, magnetic properties, and theoretical studies of three heterometallic {CrIIILnIII6} (Ln=Tb, Ho, Er) complexes, each containing a metal topology consisting of two Ln3 triangles connected via a CrIII linker, are reported. The {CrTb6} and {CrEr6} analogues display slow relaxation of magnetization in a 3000 Oe static magnetic field. Single‐crystal measurements reveal opening up of the hysteresis loop for {CrTb6} and {CrHo6} molecules at low temperatures. Ab initio calculations predict toroidal magnetic moments in the two Ln3 triangles, which are found to couple, stabilizing a con‐rotating ferrotoroidal ground state in Tb and Ho examples and extend the possibility of observing toroidal behaviour in non DyIII complexes for the first time.

Stepwise Investigation of the Influences of Steric Groups versus Counterions To Target Cu/Dy Complexes

From an investigation of varying the steric bulk of a flexible ligand, we have produced a family of structures using similar reaction conditions. Even small changes from a hydrogen atom to a methyl to an ethyl group on the ligand influences the structural outcome, which can also be steered by the nature of the metal source. We employed Schiff base ligands by combining o-vanillin and three different 2-amino-1,3-propandiol units, leading to H3L1 (R = hydrogen), H3L2 (R = methyl), and H3L3 (R = ethyl). The differing nuclearities of the three clusters, 1–3, originate mainly from the steric influence, while this effect is not seen in complexes 4–6, where the general butterfly motif is maintained. We present here the synthesis, crystal structures, and magnetic properties of six new CuII-LnIII complexes, providing valuable insight into future synthetic directions. The topological part includes a table of all CuII–DyIII complexes with nuclearities higher than four and their topological motif. The investigation of...

Axial Ligand Field in D4d Coordination Symmetry: Magnetic Relaxation of Dy SMMs Perturbed by Counteranions.

A series of mononuclear DyIII complexes with the general formula [DyLz2(salicylaldehyde)2]·X·solvent (Lz = 6-pyridin-2-yl[1,3,5]triazine-2,4-diamine; X = OH- (1·OH), Cl- (2·Cl), Br- (3·Br)) have been synthesized using mixed salicylaldehyde/pyridinyl-triazine ligands and discriminative counteranions. The DyIII ion in these three complexes resides in a similar D4d coordination geometry with counteranions perturbing the coordination environment and bond lengths and angles in the lattice. Magnetostructural studies reveal that the asymmetric distribution of salicylaldehyde/pyridinyl-triazine ligands and the presence of discriminative counteranions result in the coexistence of large anisotropy and quantum tunneling of magnetization. The magnetic anisotropy is dominated by the axial ligand field with short Dy-Osali distances and large ∠Osali-Dy-Osali angles, while the quantum tunneling relaxation is probably dictated by the π-π stacking of the Lz ligands, which induces an axial constriction of the coordinating plane. Ab initio calculations substantiate the diversity of the magnetic behaviors in these complexes and highlight the importance of axial ligand field with short Dy-Osali distances, large ∠Osali-Dy-Osali angles and less ligand stacking in these pseudo-D4d-symmetrical single-molecule magnets.

Elucidation of 1H NMR Paramagnetic Features of Heterotrimetallic Lanthanide(III)/Manganese(III) 12-MC-4 Complexes.

The paramagnetic one-dimensional 1H NMR spectra of twelve LnIIINaI(OAc)4[12-MCMnIII(N)shi-4] complexes, where LnIII is PrIII-YbIII (except PmIII) and YIII, are reported. Their solid-state isostructural nature is confirmed in methanol-d4 solution, as a similar pattern in the 1H NMR spectra is observed along the series. Notably, a relatively well-resolved spectrum is reported for the GdIII complex. The chemical shift data are analyzed using the "all lanthanides" method, and the Fermi contact and pseudo-contact contributions are calculated for the lanthanide-induced shift (LIS). For the TbIII-YbIII complexes, the pseudo-contact contributions are typically 1 order of magnitude higher than the Fermi contact contributions; however, for the GdIII complex, the Fermi contact is the main contribution to the paramagnetic chemical shift. For the methyl protons of the axial acetate (-OAc) ligands, the LIS is opposite in sign, with respect to that of the aromatic salicylhydroximate (shi3-) protons, because of structural rearrangements that occur upon dissociation of the NaI cation in solution. The calculated crystal field parameters (BLn) for the TbIII (360 cm-1), DyIII (250 cm-1), HoIII (380 cm-1), ErIII (410 cm-1), TmIII (620 cm-1), and YbIII (380 cm-1) complexes are not constant, likely as a consequence of the inaccuracy of the Bleaney's constants and, to a smaller extent, the small structural changes that occur in solution. Overall, the metallacrown scaffold retains structural integrity and similarity in solution for the entire series; however, small structural features, which do not affect the overall similarity, do likely occur.

A chiral mononuclear DyIII complex with field-induced single molecule magnet behavior

A chiral mononuclear DyIII complex, formulated [Dy(PNO)6(H2O)2]Cl3 (1) (PNO=pyridine-N-oxide), has been prepared by using an achiral ligand through spontaneous resolution. Structure analyses show that complex 1 consists of a DyIII mononuclear unit and such units interact with each other by hydrogen bonds to form helical chains along a axis. The crystals of 1 are optically active and opposite Cotton effects can be observed in the circular dichroism (CD) spectra. Magnetic studies reveal that complex 1 exhibits field-induced single molecule magnet behavior with an energy barrier of 49K.

Role of the Diamagnetic Zinc(II) Ion in Determining the Electronic Structure of Lanthanide Single-Ion Magnets.

Four complexes containing DyIII and PrIII ions and their LnIII -ZnII analogs have been synthesized in order to study the influence that a diamagnetic ZnII ion has on the electronic structure and hence, the magnetic properties of the DyIII and PrIII single ions. Single-crystal X-ray diffraction revealed the molecular structures as [DyIII (HL)2 (NO3 )3 ] (1), [PrIII (HL)2 (NO3 )3 ] (2), [ZnII DyIII (L)2 (CH3 CO2 )(NO3 )2 ] (3) and [ZnII2 PrIII (L)2 (CH3 CO2 )4 (NO3 )] (4) (where HL=2-methoxy-6-[(E)-phenyliminomethyl]phenol). The dc and ac magnetic data were collected for all four complexes. Compounds 1 and 3 display frequency dependent out-of-phase susceptibility signals (χM "), which is a characteristic signature for a single-molecule magnet (SMM). Although 1 and 3 are chemically similar, a fivefold increase in the anisotropic barrier (Ueff ) is observed experimentally for 3 (83 cm-1 ), compared to 1 (16 cm-1 ). To rationalize the larger anisotropic barrier (1 vs. 3), detailed ab initio calculations were performed. Although the ground state Kramer's doublet in both 1 and 3 are axial in nature (gzz =19.443 for 1 and 18.82 for 3), a significant difference in the energy gap (Ueff ) between the ground and first excited Kramer's doublet is calculated. This energy gap is governed by the electrostatic repulsion between the DyIII ion and the additional charge density found for the phenoxo bridging ligand in 3. This extra charge density was found to be a consequence of the presence of the diamagnetic ZnII ion present in the complex. To explore the influence of diamagnetic ions on the magnetic properties further, previously reported and structurally related Zn-DyIII complexes were analyzed. These structurally analogous complexes unambiguously suggest that the electrostatic repulsion is found to be maximal when the Zn-O-Dy-O dihedral angle is small, which is an ideal condition to maximize the anisotropic barrier in DyIII complexes.

A Trinuclear Radical‐Bridged Lanthanide Single‐Molecule Magnet

AbstractAssembly of the triangular, organic radical‐bridged complexes Cp*6Ln3(μ3‐HAN) (Cp*=pentamethylcyclopentadienyl; Ln=Gd, Tb, Dy; HAN=hexaazatrinaphthylene) proceeds through the reaction of Cp*2Ln(BPh4) with HAN under strongly reducing conditions. Significantly, magnetic susceptibility measurements of these complexes support effective magnetic coupling of all three LnIII centers through the HAN3−. radical ligand. Thorough investigation of the DyIII congener through both ac susceptibility and dc magnetic relaxation measurements reveals slow relaxation of the magnetization, with an effective thermal relaxation barrier of Ueff=51 cm−1. Magnetic coupling in the DyIII complex enables a large remnant magnetization at temperatures up to 3.0 K in the magnetic hysteresis measurements and hysteresis loops that are open at zero‐field up to 3.5 K.

Effect of coordination environment on the magnetic relaxation of mononuclear DyIII field-induced single molecule magnets

Two mononuclear DyIII complexes [Dy(H2TEG)(NO3)3]·[18-crown-6] (H2TEG=triethylene glycol) (1) and [Dy(H2TEG)Cl3]·[18-crown-6] (2) have been prepared using H2TEG as ligands. Magnetic studies revealed that both complexes show field-induced double magnetic relaxation behavior with energy barriers of 28K and 54K. Distinct magnetic dynamic properties observed in 1 and 2 are mostly attributed to the dissimilar coordination environments around DyIII centers in these two complexes.

Compartmental ligand approach for constructing 3d–4f heterometallic [CuII5LnIII2] clusters: synthesis and magnetostructural properties

The employment of a reduced Schiff-base ligand, 1,3-bis(3-methoxy-salicylamino)-2-propanol (H3L), with the assistance of acetate anions led to the isolation of eight heptanuclear heterometallic complexes containing [Cu5Ln2] cores. Single-crystal X-ray diffraction analyses have been performed for all the complexes and show that they all have dicationic [Cu5Ln2] cores with two nitrate or hexafluorophosphate anions to compensate the charge. The dicationic parts in 1–8 display centrosymmetric hexagonal-like arrangements in which one CuII ion sits on the inversion centre with six peripheral metal ions (two LnIII and four CuII) around it. The magnetic susceptibilities of all the complexes have been studied by dc magnetic measurements. The temperature dependent magnetic susceptibility data for the CuII–GdIII complex have been processed using PHI software. The results reveal that the magnetic exchange interactions between CuII and CuII ions are antiferromagnetic while those between CuII and GdIII ions are ferromagnetic. The magnetostructural correlations reveal that the bridging angles of Cu–O–Cu and Cu–O–Gd greatly influence the magnetic coupling of CuII–CuII and CuII–GdIII, respectively. Further, ac susceptibility studies have been carried out for DyIII and TbIII complexes and HoIII derivatives. The complexes CuII–HoIII and CuII–TbIII show slow magnetization relaxation behaviour of an SMM.

A NdIII enantiomeric pair: Synthesis, crystal structures and near-infrared luminescent properties

Based on enantiopure bis-bidentate N-donor ligands (−)/(+)-2,5-bis(4,5-pinene- 2-pyridyl)pyrazine (LR/LS), a new pair of NdIII enantiomers with the formula Nd(dbm)3LR/S·2H2O (R-1 and S-1 being the isomers containing the LR and LS ligands, respectively, and dbm = dibenzoylmethanate) have been isolated and characterized by X-ray crystallography and spectroscopic methods. Notably, unlike our previously reported homodinuclear EuIII and DyIII complexes based on the identical ligands (LR and LS), the dinuclear NdIII congener have not been obtained by controlling the ligand-to-metal ratio as expected, the reason of which was elucidated in this work. The crystal structure analyses of R-1 and S-1 reveal that they are mononuclear NdIII complexes and crystallize in chiral space group P212121 of the orthorhombic system. Circular dichroic (CD) spectra confirmed their chiroptical activities and enantiomeric nature. The photoluminescence investigations showed that they display characteristic near-infrared (NIR) emissions of the NdIII ions with notable emitting lifetime value.

Luminescent DyIII single ion magnets with same N6O3 donor atoms but different donor atom arrangements, ‘fac’-[DyIII(HLDL-ala)3]·8H2O and ‘mer’-[DyIII(HLDL-phe)3]·7H2O

Two DyIII complexes with same N6O3 donor atoms but different donor atom arrangements ‘fac’-[DyIII(HLDL-ala)3]·8H2O (1) and ‘mer’-[DyIII(HLDL-phe)3]·7H2O (2) were synthesized, where H2LDL-ala and H2LDL-phe are tridentate NNO ligands of N-[(imidazol-4-yl)methylidene]-dl-alanine and N-[(imidazol-4-yl)methylidene]-dl-phenylalanine, respectively. Each DyIII ion is coordinated by three mono-deprotonated mono-negative NNO tridentate ligands to form a nona-coordination geometry of a tricapped trigonal prism (TTP). 1 consists of enantiomers ‘fac’-[DyIII(HLD-ala)3] and ‘fac’-[DyIII(HLL-ala)3], while 2 consists of ‘mer’-[DyIII(HLD-phe)2(HLL-phe)] and ‘mer’-[DyIII(HLD-phe)(HLL-phe)2]. The temperature dependence of the magnetic susceptibilities and field-dependence of the magnetization of two complexes showed the different magnetic profiles and the Stark splitting of the ground state 6H15/2 due to the crystal field effect on DyIII ion (4f9, J=15/2, S=5/2, L=5, gJ=4/3, 6H15/2). Luminescence spectra were observed and the fine structures assigned to the 4F9/2→6H15/2 transitions are partially observed. 1 and 2 showed an out-of-phase signal with frequency-dependence in alternating current (ac) susceptibility under a dc bias field of 1000 Oe, indicative of field induced single ion magnet (SIM). The ac magnetic susceptibilities under 1000 Oe dc field of 2 showed the maximum peaks at the higher temperature than those of 1, indicating that the energy barrier of 2 is larger than that of 1.