Light-induced Excited Spin-state Trapping Effect Research Articles

Substituent group tuned structural dimensionalities and magnetic properties of V-shaped bis-pyridyl ligands based Fe(II) coordination polymers

A series of V-shaped thioether-based bis-pyridyl ligands containing different substituent groups have been successfully employed to assemble Fe(II)-based complexes by using H-tube diffusion method, resulting in six new coordination polymers with different structure types, [Fe(L1)(SCN)2]n·1.5nCH3OH (1), [Fe(L1)(SeCN)2]n·nCH3OH·nH2O (2), [Fe(L2)(SCN)2]n (3), [Fe(L2)(SeCN)2]n (4), [Fe(L3)(SCN)2]n (5), [Fe(L3)(SeCN)2]n (6) (L1 = 1,3-bis((pyridin-4-ylthio)methyl)benzene, L2 = 4,4′-(((2,4,6-trimethyl-1,3-phenylene)bis(methylene))bis(sulfanediyl))dipyridine, L3 = 4,4′-(((perchloro-1,3-phenylene)bis(methylene))bis(sulfanediyl))dipyridine). All the complexes have been structurally characterized by elemental analysis, FT-IR spectroscopy, single crystal and powder X-ray diffraction. The single crystal structure analysis revealed the one-dimensional (1D) chain for complexes 1–4, in which the different conformation the ligand adopted was found, and two-dimensional (2D) grid-like network for 5 and 6, respectively. Investigation of the temperature dependent magnetic susceptibilities discovered the always high spin state of the Fe(II) ion in all the compounds within the whole temperature range of 10-300 K, except complex 2 with the obvious temperature dependent color change from yellow (293 K) to violet (100 K). The thermo- and photomagnetic property study for complex 2 showed the incomplete spin transition behavior with interesting light-induced excited spin state trapping effect (LIESST). The current results indicated that the steric effect and/or the electronegativity of the substitute groups on the ligand and the conformation of the ligand could play an important role on the topologic structure of the target products, therefore putting obvious influence on spin state of the central Fe(II) ion.

Interface versus Bulk Light-Induced Switching in Spin-Crossover Molecular Ultrathin Films Adsorbed on a Metallic Surface.

Spin-crossover molecules present the unique property of having two spin states that can be controlled by light excitation at low temperature. Here, we report on the photoexcitation of [FeII((3, 5-(CH3)2Pz)3BH)2] (Pz = pyrazolyl) ultrathin films, with thicknesses ranging from 0.9 to 5.3 monolayers, adsorbed on Cu(111) substrate. Using X-ray absorption spectroscopy measurements, we confirm the anomalous light-induced spin-state switching observed for sub-monolayer coverage and demonstrate that it is confined to the first molecular layer in contact with the metallic substrate. For higher coverages, the well-known light-induced excited spin-state trapping effect is recovered. Combining continuous light excitation with thermal cycling, we demonstrate that at low temperature light-induced thermal hysteresis is measured for the thicker films, while for sub-monolayer coverage, the light enables extension of the thermal conversion over a large temperature range. Mechanoelastic simulations underline that, due to the intermolecular interactions, opposite behaviors are observed in the different layers composing the films.

A series of new Fe(II) coordination polymers based-on [Hg(XCN)3]− or [Hg(XCN)4]2− (X = S, Se) building blocks: Synthesis, crystal structure and magnetic property

Self-assembly of the tetrahedral metalloligand building block [(HgII(XCN)4]2-, where X ​= ​S or Se, a series of bis-monodentate pyridine-like ligands and iron(II) compounds has afforded seven new heterobimetallic HgII–FeII coordination polymers. Single crystal X-ray diffraction structural analysis revealed the infinite two-dimensional (2D) sheet with different topologies for all the complexes except 3, which belonged to inherent 3D-structure. The results of the temperature dependent magnetic susceptibility investigation over all the complexes discovered the paramagnetic behavior for the high spin iron(II) ion in all the complexes within the temperature range of 2–300K, except complex 6. The thermo- and photomagnetic property study for complex 6 showed incomplete spin crossover (SCO) behaviors with interesting thermomagnetic properties and light-induced excited spin state trapping effect (LIESST). The results show that the ligand field, configurations, rigidity, and polarity of the bridging ligands, as well as the coordination mode with the Fe(II) ion of the building units, are important for the design and synthesis of the targeted coordination polymers.

Light-induced thermal hysteresis and high-spin low-spin domain formation evidenced by optical microscopy in a spin-crossover single crystal

The low-temperature photoinduced effects of the spin-crossover $[{\mathrm{Fe}{(2\text{\ensuremath{-}}\mathrm{pytrz})}_{2}[\mathrm{Pd}{(\mathrm{CN})}_{4}]}].3{\mathrm{H}}_{2}\mathrm{O}$ single crystal have been investigated by means of a cryogenic optical microscopy technique down to 10 K from which the imaging and quantitative analysis of the spatiotemporal transformation are derived. The magnetic investigations revealed that this compound exhibits an incomplete spin transition between a full high-spin (HS) state at high temperature and an intermediate HS and low-spin (LS) state, where HS and LS species coexist, as a result of the existence of an elastic frustration at the molecular scale, most likely caused by the rigidity of the interconnected $[\mathrm{Pd}{(\mathrm{CN})}_{4}$] [Fe(II)/Pd(II)] two-dimensional network. At low temperature (10 K), thanks to reverse light-induced excited spin-state trapping effect, we could switch the system from the intermediate HS-LS state to the fully photoinduced LS state by irradiating the sample in near-infrared region, revealed by photomagnetic and optical microscopy studies. Optical microscopy images showed monotonous and homogeneous transformation of the crystal color along this process, corresponding to a gradual change of the spin state under light. In contrast, the thermal relaxation in the dark of this photoinduced LS-LS state shows a transition to the intermediate HS-LS state at $\ensuremath{\sim}90$ K with domain formation, which is characteristic of a first-order transition at equilibrium. Interestingly, the same behavior is also obtained during the heating process of the reverse light-induced thermal hysteresis cycle with a heating branch almost unchanged, confirming that light does not act on this transition. It is then concluded that the transition from the full LS to the intermediate HS-LS transition is of first order and therefore the LS state reached by light is a hidden stable state of the system until $\ensuremath{\sim}90$ K. These experimental results are modeled using an adapted version of the electroelastic model including photoexcitation effects and solved by Monte Carlo method. Both thermal equilibrium and light-induced thermal hysteresis are reproduced, in fair qualitative agreement with the experimental data of photomagnetism and optical microscopy.

Light-induced hidden multistability in a spin crossover metal–organic framework

An extremely rare bidirectional light-induced excited spin-state trapping effect is firstly observed in a 3D Hofmann-type metal–organic framework with 1-fluoronaphthalene guests.

Light and Thermal Induced Spin Crossover Properties of Fe(II) Compound

We synthesized a novel phenanthroline-based mononuclear Fe(II) compound [Fe(TTD)2(NCS)2]⋅CH3CN (1, TTD = 1,4,8,9-tetraaza-triphenylene-2,3-dicarbonitrile). And its crystal structure, optical and magnetic properties were analyzed. The thermally induced SCO of the compound is a one-step abrupt transition. In addition, light can also control the spin state of the compound. By using 660 nm light-excited compound, LIESST (light-induced excited spin-state trapping) effect can be achieved.

Effects of water removal on the structure and spin-crossover in an anilato-based compound

The crucial role played by a crystallization water molecule in the spin crossover (SCO) temperature and its hysteresis is described and discussed in compound [NBu4][Fe(bpp)2][Cr(C6O4Br2)3]⋅2.5H2O (1), where bpp = 2,6-bis(pyrazol-3-yl)pyridine and (C6O4Br2)2− = dianion of the 3,6-dibromo-2,5-dihydroxy-1,4-benzoquinone. The compound has isolated [Fe(bpp)2]2+ cations surrounded by chiral [Cr(C6O4Br2)3]3− anions, NBu4+ cations, and a water molecule H-bonded to one of the non-coordinated N–H groups of one bpp ligand. This complex shows a gradual almost complete two-step spin transition centered at ca. 180 and 100 K with no hysteresis. The loss of the water molecules results in a phase transition from a P21/n phase with only one independent [Fe(bpp)2]2+ cation to a chiral Pn phase with two independent [Fe(bpp)2]2+ cations. Besides, there is an increase in the SCO temperature to 195/202 K with a hysteresis of ca. 7 K. In the dehydrated phase, only one of the two independent [Fe(bpp)2]2+ cations shows the SCO, whereas the second one remains in a high spin configuration at any temperature. In addition, compound 1 exhibits the LIESST (light-induced excited spin-state trapping) effect with a TLIESST of ca. 70 K.

Thermal- and photo-induced spin crossover in the 1D coordination polymer [Fe(4-tBupy)3][Au(CN)2]2 (4-tBupy = 4-tert-butylpyridine)

Reaction of the unidentate pyridine ligand containing a bulky t-butyl substituent with Fe2+ and [Au(CN)2]− affords a new type of spin crossover (SCO) coordination polymer in the 1D compound [Fe(4-tBupy)3][Au(CN)2]2⋅0.5H2O (1), which is formed by chains of Fe(II) complexes linked through bridging [Au(CN)2]− with three terminal 4-tBupy and one monodentate [Au(CN)2]− ligands completing the octahedral coordination around Fe(II). Longer reaction times led to the minor products [Fe(4-tBupy)2][Au(CN)2]2 (2), which presents a 2D structure more similar to that found in the other SCO compounds based on [Au(CN)2]−, and the 1D compound [Fe(4-tBupy)2(MeOH)][Au(CN)2]2 (3), in which one of the three terminal 4-tBupy found in 1 is replaced by a coordinating MeOH molecule. Magnetic measurements of 1 show an abrupt spin transition with the temperature with hysteresis and light-induced excited spin-state trapping effect. Structural analysis of 2 and 3 indicates that Fe(II) remains in the high-spin state in these compounds.

Synchrotron-based Mössbauer spectroscopy characterization of sublimated spin crossover molecules.

The spin crossover (SCO) efficiency of [57Fe(bpz)2(phen)] (where bpz = bis(pyrazol-1-yl)borohydride and phen = 9,10-phenantroline) molecules deposited on gold substrates was investigated by means of synchrotron Mössbauer spectroscopy. The spin transition was driven thermally, or light induced via the LIESST (light induced excited spin-state trapping) effect. Both sets of measurements show that, once deposited on a gold substrate, the efficiency of the SCO mechanism is modified with respect to molecules in the bulk phase. A correlation in the distribution of hyperfine parameters in the sublimated films, not evidenced so far in the bulk phase, is reported. This translates into geometrical distortions of the first coordination sphere of the iron atom that seem to correlate with the decreased spin conversion. The work reported clearly shows the potentiality of synchrotron Mössbauer spectroscopy for the characterization of nanostructured Fe-based SCO systems, thus resulting as a key tool in view of their applications in innovative nanoscale devices.

Tetranuclear [FeII2FeIII2]2+ molecular switches: [FeII(bik)2(N–)2] spin-crossover complexes containing [FeIII(Tp)(CN)3]– metalloligands as N-donor

Three novel mixed valence cyanide-bridged {FeIII2FeII2} square complexes were obtained through the self-assembling of [FeIII(Tp)(CN)3]- or [FeIII(Tp*)(CN)3]− cyanido building blocks with the in situ formed [FeII(bik)2(S)2] complex (Tp = hydrotris (pyrazol-1-yl)borate, Tp* = hydrotris (3,5-dimethyl-pyrazol-1-yl)borate, bik = bis(1-methylimidazol-2-yl)ketone, S = solvent). The structures of these three complexes (2, 3 and 4) are reminiscent of that of our previously published square complex {[FeIII(Tp)(CN)3]2 [FeII(bik)2]2}·[FeIII(Tp)(CN)3]2·18H2O·4CH3OH (1). They consist of cyanide-bridged square dicationic complexes, ClO4− (2 and 3) or BF4− (4) counterions and solvate molecules. The FT-IR cyanide stretching vibrations observed at νCN ≈ 2145–60 cm−1 are typical of {FeIII–CN–FeII} moieties. The investigation of the magnetic properties of 2 reveals the occurrence of spin-crossover centered at T1/2 = 227 K. The χMT variation, ca. 7 cm3 mol−1 K, reflects the complete spin-state change occurring on both {FeII(bik)(–NC)2} moieties (–NC represents the cyanido building blocks). The Slichter–Drickamer model leads to a weak cooperativity factor, Γ = 1.6 kJ mol−1 (with Γ < 2RT1/2), which reflects the gradual spin-state change. This is in agreement with the molecular structure of 2, which does not present significant intermolecular interactions. The calculated enthalpy and entropy variations associated with the spin-state equilibrium are ΔH = 24 kJ mol−1 and ΔS = 105 J K−1 mol−1. In contrast, 3 and 4 show only partial spin-crossover in the accessible temperature range (2–400 K) as the T1/2 are shifted toward higher temperatures (ca. T1/2 > 400 K). Although no photomagnetic effect is observed for 3, compound 4 shows a moderate increase in the magnetization upon irradiation at low temperature. This phenomenon is ascribed to the light-induced excited spin-state trapping (LIESST) effect. Interestingly, the complex 2 also shows a remarkable LIESST effect, which is observed with different laser lights covering the visible and near-infrared range. The resulting χMT value obtained in the photoinduced state suggests the occurrence of a ferromagnetic interaction inside the {FeIII–CN–FeII} units. Trois nouveaux complexes carrés {FeIII2FeII2} à pont cyanure et à valence mixte ont été obtenus par auto-assemblage des précurseurs cyanurés [FeIII(Tp)(CN)3]− ou [FeIII(Tp*)(CN)3]− et du complexe cationique [FeII(bik)2(S)2] formé in situ (Tp = hydrotris (pyrazol-1-yl)borate, Tp* = hydrotris (3,5-dimethyl-pyrazol-1-yl)borate, bik = bis(1-methylimidazol-2-yl)cétone, S = solvant). Les structures de ces trois complexes (2, 3 et 4) sont similaires à celle du complexe {[FeIII(Tp)(CN)3]2[FeII(bik)2]2}[FeIII(Tp)(CN)3]2·18H2O·4CH3OH (1) préalablement publié. Elles sont constituées de complexes carrés dicationiques à pont cyanure, de contre-ions ClO4− (2 and 3) ou BF4− (4) et de molécules de solvant. Les vibrations d’élongation des cyanures, observée en spectroscopie IR à νCN ≈ 2145–60 cm−1, sont caractéristiques d'unités {FeIII–CN–FeII}. L’étude des propriétés magnétiques de 2 révèle un équilibre de spin centré à T1/2 = 227 K. La variation du produit χMT, ca. 7 cm3 mol−1 K, traduit une conversion de spin complète sur chacune des unités {FeII(bik)(–NC)2} du carré (–NC représente le complexe précurseur cyanuré). L'analyse des données par le modèle de Slichter–Drickamer conduit à un faible facteur de coopérativité, Γ = 1.6 kJ mol−1 K (with Γ < 2RT1/2), en accord avec un changement d’état de spin graduel. Ces données sont en accord avec la structure de 2 qui ne montre pas d'interactions intermoléculaires notables. Les valeurs des variations d'enthalpie et d'entropie associées à la conversion de spin sont ΔH = 24 kJ mol−1 et ΔS = 105 J K−1 mol−1. Au contraire de 2, les composés 3 and 4 présentent seulement une conversion de spin partielle dans le domaine de température exploré (2–400 K), avec des valeurs T1/2 déplacées vers les hautes températures (ca. T1/2 > 400 K). Tandis qu'on n'observe pas d'effet photomagnétique pour 3 et seulement un faible effet dans 4, le composé 2 présente une forte augmentation de son aimantation sous irradiation à basse température. Cet effet est dû au piégeage photo-induit d'un état excité de spin (effet « LIESST », Light-Induced Excited Spin-State Trapping). Il est observé avec différentes sources laser couvrant le spectre visible et le proche infrarouge. Les valeurs de χMT obtenues dans l’état photo-induit suggèrent la présence d'une interaction ferromagnétique au sein de la paire {FeIII–CN–FeII}.

Light-induced spin crossover—Solution and solid-state processes

Abstract This article overviews the different light-induced spin-crossover processes that are induced using ligand photoreaction, photothermal effects, or optical absorption of the center metallic ion. A particular attention is drawn on the light-induced excited spin-state trapping effect, the most studied phenomenon, by discussing the recent developments in terms of description of the initial photoswitching process and the mechanisms developing at different time scales, as well as the lifetime of the photoinduced state.

Intermolecular Interaction Tuning of Spin-Crossover Iron(III) Complexes with Aromatic Counteranions.

Iron(III) spin-crossover (SCO) complexes [Fe(qsal)2]BS·MeOH·H2O (1), [Fe(qsal)2](NS)·MeOH (2), [Fe(qnal)2](NS) (3), and [Fe(qnal)2]PS·MeOH·CH2Cl2 (4) (Hqsal, N-(8-quinolinyl)salicylaldimine; Hqnal, N-(8-quinolinyl)-2-hydroxy-1-naphthaldimine; BS, benzenesulfonate; NS, 1-naphthalenesulfonate; PS, 1-pyrenesulfonate) have been synthesized and characterized by X-ray structure determinations and temperature-dependent magnetic susceptibility measurements. The aromatic counteranions BS, NS, and PS can be used for the tuning of intermolecular coupling through a variety of weak interactions. All of the complexes show temperature-dependent SCO behavior. but the light-induced excited spin-state trapping (LIESST) effect was observed only for 1, 3, and 4 when the samples were illuminated (λ 808 nm) for 1 h at 5 K. In particular, 59% of the LS form of 1 was converted to the metastable HS state by illumination, equal to the highest degree of conversion yet known for LIESST in [Fe(qsal)2]+ derivatives. The lack of a LIESST effect for 2 may be due to the relatively limited degree of interaction between the cations and anions in the lattice, reflected in a much longer minimum Fe···Fe separation in this complex in comparison to the others.

Cooperative spin-crossover transition from three-dimensional purely π-stacking interactions in a neutral heteroleptic azobisphenolate FeIII complex with a N3O3 coordination sphere.

A novel neutral heteroleptic FeIII complex from two kinds of π-extended tridentate ligands was designed and prepared. The π-ligands formed a three-dimensional purely π-stacking interaction network. The present complex proved to be the first neutral spin-crossover (SCO) FeIII complex with a N3O3 coordination sphere exhibiting an abrupt SCO transition with a thermal hysteresis of 10 K and the light-induced excited spin-state trapping effect.

Structural investigation of the high spin→low spin relaxation dynamics of the porous coordination network [Fe(pz)Pt(CN)4]⋅2.6 H2O.

The Hoffman-type coordination compound [Fe(pz)Pt(CN)4]⋅2.6 H2O (pz = pyrazine) shows a cooperative thermal spin transition at around 270 K. Synchrotron powder X-Ray diffraction studies reveal that a quantitative photoinduced conversion from the low-spin (LS) state into the high-spin (HS) state, based on the light-induced excited spin-state trapping effect, can be achieved at 10 K in a microcrystalline powder. Time-resolved measurements evidence that the HS→LS relaxation proceeds by a two-step mechanism: a random HS→LS conversion at the beginning of the relaxation is followed by a nucleation and growth process, which proceeds until a quantitative HS→LS transformation has been reached.

First evidence of light-induced spin transition in molybdenum(IV).

Photo-induced spin transition in a molybdenum-zinc complex has been evidenced and fully characterized by Squid magnetometry and several spectroscopies performed under irradiation (IR, EPR, etc.). The phenomenon has been confirmed by X-ray diffraction and DFT calculations yielding a Light-Induced Excited Spin State Trapping Effect (LIESST) on a 4d transition metal ion.

Spin-crossover thermal hysteresis and light-induced effect on iron(II) complexes with tripodal tris(2-pyridyl)methanol

The X-ray crystal structure of Me4N[Fe(py3COH)(NCS)3](1-PrOH)0.5(H2O)2 [1; py3COH stands for tris(2-pyridyl)methanol] was successfully determined, clarifying that the complex has a pseudo-trigonal molecular arrangement, though the space group was P1¯. Possible π–π interaction is operative between the pyridine rings from neighboring [Fe(py3COH)(NCS)3]− ions. After annealing of 1 at 400K, the resultant compound was characterized to be Me4N[Fe(py3COH)(NCS)3](H2O) (1′), which showed a relatively abrupt spin-crossover (SCO) with thermal hysteresis. Combining the differential thermal analysis results, the SCO temperatures were determined as T1/2↓=224K and T1/2↑=246K. Compound 1′ also showed light-induced excited spin-state trapping (LIESST), as indicated with the χmT increased to a 32% level of the high-spin moment upon Xe-lamp irradiation at 5K. The LIESST effect disappeared at around 26K on heating. The complex ion [Fe(py3COH)(NCS)3]− is a rare anionic SCO and LIESST building block.

Spin-crossover and LIESST Effect for Iron(III) Complex Based on π–π Stacking by Coordination Programming

Abstract Spin-crossover (SCO) iron(III) compounds, [Fe(qnal-OMe)2]PF6·acetone (1) and [Fe(qnal-OMe)2]BPh4·2MeOH (2) (qnal-OMe: 7-methoxy-1-[(8-quinolinylimino)methyl]-2-naphthalenol), were prepared and characterized by X-ray single-crystal structure analysis, temperature-dependent magnetic susceptibility, and Mössbauer spectroscopy measurements. The compounds exhibited SCO behavior with thermal hysteresis loop (T1/2↑ = 202 K, T1/2↓ = 194 K for 1 and T1/2↑ = 304 K, T1/2↓ = 194 K for 2). Moreover, the light-induced excited spin-state trapping (LIESST) effect was observed for the compounds when the samples were illuminated (1000 nm) at 5 K. We suggest that the introduction of a strong intermolecular interaction, such as π–π stacking, can play an important role in the observed dynamic phase transition.

First glimpse of the soft x-ray induced excited spin-state trapping effect dynamics on spin cross-over molecules

The dynamics of the soft x-ray induced excited spin state trapping (SOXIESST) effect of Fe(phen)2(NCS)2 (Fe-phen) powder have been investigated by x-ray absorption spectroscopy (XAS) using the total electron yield method, in a wide temperature range. The low-spin (LS) state is excited into the metastable high-spin (HS) state at a rate that depends on the intensity of the x-ray illumination it receives, and both the temperature and the intensity of the x-ray illumination will affect the maximum HS proportion that is reached. We find that the SOXIESST HS spin state transforms back to the LS state at a rate that is similar to that found for the light induced excited spin state trapping (LIESST) effect. We show that it is possible to use the SOXIESST effect in combination with the LIESST effect to investigate the influence of cooperative behavior on the dynamics of both effects. To investigate the impact of molecular cooperativity, we compare our results on Fe-phen with those obtained for Fe{[Me2Pyrz]3BH}2 (Fe-pyrz) powder, which exhibits a similar thermal transition temperature but with a hysteresis. We find that, while the time constant of the dynamic is identical for both molecules, the SOXIESST effect is less efficient at exciting the HS state in Fe-pyrz than in Fe-phen.

Photoinduced Relaxation Dynamics in Iron(II) Spin‐Crossover Nanoparticles: The Significance of Crystallinity

A switch in time: A fast precipitation technique was used to prepare 75 nm FeII spin-crossover nanocrystals. Their photoswitching dynamics, based on the light-induced excited spin-state trapping effect, has been investigated by means of optical spectroscopy. A significant variation of the switching proprieties is observed compared to similar but amorphous nanoparticles.

Ab initiostudy of the influence of structural parameters on the potential energy surfaces of spin-crossover Fe(II) model compounds

In spin-crossover (SCO) compounds exhibiting a light induced excited spin state trapping (LIESST) effect, the thermodynamic T(1∕2) and kinetic T(LIESST) temperature values depend on the features of the potential energy surfaces (PES) of the two lowest singlet and quintet states but also on vibrational contributions, collective effects, such as electrostatics, for instance, spin-orbit couplings to a lesser extent, etc. In this work, the question of the link between the shape of the PES of SCO compounds exhibiting a LIESST effect and their first coordination sphere structure is addressed from wave function theory based ab initio calculations. Fe(II) complexes based on model ligands suited to reproduce the main characteristics of the PES of such compounds are distorted to emphasize selectively the role played by the metal-ligand distances and the ligand-metal-ligand angles. The studied angular deformations are those usually observed in many Fe(L)(2)(NCS)(2) complexes. It is shown that the larger the deformation between the low spin and high spin equilibrium geometries, the higher the energy barrier from the high spin state and the weaker the energy difference between the bottom of the wells. These results corroborate observations made by experimentalists on a large number of complexes. While the PES features only constitutes one of the contributions to these temperatures, it is worth noticing that, relating T(1∕2) to the energy difference between the bottoms of the singlet and quintet wells and the T(LIESST) to the energy barrier from the quintet bottom well, the same slope of the empirical law T(LIESST) = -0.3T(1∕2)+T(0) is observed.