1

Dynamic Jahn-Teller Character of Manganese(III) Spin-Crossover Complex[Mn(taa)] (H3taa = tris(1-(2-azolyl)-2-azabuten-4-yl)amine)

Motohiro Nakano1 and Gen-etsu MatsubayashiDepartment of Molecular Chemistry & Frontier Research Center, Graduate

School of Engineering, Osaka University, Toyonaka, Osaka 560-0043, Japan

Takasuke MatsuoDepartment of Chemistry & Research Center for Molecular Thermodynamics,Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Abstract Paraelectric behavior due to a dynamic Jahn-Teller effect has beenfound in the high-spin (HS) phase above Tc = 48 K of the manganese(III) spin-crossover complex [Mn(taa)] (H3taa = tris(1-(2-azolyl)-2-azabuten-4-yl)amine).The dielectric constant obeys the Curie-Weiss law with an asymptotic Curietemperature of 26 K, suggesting competition between a low-spin (LS) phase and aferroelectric-ordered (FO) phase at low temperatures. A phase diagram based ona 4-state Ising-Potts model incorporating both a virtual cooperative Jahn-Tellertransition (HS ⇔ FO) and a spin-crossover transition (HS ⇔ LS) is proposed to

elucidate the interrelation of the HS, LS, and FO phases.

1. Introduction2. Experimental3. Results and Discussion 3-1. Raman Spectra of [Mn(taa)] 3-2. Dielectric Behavior of [Mn(taa)] 3-3. DFT-Optimized Structure of High-Spin [Mn(taa)] Species 3-4. Phase Diagram Based on a 4-State Ising-Potts Model4. ConclusionAcknowledgmentsReferences

1 E-mail address: moto@ch.wani.osaka-u.ac.jp (Motohiro Nakano)

2

1. Introduction

Spin-crossover complexes contain octahedrally coordinate d4-d7 transitionmetal ions and have two nearly degenerate electron configurations with differentspin multiplicities, i.e. high-spin (HS) and low-spin (LS) states [1-5]. Theground state configuration of these complexes can be switched from one to theother by varying ligand-field strength. This bistability is usually accomplishedby coupling with molecular deformations, especially metal-ligand stretchingmodes, and known to be controllable through external fields includingtemperature, pressure, magnetic field, and so on. In many theoretical models,only totally-symmetric breathing mode is taken into account as the interactionmode relevant to spin-crossover phenomena. However, lower-symmetry modesmay play an important role when the orbital degeneracy is not fully quenched.Such low-symmetry deformations are sometimes noted in experimental works [6-10]. In this paper, a manganese(III) spin-crossover complex, where theanisotropic deformation induced by the Jahn-Teller effect provides a rich varietyof phase behavior, is discussed based on a simple mean-field model. The title compound [Mn(taa)] (H3taa = tris(1-(2-azolyl)-2-azabuten-4-yl)amine) is known to have an abrupt spin-crossover phase transition [11, 12].The LS phase consisting of 3T1g (t2g

4: S = 1) molecules transforms into the HSphase consisting of 5Eg (t2g

3eg1: S = 2) molecules at above Tc = 48 K. The crystal

structure of the HS phase has cubic symmetry: space group I d43 , lattice constanta = 2.031 nm, cell volume V = 8.377 nm3, and number of formula unit per unit

C3 C3+ LS

C3+ LS+ JT

A3E3

E5N

N

N

N

N

N

N

Mn

(a) (b)Fig. 1. (a) Molecular structure of [Mn(taa)] and (b) splitting of groundmultiplet under perturbations; C3 twist (C3), spin-orbit coupling (LS), and E ⊗e Jahn-Teller distortion (JT).

3

cell Z = 16 [11]. The HS molecule in the cubic lattice has a C3 axis penetratingthe central Mn(III) ion and the non-ligating N(amino) atom of the taa3- ligand (Fig.1(a)). The coordination environment of the central Mn(III) ion is approximatelyoctahedral with small twisting (9.2°) around the C3 axis from the C3v symmetry.

2. Experimental

Polycrystalline [Mn(taa)] samples were prepared according to the literaturemethod [11, 12] and tetrahedron-shaped single crystals were obtained byrecrystallization from CH2Cl2/hexane solutions. Variable-temperature Laser Raman spectra between 15-70 K were measuredfor a polycrystalline sample mounted in an Oxford CF1204 cryostat using a JascoNR-1800 Raman spectrophotometer. The dielectric permittivity was measured on a compacted disk, 0.55 mmthick and 9.0 mm in diameter, with vacuum-deposited electrodes on the circularfaces, using an HP 4284A precision LCR meter. The frequency and temperatureranges were 102-106 Hz and 15-300 K, respectively. Temperature measurementswere made by an Rh-Fe resistance thermometer fixed on the sample holder, whichwas calibrated against the ITS90. For the aid of thermal equilibration, a smallamount of He gas (~10 Pa) was introduced in the sample chamber of the lab-madevacuum cryostat. Degradation of the sample by thermal cycling, e.g. crack ofthe disk or strip-off of the Au electrodes, was negligible since no thermalhystereses of dielectric constants were detected.

3. Results and Discussion

3-1. Raman Spectra of [Mn(taa)]

The Raman spectrum of [Mn(taa)] recorded at 50 K is plotted in Fig. 2,together with a quantum-chemical simulation spectrum. The details of thetheoretical method are presented in section 3-3. Although the simulation curve isnot corrected with any scaling factors of vibrational frequencies, it is still usefulfor peak assignment. Temperature dependences of the Raman spectra are shownin Fig. 3. Some peaks showing remarkable intensity changes at around Tc areindicated by arrows. An important feature of these spectra is that most ofRaman-active vibrational modes show negligible frequency shifts across Tc, whilethe intensitis vary due to probable site-symmetry changes are observed. This

4

Fig.

2.

Ram

an s

pect

rum

of

[Mn(

taa)

] at

50

K (

uppe

r cu

rve)

and

sim

ulat

ions

for

the

geom

etry

-opt

imiz

ed h

igh-

spin

spe

cies

by

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/LA

NL

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.

5

Fig.

3.

Tem

pera

ture

dep

ende

nce

of R

aman

spe

ctra

of

[Mn(

taa)

].

Arr

ows

indi

cate

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ity c

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und

spin

-cro

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ansi

tion

Tc =

48

K.

6

behavior is in clear contrast to ordinary Fe spin-crossover complexes, wherevibrational frequencies shift to lower as the sample changes from the LS to HSspecies [1-5, 13-18]. The shifts in vibrational frequencies between the LS and HS species areresponsible for the major parts of the entropy changes ∆S in spin transitions [13].This has been repeatedly confirmed by infrared [13-15], Raman [14-17], andinelastic neutron scattering spectroscopies [18]. Since the observed entropychange 13.8 JK-1mol-1 [12] in the present compound is not explained adequatelysolely by the entropy of the spin multiplicity (Rln(5 / 3) = 4.25 JK-1mol-1).However, we cannot assign the extra entropy change to a vibrational origin, sincethe Raman spectra of the two phases differ only in intensities. One of plausible candidates for the entropy source is a dynamic structuraldisorder in the HS phase, which should be settled down in the LS phase. Thecrystallographic data for [Mn(taa)] [11] provide a clue, i.e. the presence of C3 axisin the HS molecule. An Mn(III) ion in the 5E state is a well-known Jahn-Tellerion [19]. Since the C3 site-symmetry cannot lift the orbital degeneracy of the 5Eterm (Fig. 1(b)), it is likely that the Mn ion is subjected to the E ⊗ e Jahn-Tellereffect, which gives rise to three energetically equivalent deformation structures.The apparent C3 symmetry should be observed in a time-averaged structure overthree deformed structures.

3-2. Dielectric Behavior of [Mn(taa)] The temperature dependence of dielectric constant at 1.0 kHz is plotted inFig. 4. The HS phase above the spin-crossover transition at Tc = 48 K shows acharacteristic Curie-Weiss behavior, ε∞ + C / (T – θ), indicating the presence ofdynamically disordering electric dipoles. The high-frequency dielectric constantis ε∞ = 3.0, the Curie constant C = 91 K, and the asymptotic Curie temperature θ =26 K. The positive value of θ suggests a ferroelectric interaction betweenreorienting dipoles in the HS phase. Such an interaction has a possibility ofproviding a ferroelectric phase at low temperatures, if the spin-crossover phasetransition would not prevent the development of ferroelectric long-range order. On the other hand, the Curie-Weiss behavior is fully suppressed in the LSphase below 48 K. It suggests that the complete C3-symmetry is recovered in theLS molecule and the reorienting dipoles, which are required to guarantee theapparent C3-symmetry in the dynamically disordered HS phase, disappear. Aslight growth of ε observed between 15-40 K arises from a small fraction of

7

thermally excited HS species. Analysis of this part assuming a temperaturedependence of the form T-1exp(-∆eff / kBT) for the permittivity gives the effectiveLS-HS gap ∆eff / kB = 340 K. This gap ∆eff is the energy difference between the

LS and HS states of a [Mn(taa)] molecule embedded in the LS molecules. Thus,it should differ from the LS-HS gap ∆ of an isolated molecule in vacuum by thevan der Waals' interaction exerted by the surrounding LS molecules. Thisinteraction is expected to enhance the energy gap ∆ because of mismatchedmolecular packing disturbing the uniform and equilibrium molecular array of theLS phase. A simple electrostatic model facilitates understanding the physical meaningof the Curie behavior of [Mn(taa)] in the HS phase. Electric polarization Pproduced by a number of reorienting molecular dipoles µ under a local field Eloc

obeys a simple Curie law, P = (Nµ2 / 3kBT) Eloc,where N stands for the number density of molecular dipoles. The local field Eloc

consists of the external field Eext and the Lorentz field ELorentz exerted fromneighboring molecular dipoles, Eloc = Eext + ELorentz = Eext + P / (3ε∞ε0),where ε∞ is the high-frequency dielectric constant. From the definition ofdielectric constant P = (ε – ε∞) ε0 Eext, the Curie-Weiss law is provided: ε = ε∞ + C / (T - θes),

10 100 30020020 30 50

Fig. 4. Temperature dependence of dielectric constant of [Mn(taa)] measuredat 1.0 kHz. Full curve is the Curie-Weiss law, C / (T - θ), where C = 91 K andθ = 26 K.

8

where C = Nµ2 / (3kBε0), θes = C / (3ε∞), and ε0 means the permittivity of vacuum.Based on the experimental values, C = 91 K, ε∞ = 3.0, and N = 1.91 nm-3 [11], thecalculated value of the reorienting molecular dipole moment is µ = 1.25 D. Theasymptotic Curie temperature in this electrostatic model is deduced to θes = C /(3ε∞) ≅ 10 K, which is much smaller than the observed value, θ = 26 K. If weattribute the discrepancy between the calculated θes and the experimental θ solely

to the van der Waals energy, we conclude that a neighboring pair of HS moleculesprefers parallel deformation between them. Thus, the electrostatic contributionis about 40% of whole ferroelectric interaction between HS molecules, while thevan der Waals interaction contributes up to 60 %.

3-3. DFT-Optimized Structure of High-Spin [Mn(taa)] Species

The geometry optimization of the HS [Mn(taa)] molecule was carried out bya hybrid DFT quantum chemical calculation using Gaussian98 program suite[20].In the calculation, the ECP (effective core-potential) basis functions LANL2DZwere adopted for all atoms and a hybrid density functional UB3PW91 was used.Since the C3-symmetry constraint is released, the optimized molecular structure isquite skewed (Fig. 5), so that three Mn-N(pyrrole) bond lengths are 1.9785,1.9778, and 2.2032 Å, and three Mn-N(imino) bond lengths are 2.0642, 2.0365,and 2.3144 Å. Typical Jahn-Teller elongations along a coordination axis arefound. Averaged bond lengths are 2.053 and 2.138 Å for Mn-N(pyrrole) andMn-N(imino) bonds, respectively, which correspond very well to the experimentalvalues of 2.054 and 2.148 Å [11]. If the complex molecule maintains C3 symmetry, it carries only longitudinalelectric dipole parallel to the C3 axis. Symmetry-lowering of the HS moleculeproduces the transverse component of electric dipole moment. Based on theoptimized structure and the electron distribution, the longitudinal and transversedipole moments are estimated to be 6.28 and 0.88 D, respectively. In the crystallattice, reorientation of a whole molecule is prevented by dense packing, and onlypseudo-rotation of the transverse moment is allowed. If we remember that thechoice of the pseudo-C3 axis, which affects separation of the longitudinal andtransverse components, is not unique, the value obtained for the transversemoment may be regarded close to the experimental value of the reorienting dipole1.25 D estimated from the dielectric constant. This good agreement verifies theidea of pseudo-rotating distortion dipoles attributable to the E ⊗ e Jahn-Tellereffect.

9

Fig.

5.

DFT

-opt

imiz

ed m

olec

ular

str

uctu

re o

f hi

gh-s

pin

[Mn(

taa)

].

Tw

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own.

10

Since the 16 molecules in a unit cell are grouped into four sublattices interms of their longitudinal moments, which align to four body-diagonals of thecubic unit cell, the Jahn-Teller distortions in the same direction generate non-collinear electric dipoles on different sublattices. The mutual relation of foursublattices is depicted in Fig. 6. Each octant of a unit cell contains twomolecules belonging to a same sublattice, placed on the body-diagonal. Any twooctants sharing a single corner are equivalent. Coordination axes (N-Mn-N) of amolecule are approximately parallel to the lattice vectors a, b, and c, and thetetragonal elongations of coordination octahedra by E ⊗ e Jahn-Teller effect areregarded to take place along the lattice vectors. A transverse electric dipole isinduced perpendicular to the molecular C3 axis on a coplane of the C3 andelongation axes. The lost collinearity suggests inequivalency of ferrodistortiveand ferroelectric interactions between the HS molecules. For example, aferrodistortive order with z-axis elongations makes electric polarizations ofdifferent sublattices cancel out each other resulting in an antiferroelectric order. In Fig. 5 the spin-density isosurface of 0.005 e / a.u.3 of [Mn(taa)] is alsoshown. Taking the Jahn-Teller elongation axis as z, the electron configuration isapproximately described to be (dyz)

1(dzx)1(dxy)

1(dz2)1. Most of the spin densities sit

on t2g orbitals and around the z-axis, consistent with the electron configuration.

Upper 4 octants Lower 4 octantsFig. 6. Molecular packing in [Mn(taa)] crystal. Coordination octahedra arecolored according to four sublattices discriminated by mapping a body-diagonalof the unit cell to C3 axes of member molecules. Darken side of eachoctahedron faces to the C3 axis.

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A small amount of spin densities appears on the pyrrole ring perpendicular to thez-axis, suggesting delocalization of t2g electrons over pyrrole π orbitals sharing thenodal plane. It induces energy splitting between dyz and dzx orbitals and maycause rhombic zero-field splitting term in the spin Hamiltonian.

3-4. Phase Diagram Based on a 4-State Ising-Potts Model

A 4-state Ising-Potts model is applied to the [Mn(taa)] system to elucidatethermodynamic relations [21]. An [Mn(taa)] molecule is assumed to take fourdifferent microscopic states: state 0 is the LS state and states 1-3 are the HS stateswith the elongation axis parallel to x, y, and z, respectively. Interactions areassumed only between nearest neighbor molecules. Under a mean-fieldapproximation [22], the internal energy of the [Mn(taa)] system is expressed interms of populations ρi (i = 0, 1, 2, 3) of four microscopic states, U = ∆(1 – ρ0) + J0(ρ1

2 + ρ22 + ρ3

2) + 2J1ρ0(1 – ρ0),where ∆ (> 0) is the LS-HS gap, J0 (< 0) is the Potts-type ferroelectric interaction

between the HS species, and J1 (> 0) is the Ising-type demixing interactionbetween HS and LS species [23]. The entropy S of the system consists of thecontribution of spin-multiplicity and the entropy of mixing,

S / kB = ρ0ln(2SLS + 1) + (1 – ρ0)ln(2SHS + 1) - i=

∑0

3ρilnρi,

where SLS = 1 and SHS = 2 are spin quantum numbers of the LS (i = 0) and HS (i =1, 2, 3) states, respectively. By minimizing the free energy of the system F = U–TS under a normalization condition ρ0 + ρ1 + ρ2 + ρ3 = 1, i.e. solving ∂F/∂ρi = 0, ∂2F/∂ρi∂ρj > 0, (i, j = 1, 2, 3),three stable solutions are obtained: an LS phase (ρ0 » ρ1 = ρ2 = ρ3), an HS phase(ρ0 « ρ1 = ρ2 = ρ3), and a ferroelectric-ordered (FO) phase (ρ0 « ρ1 = ρ2 < ρ3).These three phases are shown in a T-J0 phase diagram (Fig. 7). The HS phasehas the highest entropy and occupies high-temperature regions. Two distinctordered phases, LS and FO, appear at lower temperatures, and the most stablephase observable near 0 K switches from one to the other at a critical value J0 = -∆.

The phase boundary between the HS and LS phases is given by Tc(J0) = (∆ + J0 / 3) / kBln[3(2SHS + 1) / (2SLS + 1)].Both spin-crossover transitions (HS ⇔ LS, FO ⇔ LS) are first order accompanied

by definite jumps of populations, while the cooperative Jahn-Teller transition (HS⇔ FO) is weak first-order (very close to a second-order transition). It suggests apossibility of observation of hidden cooperative Jahn-Teller transition (the broken

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line in Fig. 7) between the metastable HS and FO phases, if the HS phase could besupercooled enough below the spin-crossover transition temperature Tc by a rapidcooling. The three adjustable parameters are determined, ∆ / kB = 90 K, J0 / kB = -36 K,and J1 / kB = 125 K, so as to reproduce the spin-crossover transition temperature Tc

= 48 K, the virtual Jahn-Teller transition temperature TJT ≅ θ = 26 K, and theeffective LS-HS gap in the LS phase ∆eff / kB = 340 K. (Note ∆eff is approximatedby ∆ + 2J1 in this mean-field model.) This choice of model parameters gives a

phase sequence from LS to HS with increasing temperature, corresponding to thearrow path in Fig. 7. Temperature dependence of thermodynamic quantities (Fig.8) is calculated along the path indicated by the arrow in Fig. 7, where thediscontinuities arising from the first-order spin-crossover transition arerecognized: ∆ρ0 = 0.99, ∆H = 0.64 kJ mol-1, and ∆S = 13.3 J K-1 mol-1. These

Fig. 7. Mean-field phase diagram ofthe 4-state Ising-Potts model (∆ / kB =90 K, J1 / kB = 125 K). The high-spinphase (HS), the low-spin phase (LS),and the ferroelectric-ordered phase(FO) are shown. The arrow linecorresponds to J0 / kB = -36 K,appropriate to the [Mn(taa)] system.

5

4

3

2

1

0604020

25

20

15

10

5

0604020

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0604020

1.0

0.8

0.6

0.4

0.2

0.0604020

T / K T / K

T / K T / K

1, 2, 3

0

Fig. 8. Thermodynamic quantitiesof the 4-state Ising-Potts modelalong the heating path (arrow line)in Fig. 7.

13

theoretical values compare well with the experimental ones, ∆H = 0.60 kJ mol-1

and ∆S = 13.8 J K-1 mol-1 [12]. The good agreement supports the validity of the4-state Ising-Potts model in the spin-crossover [Mn(taa)] system. Jahn-Teller effects are rarely adopted in theoretical treatments of spin-crossover phenomena, except Kambara's model for Fe(II) complexes [24] andBersuker's for Fe(III) complexes [19, 25]. In the Kambara theory, abrupt spin-crossover transitions are given an FO ⇔ LS character, while gradual transitionsare of the HS ⇔ LS type. However, experimental evidences of cooperativeJahn-Teller transitions (FO ⇔ HS) have not yet been reported for Fe(II) spin-

crossover complexes. Kambara's theory ignores the spin-orbit interaction andappears to overestimate the Jahn-Teller coupling, producing an unphysical (forFe(II) complexes) FO ⇔ HS transition.

The most interesting possibility indicated by this phase diagram is that theFO phase may be present as a metastable phase below TJT ≅ 26 K, instead of theHS phase above TJT. It suggests that physical properties of the metastable phasemay change at TJT. Recently a photo-induced metastable phase of an Fe(II) spin-crossover complex [Fe(2-pic)3]Cl2 •EtOH (2-pic = 2-aminomethylpyridine) wasreported [26-28]. Its properties are remarkably different from those of themetastable HS phase quenched by rapid cooling. Lowered symmetryaccompanying the Jahn-Teller deformation has been invoked to explain thedifference. The situation has close similarity to the present compound. Thus,[Mn(taa)] may be driven into a Jahn-Teller distorted FO phase by irradiation oflight. The strong cooperativity indicated by the large value of J1 / kB = 125 K is afavorable factor [29], even though the HS ⇔ LS transition has very small thermal

hysteresis. Recently high-field / high-frequency EPR spectra of [Mn(taa)] were recordedfor a powder sample at 1017.6 GHz. Analysis of the spectra showed the presenceof a rhombic zero-field splitting in the HS molecule [30], which is consistent withthe symmetry lowering by E ⊗ e Jahn-Teller distortions and the dynamicreorientation of deformation dipoles slower than the time scale of ~10-12 s.

4. Conclusion

Spin-crossover phase transition of a manganese(III) complex [Mn(taa)] wasstudied by variable-temperature Laser Raman spectroscopy and it was found thatthe vibrational contribution in the transition entropy is not dominant in contrast to

14

the cases of ordinary iron spin-crossover systems. The discovery of a dynamicdisorder in the HS phase by means of dielectric measurements provided analternative entropy source to explain the thermally-induced spin-crossovertransition. This dynamic disorder was attributed to the reorienting distortiondipoles accompanying the E ⊗ e Jahn-Teller effect in HS manganese(III) ions.

Acknowledgments

The authors are grateful to Mr. Mitsuo Ohama at Osaka University forrecording variable-temperature Raman spectra. This work was supported by aGrant for Basic Scientific Research from the Sumitomo Foundation, a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports,Science and Technology of Japan (MEXT), and a Strategic Research BaseUpbringing Special Coordination Fund for Promoting Science and Technology.

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