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Magneto-structural relationships for a mononuclear Co(II) complex with largezero-field splitting

B. Papánková a, R. Boca a,b,*, L. Dlhán a, I. Nemec a, J. Titiš b, I. Svoboda c, H. Fuess c

a Institute of Inorganic Chemistry, Technology and Materials (FCHPT), Slovak University of Technology, SK-812 37 Bratislava, Slovakiab Department of Chemistry, University of SS Cyril and Methodius, Trnava, Slovakiac Material Science, Darmstadt University of Technology, D-64287 Darmstadt, Germany

a r t i c l e i n f o

Article history:Received 2 June 2009Received in revised form 28 August 2009Accepted 11 September 2009Available online 16 September 2009

Keywords:Cobalt(II) complexesImidazole complexesMagnetismZero-field splittingElectronic spectrum

a b s t r a c t

A mononuclear cobalt(II) complex, [Co(ac)2(H2O)2(MeIm)2], with heteroleptic coordination sphere pos-sessing the {CoO2O02N2} chromophore has been prepared and structurally characterized. The magneticdata down to 2 K show an enhanced magnetic anisotropy manifesting itself in a large zero-field splitting(ZFS) parameter. As a consequence, the magnetization deviates substantially from the Brillouin-functionbehavior. A fit to the zero-field splitting model gave the following set of magnetic parameters:D/hc = +95 cm�1, gx = 2.530, zj/hc = �0.078, vTIP = 16.7 � 10�9 m3 mol�1, (gz = 2.0). The Griffith–Figgismodel and the Generalized Crystal-Field model lie beyond the spin-Hamiltonian formalism; they gaveanalogous, although not identical ZFS parameters: D/hc = 109 cm�1, and D/hc = 77 cm�1, respectively.The absorption spectrum taken in the FAR-IR region exhibits manifold absorption peaks referring tothe transitions among the crystal-field multiplets of the parent 4A2g + 4Eg terms (D4h), originating in acrystal-field splitting of the octahedral 4T1g ground term.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Magneto-structural relationships reflect a correlation betweenthe structural parameters of the complex under study and themagnetic parameters withdrawn from the magnetic data (temper-ature dependence of the magnetic susceptibility). The magneto-structural J-correlation is the correlation of the isotropic exchangecoupling constant (J) with the bridging angle (a = M–O–M) in dinu-clear complexes and it represents one of the best studied case [1].Recently, another type of the relationship has been reported: themagneto-structural D-correlation [2–6], where the axial zero-fieldsplitting parameter (D) has been correlated with the structural(tetragonal) distortion Dstr. The above correlation has been provenfor a series of mononuclear Ni(II) complexes possessing the groundelectron term 3A2g(Oh) ? 3B1g(D4h), where the spin–orbit couplingcauses its zero-field splitting to C5 (doublet) and C4 (singlet) mul-tiplets: D = E(C5) � E(C4). On tetragonal elongation D > 0 holdstrue, whereas on the compression there is D < 0. Hereafter, theMulliken notation (A, B, E, T) is used for the irreducible representa-tions of the ordinary point groups whereas the Bethe notation (Ci)is used for double groups (when the spin–orbit coupling is ac-counted for).

The above correlation cannot be simply transferred to other sys-tems without care of the ground electronic state. It could be validfor an analogous Cr(III) system possessing the ground electronterm 4A2g(Oh) ? 4B1g(D4h) ? {C6,C7}(D04).

The Co(II) systems (Fig. 1) differ from the above cases in the fea-ture that the ground electron term in the octahedral geometry isorbitally threefold degenerate: 4T1g(Oh). On tetragonal elongationit splits into the terms 4Eg(D4h, ground) and 4A2g(D4h, excited)and this splitting is taken as negative: Dax = E(4Eg) � E(4A2g) < 0.Their 12-membered multiplets (C6a < C6b < C7a < C7b < C6c < C7c,each representing a doublet) lie close to one another. This manifoldcannot be reduced to the traditional spin-Hamiltonian with spin-kets spanning the S;MSj i space having only four members:3=2;�1=2j i and 3=2;�3=2j i. Notice also the double-group nota-

tions: C6 M E1/2 and C7 M E3/2.On tetragonal compression the 4T1g(Oh) term splits into the

terms 4A2g(D4h, ground) and 4Eg(D4h, excited) with Dax > 0. Theordering of the multiplets is different (C6a < C7a < C6b <C6c < C7b < C7c) owing to which the four members of the former4A2g term (C6a < C7a) can be considered within the spin-Hamilto-nian formalism. The corresponding energy gap can be attributedto the zero-field splitting: 2D = E(C7a) � E(C6a) > 0.

The magnetism of metal complexes is determined by the crys-tal-field multiplets that exhibit a further splitting under the influ-ence of an applied magnetic field (Zeeman splitting) [7]. Just theCo(II) complexes represent an interesting case where severalimportant factors tune the overall magnetic behavior. Therefore

0020-1693/$ - see front matter � 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.ica.2009.09.028

* Corresponding author. Address: Institute of Inorganic Chemistry, Technologyand Materials (FCHPT), Slovak University of Technology, SK-812 37 Bratislava,Slovakia.

E-mail address: roman.boca@stuba.sk (R. Boca).

Inorganica Chimica Acta 363 (2010) 147–156

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we prepared a mononuclear hexacoordinate Co(II) complex thatexhibits an effectively compressed tetragonal bipyramid. This com-plex has been structurally characterized and subjected to magneto-chemical studies. As a complementary study, the electronic spectrahave been taken in the visible and far-infrared region with theambition to get useful magneto-structural relationships.

2. Experimental

The complex under study, 1, has a composition of [Co(a-c)2(H2O)2(MeIm)2] where MeIm is the 1-methylimidazole, ac – ace-tato ligand. Its preparation and the single-crystal X-ray structureanalysis have been briefly reported [8].

The commercial SQUID apparatus (MPMS, Quantum Design) hasbeen used in taking the temperature dependence of the magnetic

susceptibility (B = 0.1 T) and the field dependence of the magneti-zation (T = 2.0 K). Raw susceptibility data have been corrected forthe underlying magnetism with the estimate of vdia = �2.40 �10�9 m3 mol�1 (SI units) based upon the Pascal constants.

The spectrophotometer (Specord 200, Analytical Jena) has beenused in scanning the electronic spectra of the sample in Nujol mullin the visible region. The FT-IR apparatus (Magna FT-IR 750, Nicolet)has been applied in recording the absorption spectra in the FAR-IRregion (50–600 cm�1); the sample was prepared as a nylon pellet.

3. Theory

The magnetism of Co(II) complexes with the reference 4T1g(Oh)ground term can be studied at several levels of complexity asfollows.

8Dq

10Dq

15B

4F

4P

4A2g

4T2g

4T1g

4T1g

4B1g

4B2g

R3 Oh D4h(compressed) D'4 O'

Δax > 0

Δo

2G

4B+3C

Δ3 ~ 15B + 12Dq

Δ2 ~ 18Dq

4A2g

4Eg(1)

4Eg(2)

Γ6 x 2

Γ6 x 2

Γ8 x 4

Γ8 x 4

Γ6 x 2

Γ7 x 2

Γ7 x 2

Γ7 x 2

Γ6 x 2

δo = −(3/2)Aλ

CI

axial strengthening

Γ7 x 2Δ'xy

Δxy

(Γ7,Γ8) x 6

δ67 = 2D

8Dq

10Dq

15B

4F

4P

4A2g

4T2g

4T1g

4T1g

4B1g

4B2g

δ66

R3 Oh D 4h(elongated) D'4 O'

Δax < 0

Δo

2G

4B+3C

Δ3 ~ 15B + 12Dq

Δ2 ~ 18Dq

4A2g

4Eg(1)

4Eg(2)

Γ7 x 2

Γ6 x 2

Γ8 x 4

Γ8 x 4

Γ6 x 2

Γ7 x 2

Γ6 x 2

Γ6 x 2

Γ7 x 2

δo = −(3/2)Aλ

CI

axial weakening

Γ7 x 2

(Γ7,Γ8) x 6

Fig. 1. Energy levels of nearly-octahedral d7 systems on symmetry lowering (not to scale).

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(i) The simplest model assumes the basis set of four spin kets,and it refers to the zero-field splitting model (ZFS).

(ii) A more complex approach refers to the Griffith–Figgis model(GF) working in the restricted basis of 12 functions account-ing for the ground 4T1g(F) term (being eventually in the con-figuration interaction with 12 other functions of the excited4T1g(P) term).

(iii) Even more general is the model based upon the Crystal-FieldTheory (CFT) that works in the basis set of 120 functionsspanned by all terms of the d7 electron configuration.

The spin-Hamiltonian that accounts for the zero-field splitting(ZFS) and the spin-Zeeman term has the form

HS ¼ �h�2½DðS2z � S2=3Þ þ EðS2

x � S2yÞ� þ �h�1lBð~B � ��g �~SÞ ð1Þ

where the physical constants adopt their usual meaning. Here, D isthe axial zero-field splitting parameter; E is the rhombic ZFS param-eter (not mandatory). The relationships for the magnetic parame-ters occurring in the spin-Hamiltonian have been presentedelsewhere (see, for instance, Ref. [9]). The magnetic parametersare interrelated through the K-tensor (‘‘angular momentumunquenching tensor”). With the sign convention

Kab ¼ þ�h�2XK–0

0jLajKD E

KjLbj0D E

= EK � E0ð Þ ð2Þ

one gets the relationships

gab ¼ gedab � 2kKab ð3Þ

D0ab ¼ �k2Kab ð4Þ

D ¼ ð�D0xx � D0yy þ 2D0zzÞ=2! ð3=2ÞD0zz ¼ �ð3=2Þk2Kzz ð5Þ

E ¼ ðD0xx � D0yyÞ=2 ¼ �ð1=2Þk2ðKxx �KyyÞ > 0 ð6Þ

vTIP ¼ þð2=3ÞNAl0l2BðKxx þKyy þKzzÞ > 0 ð7Þ

bringing some insight into the nature of these magnetic parameters(k ¼ �n=2S is the spin–orbit splitting parameter within the groundterm, vTIP is the temperature independent paramagnetism). In asimple sentence: the magnetic parameters (gx, gy, gz, D, E, and vTIP)reflect the influence of the angular momentum La Kj i carried by theexcited electronic states Kj i through the matrix elements h0jLajKi.For the spin kets I ¼ S;MSj i one readily gets the matrix elementsHJIðBÞ ¼ hJjHSjIi [9]. The eigenvalues for the given magnetic fieldrepresent the Zeeman energy levels eiðBÞ. These enter the partitionfunction Z, from which the magnetization and the magnetic suscep-tibility can be calculated by using the formulae of the statisticalthermodynamics

Z ¼X

i

exp �eiðBÞ=kT½ � ð8Þ

Mmolð Þa ¼ RT@ ln Z@Ba

� �T

ð9Þ

~vmolð Þab ¼ l0@ðMmolÞa@Bb

� �T

ð10Þ

(In some particular cases closed formulae are available.) The fittingprocedure can be accomplished by considering the six magneticparameters as being independent. Alternatively, one can performthe fitting to three components of the K-tensor from which themagnetic parameters can be reconstructed. This is equivalent tothe procedure when two or three g-tensor components are fitted

independently and the ZFS parameters are reconstructed throughthe formulae

D ¼ k½gz � ðgx þ gyÞ=2�=2 ð11Þ

E ¼ kðgx � gyÞ=4 ð12Þ

From the formal point of view, D can be negative or positive, and E isalways taken as positive. The value of 2D opens the zero-field en-ergy gap between MS ¼ �1=2 and MS ¼ �3=2 Kramers doublets.The value of E enters that energy gap but causes no additional split-ting of the Kramers doublets (Fig. 2).

Based upon the modeling presented on Figs. 3 and 4, the follow-ing conclusions can be drawn.

1. The energy levels and the magnetization components developin the given orientation of the magnetic field differently, show-ing a magnetic anisotropy.

2. The susceptibility components develop with temperature dif-ferently, which is the fingerprint of the magnetic anisotropy.With jDj=k = 20 K the magnetic anisotropy is well pronouncedfor T < 50 K.

Bx /TBz /T

(εi/ k

)/K

-20

-10

0

10

20

0 2 4 6 8 100 2 4 6 8 10

Fig. 2. Development of energy levels for S = 3/2 ZFS system in a magnetic field. Left– parallel direction, right – perpendicular. Modeling parameters: D/k = +10 K, E/k = 3 K.

B/T

D = 0D/k = +5KD/k = +10 KD/k = +15 KD/k = +20 K

B/T

0 2 4 6 8 100 2 4 6 8 10

Mm

ol/(

NA

μB

)

0

1

2

3

D = 0D/k = −5 KD/k = −10 KD/k = −15 KD/k = −20 K

Fig. 3. Modeling the magnetization for S = 3/2 ZFS system as an average of principalcomponents at T = 4.2 K. Left – negative D, right – positive D; g = 2.0. Note: e/k(K) ¼: 0.7 e/hc (cm�1).

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3. The averaged susceptibility (or the product function vT) isinsensitive to the sign of the D-parameter (valid only for thespin S = 3/2). With increasing |D| the magnetizationdeflects progressively from the Brillouin-function behavior)characteristic for the Curie paramagnets). At the same timethe product function deviates from the straight-line behaviorand approaches a constant limit.

The above modeling has been done assuming an isotropic g-fac-tor, g = ge = 2.0. However, the asymmetry in the K-tensor compo-nents causes not only the non-zero D (and E) but also anisotropicg-factors. With different g-factors (gx < gz) the product function(or the effective magnetic moment) passes through a maximum[10].

The second theoretical approach, pioneered by Griffith and Fig-gis, accounts for the orbital angular momentum. The Hamiltonianappropriate for such a purpose can be written in the form

H ¼ �h�1lB~B � Aj~Lþ ge

~S� �

þ �h�2ksf Aj~L �~S� �

þ Dax �h�2L2z � LðLþ 1Þ=3

h ið13Þ

where different magnetic parameters occur: Dax, ksf, A, j. The firstterm contains the orbital-Zeeman operator �h�1lBð~B �~LÞ tuned bytwo additional factors. The orbital reduction factor 0 < j 6 1 re-flects the covalent character of the metal–ligand bond (j = 1 for apure ionic bond). The Figgis factor (A) accounts for the configuration

interaction of the ground 4T1g(F) and excited 4T1g(P) terms. Thismixing parameter equals to

A ¼ ½ð3=2Þ � C2�=½1þ C2�; ðstrong-fieldÞ 1 < A < 3=2 ðweak fieldÞð14Þ

where

C ¼ f3þ ð15=2ÞðB=DqÞ � ½25þ 45ðB=DqÞþ ð225=4ÞðB=DqÞ2�1=2g=4 ð15Þ

(B is the Racah parameter of electron repulsion; Dq is the crystalfield strength parameter). The spin-Zeeman operator, �h�1lBgeð~B�~SÞ, contrary to the spin-Hamiltonian approach, contains the free-electron g-factor ge. Next term in Eq. (13) describes the spin–orbitinteraction within the ground term where the spin–orbit splittingparameter taken in the strong-field limit occurs: ksf ¼ �nd=2S (theminus sign applies for configurations more than half-full, like d7);this is tuned by the Aj product. The last term reflects the symmetrylowering owing to the axial crystal field.

On applying the ‘‘Tp isomorphism”, according to which the orbi-tal angular momentum for T2g kets within the Oh group is substi-tuted for that of free-atom p-functions ~LðOhÞ ! csf~LpðR3Þ ¼�~LpðR3Þ, we arrive at the Hamiltonian

H ¼ Dax½�h�2L2z � LðLþ 1Þ=3� þ �h�2ksfðcsf Aj~Lp �~SÞ

þ �h�1lB~B � ðcsf Aj~Lp þ ge

~SÞ ð16Þ

T/KT/K

χ mol

/10

6 m

3 mol

−1

0

1

2

averaged

parallelperpendicular

T/K

(χz

−χ x)

l/106

m3 m

ol−1

-4

0

4

D > 0

D < 0

D/k = +20 K D/k = −20 K

T/KT/K

0 50 100 1500 50 100 150 0 50 100 150

0 50 100 1500 50 100 150

(χaT

/C0)

0

2

4

6

8

10D/k = +20 K D/k = −20 K

Fig. 4. Modeling the susceptibility and product function for S = 3/2 ZFS system. Dot-dashed – vjj; short dashed – v?; solid – vav. (Reduced Curie constant – C0 ¼ NAl0l2B=k).

150 B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156

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where L = 1 and csf ¼ �1 should be applied. The basis set consists ofall combinations of the orbital kets L;MLj i and the spin kets S;MSj iyielding the number N ¼ ð2Lþ 1Þð2Sþ 1Þ of spin&orbital ketsðLSÞMLMSj i. The corresponding matrix elements are already avail-

able [7,9]. Since the resulting cubic equation has not eigenvaluesin a closed form, a numerical solution is necessary.

The above-described approach can be used in describing the sit-uations that occur on departing the octahedral geometry in bothdirections (elongation and compression). The zero-field energy lev-els are schematically drawn in Fig. 5. The temperature dependenceof the magnetic susceptibility (transformed to the effective mag-netic moment) is shown in Fig. 6. It can be seen that for the elon-gated bipyramid (and for the octahedron itself), whenv � D=k P 0, the effective magnetic moment on temperature low-ering passes through a maximum. For the compressed bipyramid(v < 0) it behaves like the ZFS system with large D and large-posi-tive vTIP.

With the ground term 4A2g, and assuming Dax � jkj, we arrive atthe approximate expressions for the K-tensor components and re-lated spin-Hamiltonian parameters

Kxx ¼ A2j2x=Daxð4A2g ! 4EgÞ; Kzz ¼ 0 ð17Þ

gx ¼ ge � 2kKxx ¼ ge � 2kA2j2x=Daxð4A2g ! 4EgÞ; gz ¼ ge ð18Þ

D ¼ kðgz � gxÞ=2 ¼ k2Kxx ¼ k2A2j2x=Daxð4A2g ! 4EgÞ ð19Þ

vTIP ¼ NAl0l2Bð2=3Þ½2A2j2

x=Daxð4A2g ! 4EgÞ� ð20Þ

In the third, the most complex theoretical approach, five contribut-ing operators are considered, namely the electron repulsion, thecrystal field potential, the spin–orbit coupling, the orbital-Zeeman,and the spin-Zeeman terms [7]. The appropriate basis set consistsof all electron terms dn

: v ; L; S;ML;MS

�� �arising from the dn electron

configuration. In the case of a d7 system it consists of 4F, 4P, 2G, 2H,2P, 2

1D, 2F, 23D atomic terms (the subscript denotes the seniority

number when necessary) and the total number of the basis-set

functions equals to N ¼ 107

� �¼ 120. The matrix elements can be

computer-generated by utilizing the full battle of the irreducibletensor operator (ITO) approach. The electron repulsion is parame-terized with the help of the Racah parameters B and C. The crystalfield operator contains the even-order crystal-field poles of individ-ual ligands, F2(L) and F4(L), of which F4 = (6/10) � 10Dq. The spin–or-

bit operator contains the true spin–orbit coupling constant nd. Thespin-Zeeman term contains the free-electron g-factor (ge) whereasthe orbital reduction factors (jx, jy, jz) occur in the orbital-Zeemanterm. As a result of the eigenvalue problem, the energies of the crys-tal-field multiplets are obtained in the zero-field. With the appliedreference field Br, the Zeeman energy levels result. These enter thepartition function from which the magnetization and the magneticsusceptibility are evaluated using numerical derivatives.

The last treatment instantaneously accounts for the configura-tion interaction of crystal-field terms and multiplets. The zero-fieldsplitting parameter is read off as an energy difference of the lowestmultiplets: D13 = e(C7) � e(C6) = 2D (valid for a compressed tetrag-onal bipyramid). The variation of the zero-field energy gap withthe crystal-field strengths in the equatorial plane and axial posi-tions is displayed in Fig. 7. It can be seen:

(1) the spacing of the lowest energy levels for the elongatedbipyramid, D = e(C6b) � e(C6a), is almost constant over awide range of the crystal-field strengths and ranges asD/hc 230–280 cm�1;

(2) for the octahedron the energy gap refers to D = e(C8, quar-tet) � e(C6) and it decreases from the value of 347 atF4 = 5000 to 265 at F4 = 15 000 (all values in cm�1);

(3) for the compressed bipyramid, on the contrary, the energygap varies in a broad range; it drops progressively with thecrystal field asymmetry (on negative Dt) and approaches

R3 Oh D'4 D4h OhO'

4F x 28

4T1 x 12 4T1 x 12

Γ6 x 2

Γ8 x 4

(Γ7,Γ8) x 6

J = 5/2, ε = −(3/2)λA

J = 3/2, ε = λA

J = 1/2, ε = (5/2)λA

4A2 x 4

4E x 8

ε = −(2/3)Δax

ε = (1/3)Δax

Γ7 x 2

Γ6 x 2

Γ6 x 2

Γ7 x 2

Γ6 x 2

Γ7 x 2

CI

spin-orbit spin-orbit compressioncompression

~

Fig. 5. Zero-field energy levels for the split 4T1g ground term on tetragonal compression (not to scale); k < 0.

d 7, 4T1g, λ < 0

kT/|λ|0 1 2 3

μef

f/μ

B

3.0

3.5

4.0

4.5

5.0

v = −10

v = +10

v = 0

Fig. 6. Temperature dependence of the effective magnetic moment for the ground4T1g term within the Figgis theory. Note: v ¼ D=k.

B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156 151

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the lowest limit of 2D = 47 at F4(xy) = 4000 and F4(z) =15 000 cm�1. A normal value is about 100 cm�1.

The above findings represent a key result of the theoreticalmodeling showing that the allowed D value for tetragonally com-pressed Co(II) complexes is large and positive.

The eigenvectors for the crystal-field terms obtained by theabove approach can be used in evaluating the K-tensor compo-

nents and consequently the spin-Hamiltonian parameters (Fig. 8).It can be seen that the gz-component adopts a constant value forthe compressed tetragonal bipyramid (negative Dt) whereas thegx-component can very between 2.3 and 3.5. (On approaching theoctahedral geometry the spin-Hamiltonian formulae diverge.) Alsothe vTIP adopts substantial values, between 3 and 20 (in units of10�9 m3 mol�1). Notice, the Cu(II) systems possess the value ofonly 0.7 (same SI units).

0

100

200

300

4000

60008000

1000012000

14000

4000

60008000

1000012000

(Δ13

/hc)

/cm

-1

F 4(xy)F

4 (z)

axial strengthening - axial weakening

Γ6

Γ6

Γ6

Γ7

Γ8

4000

6000

8000

10000

12000

14000

400060008000100001200014000 F 4(x

y)

F4(z)

Fig. 7. Calculated energies (in full dn space) of the lowest multiplets (each doubly degenerate) relative to the ground state for high-spin/weak&intermediate-field Co(II)complexes; F4ðxyÞ and F4ðzÞ ranging between 4000 and 14,000 cm�1. Right – a rotated view.

Dt /hc /cm−1

χT

IP/1

09 m3 m

ol−1

0

5

10

15

20

25

Dt /hc /cm−1

g z

1.90

1.95

2.00

2.05

2.10

2.15

2.20

Dt /hc /cm−1

-1000 -500 0 500 1000-1000 -500 0 500 1000 -1000 -500 0 500 1000

g x

2.0

2.5

3.0

3.5

4.0

Fig. 8. Spin-Hamiltonian projection of magnetic parameters on tetragonal distortion of high-spin/intermediate&weak-field Co(II) complexes for F4 between 4000 and14,000 cm�1; Dt ¼ ð2=21Þ½F4ðxyÞ � F4ðzÞ�. Manifold coordinate points refer to different 10 Dq.

Fig. 9. The molecular structure of the complex [Co(ac)2(H2O)2(MeIm)2] with highlighted chromophore – left; crystal packing – right.

152 B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156

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4. Results and discussion

The structure of the complex under study is shown in Fig. 9. Thecomplex possesses an orthorhombic {CoO2O02N2} chromophorewith interatomic distances CoAO(ac) = 2.1220(12), CoAO(w) =2.1702(13), and CoAN = 2.1273(15) Å. The averaged CoAO distanceis 2.146 Å and to the first approximation the coordination polyhe-dron can be considered as a compressed tetragonal bipyramid (D4h

group).Because of the heterogeneous donor set, the distortion parame-

ter is defined as [6]

Dstr ¼ Dz � ðDy þ DxÞ=2 ð21Þ

where

Da ¼ ðdi � �diÞ ð22Þ

for a = x, y, z is a shift relative to the mean distance �di for a givenbond (i = N, O). For the N- and O-donor ligands these values havebeen taken from complexes containing the [Co(NH3)6]2+ and[Co(H2O)6]2+ units, respectively, giving rise to �dðCo�NÞ = 2.185 Åand �dðCo� OÞ = 2.085 Å [11]. Consequently, Dz(CoAN) = 0.058,Dx(CoAOw) = 0.085 and Dy(CoAO) = 0.037 yielding the distortion

parameter Dstr = 0.119 Å. Thus complex under study possess an‘‘effective compression”.

Experimental magnetic data for 1 are show in Fig. 10 along withthe fitting curves by applying the spin-Hamiltonian with the zero-field splitting (1). The magnetic parameters are: [gz = 2.0 � fixed],gx = 2.530, D/hc = +95.0 cm�1, vTIP = 16.7 � 10�9 m3 mol�1, and amolecular-field (MF) correction zj/hc = �0.078 cm�1; discrepancyfactors R(v) = 0.0043 and R(M) = 0.037). A fit of a similar qualityhas been obtained with gz� 2 and D < 0 but these values, accord-ing to the theoretical modeling, are not permitted for the com-pressed tetragonal bipyramid. The minor molecular-fieldcorrection is essential in reproducing the low-temperature suscep-tibility data below 10 K. The corrections are applied in the form

vcor ¼ v=½1� ðzj=NAl0l2BÞ � v� þ vTIP

¼ v=½1� ðzj=kC0Þ � v� þ vTIP ð23Þ

where the MF parameter (zj) includes the isotropic exchange inter-action (j) with the number of nearest neighbors (z).

The magnetic parameters recover the susceptibility data as wellas the magnetization data perfectly. The principal message fromthem is that the complex under study possesses an enhanced mag-netic anisotropy reflecting itself in very different g-components

T/K

μ eff/

μ B

0

1

2

3

4

5

6

B/T

0 50 100 150 200 250 300 0 1 2 3 4 5 6

Mm

ol/(

NA

μB

)

0

1

2

3

4

0 5 10 15 20 25

3.5

4.0 T = 2.0 K

B = 0.1 TBrillouin function

T = 4.6 K

Fig. 10. Magnetic data for 1: left temperature dependence of the effective magnetic moment; right – field dependence of the magnetization. Open points – experimental data,filled and solid line – fitted with the spin-Hamiltonian. Dashed (inset) – molecular-field correction switched off. Dotted – Brillouin function for magnetization withgav = 2.353.

Table 1Magnetic parameters for hexa- and penta-coordinate Co(II) complexes.

System Magnetic parameters, energy quantities in cm�1 a Ref.

(A) This work[Co(ac)2(H2O)2(MeIm)2] Model 1 (ZFS): D = 95, gx = 2.530, vTIP = 16.7 � 10�9 m3 mol�1, zj/hc = �0.078, [gz = 2.0]

Model 2 (GF): D = 109, Aj = 1.38, Dax = 503, zj/hc = �0.078, [n = 515, gS = 2.0]Model 3 (CFT): D = 77, B = 830, C = 5000, F4(O) = 5700, F4(N) = 6600, j(O) = 0.8, j(N) = 0.6, [n = 515, g = 2.0]

(B) Comparison with other works (hexacoordination)[Co(iphos)2(H2O)2] D = 52, E = 17, gz = 1.70, gx = 2.53 [12][Co(acac)2(H2O)2] D = 82.7; B = 980, n = 435, 10Dq = 9300, d = 550 [15][Co(pyO)6](ClO4)2 D = 25.5; B = 780, C = 3030, n = 525, 10Dq = 8900, Dep = 665 [16]

(C) Comparison with other works (pentacoordination)[Co(bzimpy)Cl2] D = 73.4, E = 3.28, gz = 1.506, gx = 2.501, gy = 2.622, zj = �0.205 [13][Co{L5

NNNOO}] D = 48.4, gz = 2.06, gx = 2.62 [14](NEt4)2[Co{L3

SSOO}]�2H2O A = 1.4, j = 1, k = 160, d = 800 [17]

a Fixed values in square brackets.

B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156 153

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and a very high axial zero-field splitting parameter D. The zero-field energy gap amounts to D/hc = 2D = 190 cm�1.

The inspection to Table 1 shows that the obtained D-parameteris the largest reported so far (but still ‘‘normal” in view of the CFTpredictions). For instance, the hexacoordinate complex [Co(aca-c)2(H2O)2] possesses the ZFS parameter D/hc = 83 cm�1. Large ZFSparameters have been quoted also for penta-coordinate Co(II)complexes.

Attempts to fit the magnetic susceptibility in terms of the Grif-fith–Figgis model (13) were also successful (Fig. 11a). In reality, thefollowing form of the Hamiltonian has been applied

H ¼ Dax½�h�2L2z � LðLþ 1Þ=3� � �h�2J12ð~j1 �~j2Þ þ �h�1lB

~B � ðg1~j1 þ g2

~j2Þð24Þ

where the correspondence between the angular momenta~j1 $~Lp

and~j2 $~S is obvious. The independent magnetic parameters thatshould be fixed by the fitting procedure are g1 = Aj (ranging be-tween �1:5 6 g1 6 �j) and Dax. The coupling parameter is con-strained through the relationship J12 � �csfksf Aj ¼ �ðn=2SÞAj ¼ðn=2SÞ � g1 with n = 515 cm�1. The resulting set is: g1 = 1.383, Dax/hc = 503 cm�1, and the additional MF correction zj/hc =�0.078 cm�1 (R(v) = 0.45%). The value of g1 reflects some orbital

T/K

μ eff/

μB

0

1

2

3

4

5

6

3.0

3.5

4.0

4.5

T /K

μ eff/

μB

0

1

2

3

4

5

6

0 50 100 150 200 250 300

0 5 10 15 20 25

0 50 100 150 200 250 300

0 5 10 15 20 253.0

3.5

4.0

4.5

(a) Fitted with the Griffith-Figgis model with (solid) and without (dashed) MF

correction

(b) Reconstructed with the crystal-field model without MF correction (dashed)

Fig. 11. Calculated magnetic susceptibility (transformed to the effective magnetic moment) for 1.

Wavenumber /103 cm−1

10 12 14 16 18 20 22 24 26 28

Inte

nsity

/a.u

.

0.0

0.1

0.2

0.3

0.4

0.5

4A2g4T1g

(4Eg,4B2g) (4B1g)

4T2g

(4A2g,4Eg)

CT

8Dq

10Dq

15B

4F

4P

4A2g

4T2g

4T1g

4T1g

4B1g

4B2g

Δax > 0

Δ1

2G

4B+3C

4A2g

4Eg

CI

4A2g

4Eg

4Eg

Δ2

Δ3

Oh D4hR3

Fig. 12. Electronic d–d spectrum of 1 in the visible region (left) and the corresponding term-diagram (right). Solid – measured, dashed – calculated for Oh group, dotted –individual Lorentzian primitives drawn from zero-level. Labels in parentheses refer to the D4h group.

154 B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156

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reduction. The reconstructed lowest energy levels (e/hc = 0, 219,567, 965, 1071, 1194 cm�1) will be useful in interpreting the lowestelectronic transition (see below).

The recorded electronic spectrum for 1 is displayed in Fig. 12along with the energy level diagram. The first band at D1/hc 9000 cm�1 is attributed to the 4T1g ?

4T2g transition in theOh group. More precisely, it consists of transitions 4A2g ? (4Eg,4B2g) in the D4h group. The second, more intense band at D2/hc 19 000 cm�1 is attributed to the allowed 4T1g ?

4A2g transi-tion. Between these bands a series of spin-forbidden transitionsto the spin-doublets (originating in the atomic 2G term) occurs.The position of the third allowed transition 4T1g ?

4T1g(P) is oddlyseen as an arm at D3/hc 20 000 cm�1. This band is followed by anintense charge-transfer (CT) band.

The electronic spectrum has been deconvoluted assuming threeLorentzian-shaped primitive curves

Ið~v iÞ ¼X4

K¼1

AK

1þ ½ð~vK � ~v iÞ=rK �2þ b ð25Þ

where AK is the height, rK the half-width, and the energy of the elec-tronic transition eK is transformed to the wavenumber ~vK ¼ eK=hc;~v i is the point of the experiment and b is the baseline. An additional

Lorentzian mimics the intense charge-transfer band. The positionsof the three allowed absorption peaks were reconstructed usingthe Racah parameters (B, C) and the crystal-field poles (F4) as theyresult from the crystal-field theory for the octahedral reference[6,7]. The calculations were performed in the complete basis setof the crystal-field terms for d7 configuration where the configura-tion interaction is naturally involved. (The decomposition of theelectronic spectrum within the D4h group is also possible but thiswould require much enlarged parameter set.) The final electronic-structure parameters are B = 830, C = 5000, F4 = 6000, and the calcu-lated transition energies are D1 = 8800, D2 = 18 800, and D3 =20 100 (all data in cm�1).

The set of {B, C, F4} parameters retrieved from electronic spectrahas been enlarged for the spin–orbit coupling constantn = 515 cm�1 and used in evaluating the crystal-field multiplets,the Zeeman levels, and the partition function subsequently pro-cessed to obtain the magnetic susceptibility. In addition, two mod-ifications were applied:

(1) the crystal-field poles have been allowed to accommodatefor the different crystal-field strength of the donor set:F4(O) = 5700, F4(N) = 6600 cm�1;

0.0

0.5

1.0

1.5

2.0

2.5

5668

106

129

166

185

214 23

927

030

3

372

501

Abs

orba

nce,

log(

i ref/i

)

Wavenumber/cm−1

0.2

0.4

0.6

0.8

1.0

1.2

6494

112

168 18

922

0 245

272

314

372 50

3Abs

orba

nce

Wavenumber/cm −1

Wavenumber/cm−1

Rel

ativ

e in

tens

ity, (

i ref/

i )

0

2

4

6

8

10

12

14

16

18

210 K160 K

(i 160)

/(i 21

0)

0.8

0.9

1.0

1.1

1.2

1.3

1.4

0 50 100 150 200 250 300 350 400 450 500 550 600

0 50 100 150 200 250 300 350 400 450 500 550 600

50 100 150 200 250 300 350 400 450 500 550 600

50 100 150 200 250 300 350 400 450 500 550 600

50 100 150 200 250 300 350 400 450 500 550 600

(ire

f/i 16

0) −

(i re

f/i 21

0)

-1

0

1

2

3

4

5

(a) Top − room-temperature spectrum, bottom – spectrum at T = 210 K, different pellet

(b) Low-temperature spectra, their intensity difference, and their ratio

Fig. 13. Absorption spectra of 1 in FAR-IR region attributed to electronic transitions among multiplets of the parent 4A2g and 4Eg terms (D4h group).

B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156 155

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(2) the different orbital reduction factors have been considered:j(O) = 0.8, j(N) = 0.6.

The results of the susceptibility calculations are presented inFig. 11b. It can be seen hat the results are approximately of thesame quality as those obtained by the GF-model. However, theCFT-model allows calculating the Figgis CI factor via Eqs. (14)and (15) as well as the direct reading-off the Dax value. The calcu-lated value of A = 1.397 matches firmly the fitted value ofAj = 1.383. The separation of the lowest crystal-field terms isDax = e(4Eg) � e(4A2g) = 393 cm�1. The lowest crystal-field multi-plets lie at 0, 154, 477, 758, 811, and 859 cm�1.

The room-temperature absorption spectrum of 1 in the far-infrared region is shown in Fig. 13. It possesses rather unusual fea-tures with a manifold peak structure. The absorption peaks refer toelectronic transitions among the crystal-field multiplets of the par-ent 4A2g and 4Eg terms (D4h group). As a result of the crystal-fieldand SOI splitting, there are 6 Kramers doublets (three C6 and threeC7), among which 15 transitions are possible (five from the groundstate C6a). The rules for the direct product of irreducible represen-tations within the D4

0 double group are

C6 � C6 ¼ C7 � C7 ¼ C1 þ C2 þ C5 ð26Þ

C6 � C7 ¼ C3 þ C4 þ C5 ð27Þ

Sine the z-component of the dipole moment belongs to C2, and the(x, y)-components belong to C5, the representation of the dipolemoment operator is contained in the direct product of the wavefunctions. Consequently all mentioned 15 transitions are allowed.

The relative intensities (iref/i) of seven transitions between 150and 350 cm�1 clearly alter on cooling between 210 K and 160 K sothat the lower-temperature transitions are more intense. There aresome more absorption bands below 150 cm�1 but these are worseresolved. The most pronounced intensity variation exhibits thetransitions at 214 (220) cm�1 at T = 298 K (T = 210 K). This transi-tion is expected to be equal to the energy gap d67 = 2D; theoreticalmodels 1–3 predict 2D = 190, 218, and 154 cm�1, respectively.

The predicted electronic transitions are collected in Table 2using models 2 and 3. One can conclude that the predicted transi-tions occur in the recorded spectrum.

The data obtained so far, along with the data from the literaturesources, cannot be used in judging which of the models (1 – ZFS, 2– GF, 3 – CFT) is more appropriate to the magnetic data fitting. Wecan only stress that the ZFS model operates with a set of six virtual

magnetic parameters within the spin-Hamiltonian formalism; thisset (gx, gy, gz, D, E, and vTIP) is regarded as molecular constants thatcan be reconstructed from three K-tensor components.

The crystal-field theory, on the other hand, operates with truephysical parameters (Racah B and C parameters expressing theinterelectron repulsion, spin–orbit coupling constant n, and thecrystal-field poles F4 and F2 of individual ligands). Therefore thistheory can be regarded as a more fundamental approach in under-standing the electronic origin of magnetic parameters.

5. Conclusions

Theoretical modeling presented in Fig. 7 shows that the spin-Hamiltonian formalism (the zero-field splitting model) is justifiedfor the compressed tetragonal bipyramid of hexacoordinate,high-spin Co(II) complexes. The value of the axial ZFS parameterD is naturally high and positive for all combinations of the axialand equatorial crystal-field strengths; it increases on approachingthe octahedral limit.

The electronic spectrum in the VIS region represents a usefulbasis for retrieving the electronic-structure parameters (B, C, F4)that can be further used in reconstructing the magnetic functionsof the complex. The absorption spectrum in the FAR-IR region re-fers to the electronic transitions among the crystal-field multipletsthat originate in the splitting of the parent ground octahedral term4T1g. into 4A2g and 4Eg terms (D4h). This allows a direct spectro-scopic reading-off of the zero-field energy gap d67 = 2D.

Acknowledgements

Grant Agencies (Slovakia: VEGA 1/0213/08, APVV 0006-07,COST-0006-06, VVCE 0004-07; Germany: DAAD) are acknowl-edged for the financial support.

References

[1] S.M. Gorun, S.J. Lippard, Inorg. Chem. 30 (1991) 1625.[2] P. Baran, M. Boca, R. Boca, A. Krutošíková, J. Miklovic, J. Pelikán, J. Titiš,

Polyhedron 24 (2005) 1510.[3] A. Mašlejová, R. Ivaniková, I. Svoboda, B. Papánková, L. Dlhán, D. Mikloš, H.

Fuess, R. Boca, Polyhedron 25 (2006) 1823.[4] R. Ivaniková, R. Boca, L. Dlhán, H. Fuess, A. Mašlejová, V. Mrázová, I. Svoboda, J.

Titiš, Polyhedron 25 (2006) 3261.[5] J. Titiš, R. Boca, L. Dlhán, T. Durceková, H. Fuess, R. Ivaniková, V. Mrázová, B.

Papánková, I. Svoboda, Polyhedron 26 (2007) 1523.[6] R. Boca, J. Titiš, in: Coordination Chemistry Research Progress, Nova, New York,

2008, p. 247.[7] R. Boca, Struct. Bond. 117 (2006) 1.[8] B. Papánková, I. Svoboda, H. Fuess, Acta Crystallogr. E 62 (2006) m1916.[9] R. Boca, Theoretical Foundations of Molecular Magnetism, Elsevier,

Amsterdam, 1999.[10] R. Boca, H. Elias, W. Haase, M. Huber, R. Klement, L. Müller, H. Paulus, I.

Svoboda, M. Valko, Inorg. Chim. Acta 278 (1998) 127.[11] Inorganic Crystal Structure Database, Fachinformationszentrum Karlsruhe,

Germany, http://www.fiz-informationsdienste.de/en/DB/icsd/index.html.[12] H. Jankovics, M. Daskalakis, C.P. Raptopoulou, A. Terzis, V. Tangoulis, J.

Giapintzakis, T. Kiss, A. Saligoglou, Inorg. Chem. 41 (2002) 3366.[13] R. Boca, L. Dlhán, W. Linert, H. Ehrenberg, H. Fuess, W. Haase, Chem. Phys. Lett.

307 (1999) 359.[14] R. Herchel, R. Boca, Dalton Trans. (2005) 1352.[15] L.L. Lohr, J.C. Miller, R.R. Sharp, J. Chem. Phys. 111 (1999) 10148.[16] D.J. Mackey, S.V. Evans, R.F. McMeeking, J. Chem. Soc., Dalton Trans. (1978)

160.[17] N. Duran, W. Clegg, L. Curucull-Sanchez, R.A. Coxall, H.R. Jimenez, J.-M.

Moratal, F. Lloret, P. Gonzalez-Duarte, Inorg. Chem. 39 (2000) 4821.

Table 2Calculated electronic transitions among multiplets in the FAR-IR region.

C6a C7a C6b C6c C7b

(a) Model 2, GF-data fitC7a 219C6b 567 348C6c 965 746 398C7b 1071 852 504 106C7c 1194 975 627 229 123

(b) Model 3, CFT data reconstructionC7a 154C6b 477 323C6c 758 604 281C7b 811 657 334 53C7c 859 705 382 101 48

156 B. Papánková et al. / Inorganica Chimica Acta 363 (2010) 147–156