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EPR investigations of trinuclear Cu(II) complexes with quartet ground states
ELSEVIER
Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
~H ~H ~H
Journalof magnotlsm and magnetic materials
EPR investigations of trinuclear Cu(II) complexes with quartet ground states P. Fleischhauer a S. Gehring a C. Saal a W. Haase a,* Z. T o m k o w i c z b C. Zanchini c, D. Gatteschi d, D. Davidov e, A.L. Barra a lnsfitutfiir Physikalische Chemie, Technische Hochschule Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany Institute of Physics, Jagellonian Unicersitv, Reymonta 4, Krakow, Poland c Department of Chemisto', Unil,ersity of Calabria, Calabria. Italy Department of Chemistr)', Unicersity of Florence, Via Maragliano 75 / 77, 1-50144 Florence, ltaly Racah Institute of Physics, Hebrew Unicersio" of Jerusalem, Ramat Gan, 52900 Jerusalem, lsrael f SerHce National des Champs Intenses, F-38042 Grenoble Cedex 9. France
Received 23 May 1995; revised 20 October 1995
Abstract
The X-band EPR powder spectrum of bis(/x-benzoato-O,O')-bis(benzoato-O)-bis[/x-(2-diethylamino)ethanolato-O,N]bis(methanol) tricopper(II) (CuEtBz' MeOH) at liquid-helium temperature is dominated by a resonance with g' --~ 4.3 (the prime indicates effective g-values). This signal shows a very unusual temperature dependent resonance shift with a variation of the effective g-value to g' ~ 2.6 at room temperature. Single-crystal EPR investigations on this compound at 4.2 K were carried out to determine the effective g-values of the quartet ground state: g'~ = 2.1(1), g'x = 4.0(1) and gi, = 4.7(1). In the temperature-dependent high-field EPR spectra recorded with a resonance frequency l, = 244.99 GHz, no resonance shifts were observed. Based on this observation and on simulations of the temperature dependence of the X-band signal, it was possible to show that the signal shift occurs because the signals of the three spin states of the molecule are not resolved in the X-band experiment. Therefore the observed signal embodies the contributions of each spin state, yielding a temperaturedependent resonance field due to the varying thermal populations of the different levels.
1. I n t r o d u c t i o n Investigations o f trinuclear transition metal c o m plexes have been o f increasing interest in recent years. O n e reason for this certainly was the lack of
* Corresponding author. Fax: d54d @hrzpub.th-darmstadt.de.
+49-6151-164298;
email:
m e t a l l o b i o m o l e c u l e s for which the trinuclear core can act as a synthetic analogue. The M C D spectroscopic p r o o f of a trinuclear active site in laccase [1], the recent discovery o f a f e r r o m a g n e t i c a l l y coupled Cu(II) triad in a subunit o f m e t h a n e m o n o - o x i g e n a s e [2], and an X-ray structure analysis o f ascorbate oxidase f r o m zucchini [3], which r e v e a l e d an angled trimeric Cu(II) unit as well as a m o n o n u c l e a r type I copper(II) centre, have all stimulated increasing interest in studies of trinuclear copper systems.
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0304-8853(95)00646-X
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
During our investigations of multinuclear copper(II) complexes [4] a number of ferromagnetically coupled linear and angled copper(II) triads (shown schematically below) have been synthesized and structurally as well as magnetically characterized.
~c'O
R
R"
o~C'o 1
"~ N ~ R
R,, ~,.O,,, ,.,O.~ /R
'o.. 1 ~ ~.o.... / cu
cu
ca
"0./ ] '~OH/ "O R'--N.._ CI O'C ~ 0 o_C__
~/
2Ry~u
I
\ cuP
/
I, R
L.~
/ R
~'R
%__0 H ~R*O__C,0 g
167
2. Experimental section 2.1. Synthesis CuEtBz • MeOH was synthesized as described by Haase and Gehring [4] by the dropwise addition of 5.5 mmol N,N-diethylaminoethanol dissolved in 5 ml methanol to a suspension of 2.75 mmol copper(II) benzoate in 45 ml boiling methanol. Slow cooling of the solution yielded blue needle-shaped crystals of CuEtBz • MeOH.
"R
2.2. EPR investigations The importance of studies of these /x-oxo/~carboxylato bridged systems does not arise only from the occurrence of this bridging unit in several metalloproteins [5]. These studies are also related to the properties of quartet ground states, to magnetostructural correlations in mixed bridged systems, to ferromagnetic exchange coupling, and to long-range coupling effects between the terminal copper centres. Since exchange coupling in copper(II) triads leads to spin states with non-integer total spin quantum numbers that are accessible to EPR spectroscopy, this technique has been proven to be a powerful tool for investigations of the structural and magnetic properties of these compounds [6]. The observation of only one signal at all temperatures for some of the compounds [7], even though signals for all the three spin states generated through exchange coupling are expected, and the fact that the effective g-values in some Cu(II) triads are found to be temperature dependent [8,9], show that the properties of this class of compounds are not yet fully understood. The very strong temperature dependence of the resonance field observed in the X-band EPR powder spectrum of bis(/x-benzoato-O,O')-bis(benzoato-O)bis[ ff-(2-diethylamino)ethanolato-O,N]-bis(methanol) tricopper(II) (CuEtBz- MeOH) [9] (see Fig. 1), with a variation in the effective g-value from g' ~- 4.3 at liquid-helium temperature to g ' ~ - 2 . 6 at room temperature, stimulated our investigations of singlecrystal X-band and high-frequency powder EPR of this compound. The results of these studies are reported in this paper.
The crystals for the single-crystal EPR investigations were oriented using a Philips PWl000 diffractometer. EPR measurements at 4.2 K and the variable temperature investigations were performed with Varian E9 X-band spectrometers. The high-field EPR spectra were recorded with a non-commercial spectrometer described in Ref. [10]. The resonance frequency was 244.99 GHz.
3. Results The X-band powder spectrum of CuEtBz • MeOH at 4.2 K is dominated by a resonance with g' ~ 4.3 (Fig. 1). Two further signals with intensities approximately two orders of magnitude smaller than the main transition are observed at 13 300 and 14 600 G (Fig. 2).
d~L" d'H
i~. d
;!
- - T=4AK - - T=60K
// I I / I/
1000 2000 3000 4000 5000 H[Gauss] Fig. ]. X-band powder spectra of CuEtBz .MeOH.
168
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
T=4,2K O:0 10
11
12
13
~:N O:c
14 15 H [103 Gouss1
Fig. 2. X-band powder spectra of CuEtBz. MeOH.
Fig. 4. Orientation of the g-tensor in the molecular frame.
The angular dependences of the resonance fields of CuEtBz • MeOH were recorded by rotating a single crystal around three orthogonal axes at 10 different temperatures from liquid helium temperature up to 93 K. For all crystal orientations, only one resonance in the investigated range up to 5000 G was observed. Fig. 3 shows the angular dependence of the X-band signal at 4.2 K; the curves were calculated using a least-squares fitting procedure described in Ref. [11]. The principal values and directions of the g-tensor are given in Table 1. As there is only one molecule in the unit cell (space group PI), the crystal g-values correspond to the molecular g-values. The directions of the principal axes in the Cu(2) molecular frame at 4.2 K are shown in Fig. 4. Fig. 5 shows the powder spectra of CuEtBz. MeOH up to 9 T obtained with a resonance frequency of 244.99 GHz.
The three copper centres in CuEtBz • MeOH form an exact linear arrangement with Cu(2) on the centre of symmetry. Two adjacent copper centres are bridged by the oxygen atom O(1) of the diethylamino-ethanolato ligand and by the two carboxylato-oxygen atoms 0(2) and O(3), of a benzoato ligand. The terminal copper atom Cu(1) is distorted square-planar coordinated by O(1), O(2), O(4), and N(1) (plane A). Cu(2) is octahedrally coordinated by O(1), O(1"), 0(3) and 0 ( 3 * ) (symmetry code for the atoms marked with asterisks: - x , - y , - z ) , which form an exact plane B and the methanolic oxygen atoms 0(6) and 0 ( 6 * ) . The dihedral angle
4. Discussion
(a)
T=4K
>d "O
The molecular structure of CuEtBz • MeOH (space group P1) is shown in Fig. 6 [4]. Table 2 lists selected interatomic distances and angles to illustrate the coordination around the copper ions.
6
7
8
H[T]
9
[(b) T = 30 ~
10 0
0
50
100
150
®to~
Fig. 3. Experimental and calculated angular dependences of g2 for the single crystal of CuEtBz.MeOH at 4.2 K.
7
8
H[T]
9
Fig. 5. High-frequency EPR spectra of CuEtBz-MeOH (vrc~ = 244.99 GHz) at (a) 4 K and (b) 30 K.
169
P. Fleischhauer et al. / J o u r n a l o f Magnetism and Magnetic Materials 159 (1996) 1 6 6 - 1 7 4
Table 1 Principal g-values and direction cosines of CuEtBz • MeOH with respect to the axes of rotation T (K)
g':
I
m
n
g'~
I
m
n
g'v
I
m
n
4.2 10 21 29 34 41 51 62 72 93
2.11(10) 2.11(10) 2.06(10) 2.06(10) 2.15(10) 2.17(10) 2.20(10) 2.19(10) 2.20(10) 2.24(10)
0.87(2) 0.89(2) 0.89(2) 0.86(3) 0.89(3) 0.87(3) 0.87(3) 0.86(3) 0.85(3) 0.87(3)
0.22(6) 0.23(6) 0.21(6) 0.20(6) 0.2l(6) 0.25(6) 0.26(6) 0.26(6) 0.24(6) 0.26(6)
0.44(4) 0.40(4) 0.40(4) 0.46(4) 0.41(4) 0.42(4) 0.41(4) 0.43(4) 0.47(4) 0.41(4)
4.01(10) 4.03(10) 3.73(10) 3.47(10) 3.35(10) 3.23(10) 3.14(10) 3.1 l(10) 3.02(10) 2.93(10)
0.21(4) 0.16(4) 0.14(4) 0.14(4) 0.15(4) 0.18(4) 0.18(4) 0.17(4) 0.22(4) 0.20(4)
0.63(9) 0.66(9) 0.71(9) 0.68(9) 0.70(9) 0.63(9) 0.60(9) 0.66(9) 0.65(9) 0.60(9)
0.74(7) 0.73(7) 0.69(7) 0.72(7) 0.70(7) 0.76(7) 0.78(7) 0.73(7) 0.72(7) 0.78(7)
4.70(10) 4.69(10) 4.41(10) 4.06(10) 3.85(10) 3.70(10) 3.57(10) 3.48(10) 3.42(10) 3.30(10)
0.44(4) 0.43(4) 0.43(4) 0.43(4) 0.43(4) 0.45(4) 0.45(4) 0.47(4) 0.48(4) 0.45(4)
0.74(6) 0.71(6) 0.67(6) 0.71(6) 0.69(6) 0.74(6) 0.74(6) 0.71(6) 0.70(6) 0.75(6)
0.50(8) 0.56(8) 0.60(8) 0.56(8) 0.58(8) 0.50(8) 0.49(8) 0.52(8) 0.52(8) 0.48(8)
Fig. 6. Molecular structure of CuEtBz. MeOH.
~AB between the two equatorial coordination planes A and B is 60.7 °. The shortest intermolecular C u - C u separation is 8.01 A. The temperature-dependent magnetic susceptibility measurements indicated that ferromagnetic exchange coupling is operative between adjacent copper centres. The exchange parameters Jl2 = 30.1(5.0) cm - j , J13 = - 6 . 1 ( 3 . 0 ) cm i ( / ~ = _ 2 J 1 2 ( ~ ~.Se
Table 2 Selected distances (~,) and angles (deg) with estimated standard deviations in parentheses for the copper environment in CuEtBz. MeOH Cu(l)-Cu(2) Cu(1)-N(I) Cu(l)-O(l) Cu(1)-O(2) Cu(l)-O(4) Cu(2)-O(I) Cu(2)-O(3) Cu(2)-O(6)
3.188(1) 2.028(4) 1.897(3) 1.940(3) 1.919(3) 1.944(3) 1.982(3) 2.478(4)
O(1)-Cu(I)-N(I) O(I)-Cu(I)-O(2) O(2)-Cu(1)-O(4) O(4)-Cu(1)-N(I) O(2)-Cu(1)-N(I) O(1)-Cu(1)-O(4) Cu( 1)-O( 1)-Cu(2) O(1)-Cu(2)-O(3) O(1)-Cu(2)-O(6) O(3)-Cu(2)-O(6)
85.2(1) 92.5(1) 88.4(1) 94.7(2) 165.9(2) 176.6(2) 112.2(1) 88.1(1) 92.0(1) 91.8(1)
+ $2" $3) - 2J,3(gL" $3)) were determined for CuEtBz • MeOH [4]. Thus the quartet state is lowest in energy with two doublet states lying 18 (11) and 90 (15) c m - ~ higher in energy, respectively (Fig. 7). Detailed SQUID measurements at low temperatures allowed the determination of the zero-field splitting parameter D. For CuEtBz • MeOH, IDI = 1.4 + 0.5 cm l was found by Tomkowicz et al. [4]. The EPR spectra of CuEtBz • MeOH were interpreted using the following total spin Hamiltonian:
-t-D[S':-½S(S-t-1)]+E[S^:-S~],
(1)
where /x B denotes the Bohr magneton, D and E represent the axial and the rhombic zero-field splitting parameters, and Si are the spin operators. The choice of the coordinate system x , y , z is arbitrary. However, the sign of E varies upon the interchange of the x and y axes. In order to specify the axes explicitly, we will follow the convention IOl > 31El and D . E > 0 [ 1 2 ] . In analyzing the EPR spectra of quartet states with large zero-field splitting (2 D >> h v, where v is ISges,SI3 > 11/2,1)
E (J12,J13) l
'2Jlz-1/2J13
I 69±13crnI 90-+15cm-1 1 11/2,0> I , -1 I 18+11cm
13/2,1)
i
312 J13 j12_1/2J13
Fig. 7. Spin states and exchange splitting for CuEtBz-MeOH as detected from temperature-dependent susceptibility measurements.
P. Fleischhaueret al. /Journal qf Magnetismand Magnetic"Materials 159 (1996) 166-174
170
the spectrometer frequency), it is most convenient to use a fictitious S' = 1 / 2 Hamiltonian rather than the true S = 3 / 2 spin Hamiltonian. The g'-values of the effective S' = 1 / 2 and the true S = 3 / 2 Hamiltoniarts are related as follows [13]: 1 -3A
not valid, the EPR transitions may be analyzed by solving the Hamiltonian matrix of the quartet state. The following solutions (3)-(5) were obtained for the magnetic field parallel to one of the principal axes [ 14]. (1) H = H.: e ( l l ) ) = ~-g: ' ]&BH + { ( D + g = /.zBH ) 2 +
g' =
3E2}
1/2
(2a)
x
g,
1
,
, g,,(l+ glr=
l+3h 1
(3a)
e(12)) = - T g' ~ l x u H
+{(D-g:tzBH)2+3E2}
l+3A l+fi--7~),
( g,
+_3/2,
M~=_+I/2, )
(2b)
~
,
,
e(13)) =
I/2 ,
(3b)
7g:l,*B H - {(D + g~:/.tBH) 2 + 3E2} '/2 1
(3c)
M,=-1-3/2,
e(14)) = --Tg~lXBH ' ,
g~=
( g:
2 ) 1+
--{(D--g:IxBH)Z+3E'I
M,=_+l/2,
(2c)
~
,
.~ 1/2
,
(3d)
(2) H = g~ ."
7gxtXBH+{g~tzi~
M,=-t-3/2,
2
+D2+3E
2
-g~ I.*, H( D - 3E)} 1/2, where A = E/D. The g'-values for transitions within the predominant M s = 4 - 1 / 2 and the predominant M, = 4- 3 / 2 Kramers doublet of the quartet state are plotted versus A in Fig. 8, assuming a true g-value of 2.15. Eqs. (2a)-(2c) are approximations that hold for the case D >> g •/x B • H. If these equations are
(4a)
e(12)) = - T g' , tzB H + {gTlz~3 " ' H2 + De + 3E2 + g x / Z B H ( D - 3E)} 1/2,
(4b)
{g2~tx2H2+ D 2 + 3 E 2 e(13)) = 7g~t~BH_ ' -g,/-*B H( D e(14)) =
-
-
BE)}
(4c)
1/2 ,
1 ~_g~tXBH-{g,2tX~") H 2 + D 2 +3E-"
+g,/XBH (D-
3E)} 1/2,
(4d)
(3) H = H,,: e ( l l ) ) = Ig,,txBH + {g.~tx~H 2 + D2Z + 3E 2 0
[ 0
. '
.
. 011
.
. "
. 02
i '
E/O
013
- g , tzBH(D + 3E)} '/2,
(5a)
~ o 2 + D 2 + 3E 2 . g~txgH e(12)) = - ' ?_g,,/xBH+{
g:l'b'
"1
+ g , . t * B H ( D + 3 E ) } '/2
(5b)
I ~ 2 2 + D 2 +3E 2 e(13)) = 7gylXBH-{g;tXBH
- g ~ I Z B H ( D + 3E)} 1/2, EID
Fig. 8. Effective g-values for transitions within (a) the predominantly 4-1/2, and (b) predominantly 4-3/2 Kramers doublet of the quartet state.
e ( [ 4 ) ) = - 2 g ~I t X B H - - { g ~ t x~B H~
2
+gytxBH(D + 3E)} 1/2.
(5c)
+ V 2 +3E 2 (5d)
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
The eigenvalues (3)-(5) are not labelled with M~ values since the corresponding eigenvectors are in general linear combinations of the basic vectors, according to li) = ail3/2) + bill/Z) +
c,I-
1/2) +
d,I-
171
G. This strongly suggests that the weak signals observed in the X-band powder spectra of CuEtBz • MeOH at 13 300 and 14 600 G arise from transitions between the Kramers doublets of the quartet state.
3/2) (6) HIIx
where 13/2), 11/2), l - 1 / 2 ) and l - 3 / 2 ) denote the basic vectors indicated with the appropriate M~ values. Fig. 9 shows the field dependence of the quartet energy levels, calculated using Eqs. (3)-(5) with g = 2.15, D = 1.0 cm i and E = 0.1 cm-L The reflection of 12) and 14) for Hllz arises from the non-crossing rule, which expresses that states of the same symmetry may not cross. The arrows in Fig. 9 indicate the allowed transitions which were obtained by calculating the transition probability P, which is given by P = 1~mlS~ + iS/j ]n)l 2,
I1> 2"
~.oo
13>
ILl -2"
-4-
I
50OO
,
I
1O000
,
I
15OOO
,
~DOOO
H [Gauu.I
4t
(7)
where ]rn) and In) are eigenvectors according to Eq. (6) and c~,/3 denote x, y, z, the components perpendicular to the main field. Transitions are allowed within the + 1 / 2 and + 3 / 2 Kramers doublets, since the latter states are not pure _+3/2 states as discussed above. Transitions between levels W2) and 14) belonging to different Kramers doublets are forbidden for HI] z, but are allowed for all other orientations. With the theoretical background elaborated so far, the EPR spectra of CuEtBz-MeOH will be interpreted in the following. From the angular dependence of the single-crystal resonance, the principal g-values of g':=2.1(1), gi~ = 4.0(1), g'~ = 4.7(1) (at 4.2 K) were determined for CuEtBz. MeOH. These values are characteristic for transitions within the predominantly M~ = _+ 1/2 Kramers doublet of the quartet state. From the principal g-values an [E/D] ratio of A = 0.054(3) is calculated using Eqs. (2a-c) and a true g-value of 2.15. A plot of the energy levels of the quartet state with ]D]= 1.4 cm -1 (obtained from the SQUID experiments) and A=0.054, reveals that for HIPz the resonance condition is fulfilled for transitions between the Kramers doublets at 13300 and 14800
12>
.,-,
Hlly
21
~
I1>
o.!.
0
50O0
1OOOO
15O0O
20OOO
H IGauul
HIIz
2-
~O-
12>
I,LI -2-
13> -40
,
I
,
I
lOIx~o
,
I
1500o
,
H l~uml Fig. 9. Field dependence of the quartet levels calculated using Eqs. ( 3 ) - ( 5 ) with g = 2 . 1 5 , D = I . 0 cm - I and E = 0 . 1 c m - l . The arrows indicate allowed transitions for A E = 0.3 c m - l .
172
P. Fleischhauer et al. / Journal q['Magnetism and Magnetic Materials 159 (1996) 166-174
Table 3 g-tensors for the different levels of SE= Sil = S[u = l/2 systems Multiplet ISge~,St3)
g-tensor
13/2, 1) 11/2,0) 11/2, 1)
gH
1/3g I + 2/3g I -
l/3gli + 1/3gli I
different contributions of this state to the observed signal due to the changes in the thermal population of the levels. The variation in the position of the composed signal can be simulated with the following formula, which simply weights the resonance fields
I/3g u +2/3gHi 15
As discussed above, these transitions are forbidden for H ] l z but become allowed for rotating the : axis away from the main field direction, and may therefore be observed. Nevertheless, for a definite assignment of the signals, single-crystal EPR investigations are necessary. The orientations of the principal axes in the molecular frame, as determined from the singlecrystal EPR investigations will be discussed in the following. As shown in Fig. 4, the g~ axis lies close to the Cu(2)-O(6) bond (4°), while the deviation of the g2 and g3 axes from both the Cu(2)-O(3) and Cu(2)O(1) bonds is approximately 12 °. It is well known that the g-tensor of exchangecoupled systems can be expressed as a linear combination of the local g-tensors. For symmetric triads with S = 1 / 2 centres, the relations given in Table 3 hold [6]. From Table 3 it is obvious that the three metal centres contribute equally to the g-tensor of the quartet state. Since the dihedral angle between the coordination planes of adjacent copper ions is 60.7 °, the observed g-values result from a complete average of the tensors of individual ions. In fact, using Eq. (2), with the observed effective g-values and A = 0.054, the true g-values of g, ~ g,. ~ 2.18 and g~ ~ 2.12 can be calculated. It is clear that the quasi-isotropic g-values are the result of an averaging process, due to the misalignment of the local axes of the three tensors. This is also the reason why no change in the orientation of the g-tensor with increasing temperature is observed (Table 1). It is possible to explain the strong temperature dependence of the resonance field observed in the powder spectra of C u E t B z - M e O H (Fig. 1) by assuming that in the X-band experiment the signals of the three spin states of the system are not resolved. Thus the observed signal embodies contributions of the [3/2,1), the ]1/2,1) and the l l / 2 , 0 ) states. The temperature-dependent resonance position arises from
~0
•
"10t -15
I
' 0
,
~
I
,
~
I
'
I
I
'
I
~
H l~uul 15-
10-
5-
UI -5-10• -15H lGau~] 15
10,
5,
W -5-
-10-15
,
I
,
I
,
H l~,u,,l
Fig. 10. Field dependence of the quartet levels calculated using Eqs. (3)-(5) and g = 2 . 1 5 , D = 1 . 4 cm -I and A=0.054. The
arrows indicate allowed transitions for A E = 8.2 cm- ].
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
of the different spin states according to the Boltzmann distribution:
H ...... ic =
E tOi nres,i e x p { -- a g i / k T } i E toi exp{ - A EykT} '
(8)
i where //re ~ is the resonance field; to is the multiplicity; AE~ is the energy separation between ]3/2,1) and 11/2,0), and A E 2 is the energy separation between ]3/2,1) and ll/2,1). Good agreement between the observed and calculated temperature dependences of Hre~ has been obtained (see Ref. [9]). It is also possible to describe the temperature dependence of the principal g-values of CuEtBz. MeOH (see Table 1) using Eq. (8). The principal g-values of the doublet states of CuEtBz • MeOH are not known, but their choice strongly influences the energy separations obtained when fitting Eq. (8) to the experimental values. It is therefore rather pointless to give numerical data for the kEg values obtained from the analysis of the resonance shifts in the single-crystal experiment. Nevertheless the agreement between the simulated and observed results supports the above explanation of this effect. It is well known that the coalescence of different spectroscopic signals can be suppressed if the energy difference of the signals is enhanced [15]. In the EPR experiment, this can be achieved by operating with a higher resonance frequency. In Fig. 5 the highfrequency powder spectra of CuEtBz. MeOH, obtained with a resonance frequency of 244.99 GHz are shown. A sharp signal at 65000 G ( g ' = 2 . 7 ) is observed in the spectrum at 4 K. Fig. 10 shows the energy levels of the quartet state, again calculated using Eqs. (3)-(5), up to 90 000 G for g = 2.15, D = l . 4 c m 1 andA=0.054. The allowed transitions for the resonance frequency of 244.99 GHz are indicated as arrows. Since the Zeeman splitting at 8 T corresponds roughly to 12 K, in the spectrum at 4 K only the transitions from the lowest state occur. Thus transitions at 70000 and 66000 G for Hllx and HII y, respectively, are expected in the high-field spectra of CuEtBz. MeOH. The observed signal at 65 000 G can be attributed to the transition from the lowest state for Hlly. The missing signal at 70000 G, which is expected for Hllx, indicates that the
173
sample is oriented by the strong magnetic field roughly along the y-axis. Attempts to suppress the orientation with mineral oil or araldite were hampered by the decomposition of the compound. The large Zeeman splitting in the high-frequency experiment in comparison with the thermal energy at 4 K allows the determination of the sign of the D parameter. For D = - 1 . 4 cm-J only one transition from the lowest level at 54000 G is expected (HI] z), indicating that the positive sign for D is the correct choice. As expected, the position of the resonance field is not affected by increasing temperature in the highfield experiment. Instead, an additional signal at H = 81 800 G ( g ' ~ 2.14) gains intensity with increasing temperature. As shown in Fig. 1, signals near 80000 G are possible for orientations along x and y. In addition, the doublet spin states of the cluster become populated, for which signals of the order of 80000 G are also expected. The observation of separate signals as at 8600 G for the doublets should be expected in the high-field experiment, because the difference in resonance fields becomes large, and relaxation can no longer average the signals. The results presented so far prove that the observed temperature-dependent resonance field in the X-band spectra of CuEtBz - MeOH is due to the fact that the signals of the different spin states of the molecule are not resolved. The merging of spectroscopic signals attributed to different states is a well known phenomenon, and is a manifestation of the Heisenberg uncertainty principle, which can be expressed as A t - A u ~ 27r,
(9)
where A~, is the separation of the signals in frequency units, and At is the smallest time during which the states may be distinguished. If the mean lifetime ~- of the states becomes smaller than At, the signals coalesce into one line. In order to observe the coalescence of the signals related to the quartet and the doublets of CuEtBzMeOH in the X-band spectra a mean lifetime of ~ - < 3 × 10 - ~ s is estimated using Eq. (9). Two mechanisms may be responsible for the small lifetimes: (i) spin-spin relaxation, and (ii) spin-lattice relaxation.
174
P. Fleischhauer et al. / Journal of Magnetism and Magnetic: Materials 159 (1996) 166 174
Further investigations on this interesting topic are now under way to identify which of these mechanisms is operative in our case.
Acknowledgements We thank Dr N. Bontemps and Professor Dr P. Monod, Ecole Normal Superieur, Paris, for giving us the opportunity to record X-band EPR spectra up to 16000 G.
[5]
[6]
References [7] [1] D.J. Spira-Solomon, M. Allendorf and E.I. Solomon, J. Am. Chem. Soc. 108 (1986) 5316. [2] (a) S.I. Chan, H.-H.T. Nguyen, A.K. Shiemke and M.E. Lidstrom, in: Bioinorganic Chemistry of Copper, eds. K.D. Karlin and Z. Tyeklar (Chapman & Hall, New York, 1993) p. 184. (b) H.-H.T. Nguyen, A.K. Shiemke, S.J. Jacobs, B.J. Hales, M.E Lidstrom and S.I. Chan, J. Biol, Chem. 269 (1994) 14995. [3] (a) A. Messerschmidt, A. Rossi, R. Ladenstein, R. Huber, M. Bolognesi, G. Gatti, A. Marchesini, R. Petruzzelli and A. Finazzi-Agr~), J. Mol. Biol. 206 (1989) 513. (b) A. Messerschmidt and R. Huber, Eur. J. Biochem. 187 (1990) 341. (c) A. Messerschmidt, in: Bioinorganic Chemistry of Copper, eds. K.D. Karlin and Z. Tyeklar (Chapman & Hall, New York, 1993) p. 471. [4] (a) W. Haase and S. Gehring, J. Chem. Soc., Dalton Trans. (1985) 2609. (b) S. Gehring, P. Fleischhauer, H. Paulus and W. Haase, Inorg. Chem. 32 (1993) 54. (c) Z. Tomkowicz, P.
[8] [9] [10] [11] [12]
[13] [14] [15]
Fleischhauer, W. Haase, M. Baran, R. Szymczak and A.J. Zaleski, J. Magn. Magn. Mater. 127 (1993) LII. (d) S. Gehring, PhD Thesis, Technische Hochschule Darmstadt, Germany (!990). (e) P. Fleischhauer, PhD Thesis, Technische Hochschale Darmstadt (1994) Germany. (f) S. Gehring, H. Paulus, W. Haase, E. Bill and A.X. Trautwein, Z. Kristallogr. 186 (1990) 83. (g) S. Gehring, W. Haase and H. Paulus, Acta Cryst. C 47 (1991) 1814. (a) R.E. Stenkamp, L.C. Sieker and L.H. Jensen, J. Am. Chem. Soc. 106 (1984) 618. (b) P. Nordlund, B.-M. SjiSberg and H. Eklund, Nature 345 (1990) 593. (c) B. Salvato and M. Beltramini, Life Chem. Rep. 8 (1990) 1. (a) A. Bencini and D. Gatteschi, EPR of Exchange-Coupled Systems (Springer, Berlin, 1990). (b) L. Banci, A. Bencini, A. Dei, D. Gatteschi, lnorg. Chem. 22 (1983) 4018. (c) Y. Journaux, F. LLoret and O. Kahn, Inorg. Chem. 29 (1990) 3048. C. Benelli, D. Gatteschi, C. Zanchini, J.M. Latour and P. Rey, Inorg. Chem. 25 (1986) 4242. L. Banci, A. Bencini and D. Gatteschi, lnorg. Chem. 22 (1983) 2681. P. Fleischhauer, S. Gehring and W. Haase, Ber. Bunsenges. Phys. Chem. 96 (1992) 1701. A.L. Barra, L.C. Brunel and J.B. Robert, Chem. Phys. Lett. 165 (1990) 107. B.J. Hathaway and D.E. Billing, Coordin. Chem. Rev. 5 (1970) 143. S.P. McGlynn, T. Azumi and M. Kinoshita, Molecular Spectroscopy of the Triplet State (Prentice-Hall, Englewood Cliffs, NJ, 1969). L. Banci, A. Bencini, C. Benelli, D. Gatteschi and C. Zanchini, Structure and Bonding 52 (1982) 37. B.R, McGarvey, in: Transition Metal Chemistry, ed. R.I. Carlin (Marcel Dekker, New York, 1972) p. 89. D.M.S. Bagguley and J.H.E. Griffiths, Proc. R. Soc, A 214 (1950) 451.
Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
~H ~H ~H
Journalof magnotlsm and magnetic materials
EPR investigations of trinuclear Cu(II) complexes with quartet ground states P. Fleischhauer a S. Gehring a C. Saal a W. Haase a,* Z. T o m k o w i c z b C. Zanchini c, D. Gatteschi d, D. Davidov e, A.L. Barra a lnsfitutfiir Physikalische Chemie, Technische Hochschule Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany Institute of Physics, Jagellonian Unicersitv, Reymonta 4, Krakow, Poland c Department of Chemisto', Unil,ersity of Calabria, Calabria. Italy Department of Chemistr)', Unicersity of Florence, Via Maragliano 75 / 77, 1-50144 Florence, ltaly Racah Institute of Physics, Hebrew Unicersio" of Jerusalem, Ramat Gan, 52900 Jerusalem, lsrael f SerHce National des Champs Intenses, F-38042 Grenoble Cedex 9. France
Received 23 May 1995; revised 20 October 1995
Abstract
The X-band EPR powder spectrum of bis(/x-benzoato-O,O')-bis(benzoato-O)-bis[/x-(2-diethylamino)ethanolato-O,N]bis(methanol) tricopper(II) (CuEtBz' MeOH) at liquid-helium temperature is dominated by a resonance with g' --~ 4.3 (the prime indicates effective g-values). This signal shows a very unusual temperature dependent resonance shift with a variation of the effective g-value to g' ~ 2.6 at room temperature. Single-crystal EPR investigations on this compound at 4.2 K were carried out to determine the effective g-values of the quartet ground state: g'~ = 2.1(1), g'x = 4.0(1) and gi, = 4.7(1). In the temperature-dependent high-field EPR spectra recorded with a resonance frequency l, = 244.99 GHz, no resonance shifts were observed. Based on this observation and on simulations of the temperature dependence of the X-band signal, it was possible to show that the signal shift occurs because the signals of the three spin states of the molecule are not resolved in the X-band experiment. Therefore the observed signal embodies the contributions of each spin state, yielding a temperaturedependent resonance field due to the varying thermal populations of the different levels.
1. I n t r o d u c t i o n Investigations o f trinuclear transition metal c o m plexes have been o f increasing interest in recent years. O n e reason for this certainly was the lack of
* Corresponding author. Fax: d54d @hrzpub.th-darmstadt.de.
+49-6151-164298;
email:
m e t a l l o b i o m o l e c u l e s for which the trinuclear core can act as a synthetic analogue. The M C D spectroscopic p r o o f of a trinuclear active site in laccase [1], the recent discovery o f a f e r r o m a g n e t i c a l l y coupled Cu(II) triad in a subunit o f m e t h a n e m o n o - o x i g e n a s e [2], and an X-ray structure analysis o f ascorbate oxidase f r o m zucchini [3], which r e v e a l e d an angled trimeric Cu(II) unit as well as a m o n o n u c l e a r type I copper(II) centre, have all stimulated increasing interest in studies of trinuclear copper systems.
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0304-8853(95)00646-X
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
During our investigations of multinuclear copper(II) complexes [4] a number of ferromagnetically coupled linear and angled copper(II) triads (shown schematically below) have been synthesized and structurally as well as magnetically characterized.
~c'O
R
R"
o~C'o 1
"~ N ~ R
R,, ~,.O,,, ,.,O.~ /R
'o.. 1 ~ ~.o.... / cu
cu
ca
"0./ ] '~OH/ "O R'--N.._ CI O'C ~ 0 o_C__
~/
2Ry~u
I
\ cuP
/
I, R
L.~
/ R
~'R
%__0 H ~R*O__C,0 g
167
2. Experimental section 2.1. Synthesis CuEtBz • MeOH was synthesized as described by Haase and Gehring [4] by the dropwise addition of 5.5 mmol N,N-diethylaminoethanol dissolved in 5 ml methanol to a suspension of 2.75 mmol copper(II) benzoate in 45 ml boiling methanol. Slow cooling of the solution yielded blue needle-shaped crystals of CuEtBz • MeOH.
"R
2.2. EPR investigations The importance of studies of these /x-oxo/~carboxylato bridged systems does not arise only from the occurrence of this bridging unit in several metalloproteins [5]. These studies are also related to the properties of quartet ground states, to magnetostructural correlations in mixed bridged systems, to ferromagnetic exchange coupling, and to long-range coupling effects between the terminal copper centres. Since exchange coupling in copper(II) triads leads to spin states with non-integer total spin quantum numbers that are accessible to EPR spectroscopy, this technique has been proven to be a powerful tool for investigations of the structural and magnetic properties of these compounds [6]. The observation of only one signal at all temperatures for some of the compounds [7], even though signals for all the three spin states generated through exchange coupling are expected, and the fact that the effective g-values in some Cu(II) triads are found to be temperature dependent [8,9], show that the properties of this class of compounds are not yet fully understood. The very strong temperature dependence of the resonance field observed in the X-band EPR powder spectrum of bis(/x-benzoato-O,O')-bis(benzoato-O)bis[ ff-(2-diethylamino)ethanolato-O,N]-bis(methanol) tricopper(II) (CuEtBz- MeOH) [9] (see Fig. 1), with a variation in the effective g-value from g' ~- 4.3 at liquid-helium temperature to g ' ~ - 2 . 6 at room temperature, stimulated our investigations of singlecrystal X-band and high-frequency powder EPR of this compound. The results of these studies are reported in this paper.
The crystals for the single-crystal EPR investigations were oriented using a Philips PWl000 diffractometer. EPR measurements at 4.2 K and the variable temperature investigations were performed with Varian E9 X-band spectrometers. The high-field EPR spectra were recorded with a non-commercial spectrometer described in Ref. [10]. The resonance frequency was 244.99 GHz.
3. Results The X-band powder spectrum of CuEtBz • MeOH at 4.2 K is dominated by a resonance with g' ~ 4.3 (Fig. 1). Two further signals with intensities approximately two orders of magnitude smaller than the main transition are observed at 13 300 and 14 600 G (Fig. 2).
d~L" d'H
i~. d
;!
- - T=4AK - - T=60K
// I I / I/
1000 2000 3000 4000 5000 H[Gauss] Fig. ]. X-band powder spectra of CuEtBz .MeOH.
168
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
T=4,2K O:0 10
11
12
13
~:N O:c
14 15 H [103 Gouss1
Fig. 2. X-band powder spectra of CuEtBz. MeOH.
Fig. 4. Orientation of the g-tensor in the molecular frame.
The angular dependences of the resonance fields of CuEtBz • MeOH were recorded by rotating a single crystal around three orthogonal axes at 10 different temperatures from liquid helium temperature up to 93 K. For all crystal orientations, only one resonance in the investigated range up to 5000 G was observed. Fig. 3 shows the angular dependence of the X-band signal at 4.2 K; the curves were calculated using a least-squares fitting procedure described in Ref. [11]. The principal values and directions of the g-tensor are given in Table 1. As there is only one molecule in the unit cell (space group PI), the crystal g-values correspond to the molecular g-values. The directions of the principal axes in the Cu(2) molecular frame at 4.2 K are shown in Fig. 4. Fig. 5 shows the powder spectra of CuEtBz. MeOH up to 9 T obtained with a resonance frequency of 244.99 GHz.
The three copper centres in CuEtBz • MeOH form an exact linear arrangement with Cu(2) on the centre of symmetry. Two adjacent copper centres are bridged by the oxygen atom O(1) of the diethylamino-ethanolato ligand and by the two carboxylato-oxygen atoms 0(2) and O(3), of a benzoato ligand. The terminal copper atom Cu(1) is distorted square-planar coordinated by O(1), O(2), O(4), and N(1) (plane A). Cu(2) is octahedrally coordinated by O(1), O(1"), 0(3) and 0 ( 3 * ) (symmetry code for the atoms marked with asterisks: - x , - y , - z ) , which form an exact plane B and the methanolic oxygen atoms 0(6) and 0 ( 6 * ) . The dihedral angle
4. Discussion
(a)
T=4K
>d "O
The molecular structure of CuEtBz • MeOH (space group P1) is shown in Fig. 6 [4]. Table 2 lists selected interatomic distances and angles to illustrate the coordination around the copper ions.
6
7
8
H[T]
9
[(b) T = 30 ~
10 0
0
50
100
150
®to~
Fig. 3. Experimental and calculated angular dependences of g2 for the single crystal of CuEtBz.MeOH at 4.2 K.
7
8
H[T]
9
Fig. 5. High-frequency EPR spectra of CuEtBz-MeOH (vrc~ = 244.99 GHz) at (a) 4 K and (b) 30 K.
169
P. Fleischhauer et al. / J o u r n a l o f Magnetism and Magnetic Materials 159 (1996) 1 6 6 - 1 7 4
Table 1 Principal g-values and direction cosines of CuEtBz • MeOH with respect to the axes of rotation T (K)
g':
I
m
n
g'~
I
m
n
g'v
I
m
n
4.2 10 21 29 34 41 51 62 72 93
2.11(10) 2.11(10) 2.06(10) 2.06(10) 2.15(10) 2.17(10) 2.20(10) 2.19(10) 2.20(10) 2.24(10)
0.87(2) 0.89(2) 0.89(2) 0.86(3) 0.89(3) 0.87(3) 0.87(3) 0.86(3) 0.85(3) 0.87(3)
0.22(6) 0.23(6) 0.21(6) 0.20(6) 0.2l(6) 0.25(6) 0.26(6) 0.26(6) 0.24(6) 0.26(6)
0.44(4) 0.40(4) 0.40(4) 0.46(4) 0.41(4) 0.42(4) 0.41(4) 0.43(4) 0.47(4) 0.41(4)
4.01(10) 4.03(10) 3.73(10) 3.47(10) 3.35(10) 3.23(10) 3.14(10) 3.1 l(10) 3.02(10) 2.93(10)
0.21(4) 0.16(4) 0.14(4) 0.14(4) 0.15(4) 0.18(4) 0.18(4) 0.17(4) 0.22(4) 0.20(4)
0.63(9) 0.66(9) 0.71(9) 0.68(9) 0.70(9) 0.63(9) 0.60(9) 0.66(9) 0.65(9) 0.60(9)
0.74(7) 0.73(7) 0.69(7) 0.72(7) 0.70(7) 0.76(7) 0.78(7) 0.73(7) 0.72(7) 0.78(7)
4.70(10) 4.69(10) 4.41(10) 4.06(10) 3.85(10) 3.70(10) 3.57(10) 3.48(10) 3.42(10) 3.30(10)
0.44(4) 0.43(4) 0.43(4) 0.43(4) 0.43(4) 0.45(4) 0.45(4) 0.47(4) 0.48(4) 0.45(4)
0.74(6) 0.71(6) 0.67(6) 0.71(6) 0.69(6) 0.74(6) 0.74(6) 0.71(6) 0.70(6) 0.75(6)
0.50(8) 0.56(8) 0.60(8) 0.56(8) 0.58(8) 0.50(8) 0.49(8) 0.52(8) 0.52(8) 0.48(8)
Fig. 6. Molecular structure of CuEtBz. MeOH.
~AB between the two equatorial coordination planes A and B is 60.7 °. The shortest intermolecular C u - C u separation is 8.01 A. The temperature-dependent magnetic susceptibility measurements indicated that ferromagnetic exchange coupling is operative between adjacent copper centres. The exchange parameters Jl2 = 30.1(5.0) cm - j , J13 = - 6 . 1 ( 3 . 0 ) cm i ( / ~ = _ 2 J 1 2 ( ~ ~.Se
Table 2 Selected distances (~,) and angles (deg) with estimated standard deviations in parentheses for the copper environment in CuEtBz. MeOH Cu(l)-Cu(2) Cu(1)-N(I) Cu(l)-O(l) Cu(1)-O(2) Cu(l)-O(4) Cu(2)-O(I) Cu(2)-O(3) Cu(2)-O(6)
3.188(1) 2.028(4) 1.897(3) 1.940(3) 1.919(3) 1.944(3) 1.982(3) 2.478(4)
O(1)-Cu(I)-N(I) O(I)-Cu(I)-O(2) O(2)-Cu(1)-O(4) O(4)-Cu(1)-N(I) O(2)-Cu(1)-N(I) O(1)-Cu(1)-O(4) Cu( 1)-O( 1)-Cu(2) O(1)-Cu(2)-O(3) O(1)-Cu(2)-O(6) O(3)-Cu(2)-O(6)
85.2(1) 92.5(1) 88.4(1) 94.7(2) 165.9(2) 176.6(2) 112.2(1) 88.1(1) 92.0(1) 91.8(1)
+ $2" $3) - 2J,3(gL" $3)) were determined for CuEtBz • MeOH [4]. Thus the quartet state is lowest in energy with two doublet states lying 18 (11) and 90 (15) c m - ~ higher in energy, respectively (Fig. 7). Detailed SQUID measurements at low temperatures allowed the determination of the zero-field splitting parameter D. For CuEtBz • MeOH, IDI = 1.4 + 0.5 cm l was found by Tomkowicz et al. [4]. The EPR spectra of CuEtBz • MeOH were interpreted using the following total spin Hamiltonian:
-t-D[S':-½S(S-t-1)]+E[S^:-S~],
(1)
where /x B denotes the Bohr magneton, D and E represent the axial and the rhombic zero-field splitting parameters, and Si are the spin operators. The choice of the coordinate system x , y , z is arbitrary. However, the sign of E varies upon the interchange of the x and y axes. In order to specify the axes explicitly, we will follow the convention IOl > 31El and D . E > 0 [ 1 2 ] . In analyzing the EPR spectra of quartet states with large zero-field splitting (2 D >> h v, where v is ISges,SI3 > 11/2,1)
E (J12,J13) l
'2Jlz-1/2J13
I 69±13crnI 90-+15cm-1 1 11/2,0> I , -1 I 18+11cm
13/2,1)
i
312 J13 j12_1/2J13
Fig. 7. Spin states and exchange splitting for CuEtBz-MeOH as detected from temperature-dependent susceptibility measurements.
P. Fleischhaueret al. /Journal qf Magnetismand Magnetic"Materials 159 (1996) 166-174
170
the spectrometer frequency), it is most convenient to use a fictitious S' = 1 / 2 Hamiltonian rather than the true S = 3 / 2 spin Hamiltonian. The g'-values of the effective S' = 1 / 2 and the true S = 3 / 2 Hamiltoniarts are related as follows [13]: 1 -3A
not valid, the EPR transitions may be analyzed by solving the Hamiltonian matrix of the quartet state. The following solutions (3)-(5) were obtained for the magnetic field parallel to one of the principal axes [ 14]. (1) H = H.: e ( l l ) ) = ~-g: ' ]&BH + { ( D + g = /.zBH ) 2 +
g' =
3E2}
1/2
(2a)
x
g,
1
,
, g,,(l+ glr=
l+3h 1
(3a)
e(12)) = - T g' ~ l x u H
+{(D-g:tzBH)2+3E2}
l+3A l+fi--7~),
( g,
+_3/2,
M~=_+I/2, )
(2b)
~
,
,
e(13)) =
I/2 ,
(3b)
7g:l,*B H - {(D + g~:/.tBH) 2 + 3E2} '/2 1
(3c)
M,=-1-3/2,
e(14)) = --Tg~lXBH ' ,
g~=
( g:
2 ) 1+
--{(D--g:IxBH)Z+3E'I
M,=_+l/2,
(2c)
~
,
.~ 1/2
,
(3d)
(2) H = g~ ."
7gxtXBH+{g~tzi~
M,=-t-3/2,
2
+D2+3E
2
-g~ I.*, H( D - 3E)} 1/2, where A = E/D. The g'-values for transitions within the predominant M s = 4 - 1 / 2 and the predominant M, = 4- 3 / 2 Kramers doublet of the quartet state are plotted versus A in Fig. 8, assuming a true g-value of 2.15. Eqs. (2a)-(2c) are approximations that hold for the case D >> g •/x B • H. If these equations are
(4a)
e(12)) = - T g' , tzB H + {gTlz~3 " ' H2 + De + 3E2 + g x / Z B H ( D - 3E)} 1/2,
(4b)
{g2~tx2H2+ D 2 + 3 E 2 e(13)) = 7g~t~BH_ ' -g,/-*B H( D e(14)) =
-
-
BE)}
(4c)
1/2 ,
1 ~_g~tXBH-{g,2tX~") H 2 + D 2 +3E-"
+g,/XBH (D-
3E)} 1/2,
(4d)
(3) H = H,,: e ( l l ) ) = Ig,,txBH + {g.~tx~H 2 + D2Z + 3E 2 0
[ 0
. '
.
. 011
.
. "
. 02
i '
E/O
013
- g , tzBH(D + 3E)} '/2,
(5a)
~ o 2 + D 2 + 3E 2 . g~txgH e(12)) = - ' ?_g,,/xBH+{
g:l'b'
"1
+ g , . t * B H ( D + 3 E ) } '/2
(5b)
I ~ 2 2 + D 2 +3E 2 e(13)) = 7gylXBH-{g;tXBH
- g ~ I Z B H ( D + 3E)} 1/2, EID
Fig. 8. Effective g-values for transitions within (a) the predominantly 4-1/2, and (b) predominantly 4-3/2 Kramers doublet of the quartet state.
e ( [ 4 ) ) = - 2 g ~I t X B H - - { g ~ t x~B H~
2
+gytxBH(D + 3E)} 1/2.
(5c)
+ V 2 +3E 2 (5d)
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
The eigenvalues (3)-(5) are not labelled with M~ values since the corresponding eigenvectors are in general linear combinations of the basic vectors, according to li) = ail3/2) + bill/Z) +
c,I-
1/2) +
d,I-
171
G. This strongly suggests that the weak signals observed in the X-band powder spectra of CuEtBz • MeOH at 13 300 and 14 600 G arise from transitions between the Kramers doublets of the quartet state.
3/2) (6) HIIx
where 13/2), 11/2), l - 1 / 2 ) and l - 3 / 2 ) denote the basic vectors indicated with the appropriate M~ values. Fig. 9 shows the field dependence of the quartet energy levels, calculated using Eqs. (3)-(5) with g = 2.15, D = 1.0 cm i and E = 0.1 cm-L The reflection of 12) and 14) for Hllz arises from the non-crossing rule, which expresses that states of the same symmetry may not cross. The arrows in Fig. 9 indicate the allowed transitions which were obtained by calculating the transition probability P, which is given by P = 1~mlS~ + iS/j ]n)l 2,
I1> 2"
~.oo
13>
ILl -2"
-4-
I
50OO
,
I
1O000
,
I
15OOO
,
~DOOO
H [Gauu.I
4t
(7)
where ]rn) and In) are eigenvectors according to Eq. (6) and c~,/3 denote x, y, z, the components perpendicular to the main field. Transitions are allowed within the + 1 / 2 and + 3 / 2 Kramers doublets, since the latter states are not pure _+3/2 states as discussed above. Transitions between levels W2) and 14) belonging to different Kramers doublets are forbidden for HI] z, but are allowed for all other orientations. With the theoretical background elaborated so far, the EPR spectra of CuEtBz-MeOH will be interpreted in the following. From the angular dependence of the single-crystal resonance, the principal g-values of g':=2.1(1), gi~ = 4.0(1), g'~ = 4.7(1) (at 4.2 K) were determined for CuEtBz. MeOH. These values are characteristic for transitions within the predominantly M~ = _+ 1/2 Kramers doublet of the quartet state. From the principal g-values an [E/D] ratio of A = 0.054(3) is calculated using Eqs. (2a-c) and a true g-value of 2.15. A plot of the energy levels of the quartet state with ]D]= 1.4 cm -1 (obtained from the SQUID experiments) and A=0.054, reveals that for HIPz the resonance condition is fulfilled for transitions between the Kramers doublets at 13300 and 14800
12>
.,-,
Hlly
21
~
I1>
o.!.
0
50O0
1OOOO
15O0O
20OOO
H IGauul
HIIz
2-
~O-
12>
I,LI -2-
13> -40
,
I
,
I
lOIx~o
,
I
1500o
,
H l~uml Fig. 9. Field dependence of the quartet levels calculated using Eqs. ( 3 ) - ( 5 ) with g = 2 . 1 5 , D = I . 0 cm - I and E = 0 . 1 c m - l . The arrows indicate allowed transitions for A E = 0.3 c m - l .
172
P. Fleischhauer et al. / Journal q['Magnetism and Magnetic Materials 159 (1996) 166-174
Table 3 g-tensors for the different levels of SE= Sil = S[u = l/2 systems Multiplet ISge~,St3)
g-tensor
13/2, 1) 11/2,0) 11/2, 1)
gH
1/3g I + 2/3g I -
l/3gli + 1/3gli I
different contributions of this state to the observed signal due to the changes in the thermal population of the levels. The variation in the position of the composed signal can be simulated with the following formula, which simply weights the resonance fields
I/3g u +2/3gHi 15
As discussed above, these transitions are forbidden for H ] l z but become allowed for rotating the : axis away from the main field direction, and may therefore be observed. Nevertheless, for a definite assignment of the signals, single-crystal EPR investigations are necessary. The orientations of the principal axes in the molecular frame, as determined from the singlecrystal EPR investigations will be discussed in the following. As shown in Fig. 4, the g~ axis lies close to the Cu(2)-O(6) bond (4°), while the deviation of the g2 and g3 axes from both the Cu(2)-O(3) and Cu(2)O(1) bonds is approximately 12 °. It is well known that the g-tensor of exchangecoupled systems can be expressed as a linear combination of the local g-tensors. For symmetric triads with S = 1 / 2 centres, the relations given in Table 3 hold [6]. From Table 3 it is obvious that the three metal centres contribute equally to the g-tensor of the quartet state. Since the dihedral angle between the coordination planes of adjacent copper ions is 60.7 °, the observed g-values result from a complete average of the tensors of individual ions. In fact, using Eq. (2), with the observed effective g-values and A = 0.054, the true g-values of g, ~ g,. ~ 2.18 and g~ ~ 2.12 can be calculated. It is clear that the quasi-isotropic g-values are the result of an averaging process, due to the misalignment of the local axes of the three tensors. This is also the reason why no change in the orientation of the g-tensor with increasing temperature is observed (Table 1). It is possible to explain the strong temperature dependence of the resonance field observed in the powder spectra of C u E t B z - M e O H (Fig. 1) by assuming that in the X-band experiment the signals of the three spin states of the system are not resolved. Thus the observed signal embodies contributions of the [3/2,1), the ]1/2,1) and the l l / 2 , 0 ) states. The temperature-dependent resonance position arises from
~0
•
"10t -15
I
' 0
,
~
I
,
~
I
'
I
I
'
I
~
H l~uul 15-
10-
5-
UI -5-10• -15H lGau~] 15
10,
5,
W -5-
-10-15
,
I
,
I
,
H l~,u,,l
Fig. 10. Field dependence of the quartet levels calculated using Eqs. (3)-(5) and g = 2 . 1 5 , D = 1 . 4 cm -I and A=0.054. The
arrows indicate allowed transitions for A E = 8.2 cm- ].
P. Fleischhauer et al. / Journal of Magnetism and Magnetic Materials 159 (1996) 166-174
of the different spin states according to the Boltzmann distribution:
H ...... ic =
E tOi nres,i e x p { -- a g i / k T } i E toi exp{ - A EykT} '
(8)
i where //re ~ is the resonance field; to is the multiplicity; AE~ is the energy separation between ]3/2,1) and 11/2,0), and A E 2 is the energy separation between ]3/2,1) and ll/2,1). Good agreement between the observed and calculated temperature dependences of Hre~ has been obtained (see Ref. [9]). It is also possible to describe the temperature dependence of the principal g-values of CuEtBz. MeOH (see Table 1) using Eq. (8). The principal g-values of the doublet states of CuEtBz • MeOH are not known, but their choice strongly influences the energy separations obtained when fitting Eq. (8) to the experimental values. It is therefore rather pointless to give numerical data for the kEg values obtained from the analysis of the resonance shifts in the single-crystal experiment. Nevertheless the agreement between the simulated and observed results supports the above explanation of this effect. It is well known that the coalescence of different spectroscopic signals can be suppressed if the energy difference of the signals is enhanced [15]. In the EPR experiment, this can be achieved by operating with a higher resonance frequency. In Fig. 5 the highfrequency powder spectra of CuEtBz. MeOH, obtained with a resonance frequency of 244.99 GHz are shown. A sharp signal at 65000 G ( g ' = 2 . 7 ) is observed in the spectrum at 4 K. Fig. 10 shows the energy levels of the quartet state, again calculated using Eqs. (3)-(5), up to 90 000 G for g = 2.15, D = l . 4 c m 1 andA=0.054. The allowed transitions for the resonance frequency of 244.99 GHz are indicated as arrows. Since the Zeeman splitting at 8 T corresponds roughly to 12 K, in the spectrum at 4 K only the transitions from the lowest state occur. Thus transitions at 70000 and 66000 G for Hllx and HII y, respectively, are expected in the high-field spectra of CuEtBz. MeOH. The observed signal at 65 000 G can be attributed to the transition from the lowest state for Hlly. The missing signal at 70000 G, which is expected for Hllx, indicates that the
173
sample is oriented by the strong magnetic field roughly along the y-axis. Attempts to suppress the orientation with mineral oil or araldite were hampered by the decomposition of the compound. The large Zeeman splitting in the high-frequency experiment in comparison with the thermal energy at 4 K allows the determination of the sign of the D parameter. For D = - 1 . 4 cm-J only one transition from the lowest level at 54000 G is expected (HI] z), indicating that the positive sign for D is the correct choice. As expected, the position of the resonance field is not affected by increasing temperature in the highfield experiment. Instead, an additional signal at H = 81 800 G ( g ' ~ 2.14) gains intensity with increasing temperature. As shown in Fig. 1, signals near 80000 G are possible for orientations along x and y. In addition, the doublet spin states of the cluster become populated, for which signals of the order of 80000 G are also expected. The observation of separate signals as at 8600 G for the doublets should be expected in the high-field experiment, because the difference in resonance fields becomes large, and relaxation can no longer average the signals. The results presented so far prove that the observed temperature-dependent resonance field in the X-band spectra of CuEtBz - MeOH is due to the fact that the signals of the different spin states of the molecule are not resolved. The merging of spectroscopic signals attributed to different states is a well known phenomenon, and is a manifestation of the Heisenberg uncertainty principle, which can be expressed as A t - A u ~ 27r,
(9)
where A~, is the separation of the signals in frequency units, and At is the smallest time during which the states may be distinguished. If the mean lifetime ~- of the states becomes smaller than At, the signals coalesce into one line. In order to observe the coalescence of the signals related to the quartet and the doublets of CuEtBzMeOH in the X-band spectra a mean lifetime of ~ - < 3 × 10 - ~ s is estimated using Eq. (9). Two mechanisms may be responsible for the small lifetimes: (i) spin-spin relaxation, and (ii) spin-lattice relaxation.
174
P. Fleischhauer et al. / Journal of Magnetism and Magnetic: Materials 159 (1996) 166 174
Further investigations on this interesting topic are now under way to identify which of these mechanisms is operative in our case.
Acknowledgements We thank Dr N. Bontemps and Professor Dr P. Monod, Ecole Normal Superieur, Paris, for giving us the opportunity to record X-band EPR spectra up to 16000 G.
[5]
[6]
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