Specfrochimica Aclo,Vol. 38A.No. 11,~~. 1221-1229, I982 Printed in Great Britain.

0584-8539/82/111221-09503.00/0 @I 1982 Pergamon Press Ltd.

Metal pair spectra and exchange coupling parameters of di-p-hydroxo-his [tetraamine chromium (III)] bromide

MAKOTOMORITA,* THOMAS SCHONHERR,ROLFLINDER~~~ HANS-HERBERT~CHMIDTKE~

Institut fur Theoretische Chemie der Universitit Dusseldorf, D-4000 Dusseldorf 1, Federal Republic of Germany

(Received 11 May 1982)

Abstract-The absorption, luminescence, and far i.r. spectra of the title compound have been recorded at various temperatures. A computer-assisted assignment of all peaks measured in the vibronic spectra has been carried out using an energy level scheme for the exchange coupled ‘A2e4A2, and ‘Azs2E, manifolds, calculated from a model considering only bilinear coupling terms in the excited states. Optimal agreement with the experiment is obtained if the energy levels are calculated from the exchange coupling parameters (in cm-‘) .I = 30, j = - 0.3 for the ground state, .I,, = 0, J,, = 125, Jn = - 48, .13r = 186 for the excited state manifold, from the low symmetry ligand field parameter V= 46, and an energy gap of AE = 14445. The importance of vibronically induced transitions in the assignment of band peaks is emphasized: frequencies due to this transition mechanism are obtained by comparison with the i.r. spectrum and with the electronic transition energies calculated from the model.

1. INTRODUCTION Antiferromagnetic exchange interactions between open-shell metal ions in polynuclear complex compounds have been widely investigated using magnetic [ 11 and spectroscopic I21 methods. The pair spectra of Cr(III), Mn(I1) and other ions in various host crystals are well resolved and have been carefully investigated[3-71. Sign&ant pro- gress has recently been made in interpreting spec- tra of binuclear complexes of Cr(III)[8-111. The transitions observed in the optical spectra of these compounds gain their intensity by several mechanisms which add to the oscillator strengths by varying amounts. The primary effect is an exchange induced electric dipole mechanism[l2,13], which arises from the inter- action of nearest neighbor ion pairs. Apart from this, all other intensity borrowing mechanisms, e.g. through spin-orbit coupling and vibronic inter- action, which are common to mononuclear chromophores, will contribute to the intensity. For double excitations a vibronically induced exchange mechanism has also been proposed[l4,15]. In the discussion of well-resolved pair spectra, therefore, vibronically induced transitions must also be con- sidered, which for mononuclear compounds have oscillator strengths which are comparable with zero phonon transitions[l6-181. In the past, however, band peaks of pair spectra have been explained preferentially by pure electronic (zero phonon) transitions; the coupling with vibrational modes, as determined for example, from i.r. ‘and

*Permanent address: Department of Industrial Chem- istry, Seikei University, Richijoji, Tokyo 180, Japan.

tTo whom correspondence should be addressed.

Raman spectra, has not previously been included in discussions of spectral data assignment.

This work will focus on the compound [(NHs)4Cr(OH)2Cr(NH&lBr~-4H20, which yields well-resolved vibronic and far i.r. spectra at low temperature, and attempts are made to assign the optical data to the energy levels of the ground and singly excited 4A2,2E, pair states. While for the ground pair states the symmetry types and the level scheme seem to be well established from magnetic and spectroscopic investigations, the structure of the level system for the excited pair states is still rather uncertain.

This paper uses the theoretical model of DUBICKI and TANABE[19] to calculate the energy level scheme. This theory is preferable to earlier procedures, in that the tensor operator techni&e employed results in a parameterization of the + I’S multiplets by means of the usual orbital J,, terms, simplifying the calculations significantly. In order to consider a comprehensive set of possible assignments, extensive use was made of a com- puter program that rejects those calculations which lead to parameters outside a given range of possible values. Bands assigned to vibronic tran- sitions were compared with the i.r. spectrum. For this purpose the bromide salt was preferred to the dithionate[20], since its far i.r. spectrum is not complicated by vibrational peaks of the anion. Recently, the exchange interaction in the cor- responding chromium 1,2-diaminoethane complex has been investigated using structural, magneto- chemical and spectroscopic methods [21]. Since the main subject of that work was the in- vestigation of the splitting in the ground state manifold, the levels associated with excited pair

SAA Vol. 38, No. 11-H 1221

1222 M. MORITA et al.

states and their coupling parameters were not determined in detail. This is, however, the main objective of this paper.

2. EXPERIMENTAL 2.1.. Mfzterials

The dihydroxy complex, [(NH&Zr(OH)$r(NH,).J Br.,.4Hz0 (red powder) was furnished to us by SPRINGBORG[~~]. The compound was stored at 5°C avoi- ding exposure to daylight as far as possible. The dithionate salt was prepared following an established procedure by DUBSKY 1231.

2.2. Spectroscopy All measurements in the far i.r. and in absorption and

emission at low and higher temperatures were carried out as described earlier[24]. For the i.r. spectra the samples were pressed into polyethylene mulls, for absorption and emission measurements transparent KBr disks were pre- pared. In emission pure powders were also investigated. Temperature control was achieved by a thermocouple which was affixed to the sample.

3. THEORETICAL For the ground pair states the common isotropic

effective exchange Hamiltonian

x ground = JS. - Sb - i(S, - Sd (1)

was used with IJI * ]j]. The corresponding wave functions belonging to the pair states formed by the ionic ground states, I.& and I&, of central ions a and 6, are ]I’,SJ,S,;SMs) where S is the total spin of the pair state and MS is the projection of S along the common axis. Applying equation (1) to the 4Azg4A2, state manifold for a system of equivalent pairs of ions yields the energy levels

-$ s2(s+ 1)2-15s(s+ l)+y I I

. (2)

For singly excited pair states the Hamiltonian of DUBICKI and TANABE [19] contains an exchange part %‘=, and a single ion contribution Y&i, which is comprised primarily of the low symmetry ligand field and the spin-orbit coupling.

The symmetry adapted wave function for an equivalent pair of ions, one in the 4A2, ground state and the other in the ‘E, state, is

*IE; M;A&.;; SMd} (3)

with component pair functions built up from single ion functions of t:, electron contIguration in tetragonal quantization [3]

Using this basis, the bilinear coupling parameters J(M., ML) and K(M., Mb) in the exchange opera- tor L,[19] are calculated as

J(u, u) = 5 (2X, + Xs). J(u, u) = 0

1 J(u, u) = - (4J,, + 451, + 251, - J33)

9

K(u, u) = J,, - J,2, K(u, u) = 0

1 K(u, u) = -(J,, + J,2 - 4519 + 2x3)

3 (5)

where the Jij are the common first-order superex- change coupling parameters between tzg orbitals, which by adaptation to D2,, symmetry form the parameter matrix

(6)

Biquadratic exchange coupling terms which would significantly increase the number of parameters in the model were not considered.

With the wave functions of equation (3) the energy matrix of the exchange operator Z, has only diagonal elements, which can be expressed in terms of Js and KS by

E(kSM)‘=$J(M,M)[S(S+l)-;]

1 kiz K(M, M)S(S + 1) (7)

with M = u or u and S = 1 or 2. If the complex molecule contains an inversion centre, as has been found for [en2Cr(OH)2Cr en2]X4[21, 253, the parity is a good quantum number and corresponding selection rules must. hold. Another selection rule operates with respect to total spins. Due to spin- orbit coupling effects, transitions between energy levels should only be allowed[19] if they differ in spin by AS = 0, + 1. Since spin forces are rela- tively small in chromium(II1) compounds, they will be neglected, so that the single ion contribution Yt?si contains only the ligand field term [ 191

Xi = F( “v, + grb) (8)

which represents the effects of low symmetry on the energy levels of ions a and 6. Assignments of the peaks in the absorption and emission spectra were obtained on the basis of parity and spin

Metal pair spectra and exchange coupling parameters 1223

selection rules, and by considering intensity changes at different temperatures in relation to Boltzmann distributions.

4. RESULTS AND DISCUSSION In Figs. l-3 the absorption, luminescence and

far i.r. spectra of KNH3)4Cr(OH)Kr* (NH3)4]Br4.4H20 at various temperatures are shown. Reference to the recording technique used is given in the Experimental section. A Raman spectrum could not be recorded due to the extreme light sensitivity of the com- pound. The best resolved spectrum obtained was that in absorption, which, in part, exhibits some drastic temperature effects. The infrared results demonstrate that it is necessary to record vibra- tional spectra at low temperature when they are to be compared with vibronic data measured at the same conditions: all peaks were shifted to higher frequency on going from 160 to 36 K.

4.1. 4Azs4A2, ground state splitting For the majority of chromium(II1) pair com-

plexes the energies of the ground state manifold ( f S) lie in the order

(+O)c(-1)<(+2)<(-3) (9)

which is obtained from the exchange Hamiltonian of equation (1) with parameter values .I>0 representing antiferromagnetic coupling[2,9,10,21,25]. However, since the magnitude of the splitting varies over a wide range[26], before beginning the discussion of the vibronic band assignment, the parameters ap- propriate to the present compound must be determined at least approximately. These can be

149 147 WAVENUMBER (kK1

14.5

Fig. 1. Absorption spectrum of l(NHr)4Cr(0H)2. Cr(NHJ)4]Br4.4H20 in a transparent KBr disk between 670 and 690nm at 30K (-) and 82 K (- - -). At higher frequencies absorption due to 4A2i T,,

pair states are observed with lower intensities.

estimated from the temperature dependence of absorption band intensities when related to the Boltzmann distribution over the two lower levels of equation (9). The intensity fractions of prom- inent bands in the 80 and 30K absorption spec-

s -. ‘A___

Old.30 I I 1 _ I I ,

14.50 14.70 14.

WAVENUMBER Ck Kl 90

Fig. 2. Luminescence spectrum of [(NHp)4Cr(OH)zCr(NHr)41Br4.4Hz0 in a transparent i(Br disk at 50 K (-) and 100 K (---) obtained from excitation by the 488 run argon laser line. Some lower

frequencies with smaller intensities are omitted.

1224 M. MORITA et al.

Fig. 3. l&200

’ :: I I

“210.00 t 170.00 I I I , I I 1 I 1

130.00 90.00 50.00 10.00

WAVENUMBER (CM-‘)

Far i.r. spectrum of [(NH,),Cr(OH),Cr(NH,)JBrd.4H,0 in a polyethylene mull in the range cm-’ at 36 K (-) and 160 K (---). Other 36 K band peaks obtained at higher frequencies

are 286,307,368 and 398 cm-‘.

trum can be grouped into the following ranges:

(a) Al, A7, A9, Al2 Iso/~~, = 0.7 - 0.85

(b) A4, AS = 1.3- 1.6

(c) A4 > 10. (10)

Most of the other bands can be adjoined to one of these groups although actual numbers cannot be given due to multiple superpositions with other bands. The temperature characteristics indicate that bands (a) should be assigned to transitions originating from the lowest state (+ 0), bands (b) from the (- 1) level, and the band (c) from the ( + 2) level. Introducing the intensity quotients obtained from the experiment into the Boltzmann formula yields an estimate of J = 25 - 35 cm-’ for the first-order coupling constant of the ground state which compares well with the halogenides of corresponding ethylenediamine complex salts [21]. This parameter value moves the (- 3) level to rather high energy with very small thermal occu- pations, so that few transitions from this level would be expected.

4.2. 4A,,*E, pair states From equation (7) the energy levels due to

superexchange coupling in the excited pair states are calculated in terms of fZg coupling parameters [equation (5)]

The single ion Hamiltonian, equation (8), accounts for the low symmetry ligand field splitting, and gives rise to additional shifts of the u and u components of each of the ( f S)’ levels. The sign and magnitude of this splitting is defined by the parameter V = E( + Su)’ - E( k Su)’ for each f S. The analogous effect in mononuclear tetragonal complexes is the splitting of the *E,-level, which is generally lCL70 cm-‘; for [Cr(NH&(OH)]” the splitting ‘E, has been determined to be 61 cm-’ [27]. In some cases, e.g. for [Cr(NH&Xl” (X = halogen or oxygen donors) and [CrWHMNCO)l*‘, even larger splittings have been reported [24,28].

Assuming a coupling mechanism by superex- change interaction which is propagated only through the orbitals of the bridging oxygen ligands, the t,,-orbital coupling parameters have the signs and relations given by NAITO [4]

J,,=O; J,2>O; J,,<O; .L>O with IJI,l Q J12, Ju. (12)

Metal pair spectra and exchange coupling parameters 1225

With these constraints the following relations within the u and u component series of (+ S) levels are calculated from equation (11)

(+lu)‘<(-l1u)‘~(+2u)‘<(-2u) and

(-2v)‘I(-lu)‘<(+lu)‘<(+2u)‘. (13)

This level arrangement is an important basis for discussing vibronic band assignments.

4.3. Band assignments to 4Atg4A2g++4A2g2Eg transitions

Examining the vibronic spectra in Figs. 1 and 2, it is apparent that the number of bands exceeds the number of possible electric dipole induced zero phonon transitions if the parity and spin selection rules (AS = 0, & 1) are operative. This would restrict the total number of possible tran- sitions between all level components of the ground and excited pair state manifolds to just twelve. Some of the components involving higher mem- bers of the ground state manifold would yield very low intensities and may not even be detected. Since spin-orbit coupling in 4A,, and *E, states of mononuclear chromium-amine complexes is very small [29], it is reasonable ‘to assume similar con- ditions for binuclear compounds, so it can reasonably be neglected. Also no evidence for non-equivalent sites in the crystal could be detec- ted in the spectrum; different complex molecules would not be expected in view of the fact that the number of formula units in the crystallographic cell for the corresponding ethylenediamine com- plex has been determined to be Z = 1[21]. There- fore a significant number of peaks observed in the spectra must be due to vibronic origins. In prin- ciple, because of the low symmetry, all vibrational modes found in the i.r. spectrum can be candidates for inducing vibronic transitions between elec- tronic states of equal parity. Apart from these, even gerade vibrational modes can give rise to vibronic transitions between states of different parity if symmetry rules are obeyed.

In order to arrive at definitive assignments, the band positions and the temperature dependences of the intensities will be compared with the level orders of equation (13) under the regime of selections rules for transitions between all level components of the two pair state manifolds. While the main peak in absorption (Al) loses intensity at higher temperature, the corresponding band in emission, (L6), (Stokes shifts for 2E states in chromium complexes can be neglected [16-l& 24, 27, 281) exhibits the reverse temperature behaviour. This property and the selection rules assign this peak to a transition from the ground state level (+0) to one of the (- 1)’ levels of the excited state manifold. Since other absorptions with similar temperature quotients ( < 1) are found only at higher frequencies, the absorption (Al)

must belong to the lower component of (- l)‘, which on the other hand is a higher level of the ‘A2,‘E, manifold, as evidenced by the tem- perature behavior of the emission peak (L6). With the relations given by equation (13), it can be concluded that the band (Al) must represent the ( + 0) + ( - 1 v)’ transition, since for an assignment to ( - 1~)’ the allowed transition ( - l)+ (+ 1 U) would be at lower frequency, because (+0) < ( - 1) and ( + 1~)’ < ( - 1 u)‘. A transition from (- 1) should, however, have the type (b) tem- perature behavior of equation (lo), which is not present in the energy range below the transition (Al). Therefore peaks (Al) and (L6) are assigned to (+ O)*( - 1 u)’ and the lowest levels of the excited state manifold have the order (-2u)‘< (-lu)l< *a*.

The most intense luminescence band (LlO) of the 50K spectrum (cf. Fig. 2) is at 14540cm-‘. Since it loses much of its intensity on temperature increase, the transition must originate from the lowest level of the 4A2S2E, manifold, which has been determined to be (-2~)‘. Spin and parity selection rules assign the transition to (- 2u)‘+ (+ 2) in agreement with the corresponding ab- sorption peak (A4’) at 14537 cm-‘, which is observed only at higher temperatures, exhibiting type (c) intensity behavior, characteristic of a transition from the (+ 2) level.

With the identification of these energy levels the assignment of another transition can be obtained. The allowed ( + 2) + ( - 1 u)’ transition should have significant intensity only a higher temperatures, with frequencies 75-105 cm-’ (i.e. approximately 3 J) lower in energy than the peak (Al). In this region a band at 14567 cm-’ (A3’) is observed which corresponds to the (L9)-peak in lumines- cence, exhibiting the expected temperature behavior; therefore an assignment to this tran- sition seems to be reliable.

The other excited state levels cannot be deter- mined in as straightforward a manner, since it is always possible to explain certain peaks by various allowed electronic transitions. However, the constraints generated thus far, in particular equations (10) and (13), furnish several experi- mental and theoretical footholds by which the number of possible assignments can be significantly limited:

1. The main absorptions (A7), (A9), and (A12) which lose intensity with increasing temperature must originate from the gound state level (+ 0). Since the selection rules predict only one allowed electronic transitions, i.e. (+ O)+( - lo)), two of them must be vibrationally induced transitions from (+0) into (+l)‘+v- or (-l)‘+v’ vibronic levels (v- and v+ are odd and even vibrational modes, respectively).

2. The characteristic intensity increase of the peaks (A4) and (A5) with higher temperature sug- gests an assignment to the transitions (- l)+

1226 M. hiORlTA et al.

(+ la)’ and/or (+ Iv)‘. This is supported by the observed temperature behavior of the correspond- ing luminescence bands, (L4) and (LS), which acquire intensity only when the temperature is increased.

3. In addition to the intense transition ( + 2)+ (- 2u)‘, which gives rise to the prominent peak (A4’), another hot band with a similar temperature. behavior, arising from the transition ( + 2) --, ( - 21r)‘, should occur. Since no band of this kind is obser- ved between (Al) and (A4’) this transition is either hidden under the peak (A4’) or is covered by the large group of absorptions at energies higher than (Al). A superposition on the (+ 2) + ( - 2~‘) tran- sition, which gives rise to the (A4’) band, is ruled out because of the sequence (- 2~)’ < (- lo)’ < . - * for the excited state manifold, as was derived

from (Al) and (A4’) peak assignments. The ( + 2) --, (- 2~)’ transition therefore must be hidden by the group of bands higher in energy. A closer analysis of the absorption spectrum between (Al) and (A14) shows that a band between 14760 and 1479Ocm-’ must be present with a temperature behavior similar to type (c). It is dithcult to detect, since this part of the spectrum is populated by other bands, e.g. (A9) and (A12), with reverse temperature characteristics.

4. The low frequency absorptions (AS) and (A6’) are apparently due to transitions from the (-3) level of the ground state manifold, since transitions from lower levels should occur at higher frequency. Spin and electric dipole allowed transitions in this part of the spectrum therefore must be assigned to ( - 3) + (+ 2)’ electronic (zero phonon) or ( - 3) + ( - 2~)’ + v- vibronic transitions.

With these guidelines all possible band assign- ments which fit into the framework described above have been checked and put into relation to transition energies calculated from a set of model parameters. These parameters are J and j for the ground states, .I,, = 0, &, Jls, JsJ for the excited state manifold, V for the ligand field splitting and AE for the 4Aza4A2, -“AzlE, energy gap. An assignment was rejected if the parameters did not agree with the relations of equation (12) and the level order of the ground state manifold, equation (9). Since the assignment of only three bands (Al, A3’, A4’) can be considered certain, in this pro- cedure each trial was initiated with four further tentative assignments, from which a set of seven parameters could be calculated. In the few cases where the parameter values were within the given limits, the total energy level scheme was cal- culated and all possible electronic transitions were compared with the peaks in absorption and luminescence, and the temperature behavior checked. The testing also included vibronic tran- sitions induced by odd vibrational modes, which were’ known from the i.r. spectrum (Fig. 3). The criteria for the quality of the assignment obtained

by this procedure were the following:

(a) all intense bands in the spectra should be assigned;

(b) the observed temperature dependence of the intensities had to be reproduced correctly;

(c) no allowed electronic transitions should be predicted within an energy region where no bands were observed;

(d) previous results with respect to level orders, e.g. (-2u)‘<(-lu)‘< a.*, and intensity relations had to be confirmed.

As a result the calculations supplied a single solu- tion to the problem which fulfilled all of the above conditions, leading to definite assignments for four other bands, i.e. (A4, AS, A9, All) as given in Table 1. Finally, the parameter set calculated from this assignment was varied, this time witbin a small range, in order to get optimal agreement between theoretical transition energies and the rest of the peaks in the optical spectra. The parameters thus obtained, together with their error limits, were (in cm-‘)

J=30+3, j= -0.3+0.5, JtZ= 125*5, J,, = -48a5

J,,=186+5, V=46-+5, AE=(-2u)‘-(-3) = 14 445.

The energy level scheme calculated from the optimal parameter values is shown in Fig. 4. Table 1 compiles all experimental and calculated band maxima together with the proposed assignments. Apart from peaks (Al’) and (A7), all others are explained either by spin and parity allowed zero phonon transitions or by vibronic transitions in- duced by odd vibrational modes, and all intensities have the correct temperature dependence. A glance at Fig. 3 shows that all the vibrational frequencies in Table 1 which serve to induce elec- tronically forbidden transitions occur in the i.r. spectrum as well, i.e.: 43, 77, 110, 131, 163, 177, 286, 307 cm-‘, which is in support of the assign- ments given.

Due to the low symmetry of the molecule (&, or even lower), most of the possible vibronic combinations, calculated using the i.r. frequencies, would lead to allowed transitions. An N&r&- 0),CrN4 chromophore has six primarily stretching vibrations (b,,, 2b2., 3bd and seven angular vibrations (3 blu, 2bzu, 2b9.), which are all i.r. active. If one assumes that those vibrational modes are coupled with electronic states of the chromium pair which involve extensively atoms in the Cr(p-O)zCr plane, then the odd vibrations which can induce parity forbidden electronic transitions are the b,. out-of-plane angular mode and the b2,, and bsU in-plane vibrations. The

Metal pair spectra and exchange coupling parameters 1227

Table 1. Proposed assignment of absorption and luminescence band maxima as compared with theoretical transition energies obtained from

the level scheme of Fig. 4 and relevant vibrational frequencies

Absorption* Llunlnescenc~ Assignment Y (CdC. 10

A 6’ 402

A 5’

A 4’

A 3’

514

537

567

A 2’ 585

A 1’ 626

A 1 652

A2 663

A3 675

A4 679

A5 695

A6 701

A7 725

A8 735

A9 753

A 10 763

A 11 760

A 12 782

A 13 708

A 14 801

A 15 828

A 16 862

A 17 899

A 18 910

L 14

L 13

L 12

L 11

L 10

L9

LB

409

430

476

531

540

567

583

Ll 631

L6 653

L5

L4

L 3

L2

L 1

680

695

750

702

(+0)+307- c-(+lu) ’ 401

(+0)+286- <-(+lu) ’ 422

(+2)+177- <-(+lv)’ 474

C-3) -> (-ZV) *+43- 480

(+0)+177- <-c+1u1 534

C-3) -> (-2~) ‘+77- 522

(+2) <-> (-ZV) ’ 537

(+2) <-> (-1v) ’ 565

(+0)+131- <-(+lu)’ 577

f-3) -> (-Zv) 1+131- 576

f-1 1 <-> (-1v) ’ ? 624

(+o) <-> (-1v) ’ 652

C-1) -> (-1u) 1+43- 667

(+2) -> (-1u) ’ 663

C-1) -> (-2v) 1+77- 673

f-1) <-> (+lu) ’ 680

f-1) <-> (+lv) ’ 700

f-1) -> (+zu) ’ 699

(+o) <-> (-1V) 1+73+ 725

(+o) <-> (+lv) ’ 7 728

f-1) -> (-1v) ‘+l lo- 734

(+o) c-> (+lu) 1+43- 751

(+o) <-> (-1u) ’ 750

f-1) -> (-1u) ‘+43- 765

(+2) c-> (-2u) ’ 765

(+o) -> (+lu) *+77- 785

(-1) -> (-1~) ‘+163- 787

(+o) -> (+lv) 1+77- 805

C-1) I -> (+zv) ’ 825

(+O) -> (+lv) 1+131- 859

(+o) -> (+lv) 1+177- 904

C-1) -> (-1~) ‘+286- 910

*Wavenumbers (cm-‘) are given as v-14 000.

frequencies 43 and 77 cm-’ measured in the far i.r. strengths are smaller due to the divided ligand field spectrum, which also occur as combinations in the and the dilTerent sp hybridization on the oxygen. absorption spectrum, can therefore be assigned to Ds and Dt for cis-configurations are given in two of these angular vibrations. terms of angular overlap parameters by

Finally a word must be said concerning the value V=46+5cm-’ obtained for the low sym- metry ligand field parameter. In mononuclear tetragonal or quadrate complexes this parameter corresponds to the splitting of the octahedral *E, level and is defined as V = E(*A?) - E(*B?). For [Cr(NH,),(OH)]*’ this parameter has been deter- mined from the experiment to be v= + 61 cm-’ [27]. Ligand field theory, e.g. is able to explain this level sequence for negative parameters K = Ds/Dt. Such K-VdUeS ako result from the interpretation of the tr[Cr(enh(OH)2]’ spectrum[30], which has been explained by the sign inversion of the Ds parameter due to large u- and r-bonding of hydroxo ligands. In the angular overlap model expression, Ds is equal to (2/7). (- emN - e-N + emOH + &OH) for tr[CrN,O,]- chromophores. For binuclear complexes with bridging hydroxo ligands the u- and r-bonding

= 3 t&N - DqoH). (14)

If the W- and v-bonding parameters for hydroxide are small enough, the Ds parameter will be pos- sitive and, since Dt > 0 due to the position of NH, and OH- ligands in the spectrochemical series, the K-parameter will be positive yielding positive values for V.

5. CONCLUSION The proposed level scheme in the ground and

excited state manifold is able to explain all band

1228 M. MORITA et al.

(-lu) ’

4A *E (+*u) ' *g g (+lv)'

(+lu)'

(-3)

4A 4A (+*)

*?I 29 C-1)

(+o)

14150

14728 14727

14708

14652

14624

179

a7

28

0

Fig. 4. Calculated level scheme for the ground and excited state (4A2iE,) manifolds obtained from the optimal parameter set given in the text. Prominent transitions assigned to absorption (A) and

luminescence (L) band peaks are displayed.

features in the absorption and emission spectrum as well as the intensity changes due to temperature variation. The validity of spin and parity selection rules and of limitations [equation (12)] imposed on the Jii-parameters[4] were used as constraints. In ordei to interpret electronic spectra of exchange coupled compounds, the inclusion of vibronic transitions should be emphasized to a greater extent than previously.

Acknowledgements-The authors thank Dr. J. SPRING- BORG, Copenhagen, for providing to us a sample of the dihydroxy complex. One of us (M. M.) thanks the Alex- ander van Humboldt Stiftung, Bonn-Bad Codesberg, and to Seikei University, Tokyo, for financial support. We are also grateful to Professor S. SHIONOYA, Tokyo, for continuous interest and encouragement.

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