Magnetic Circular Dichroism and the Assignment of Charge Transfer Transitions in Tetrahalide Complexes BY B. D. BIRD,* B. BRIAT,? P DAY * AND J. c. RIVOAL t *Inorganic Chemistry Laboratory South Parks Road Oxford "f.P.C.T. 10 Rue Vauquelin Paris-Ve France. Received 17th October 1969 Magnetic circular dichroism (MCD) spectra are reported for the charge transfer transitions in a large number of tetrahalide complexes of first transition series ions. Spectra of all the compounds have been obtained from solutions at room temperature and also for Co1:- and NiIi- from evaporated films and doped crystals at various temperatures down to liquid helium temperature. Assignments are discussed in terms of models based on Russell-Saunders first-order spin-orbit or j,j-coupling depending on the size of the halogen spin-orbit coupling constant.Precise unambiguous assignments of charge transfer spectra in metal complexes are difficult to obtain. At present there is no theoretical model available which will reliably predict the energies of such transitions so we must seek other observable properties of the spectra. Observables depending on the angular momenta of ground and excited states are likely to be most useful and MCD spectra have already provided valuable information about charge transfer transiti0ns.l. In this paper we report MCD measurements on charge transfer bands in tetra-halide complexes of first transition series ions both on solutions at room temperature and in some cases on films and doped crystals down to liquid helium temperatures.Our theoretical framework for analyzing the MCD data follows the basic approach laid down in our earlier paper on the intensities and spin-orbit splittings in tetra-halide charge transfer spectra i.e. we use vector-coupling methods in the formalism given by Griffith4 to derive expressions for the MCD in terms of the parameters conventionally called A B and C for the various configurations and states concerned. The latter are expressed in terms of reduced matrix elements of orbital and spin angular momentum. At first we derive state reduced matrix elements and then further reduce them to one-electron matrix elements. At that stage one may con-front theory and observation by adopting an LCAO molecular orbital scheme and expressing the one-electron reduced matrix elements in terms of atomic eigenvectors, obtainable from theoretical calculation.Our hope however is that even without making use of the precise numerical values of these matrix elements symmetry arguments alone may yield predictions about signs and magnitudes of the MCD parameters associated with the various possible configurations and states so that definite assignments of the observed bands can be established. EXPERIMENTAL The tetrahalide complexes were prepared as tetraethylammonium salts by standard methods.6 Samples were dissolved in CH2Cl containing a large excess of halide ion to prevent solvolysis. Evaporated films were prepared by the method used previo~sly.~ MCD of the CoIi- solution was essentially similar to that of the evaporated film and hence is not reported here.The MCD and absorption spectrometers and the cryostat used have 7 B . D . BTRD B . BRIAT P . D A Y A N D J. C . RIVOAL 71 been described elsewhere.* Low temperature absorption spectra of the crystals were measured both in Oxford and in Paris with good agreement. Crystals of (N(C2H5)&Zn14 doped with either CoIi- or NiIi- were grown by slow evaporation from CH3N02 solutions. To obtain reliable baselines for the low temperature MCD measurements spectra were first recorded in zero magnetic field. RESULTS MCD is expressed in terms of the magnetic dichroic optical density per unit magnetic field [AD] and absorption in terms of optical density D. At room temperature and even in some cases at liquid helium temperature (e.g. NiTi-) there are many absorption and MCD bands which overlap strongly and hence extraction of parameters from the data is difficult.For CuC1;-(300") and NiIi- (6") the components were extracted by a method described else-where? In all other cases only rough estimates of the magnitudes of the absorption and MCD components were made by considering the halfwidths and peak-trough separations in the spectra. Hence in comparing theory and observation we place little weight on the precise values either of the theoretical or experimentally derived parameters. Only the signs and relative magnitudes are considered significant. The results are presented in fig. 1-6. FIG. 1 . I I 5 0.5 n 1 (nm) CHzCll solution at room temperature. -MCD (full lines) and absorption spectra (dotted lines) of (a) FeCI and (b) FeBr; i 72 Of 0 -05 - I I - I CHARGE TRANSFER IN TETRAHALIDES -___I- c u a,*- solution I I- I FIG.2.-MCD (full lines) and absorption spectra (dotted lines) of (a) CuC1:- and (b) CuBri- in CH2C12 solution at room tem- 7 I 0 - FIG. 3.-MCD (full line) and absorption spectrum (dotted line) of CoBrz- in 9 CH2C12 at room temperature. 2 - I -2 perature. solution B \ \ \ 8 1 \250 I \ \ I 1 3.5 B. D . BIRD B . BRIAT P. DAY A N D J . C. RIVOAL 73 0.5 0 A (nm) [Fig. 4 continued overlea 74 CHARGE TRANSFER I N TETRAHALIDES A (nm) FIG. 4.-MCD (full lines) and absorption spectra (dotted lines) of CoIi- (a) as an evaporated film of the tetra-n-butylammonium salt at 300 K and 100 K and (b) doped into a crystal of [(C2H5)4N]2ZnT4 at 29 9.3 and 7.2 K.A (nrn) (4 FIG. 5.-MCD (full lines) and absorption spectra (dotted lines) of tetrahalogenonickelate(I1) ions in CH,Cl at room temperature (a) NiCIz- (b) NiBri- (c) NiTi-B . D . BIRD B. BRIAT P . D A Y AND J . C. RIVOAL 5 - 5 T = 102 K I I 75 1 0.5 0 I 3.5 0 FIG. 6.-MCD (full lines) and absorption spectra (dotted lines) of Nig- doped into a crystal of [(C2H5)4N]2Zn14 at 300 102 and 6.5 K 76 CHARGE TRANSFER I N TETRAHALIDES THEORY AND ASSIGNMENTS Employing a basis set consisting of the valence-shell s- and p-orbitals of the halogen and the d-shell of the metal the ground-state configurations and terms of the ions we are interested in are as follows : FeX, ( le)4(3 2)6(t 1)6(2e)2(4t2)3 ; 6Al COX - (1 e)4(3 t 2)6( t 6(2e)4(4t 2)3 ; 4A Nix - ( le)4(3t2)6(t 1)6(2e)4(4t2)4 ; Tl CuXz- (le)4(3t2)6(t1)6(2e)4(4t2)5 ; r2 In the CuXi- however there is a lowering of point symmetry from T d to D2d with the result that e+al + bl tl -+a2 + e and t2-+b2 + e.Paramagnetic resonance has shown that the ground state is the orbital singlet 2Bz(. . . e4bi). Our previous work on the intensity and spin-orbit splitting of the charge transfer states in the tetrahalides suggested the orderingof the n-orbitals of mainly ligand character was (le) <(3t2) < ( t l ) and so we are concerned with excited configurations such as ( le)4(3t2)6( t 1)5(2e)3(4t2)3(FeX,) and the terms arising from them. Spin-orbit coupling at the halogen is an important feature lo of the charge transfer spectra of halide complexes because the electrons are excited from orbitals of pre-dominantly ligand character.On the other hand the effect of electron repulsion on the terms of a charge transfer configuration has hardly received attention and little is known about the magnitude of the possible splittings. Thus it seems wise, in attempting to assign a wide range of halide charge transfer spectra to consider both of the extreme situations of negligible and dominant spin-orbit coupling energy, i.e. pure Russell-Saunders and purejj and also as far as possible for such complicated excited states intermediate coupling. We take each of these cases in turn using as illustrations those halides for which we expect each type of approximation to be most valid.(1) RUSSELL-SAUNDERS COUPLING In the Russell-Saunders limit electric-dipole-allowed transitions can occur from 6T2~6Al(FeX:) 4T1 t4A2(CoXi-) 3A2 3E1,3T1 3T2+-3Tl(NiX$-) and 2A1, 2Et2B2(C~Xi-) so that for all except the nickel (11) compounds a single allowed term exists for each charge transfer excited configuration. Furthermore in all cases except Nix:- the ground states are orbital singlets and hence in the Russell-Saunders approximation C-terms need not be considered. On the other hand all the excited states except 3A2 of NIX:- and 2A of CuXz- are orbitally degenerate, so that A-terms are expected in most cases. Referring to fig. 1-6 pronounced A-terms are indeed observed in CuX$- and FeX:. We therefore consider these in greater detail. For FeXz where the transitions are 6T2t6A1 the expression for AID is the same as that given by Schatz et aZ.l for the IT2+- ‘ A transitions in Mn04 because the spin wave functions are separable.Thus * AID = -<i/Js)(T2 II L II T2). {arx I gj I a’rx’) = ( l / ~ / A ( a ) ) ( - l ) a + a ’ + b ( a II gb II a’><ba’pct’ I act), (1) * Throughout this paper we define reduce matrix elements <a jl gb II a’> according to the equation : where A(a) is the degeneracy of the state a B . D . B I R D B . BRIAT P . DAY AND J . C . RIVOAL 77 Values of (Tz I] L 11 T2) are then compiled for each of the orbital excitations e e t , t 2 e t l etc. and are given in table 1. All the excited configurations resulting from such one-electron transitions contain three open-shells so a further generalization of the equation given by Griffith (e.g.10-15 ref. (4)) is required to evaluate them. Finally the one-electron reduced matrix elements in table 1 are expressed in terms of LCAO eigenvectors by expanding the molecular orbitals and eliminating two-centre terms. At the same time the operator I centred on the metal atoms must be transformed to each of the ligand coordinate systems. As before the orbital combina-tions defined by Gray and Ballhausen are also employed giving where c1 and c2 are the coefficients of the metal 4p and 3d and c3 and c4 are those of the ligandpn and p a . Substitution of the appropriate eigenvectors from a self-consistent field MO calculation l2 on FeBri yields the predicted values for AID shown in table 1. The MCD spectra in fig.1 contain a clea-rly-defined negative A-term under the lowest energy transition in agreement with our previous assignment of this band as e t t . As for MnO and TiC14 the sign and magnitude of AID for the e t t , transition does not depend on our choice of eigenvectors. The other clearly defined A-term lies under the fourth transition of FeBr; at 282 nm with the possibility of an analogous band at 243 nm in FeC14. On the grounds of their dipole strength these bands have previously been assigned to 4t2+-3t2 excitation. The observed positive sign of A at 282 nm in FeBri is compatible with this assignment (see table l) but the other MCD terms overlap so strongly that no other firm conclusions can be drawn. To interpret the A-terms observed in CuCIi- and CuBri- calculations must be performed within the D2d point group.A-terms can arise from E t 2 B 2 transitions resulting from excitations which in Td would be 4t2ctl or 4t2c3t,. We must consider for example a transition from the (x y ) components of tl(Td) transforming as e in D2d to xy the [-component of 4t2(Td) which transforms as b in Dad. Hence the calculation of AID for 4 t 2 t t (Td) can be performed without introducing eigen-vectors for 4t2 the degeneracy of the latter having been lifted. Then AID for 2 E e 2B2(4t2 f- t,) is equal to + $ and for ' E f - ,B2(4t2 +-3t2) is - ( J$)(icg - c$ -J2c3c,) where the eigenvectors relate to 3t2(Td). Taking eigenvectors for 3t2 from the calculation performed by R0s,13 AID for 4t2t3t2(Td) is predicted to be +0.60.Experimentally we find positive A-terms under the two major bands in the spectra (410 and 294 nm in CuCIi- and 515 and 350 nm in CuBri-). These bands had previously been assigned as the 2E(4t2ttl) and 2E(4t2t3t2) a con-clusion now reinforced by the MCD spectra. For CuCli- the MCD spectrum has been resolved into its components and we find experimental values of AID equal to +0.15 at 410 nm and +0.60 at 294 nm 78 CHARGE TRANSFER IN TETRAHALIDES The excellent agreement of the observed and calculated parameters suggests that a Russell-Saunders coupling scheme is a good approximation at least for these transitions. (2) FIRST-ORDER SPIN-ORBIT EFFECTS The most straightforward method of including the effect of spin-orbit coupling on charge transfer states is to assume that each Russell-Saunders state to which transitions are electric-dipole-allowed is split in first order only.That is we ignore the possibility of interaction between successive Russell-Saunders terms belonging to different excited configurations and also ignore states which would be dipole-for-bidden in the absence of spin-orbit coupling. Thus we could calculate A-terms for each degenerate spin-orbit component and also the B-terms resulting from mixing between them. There is also the possibility that C-terms could arise from the spin part of the magnetic moment operator in the ground state. in CoBri- where reasonable agreement between theory and observation was also found. A 4T1 state splits into E’ E” Ui and U; E and U& remaining degenerate to first-order.The energy difference between the El’ U& pair and U i is 5k and between U$ and E’ is 3k where for 4t2+tl The reduced matrix elements of the spin-orbit operator su defined previ~usly,~ can be evaluated like those of the magnetic moment operator using theoretically calculated eigenvectors. In this way it was found that the direction and magnitude of the splitting of 4T1 (4tzttl) and also the relative intensities of the spin-orbit components agreed with the assignment of the first three bands in the absorption spectrum. Thus we have calculated the MCD parameters for these transitions. An example to which the first-order theory has been applied in some detail k = (1/36)C(& II su TI 3tl> +(W2 II su II 34t2>l. (3) 3 1 1 3 FIG. 7.4ntensities and polarizations of the components of 4T1(E‘) -f4A2(U’) in a magnetic field.Under spin-orbit coupling the 4A2 ground state becomes U’ and we consider as an example the transition E‘(4T,)t U’(4A2). Both orbital and spin contributions to the diagonal matrix elements ( a 11 p z 11 a) where p z = -pB(L,+2S,) must now be included and in fact the spin part predominates. For example (E’a I 2Sz I E’a) = 5 while (E’cr I L I E‘a) has the magnitude & for a 4t2+-t transition. To determine the relative contributions from A and C to the experimental curve under these circumstances a particularly straightforward approach is that used b B . D . B I R D B . BRIA’T P . DAY A N D J . C . RIVOAL 79 Luty and Mort.14 The situation for E ’ t U’ is shown in fig. 7 which includes the relative intensities and polarizations of the four components.[AD] is found to be wherefis the shape of the individual lines. The spin-only g-values are 10/3 and 2 for E’ and U‘ respectively so that 2o df 5/’!Bf [AD] cc -pB-+-6 dv k T ’ Assuming that the half-width at room temperature is about 1000 cm-l (see fig. 3) the major contribution to [AD] can be shown to arise from the second term in eqn (4) i.e. the C-term. In table 3 we give the C / D terms for all the spin-orbit com-ponents of 4T1 and also the contribution C/kT to the MCD at 300 K. To compare these predictions with observation it is now necessary to estimate the relative magni-tudes of the C and B terms. In evaluating the B-terms resulting from mixing between the spin-orbit components it is again important to consider both the orbital and spin contributions to the off-diagonal matrix elements ( j ] pz I k).For example, When the eigenvectors from a self-consistent-field calculation l2 on CoBri- are substituted into the expression for (TI 11 L 11 Tl} it is found that the second spin, term in eqn (5) is approximately an order of magnitude greater than the orbital term. In table 2 we give both orbital and spin contributions to B for each pair of TABLE 2.-MCD B-TERMS FROM INTERACTION BETWEEN THE SPIN-ORBIT COMPONENTS OF 4T1 IN COX:-E‘ E“ LJi G E’ - 0 10 ip 20 _ _ _ _ - _ 2 7 4 6 9 0 - 2 ip 4 i 5 a - 5 32 ip 32 +- 1 3 5 4 6 15 - __ spin-orbit components of 4T1 in units of rn2/AE where m = (4A2 11 Y 11 4T1) and AE is the energy difference between the pairs of components.If the orbital contri-bution is neglected and the first-order energies of the components are used to evaluate the various AE we obtain expressions for B which involve only the k defined in eqn (3). E” and U& present a problem since they are accidentally degenerate in first order which would lead to two infinite B-terms of opposite sign i.e. a resultant of zero. We have assumed arbitrarily that they are split by k as a result of second-order effects and then have two predictions for the B-terms of those states depending on the order of energies chosen. k can be taken from the observed separation of the spin-orbit components in the absorption spectrum or estimated from the SCF calculation. Choosing the former alternative k - 500 cni-’ and the resulting value 80 CHARGE TRANSFER I N TETRAHALIDES of B are given in table 3.The dominant feature of the B-term contribution to the MCD is thus expected to be the two bands of opposite sign under the lowest energy absorption band. Two such bands are indeed found in the CoBri- spectrum, though with relative signs which do not agree with the predictions of table 3. The main conclusion to be drawn from table 3 is that at room temperature B and C contributions have comparable magnitudes and hence could only be separately estimated from temperature dependence experiments. However the sign of the U . band to which B and C contribute with the same sign is correctly predicted. TABLE 3.-cONTRIBUTIONS OF c AND B TO THE ROOM-TEMPERATURE MCD OF COX:-B U' lowest t 4T1 4A 2 D Cl D C/kT En lowest 1 1 6 +% +1.25 + 4.00 - 4.58 1 6 - 2.08 + 1.48 + 1.48 U& c U' - +* +2.50 - 4.48 + 4.08 E" t U' --1 - 1.67 - 1-00 - 0.99 E' c U' - - 5 u; t U' -D the dipole strength is in units of m2 where m = ( A 2 11 Y 11 T I ) ; C / D in pug ; C/kT and B in pg cm3 lo3.(3) INTERMEDIATE AND j j COUPLING For CoIi- on the other hand where we have been fortunate in obtaining spectra over a wide temperature range (fig. 4) it is certain that the major contribution to the observed MCD is derived from C-terms. However for iodides (cI = 5040cm-l) the simple first-order spin-orbit theory is unlikely to prove adequate. Its breakdown will be manifested in two ways transitions which would have been dipole- or spin-forbidden in the absence of spin-orbit coupling may appear strongly and interaction between excited states derived from configurations t 24t," and 3t24t," may become important since the separation of the baricentres of these two configurations is comparable to the spread of spin-orbit states arising from each.Our attempts to interpret the data of fig. 4 have therefore centred on diagonalization of the spin-orbit matrices for all the Russell-Saunders terms arising from each excited configuration. As a starting hypothesis we have assumed that interelectron repulsion is in-significant compared with spin-orbit coupling in splitting the charge transfer states, and have hence set all the Russell-Saunders terms of each configuration degenerate. If the complete set of Russell-Saunders terms were included in the spin-orbit diagon-alization this would be equivalent to a j j coupling scheme.The first excited con-figuration t24t," then gives rise to four bands corresponding to the excitations 4t,(y,,y,)tt1(y6,yk) with a major splitting of $cI and a minor one of 4Cmetal. Although two major band systems are indeed seen in the low-temperature absorption spectrum of CoIi- at 25 600 and 30 000 cm-l with separations corresponding to expectation (& = 3900cm-l) the spectrum in fig. 4(b) is clearly more complicated than this. One reason is almost certainly that the j,j-coupling approximation is not adequate for the ground state or for those parts of the excited configurations which are localized on the metal. For example the configuration y ' i y t is probably heavily mixed with y'&Q+ by interelectron repulsion within the d-shell.For the 4t part of the excited configuration it may therefore be more realistic to return to the Russell-Saunders limit. Then one may estimate that the three singlet terms lA1 lE lT2 of 4t; lie at least 6B+ 2C above the only triplet 3T1 a splitting of at least 12 000 cm-l. We have therefore constructed and diagonalized the spin-orbit matrices of all the Russell-Saunders quartets arising from t :4t; and of those doublets arising from 3T1(4t24). The individual matrix elements l 5 were finally expressed in terms of th B . D . B I R D €3. BRIAT P . DAY A N D J . C. RIVOAL 81 one-electron reduced matrix elements ( i t l 11 su 11 $t,) and (34t2 11 su 11 34t2). No MO calculations on CoIi- have been reported so to estimate these matrix elements, LCAO eigenvectors were taken from the same self-consistent-field calculation on CoBri-.The resulting wave-functions were used to calculate the dipole-strengths of all the transitions together with the signs and magnitudes of the C-terms in the MCD spectrum. Since the Russell-Saunders ground state is an orbital singlet we have made the same approximation as in the treatment of CoBri- in the previous section and considered only the spin contribution to pz. Fig. 8 shows the calculated absorption and MCD spectra. Both show some resemblance to fig. 4(b) the transitions are grouped into two regions corresponding to 4t + t l ( y 8 ) and 4t2 .+ t l ( Y 6 ) ~ the former with C-terms of mixed sign the latter with predominantly negative C-terms.The observed and calculated MCD both have negative contributions at lowest energy. Many more trial calculations will have to be performed to clarify the picture further but we believe that for the present a useful qualitative view of this complicated spectrum has begun to emerge. Absorption I I I I I -I-32 31 3 0 29 20 27 I MCD 1 26 I 25 FIG. 8.-Calculated absorption and MCD spectra of GI:-. (4) TETRA I o D ONI c K E LA T E ( I I) For NiIi- the situation is even more complicated for not only must one consider strong spin-orbit coupling in the excited states but also in the orbitally-degenerate ground-state. Furthermore there are several terms of each charge transfer con-figuration having spin-orbit Components to which transitions are allowed from one or other of the spin-orbit components of the ground term.To first order the 3T1 ground term of a tetrahedral d8 complex is split by spin-orbit coupling into A - 3c) Tl( - $5) and E T2( + Pc) where 5 = 2/9(+4t2 11 su 11 t4t2>. The temperature dependences of the magnetic susceptibilities of many tetrahedral nickel(II) complexes including salts of Nil$- have been fitted l 6 to values of 5 i 82 CHAKGE TRANSFER I N TETRAHALIDES the range 130-200 cm-l. On this basis we expect the spin-orbit ground state to be Al with Tl roughly 100-150 cm-l above. Now whilst transitions are allowed from Tl to A Z E TI and T2 states examples of which arise from most terms of each excited configuration from A l they are only allowed to T2. Therefore on lowering the temperature one would expect both the absorption and the MCD spectra to be drastically simplified.Fig. 6 shows that this does not occur. Some small variations in the relative intensitites of the absorption bands are seen between 77 and 6 K but these are much less pronounced than one would expect if the Tl state had been completely depopulated. Furthermore the variation of the MCD spectrum with temperature shows clearly that the major contribution comes from C-terms even at 6 K. Two alternative explanations for this striking observation are first that the multiplet splitting of 3T1 has almost completely collapsed the total spread being no more than about 10 cm-I or secondly that the sign of 5 and hence the multiplet, are inverted. Rationalization of the former might lie in the Ham effect (quenching of orbital angular momentum by a dynamic Jahn-Teller effect 17) or of the latter in the opposing contributions of cNi and the much larger [I to [.Some support for the former hypothesis comes from a calculation of the signs and magnitudes of the C-terms associated with transitions from T1(3T1) (table 4). TABLE 4.-MCD AND ABSORPTION PARAMETERS FOR TRANSITIONS FROM 3T1(T1) OF t f 4 t ; TO ALL STATES OF t:4t; in Nix;-C D CID 1 z 1 -3 T2 1/72 1/36 E - 1/24 1/12 -1 - 1/48 1/24 T1 T2 1/48 1/24 2 3T2 A2 1 /l8 1/18 1 E - 1/72 1/36 ; - 1/48 1/24 _ - Tl T2 1/48 1 124 -1 3Az T2 1 19 2/9 3E TI - 1/24 1/12 Tl -1 1 - -_ -1 C is in units of pm2 where p = -(i/22/6)(4t2 11 1.1 11 4t2) and rn = ( t l 11 r I( 4t2) ; L) is m2.Five out of ten of the spin-orbit states resulting from ts4t25 should have negative C-terms which if 41 is assumed to consist mainly of 3d(Ni) should have magnitudes in the range 0.25-0.5 pB (C/O). A curve analysis of the 6.5 K MCD spectrum using the method described elsewhere in this Symposium * confirms these predictions (fig. 9). Our hope is that accurate measurements of the MCD spectrum at various temperatures between 4 and 77 K will serve to resolve the question. CONCLUSIONS In few if any cases have we reached definitive conclusions about the assignment of these charge transfer spectra. Our account has much the nature of a progress report. On the experimental side temperature dependence experiments are manda-tory for separating B and C-term contributions and more theoretical work is needed on the coupling schemes most appropriate to composite states containing both strong and weak spin-orbit coupling.Nevertheless MCD has proved a subtle and sensitive tool for the assignment of these extremely complicated spectra B . D. B l R D B . BRIAT P . D A Y AND J . C . RIVOAL I n 83 A (nm) FIG. 9. Analysis of the MCD and absorption spectra of Ni12- at 6.5 K (see fig. 7). We are grateful to Dr I. H. Hillier and Dr R. M. Canadine for communicating the results of their MO calculations on FeBrz and CoBri- in advance of publication. The crystals of ((C2H5)4N)2Zn14 doped with CoI$- and NiI$- were grown by Mr G. A. 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