Magnetic Circular Dichroisrn of the Tetrachlorocobaltate Ion BY R. G. DENNING AND J. A. SPENCER W. A. Noyes Laboratory University of Illinois Urbana Illinois U.S.A. Received 6th October 1969 The absorption and magnetic circular dichroism spectra of the tetrachloro-cobaltate ion have been measured as a function of temperature in a single crystal. The major contribution to the Faraday effect of the 4Az -t4T1(P) transition is temperature dependent. The source of this effect and the assignment of the spectra are discussed. A theoretical treatment of the Faraday effect of CoCl;4- by Stephens stimulated the measurement of the magnetic circular dichroism (MCD) of Co Xi-(X = Cl-, Br- I-). Stephens’s work primarily a demonstration of the potential of the tech-nique assumed spin-orbit coupling to be zero and predicted the major MCD for the transition to 4T1(P) to be a B term arising from the 4A2 4T2 second-order Zeeman interaction and an A term associated with orbital angular momentum in the excited state.5 The experimental work showed this approach to be inadequate.The fine structure precluded a single A term analysis and the integrated B term was opposite in sign to that predicted. We show here that the inclusion of spin-orbit coupling accounts for the main features of the MCD spectrum which has now been studied as a function of tempera-ture. EXPERIMENTAL Single crystals of tetra-ethylammonium tetra-chloro zincate containing ca. 0.1 of cobalt(I1) by weight were grown by evaporation from nitromethane solution. These crystals are isomorphous with the analogous nickel(I1) salt whose crystal structure belongs to the tetragonal space group P4/nrnc6 The CoCIi- ion is detectably tetragonally distorted from tetrahedral.The optic axis which is perpendicular to a large rectangular face is coincident with the S4 axis of the tetrahedron. For spectroscopy the crystals were mounted on this face. The crystal used for absorption spectroscopy contained 0.051 % Co(I1) by eight,^ was 1.89 mm thick and had a density of 1.26 g CM-~. We can therefore obtain molar values for extinction coefficients dipole strengths and MCD parameters. The crystal was mounted on a copper disc in a variable temperature cell closed by quartz windows. Measurements were made in the range 224-423 K. Cooling the crystal below 220 K invariably shattered it.A phase transition ascribed to ordering of the ethyl groups has been observed at ca. 218 K by Gerloch * in the isomorphous nickel salt where it results in a large decrease in the anisotropy of the magnetic susceptibility. Spectra were obtained with the apparatus previously de~cribed.~ CD was calibrated with naturally optically active standards and the magnetic field with a Rawson rotating coil gaussmeter. Magnetic fields were about 42,000 G. A series of measurements was made at nine different temperatures without changing the magnet current. RESULTS The absorption and MCD spectra at some representative temperatures are shown Four principal bands are apparent and are numbered. 84 in arbitrary units in fig. 1 R . G . DENNING AND J . A.SPENCER 85 Both types of spectra suggest small extra components. Extracting meaningful parameters for each band is the most uncertain part of our procedure. The absorp-tion spectrum was subjected to an iterative curve-fitting routine involving gaussian components based on method (V) of Jones.9 Band energies half-widths and in-tensities were obtained and the dipole strength of the band envelope was also obtained directly from the experimental points by incremental integration. With these band energies as fixed parameters and with the Faraday parameters and half-widths as variables the same procedure was applied to the MCD spectra. This procedure was repeated at each temperature. The most reliable parameters obtained are those for the total band envelope. As a numerical check the values at room temperature of (B+ C/kT) and D the dipole strength can be compared against the solution values of ref.(4). We find D = 0.692 (B+C/kT) = 2.37 x compared with solution values of D = 0.687 (B+ C/kT) = 0.615 x The large difference in the Faraday parameters is due to a factor of 3 in the definition used here,5 compared to the defini-tions used in ref. (4).3 700 6 0 0 wavelength (nm) FIG. 1 .-Experimental absorption and MCD spectra at 423 K . . . . 399 K - . -7 290°K - - - and 229 K -. In analyzing bands (1)-(4) progressively more scattered results are obtained. In particular uncertainties arise in band (4) due to a small band at 605 nm which increases in intensity at high temperatures. The intrinsic variation of the dipole strength with temperature complicates the identification of C terms.For simplicity we assume that the Franck-Condon factors have parallel effects on the amplitude of both the dipole strength and the MCD parameters. We consequently take the experimental values of (B+ C/kT)/D and AI 86 TETRAHEDRAL COBALT as suitable quantities for interpretation. For bands (1) and (2) we find AID to be small and reasonably constant with temperature as expected; but its value in bands (3) and (4) is greatly dependent on the shortcomings of the curve-fitting procedure. In fig. 2 we plot (B+ C/RT)/D for the total band envelope and for bands (I) (2) and (3). The intercept at 1/T = 0 gives B / D and the slope C/D. The results for band (4) were too erratic to plot but inspection clearly shows a negative C term and a positive A term.The values obtained or estimated are collected in table 1. Fig. 2 demonstrates that most of the MCD at room temperature is C term in origin. 1 1 I I FIG. 2.-Temperature dependence of the MCD parameters of (3 band 1 ; @ band 2; & band 3 ; @ total band envelope. TABLE 1 .-OBSERVED MCD PARAMETERS band CID(8) BlmBlm-1) AID(B) 1 + 1.45 +o.i x 10-3 +0.1 2 + 0.98 + 0.0 x 10-3 +0.1 3 - 2.50 +9.5 x 10-3 + 0.9 4 - ve ? + 4.0 total + 0.51 + 0.4 x 10-3 -DISCUSSION The cobalt (11) ion in the host lattice is in a slightly distorted tetrahedral environ-ment. The S axis bisects a Cl-Co-C1 angle of 106.8°.6 The electronic mani-festations of the distortion are neglected here on the following grounds. The same ion in the tetragonal crystal Cs,CoCl has the S axis bisecting an angle of 106.1°,10 and the zero-field splitting is 4.31 cm-l.ll We therefore assume a similar or smaller splitting in the present lattice.At the temperatures above 210 K used here the C term summations will not be affected. Further a complete crystal-field calculation with the exact geometry for the ion predicts e.g. that 5/2 U'(4T1(P)) will be split by less than 20 cm-1 by the low symmetry field.12 With band widths of about 500 cm-l this splitting need not concern us R . G. DENNING AND J . A . SPENCER 87 for 4T1(P) for the tetrahedral cobalt ion in zinc oxide. We give this in fig. 3. The El’ *Ul degeneracy is resolved by second-order spin-orbit interactions. Weakliem calculated relative intensities on a d - p mixing or a-bonding model finding that the components of ’G, which are close in energy to 4T,(P) are nevertheless very weak.We therefore assume with him that the main features of the spectrum observed near 15,000 cm-l are transitions to 4T,(P). In this we differ from Ferguson l4 who believed that com-plex excited state vibronic effects prohibited any meaningful assignment. We rely on the energy level scheme calculated by Weaklieni E’ ‘ / / / ‘ fEa I FIG. 3.Excited state energy level diagram. We now calculate the predicted Faraday parameters for the spin-orbit components of 4T1(P). We present results for two levels of approximation calculated (i) under first-order spin-orbit coupling giving quantities subscripted zero ; (ii) under second-order spin-orbit coupling giving quantities subscripted I and 11.We work in the strong-field basis using unspecified symmetry adapted orbitals. We later make the assumption of a d orbital basis set in order to give results for the weak-field limit and an appropriate intermediate field. We use the double group TJFd and expand the strong-field states in space-spin product functions using the coupling coefficients of Griffith.15 This procedure uses the isomorphism of the Td and 0 groups. After spin integration the electric dipole and orbital magnetic moment matrix elements are expressed in terms of seven electron reduced matrix elements using the same coupling coefficient^.'^ The spin magnetic moments can be obtained after spatial integration. With these matrices which are independent of the explicit form of wavefunction the Faraday parameters are readily obtained.In table 2, spin-dependent quantities are given in units of p the Bohr magneton while orbitally dependent quantities are given in units of seven-electron reduced matrix elements. These units can be expressed in terms of one-electron reduced matrix elements by explicit evaluation of a typical element using the seven-electron strong-field wave-functions of Griffith.16 These relations are summarized for all the strong-field quartet states in table 3. We now discuss Co/Do. The presence of these terms is an example of C terms arising from spin-orbit coupling in the excited state but not in the ground state. The use of coupled excited state wave-functions forces spin selection on the electric dipole transition moments such that the C term for individual components need not vanish.However Co vanishes when summed over all components consistent with the limit of zero spin-orbit coupling. We give Co/Do in table 2 for comparison with experiment. The signs and magnitudes are in general agreement with the assignment ; band (I) 88 TETRAHEDRAL COBALT 5 U’ ; band (2) E’’ ; band (3) 3 U’ ; band (4) E’. This is the order given by a crystal field calculation (fig. 3). Values of Ao/Do are given separately for the spin and orbital contributions to the angular momentum. The former should be inde-pendent of bonding factors while the latter requires more careful consideration. Unlike the Co terms the A . spin terms need not sum to zero since inter-component B terms also dependent on spin angular momentum originate from A terms in the DO CO COlDO TABLE 2.-cALCULATED CONTRIBUTIONS TO MCD a 116 113 116 113 1 - 512 -113 114 1 / 2 0 - 512 - 1 312 312 0 E’ 312 U’ E” 5/2U’ total C TABLE 3 .-ANGULAR MOMENTUM AND ELECTRIC DIPOLE MOMENT MATRICES 4A2 4 T ~ T I (tfe3) 4Tl(tZe2) 4Az 0 ‘d2 - lb -2/2.mb 0 [ = 0 limit.The intrastate B terms are given in table 2 as &/Do with spin and orbital contributions again separated. The energy denominators are the separations given in fig. 3. The B term arising from 4A2 4T2 interaction considered by step hen^,^ is given for each spin-orbit component and for the band as a whole as Bo/Do in table 2. To include the orbital contributions to B&/Do and Ao/Do we require the quantity pl = (p/ili)(4T1 11 I l l 4T1).This depends on the explicit composition of the 4T1(P) excited state. We write For simplicity we now adopt a d orbital approximation and solve the d7 secular determinant which gives c1 = 2/d5 c2 = - 1/J5. With A/B = 5.0 (a realistic I 47’1(p)> = c1 I 4~1(t:e3))+~2 I 4T1(tze2)) R . G. DENNING AND J . A . SPENCER 89 value) c1 = 0.811 c2 = -0.585. Using the values in table 3 we obtain for the general case, In the weak field limit, Following Stephens we now neglect n-bonding and give values for the one-electron matrix elements in terms of the a-bonding molecular orbital coefficient of Ballhausen and Liehr.17 With ( e 11 I [I t 2 ) = - ,/6ihN,a ( t2 11 I 11 t 2 ) = 4 2 ihNza2 and A/B = 5.0 we obtain p1 = - 1.34N,a p. We now take Naa as 0.80 to imply a dominance of metal d orbitals in the molecular orbitals.We give the values for A o / D calculated with this choice in table 4. TABLE 4.-cALCULATED MCD PARAMETERS E' 3/2U' E" 5/2U' total Ao(spin)lDo 1.66 1.73 - 1.00 - 0.20 Ao(orbital)/Do 0.13 0.10 0.13 0.33 1.79 1.83 - 0.87 0.13 - AOlDO B$spin) /Do 9 . 2 ~ 10-3 - 1.1 x 10-3 - 1 0 . 6 ~ 10-3 1 . 8 ~ 10-3 0 B6(orbital)/Do 3.4 x - 0 . 9 ~ 10-3 osx 10-3 - 1 . 2 ~ 10-3 0 B(p0 1 2 . 6 ~ 10-3 - 2 . 0 ~ 10-3 - 10.1 x 10-3 o . 6 ~ 10-3 0 <co +CI)PO - 2.94 - 1.18 1.76 1.76 0 Cr1IDo 0.25 0.20 0.46 0.46 0.51 C/DO - 2.70 - 0.98 2.22 2.22 0.51 BOD0 o . 4 ~ 10-3 o . 4 ~ 10-3 o . 4 ~ 10-3 o . 4 ~ 10-3 o . 4 ~ 10-3 It is clear that spin contributions dominate and that a cancellation of effects virtually removes the A term in the transition to 3U'.The predicted A terms agree broadly with the results of table 1. We stress the unreliability of the experimental values which are sensitive to the curve-fitting procedure. A visual assessment of the A terms of the three COX:- ions of ref. (4) confirms the dominant positive A terms of the E' and 4U' components especially in the MCD spectrum of CoIz-. These results then strongly support the assignment made on the basis of the C terms. 360cm-l taken from the experimental spectrum the intra-state B terms can be calculated and are given as &/Do in table 4. These results do not agree well with experiment. However since the B term originating from the 4A2 4T2 interaction makes a uniform contribution to Bo/Do for each component it may be significant that the transition to E has the most negative B term both experimentally and theoretically.It is possible that doublet states are contributing to the B terms or that experimental uncertainties are responsible. Intra-state B terms must vanish when summed over the whole band and it follows that BID obtained from the separate integration of (B+C/kT) and D over the band envelope is a measure of inter-state B terms. We examine shortly the possibility that the experimental non-zero value of BID arises from 4A2 4T2 interaction. Using the same value of p1 and with El = 590 cm-l E2 = 700 cm-l E3 90 TETRAHEDRAL COBALT The total band values of C / D and BID are independent of curve-fitting procedures, being obtained by direct integration.With these relatively reliable results we now ask why C / D is experimentally non-zero. We consider therefore the effects of second order spin-orbit coupling. 4T1 (F) and 4T1 (P) are separated by 9000 cm-l, and we assume that doublet inixing will not appreciably affect the transition moments to 4T1(P). We therefore neglect these interactions. 4T2 is the only quartet mixed with 4A2 and we consider this the dominant second-order effect. We expand the ground state as I a> = I ao)+Y I bo) substitute in the expression for C and collect term to first order in y. We find two new contributions to the C term, 2 The C contribution is due to the modification of the ground state magnetic moment, the electric dipole selection rules remaining unchanged.This modification is realized in the experimental g-value. Taking g = 2.37 the mean experimental value,ll we obtain the values of (Co + C,)/Do in table 4. The band summation for this quantity still vanishes but for C, it does not vanish. CII/Do is given in table 2 in units of ym2/ml. Both Bo/Do and CII/Do contain the quantity m2/m1. Their ratio is given by Bo/CI1 = -p21J5 E,Y, where Eo is the 4T2 4A2 energy difference. y is best obtained from the experimental g-value since In the same model as before y = O.179/Naa. Also p 2 = -2 J 3 ~ a a whence g = 2(1 -y(2J2/3 J5)(e I[ I I[ t2)) = 2.37. Bo/CII = 8.65N2a2/Eo. We now assume that we have found the source of both B and C terms. Taking the experimental values from table 1 and Eo = 3130 cm-l from Cotton l1 we obtain N&:a = 0.54.Unfortunately the extrapolation to obtain B gives wide error limits and it is probably fortuitous that this value agrees with that given by Ballhausen and Liehr. However the reasonable value obtained does support the suggestion that Bo and C, are related. With more accurate experimental data over a wider range of temperature an accurate value of Naa could in principle be measured. We now consider the quantity m2/m1. With table 3 it is easily shown that m2h1 = (- 1/J6)[(3/2)((t ll m I1 t2)/<e II m I1 t2>)+cz/c1l. In the weak field limit this gives a value of Bo identical to that of step hen^.^ We work in the intermediate field (A/B = 5.00). From table 2 CII/Do = J10ym2/m and with the same value of y used earlier we obtain a value of the ratio, < t 2 [I m 11 t2)/(e 11 7n I[ 12) = 4 = -1.47Na~+O.48.With Naa = 0.8 q = -0.70. In table 4 we give CII/Do for each component using this value of m2/ml R. G . DENNING AND J . A . SPENCER 91 This value of q is unexpected. A d - p mixing model predicts q = 2 and a a-bonding molecular orbital model predicts a value 0 <q< 2. We do not speculate here on the significance of this figure. It is easy to imagine that B term interactions have been neglected in our treatment. Thus interactions with charge-transfer type excited states could contribute large moments although with small mixing parameters. The non-vanishing positive C term is however more difficult to explain since it involves only the ground and excited state wave-functions. If q is positive the experimental results imply large second-order effects in the excited state which provide C terms of opposite sign to those arising from CII.The role of the *G components in this context must await more detailed variable temperature work, over a wider range in crystals which do not shatter at low temperatures. In summary we present results which demonstrate that the major MCD at room temperature is temperature dependent and whose broad features agree well with A and C terms calculated with a conventional energy level assignment. We believe that this implies more simplicity in the structure of the band than Ferguson l4 thought possible. We demonstrate how other experimental results may be used to obtain molecular orbital parameters and one-electron electric dipole transition moments, although more work is required before these can be fully understood.We are indebted for support to the Materials Research Laboratory University of Illinois and to the National Science Foundation. present address Inorganic Chemistry Laboratory South Parks Road Oxford England. present address University of Virginia Charlottesville Virginia U.S.A. P. J. Stephens J. Chem. Phys. 1965 43,4444. R. G. Denning J. Chem. Phys. 1966,45 1307. For a definition of the Faraday parameters used here see P. N. Schatz A. J. McCaffery, W. Suetaka G. N. Henning A. B. Ritchie and P. J. Stephens J. Chem. Phys. 1966,45,722. G. D. Stucky J. B. Folkers and T. J. Kistenmacher Acta. Cryst. 1967 23 1064. Atomic Absorption Analysis (Materials Research Laboratory University of Illinois). * M. Gerloch and R. C. Slade J. Chem. SOC. A 1969 1022. J. Pitha and R. N. Jones Can. J. Chem. 1966,44,3031. H. G. Belgers P. F. Bongers R. P. Van Stapele and H. Zijlstra Phys. Letters 1964 12 81. l o B. N. Figgis M. Gerlock and R. Mason Acfa. Cryst. 1964 17 506. I2 J. A. Spencer unpublished results. l3 H. A. Weakliem J. Chem. Phys. 1962,36,2117. l4 J. Ferguson J. Chem. Phys. 1963,39 116. l 5 J. S. Griffith The Theory of Transition Metal Ions (Cambridge University Press 1961) Table A.20. ibid. Table A.24. l 7 C. J. Ballhausen and A. D. Liehr J. MoZ. Spectr. 1958 2 342 ; 1960,4 190. l o F. A. Cotton and D. M. L. Goodgame J. Amer. Chem. SOC. 1961 83,4690