71
J. Phys. Chem. 1994,98, 71-76
Magnetic Circular Dichroism and Absorption Spectra of Hexacyanoferrate(111) in a Poly(vinyl alcohol) Film Andrew H. P. Upton and Bryce E. Williamson' Department of Chemistry, University of Canterbury, Christchurch 1 , New Zealand Received: September 8, 1993' Magnetic circular dichroism (MCD) and absorption spectra have been measured, at temperatures between 1.45 and 180 K, for the lowest energy ligand-to-metal charge-transfer transition of hexacyanoferrate(II1) in poly(vinyl alcohol) films. The temperature dependence permits determination of the orbital reduction factor ( K = 0.76f 0.03) and the relative importance of 2-and &term contributions to the MCD. An empirical relation is obtained to allow such samples to be used for temperature calibrations up to -85 K.
I. Introduction The hexacyanoferrate(II1) ion (Fe(CN)63-, also known as ferricyanide) has been a subject of a great deal of spectroscopic scrutiny. In the visible and near-ultraviolet regions it exhibits threestrong transitions (Figure l), which have long been ascribed to ligand-to-metal charge-transfer (LMCT) transitions. However, until the mid 19609, the precise assignments of these transitions were a subject of some controversy.'-3 At about that time, the Faraday effect was beginning to be applied to problems of molecular spectroscopy. In a couple of exploratory papers the magnetic optical rotatory dispersion (MORD)4and magneticcirculardichroism (MCD)S of Fe(CN)6> were measured, but no attempt was made to interpret the data. Indeed, Foss and McCarvilleSsuggested that there seemed to be no simple relationship between the spectra and the electronic state symmetry. Soon after, Buckingham and Stephens@ published their theoretical formulation of the Faraday effect, in which contributions to the spectra are separated into 34, 93, and @ terms (section IV). In one of its earliest applications,Stephens9showed that if the MORD of Fe(CN)6> is assumed to be dominated by 6 terms then the transitions LMCTl and LMCT2 must respectively involve excitations of the type tl,(r+u) --.* tze(d) and tzu(r) tZg(d) (Figure 1). A year later, Schatz et al.lOJ1found semiquantitative agreement between Stephens' assignments and the MCD, as well as showing that LMCT3 involves tl,(u+r) --.* t2Ad). In 1970, Kobayashiet a1.I2pointed out that ground-state spinorbit (SO)coupling can lead to potentially significant 93 terms. For Fe(CN)6> in a poly(viny1alcohol) (PVA) film they reported the temperature dependence of the MCD between 300 and 77 K to be weak and hence concluded that the spectrum is dominated by 93 terms rather than the @ terms that had previously been assumed.9-1' This result was later refuted by Gale and McCaffery,l3,14 who found strong temperature dependence, between 290 and 12 K, for Fe(CN)6> doped in KCl crystals and in poly(methy1 methacrylate) (PMM) films. It now appears that the results of Kobayashi et a1.'2 were subject to thermometry errors resulting from the poor thermal conductivity of PVA. Gale and McCaffery were also the first to consider the effect of covalent ligand-metal interactions on the MCD spectrum of Fe(CN)6>.14 For LMCTl, they found the MCD to be quantitatively consistent with a reduction of the ground-state orbital angular momentum by a factor K = 0.87, apparently in agreement with the orbital g value obtained from electron-spin resonance (ESR) spectra of K3Fe(CN)6.1S.16However, their data were restricted to only two temperatures (12 and 290 K),and although they considered SO coupling in their assignments, their MCD
-.
Abstract published in
Aduance ACS Abstracts,
December 1, 1993.
0022-3654/94/2098-007 1$04.50/0
AA
A
0
40000
CRcm.') Figure 1. Absorption (A, lower) and MCD (AA, upper) spectra of the ligand-to-metalcharge-transfer (LMCT) transitions of K#e(CN)6 in aqueous solution (adapted from refs 10, 11, and 18). The principal excitations contributing to each band are illustrated on the right.
analysis applies to the case of zero SO coupling. Since then, Stephens" and Piepho and Schatz18have extended the theory to include SO coupling, and the latter authors have also described a method by which K can be determined from the temperature dependence of the MCD.18 For the past 2 decades there has been no'significant experimental work concerning the optical electronic spectroscopy of Fe(CN)6'-. The assignments of Sephensg and Schatz et al.'OJ1 and the domination of the magnetoopticalspectra by temperaturedependent @ terms, are generally accepted. It is the latter of these points that is responsible for one of the current spectroscopic used of Fe(CN)&. Precise measurement of the temperature dependenceof MCD is the source of a wealth of information, but thermometry errors, of the type that appear to have influenced the interpretation of Kobayashi et a1.,'2 are a major problem when the sample is mounted in a vacuum and cooled by thermal conduction.19 These conditionsare prevalent in matrix-isolation studies, where the preparation of the sample requires a vacuum. In such cases, the temperatureat thesample position issometimes calibrated by measuring the MCD of a F c ( C N ) ~ ~ / P Vfilm A mounted on the back side of the deposition window and assuming dominant 6 terms with a reciprocal temperature dependence. Despite this use, there has been no definitive demonstration that @ terms are dominant over a wide temperature range, nor has a detailed, accurate calibration of the temperature dependence been reported. Q 1994 American Chemical Society
72 The Journal of Physical Chemistry, Vol. 98, No. 1, 1994
In this work, we report the MCD of the LMCTl transition of Fe(CN)&/PVA over the temperature range 180-1.45 K. The sample is immersed in cryogenic fluid, ensuring accurate and precise determination of temperature. A modification of the method described by Piepho and Schatzl*permits determination of the effective value of the orbital reduction factor, K , which is then used to determine the relative contributions of 23 and e terms to the MCD zeroth moment. Finally we comment on the suitability of Fe(CN)&/PVA films for use in thermometric calibrations. 11. Experimental Section
Solutions of K#e(CN)6 (typically 0.25 g of BDH, Analar grade crystals in 20 mL of distilled water) and PVA (Koch-Light Laboratories; -2 g in 20 mL, heated to -80 "C)were prepared separately and then mixed in various proportions on glass slides. After drying in the dark for up to several days, the clearest and most homogeneous films were removed from the slides by using a razor blade, and their optical densities and depolarizing properties were checked a t room temperature. Samples showing excessive absorption or causing significant depolarization were discarded. The results described in this work were obtained from six independently prepared films whose optical densities (A,,, at A, = 420 nm) varied between 0.3 and 1.0. Films were mounted, free standing, in the 1-cm bore of a copper sample holder. The sample holder, fixed to the end of one of three sample rods, was inserted into the sample chamber of a top-loading, split-coil, superconducting magnetocryogenic system (Oxford Instruments, SM4). The sample was cooled by flooding the sample chamber with liquid ( T < 4.2 K) or cold gaseous ( T > 4.2 K) He. We emphasize that the sample was in direct contact with the cryogenic fluid, and to minimize thermal gradients we did not use resistive heating elements to control the temperature at any point during our measurements. Temperatures below 4.2 K were achieved by pumping on the sample chamber with a rotary vanepump(We1ch 1397;450Lmin-l) whilecontrolling thevapor pressure over the liquid with a manostat (Oxford Instruments MNT) . Above 4.2 K, the temperature was measured by monitoring the resistance of a 1/4-Wcarbon resistor and/or Rh/Fe resistor mounted close to the sample. Between 4.2 and 2.0 K, the carbonresistor measurements were augmented by readings from a calibrated carbon-glass resistor (Lake Shore Cryogenics). Finally, below 2.5 K, temperatures were also determined by monitoring the He-vapor pressure using a 100-Torr capacitance manometer (MKS Instruments, 122-AA Baratron). The agreement between the temperatures determined using different sensors in overlapping regions was excellent, and we believe the precision to be better than 1% throughout the entire range (1.45-1 80 K) over which spectra were obtained. MCD and double-beam absorption spectra were measured simultaneously using a spectrometer based on the principles outlined by Collingwood et a1.20 and described in detail by Misener.2l Light from a 500-W Xe-arc lamp is dispersed by a doubleprism Czerny-Turner monochromator (Jasco ORD/UV5 ) , collimated, and then polarized by a Rochon prism. The ordinary ray from the prism passes through a photoelastic modulator (Hinds International, PEM-80) with the result that the emerging light is modulated between left and right circular polarization a t a frequency of -50 kHz. A -200-Hz chopper successively blocks the light, deflects it through a reference path or allows it to pass through the sample to a photomultiplier tube (PMT; Hamamatsu R-376). After preamplification, the PMT signal is processed by electronic circuitry to yield signals proportional to the MCD and absorption. The data are accumulated on an IBM-compatible XT-PC computer, which also controls the wavelength scan and the driving voltage of the PEM80.
Upton and Williamson
1
*"-I,I, 7, I 0.2
I
/I
~------I__- - _. _, _ - - -
...-.....--..-
0.0
22000
24000
28000
28000
&'(cm.')
Figure 2. Temperature dependence of the MCD per tesla (AAIE,upper spectra) of LMCTl. The absorption (A, lower spectrum) is almost independent of temperature over the range (1.45-35 K) illustrated. The dashed curve is the estimated contribution of LMCT2 to the absorbance, while the vertical dotted lines show the limits between which the moment analysis was applied. A shoulder that must be included in the analysis (section IV) is indicated by an arrow. AAmax'Amax
(TI 0.3
0.2
0.1
0.0
Figure 3. l/Tdependence of the MCD-to-absorbance ratio (per tesla) of LMCTl at A, = 420 nm (23 800 cm-I). The full line is the linear least-squares fit given by eq 1, and the dashed lines represent * 5 % error limits.
Instrument calibration was performed for each sample by measuring the absorbance and natural CD of standard solutions of camphorsulfonic acid-10-&2 and showed no significant variation over the period of several months that measurements were made. Depolarization of circularly polarized light by the sample was checked by periodically measuring the CD of A-cobalt(II1) (tris1,2-diaminoethane) placed after the sample, and was found to be negligible. Spectral resolution and magnetic inductance were 1.2 nm (-60 cm-1 a t Amx) and 0.25 T, respectively. 111. Results
Spectra from a sample with A,, = 0.34 are shown in Figure 2 over the temperature range 1.45-35 K. The absorption remains relatively temperature independent over this range, but the MCD is strongly temperature dependent. This is clearly illustrated in Figure 3, where the ratio of the maximum MCD to A, per tesla ((AAmx/Amx)/B)is plotted against 1/T. The plot is nearly linear, a least-squares fit (restricted to pass through the origin) of all 202 data points yielding
(M,,/A,,)/B
= (0.555 f 0.004)/T
(1)
The error limits represent two standard deviations of the slope. Data obtained from individual samples give slightly different results with larger uncertainties, but all agree with eq 1 to within i5% (dashed lines Figure 3). The evidence for dominant 6 terms in eq 1 and Figures 2 and 3 seems compelling. However, closer inspection of Figure 3 shows
The Journal of Physical Chemistry, Vol. 98, NO.1 , I994 73
MCD and Absorption of Fe(CN)63-/PVA’
1
Tlu
T2”
determined principallyby the cyano ligandsand are much smaller than for the ground-state manifold. We avoid having to explicitly consider such excited-state effects by ensuring that theoretical expressions are summed over all excited-state components and that numerical integrations are carried over the full envelope of the transition (vide infra). In the experimental configuration used in MCD, the exciting radiation propagates along the magnetic-field direction and the absorbance ( A ) and MCD (AA)are defined by18
LMCT states
*TI“
A = ( A L+ 4 ) / 2
G#O
8=0
B#O
Figure 4. Spin-orbit and Zeeman energies (not to scale) for the groundstate (q,) manifold of Fe(CN)s3-. Parameters are defined in the text. Left (lcp) and right circularly polarized (rcp) transitions from the lowest Zeeman level to the ligand-to-metal charge-transfer (LMCT) states are illustrated, respectively, by full and dotted vertical lines.
significant, systematicdeviationsfrom exact 1/ Tdependence for the data at higher temperatures, which suggest that B terms may be important above 10 K (section IV).
-
(6)
AA = AL-AR (7) where AL and AR are, respectively, the absorbance of left and right circularly polarized light. In the presence of a magnetic field and at low temperatures the E/(2T2g) 8” level of Fe(CN)6’ will be the most populated. In that case, it is a simple matter to show that the MCD associated with 2T2g 2Tluwill be positive, while that associated with 2Tzg 2T2uwill be negative (Figure 4). (Note hereafter that we use the convention in designating transitions that the lower state is written on the left; thus A J represents absorption.) It was on a similar, qualitative basis that Stephens9and Schatz et a1.I0J1assigned the LMCT transitions in Figure 1. The quantitative expressions for A and AA of an allowed transition between Born-Oppenheimer states are18 +
-
+
IV. Discussion Theoctahedral Fe(CN)&ion has a low-spin 2Tzg(t2,5) groundstate term, which is split by SO couplinginto a doubly degenerate E/ and a four-fold degenerate U; level (Figure 4). The magnitude of this splitting is 3/2{, where { is the empirical SO coupling constant for a t2g electron. Under the influence of a magnetic field, the degeneracies are further lowered by the Zeeman effect (Figure 4). For small fields ( p 5 = --K& (5) Ineq 12,Kisan intermediatestatewithpartnerlabelrc,%denotes 2 T ~(LMCTl u and LMCT3) and 2T2u(LMCT2) terms undergo that real part of everything to the right and W is the zero-field splittings similar to those of 2T2, but the SO separations are now electronic energy of the state denoted by a subscript. m+l and
&
14 The Journal of Physical Chemistry, Vol. 98, No. 1, 1994
m-1 are circularly polarized components of the electric dipole operator, defined by
Upton and Williamson The fractional Boltzmann population of the E/(2T2,J
level is
*
m+l = = ~ ( l / f i ) ( r n ~irn,,) (14) Equations 9 and 1 1-1 3 predict that the MCD will comprisethree types of features whose intensities depend on the Faraday parameters. 34 terms arise from first-order Zeeman splittings of the ground and excited state, have a derivativeband shape and are temperature independent. 23 terms, which are also temperature independent, are associated with higher-order interstate Zeeman interactions and have a single-signed band shape (either positive or negative). Finally, @ terms account for the Boltzmann populations of Zeeman-split ground-state levels. They have a single-signed band shape and (in the linear limit) a magnitude that is inversely proportional to temperature. The dipole strengths for the LMCT transitions are obtained by summing over all excited state components to give D0(E,”(2T2,)
-
’Ti,) = a)o(U,’(2T2g)
-
where aiis a reduced transition moment
2Ti,) = I.M,l2/9 (15)
The determinationof Faraday parameters is substantiallymore complicated and is described in detail by Piepho and Schatz.l* Accurate experimental determination of higher MCD moments is difficult in the presence of strongly dominant zeroth moments, so we consider only the zeroth-moment parameters BOand eo. The results are
Equations 17 and 18 assume that the SO splittings are small compared with the energy differences between terms so that 23 terms arise exclusively from field-induced interactions between SO components within the same term manifold. To connect these expressionswith experiment,we definezeroth moments:
M, = J ( A A / E ) d l
(22)
Theoretical expressions for A0 and MOare obtained by using eqs 8, 9, IS, and 17-22 and by summing over all ground-state componentsafter weighting by the appropriate Boltzmann factors. Assuming that the temperature is sufficiently low that only the SO components of the 2T2, terms are significantly populated, then
and 1 - 6 is the fractional population of U,’(ZTz,). It is convenient to take the ratio of MOand A0 per tesla, which eliminates common factors and means that the concentration, path length, and transition moments need not be assessed. Represessing the g values in terms of K (eqs 3-5) then gives, for LMCTl
Fo” = 2(36 - 1)(2 + K ) / 3 5 Foe = (b(7 - K )
+ 5 ( K - 1))/2kT
(27) (28)
Fo” and Foe are, respectively, the contributions from B and 8 terms. Note that Fo@will not shown exact 11Tdependence due to the appearance of 6 in eq 28. Furthermore, FoS is temperature dependent due to appearance of 6 in eq 27; it decreases with increasing temperature, but at a much slower rate than Foe,so that 93 terms become relatively more important at higher temperature. An important point concerning eqs 15 and 17-20 is that they are invariant to unitary transformationsof the excited-statebases, which confers useful properties on eqs 26-28. Not only does it remove the necessity to explicitly account for SO and Zeeman interactions within excited-statemanifolds,but it also means that these equations are independent of other first-order excited-state effects, such as crystal-field and Jahn-Teller interactions. However, it does have the disadvantages that it requires the evaluation of experimental moments to be carried over the full envelope of the transition and that contributions from separate electronic transitions be excluded. With regard to the last point, there are two features of the spectra that need to be considered. The first is the shoulder near 25 OOOcm-1(arrowedin Figure2). Thismay beduetovibrational overtones or first-order excited-stated vibronic, crystal-field or SO effects, in which case it must be included in the analysis. Alternatively, it has been assigned to a parity-forbidden LMCT or 2T2, 2A1,23.25926), which transition (either 2 T a 2T1,14*23.24 gains intensity through vibronic coupling with LMCT1. In the latter case, the shoulder should still be included in the analysis; the vibronic coupling will redistribute the absorption and MCD intensities, but will leave the net zeroth moments unaffected, so long as integration is carried over both transitions. Second, it is clear from Figures 1 and 2 that the bands we wish to analyse overlap with LMCT2 in the region near 28 000 cm-I, and we therefore require some means by which to exclude the contribution of the latter. We adopt an approach similar to that used by Rose et al.19 The MCD is integrated between the limits to either side of the band where it reaches zero (21 500 and 28 000cm-1; dotted vertical lines, Figure 2). The estimated contribution of LMCT2 (dashed curve, Figure 2) is then subtracted from the absorption, and integration is carried over the same region as for the MCD. Although this method is somewhat arbitrary, it can be applied consistently and reproducibly to all of the samples we have examined, and it allows us to retain the advantages inherent in the use of moment ratios. The results are plotted in Figure 5 against l/kT. The high degree of linearity is again suggestive of 8 terms, while the low scatter of the data is a reflection of the consistency with which the method for obtaining MolAo can be applied. For given B and T, eq 26 is a function of only 5 and K. It is therefore relatively straightforward to extract these parameters from the experimental data. First, we note 6 1 at low
-
-
The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 75
MCD and Absorption of Fe(CN)63-/PVA
@ terms were assumed in that earlier work, the actual CIDvalues were obtained from the ratio of zeroth moments. (C/D refers to an obsolete definitionof the Faraday parameters; C/D = - p ~ @ o / 23J0.9 The appropriate conversion is
0.0
Figure 5. Dependence of the ratio of zeroth moments per tesla ((Mol Ao)/B) on 1/kT.The method by which Mo/Ao was obtained is described in section IV. The curve drawn through the points is obtained from eqs 2 6 2 8 with { = 300 cm-I and K = 0.76.
temperatures, and so Mo/Ao l i4 m ( 7 ) T
~g
4(2
+ K)
+
= T ( T
(1 + 2K)
kT Hence the slope of a linear fit to the data at high values of l / k T gives an initial estimate of K , which, when combined with the ordinate intercept, gives an initial value of {. These values can then be iteratively refined to eqs 26-28 using least-squares and steepest-descent methods. An unrestrained fit yields { = 600 f 800 cm-I and K = 0.77 f 0.01 cm-I. This result is quite robust, being independent of artifically imposed variations of the initial estimates. However, the precision with which {is determined is poor (a consequence of extreme dependenceof this parameter on the data at the highest temperatures), and much more precise estimates are available from the literature. For the free Fe3+ion, {a450 cm-1,16,27 but this is substantially reduced in Fe(CN)63- (as a consequence of covalency) and has been estimated to be -280 cm-I by fitting to the temperature dependence of the magnetic susceptibility of K3Fe(CN)6.16 Fortunately, K is only weakly dependent on {over a large range; fixing {between 200 and 400 cm-1 gives K = 0.76 f 0.01. To check that the method for determining Mo/Ao does not introduce significant errors, we have repeated the analysis in an approximate form where (AA-/Amx)/B (which should be relatively freeofcontributions from LMCT2) is used on therighthand side of eq 26. The result (again assuming { = 300 f 100 cm-1) is K = 0.73 f 0.03, which agrees closely with that obtained by moment analysis. (The larger error limits arise from thegreater scatter of the data; Figure 3.) After taking into account sources of experimental error, we concludethat K = 0.76 f 0.03 accurately represents the orbital reduction for Fe(CN)&/PVA. We are now in a position to determine the relativecontributions of 23 and @ terms to the MCD by inserting K = 0.76 f 0.03 and { = 300 f 100 cm-I into eqs 27 and 28. In fact, the ratio FOB/ Foe is almost linearly dependent on T. At low temperatures 6 * 1 and
Fo” 2kT Fgb=dl+&) At higher temperatures, 6 differs significantly from unity, but its appearance in both the numerator and denominator of FoB/Foe (eqs 27 and 28) means that eq 30 remains accurate to within 6% up to 300 K. 3 terms are found to be insignificant (52% of Mo) only below -6 K. They constitute 10%of the MCD intensity at -35 K and about 50% at 300 K. Clearly, an assumption of dominant @ terms is invalid at high temperatures; however, it is still possible to compare our results with previous MCD measurements.~OJ3J~Although dominant
-
C / D = -‘/Z(Mo/Ao)(kT/B) (31) Extrapolating to T = 300 K, we obtain C / D = (-0.61 f 0.08)p~, in excellent agreement with C / D = - 0 . 6 0 5 ~found ~ for aqueous K3Fe(CN)6 by Schatz et a1.I0 Gale and McCaffery, however, obtained significantly different values; - 0 . 5 0 p ~for Fe(CN)&/ KCl and -0.44pB for Fe(CN)6’-/PMM at 290 K.13J4 The latter workers interpreted their results to be consistent with K 0.87,14 but after inclusion of 23 terms we find that their results give K * 0.4. Analyses of ESR spectra yield orbital g values of 0.87 for K3Fe(CN)6,I5 and 0.91 and 0.92 for two sites of Fe(CN)%/ KCl.28 That these are significantly larger than the value of K obtained in this work is a consequence of the manner in which the environment of the complex ion treated. In a polymeric medium, such as PVA, ions reside at a very large number of inequivalent, randomly oriented sites of low symmetry. Components of the associated “crystal-field” potential can mix the E,”(2T2g) and Ui(2T2g)states with a subsequent reduction of K . In single-crystal ESR studies, however, the determination of principal g-tensor components for discrete sites allows this sitedependent mixing to be treated separately, so that the orbital g value effectively represents only the covalent contribution to the orbital reduction factor. Finally, we consider the use of the MCD of Fe(CN)&/PVA films for thermometric calibrations. Equations 26-28 indicate that exact 1/Tdependenceof (AA,/A,)/Bcannot beassumed. In fact, above 15 K the temperatures obtained by substituting values of (AAmx/Amax)/B into eq 1systematicallyunderestimate the true temperature, the error amounting to 10%at 30 K and 50%at 100 K. Furthermore,sincethe@-and 3-term intensities are not necessarily distributed uniformly over the envelope of the transition, it is not a simple matter to derive an analytical expression for the temperature dependence from the results of the moment analysis. Rather than attempting to do this, we have taken an empirical approach. We find the expression
-
-
-
T = 0.560[ (Mmax’Amax)]-’ B
+ 0.00183 [(Wnax/AmJ]
-’
(32) to be accurate within f5% up to 85 K, a temperature range that should be satisfactory for most matrix-isolation studies.
V. Conclusion Temperature dependenceof the MCD of the LMCTl transition of Fe(CN)6%/PVA permits determination of an orbital reduction factor, K = 0.76 f 0.03. This is significantly smaller than the orbital g value for Fe(CN)& in crystalline h o ~ t s , ~ 5 Jas 6 ~a~ ~ consequence of a low-symmetry outer-sphere crystal field. Although the magnitude of the MCD appears to be linear with reciprocal temperature at low temperatures, 6‘terms are truly dominant (>98% of the total MCD intensity) only below -6 K, and at 300 K about half the MCD intensity arises from 23 terms. The assumption of 1/ T dependence of the ratio (PA,/A,,)/ B (eq 1) is significantly in error above 15 K, but an empirical relationship (eq 34) should allow Fe(CN)&/PVA to be used for temperature calibrations that are accurate to within *5% below -85 K.
-
Acknowledgment. We are very grateful for the helpful advice of Prof. Paul N. Schatz. This work was supported by the New Zealand University Grants Council (542453) and the New Zealand Lottery Board (SR 7548).
76 The Journal of Physical Chemistry, Vol. 98, No. 1 , 1994
References and Notes (1) Naiman, C.
S.J . Chem. Phys. 1961, 35, 323-328.
(2) Basu, G.; Belford, R. L. J . Chem. Phys. 1962, 37, 1933-1935. (3) Naiman, C. S.J . Chem. Phys. 1963, 39, 1900-1901. (4) Shashoua, V. E. J . Am. Chem. SOC.1964,86, 2109-2115. ( 5 ) Foss,J. G.;McCarville, M. E. J . Am. Chem.Soc. 1965,87,228-230. (6) Buckingham, A. D.; Stephens, P. J. Annu. Rev.Phys. Chem. 1966, 17, 399-432. (7) Stephens, P. J. J . Chem. Phys. 1970, 52, 3489-3516. (8) Stephens, P. J. Adu. Phys. Chem. 1974, 35, 197-264. (9) Stephens, P. J. Inorg. Chem. 1965,4, 1690-1692. (10) Schatz,P. N.;McCaffery,A.J.;Suetake, W.;Henning,G.N.;Ritchie, A. B.; Stephens, P. J. J . Chem. Phys. 1966,45, 722-734. (11) Schatz, P. N.; McCaffery, A. J. Q. Rev. 1969, 23, 552-584. (12) Kobayashi, H.; Shimizu, M.; Kaizu, Y . Bull. Chem. SOC.Jpn. 1970, 43, 2321-2325. (13) Gale, R.; McCaffery, A. J. J . Chem. SOC.,Chem. Commun. 1972, 832-833. (14) Gale, R., McCaffery, A. J. J . Chem. Soc.,Dalton, Trans. 1973,13441351. (15) Baker, J. M.; Bleaney, B.; Bowers, K. D. Proc. Phys. SOC.1956,869, 1205-1 2 15.
Upton and Williamson (16) Bleaney, B.; O’Brien, M. C. M. Proc. Phys. SOC.1956,869, 1216-
.**A
IL5V.
(17) Stephens, P. J. Unpublished work. (18) Piepho, S. B.; Schatz, P. N. Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism; Wiley: New York, 1983. (19) Rose, J. L.; Smith, D.; Williamson, B. E.;Schatz,P. N.;OBrien, M. C. M. J. Phys. Chem. 1986, 90, 2608-2615. (20) Collingwood, J. C.; Day, P.; Denning, R. C.; Quested, P. N.;Snellgrove. T. R. J. Phys. E 1974, 7, 991-996. (21) Misener, G. C. Ph.D. Thesis, University of Virginia, 1987. (22) Chen, G. C.; Yang, J. T. Anal. Lett. 1977, I O , 1195-1207. (23) Guenzburger, D.; Maffeo, B.; Larsson, S.In?. J . Quantum Chem. 1977, 12, 383-396. (24) Aizman, A.; Case, D. Inorg. Chem. 1981, 20. 528-533. (25) Alexander, J. J.; Gray, H.B. J . Am. Chem. SOC.1968, 90,4260427 1. (26) Jain, S.C.; Warrier, A. V. R.; Sehgal, H.K. J . Phys. C: SolidStaie PhyS. 1973,6, 193-200. (27) Blume, M.; Watson, R. E. Proc. R. SOC.(London) I963,271A, 565578. (28) Wang, D. M.; de Boer, E. J . Chem. Phys. 1990, 92.46984707.
