Dynamic metal-ligand coupling in the infrared MCD spectra of the cobalt(II) tetrahalides

- Volume 38, number 3.

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CHEkCAL- PHYSICSLEtiERS

. .._~.._ . . Vi

~~~~C.M~TAL-~rGA~~

COUPLI[NG IN THE INFRARED MCD SPECTRA

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OF THE COBALT(II) TETRAHALIDE!3 . Rodney GALE, Robin E. GODFREY and Stephen F. MASON

s Received 3 Oct&ber 1975

The it.xM singk-crystaf magnetic circul-JSdichroisn spectra of Cs$M3&Yo2* and Cs~ZnBr&oZ+ have been measured over the 400~-700~ cm-’ region of t&e 4Aa - ’ Tt
C/D terms obtained give transition moment ratios, (t~llmIlt~)/~eilmIIt~),in accord with the value required dynamic ligand-polarization model for d-electron transition probabilities in tetrahedral metd complexes.

metal-ion

1. Introduction The preceding communication [ 13 demonstrates dependence of the intensities of quadrupoiar d-electron transitions in tetrahedral cobalt(I1) tetrahalides conform to the expectations of a general dynamic Iigand-polarisation theory of f-electron f23 and d-electron [3,4] transition Probabilities in metSal coordination compounds. The theory is based OR the model that transient induced dipoles in the ligands are correlated coulombically by the potential of the leading electric multipole of the metal-ion transition, the rest&ant first-order elect& dipole transition moment being non-zero if the multipole component and the correlated dipole component transform under a common representation in the point-group of the compiex f2-41. For a qua.drupole-allowed metal-ion trat-kition MO + Ma the ol-component of the first-order electric dipole moment, m&, follows from the expresGon, that the temperature

(1) where Z(t) is the tiean ~olarisability of the ligand L at the frequency of-the met&-ion transition and f@ is the &component of the quadrupole moment of that transition. The radia! and angular factors governing +&epotential between the &-component of a dipole Iocated in the ligand ir; and the ~~~omponent of the 446,

quadrupclfe 2re represented

(-3”2/2”2) by a

by the tensor

CL ww

The variation of the tensor Gf;,ov with temperature is considered in the preceding note [ 11, and here we investigate the phase relationship between the two main types of d-electron quadrupole transition moment in tetrahedral complexes and the MCD consequences in the case of the cobalt(i1) tetrahalides. The two types ofd-electron excitation considered are, firstly, those connecting an e with a t2 cubic d-orbital and, secondly, those connecting two different t7 orbitals. The evaluation of a particular quadrupolemoment of each type, following the defimitions and procedure of Criffrth IS], and subsequent reduction gives the two types of matrix efement in the ratio, /cellallt,, = -3i+“? The ratio of the corte~ond~~ tion moments,

(2) electric dipole transi-

~t,fimt~t,,l~ellmit~~) = 4

(3)

has the same value (q = -31j2f21j2) according to fhe dynamic coupling theory since the resultant of the ligand electric dipole rnorn~~~s is proportions to the metal-ion quadrupole transition moment and is correfated to follow the latter’s phase [eq. (I)] _The crystal field theory of the intensities of d-eledtron transitions in tetrahedral complexes, where the first-order electric dipole moment derives from a 3d + 4p contri-

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Volume 38, number 3 butiop mixed in under the &tic

15 XIarch1976

CHEMICALPHYSICS LETTERS field.d’ofthe

figands, indicates a positive value for the ratio, q = +2 f6] _

The o-bonding molecular orbital model for the d-elec-

tron intensities of the divalent transition metal tetrahalides requires a positive value for the ratio in the range, t2g2 < q < 1-2 [6], md the addition of ~0 bonding does not change the expectation that 4 is positive in the case of [CoCI, Jz- and [CO&,]~-- [7]. An estimate of the transition moment ratio, g, is afforded by MCD measurements of th.e B-terms [8] and the C-terms [Y] of the quadrupole-atlowed d-electron transitions in tetrahedral cobaIt(i1) complexes, 4A2 + 4Tl(F), 4Tr(P) near 5 kK and 14 kR, respectively. Derming found f ZO] that the v&es of @I- C/fil‘, for the 4 A2 --, 4T, (P) transition of each of the three cobalt(I1) tetrahalides at ambient temperature are positive, whereas a negative sign is expected f8] from either the crystal field theory or the o-bonding MO model. From a single-crystal MCD study of jEt,N),ZnCi,/Cc+ over the temperature range 229-423 K, Denning and Spencer [9] measured the overall B/D and C/D values of the 4Az 4 4T, (P) bznd system of [CoC!,]2-, obtaining a negative value for the transition moment ratio, Q [eq. (3)1. The negative sign of the ratio, 4. then appeared to be anomalous from the standpoint of either crystal field or MO theory, and it was suggested [9] that the negative Q value might arise from B-term interactions with higherenergy charge-transfer excited s&&es, and from substantial second-order interactions between the 4T,(P) state and neighbouring components of the free-ion 2G state, which reverse the expected sign of the C term. The 4T, (F) state of the cob&(H) tetrahalides lies some S-9 kK below the corresponding 4T1(P) state and it is separated from the nearest doublet states by a similar frequency interval. The coupling of the 4T1CF) state to any doublet state is unlikely to be significant, and mixing with higher-energy charge-transfer excited states is necessarily of less importance for the 4T1(F) than for the 4T,(F) state. Accordingly we have measured the axial single-crystal KCD spectrum of Cs,ZnC1&ozc and of CsSZnBr jCo2+ over the 4Tl(F) region, 4000-7000 cm- 5 , at ambient and at liquid-helium temperature, in order to obtain a less uncertain estimate of the transition moment ratio, Q, and for a detailed spectroscopic anaIysis which will be discussed elsewhere. The overaH values of BfD and C/ZJ for the 4A2 + 4Tr(F) band system of [COC~,]~-

.

Table i

ObservedMCDparametersS!D and C/D for d-electron transitions to the 4Tz states from the gramd &se 6f fCofCq I’complexes and the derivedv&e of the transition moment ra:io,q [eqs. i3),_(7) and (S)] 9

Compiesl:

State

B/~~~c~-~ 1 q

[COCI,J]*-

‘&(F)

-0.58~10-~

-G.6 +0.097 -1.4

4TI(P)a)

+A4 x10-”

--0’

i-o.51

-111

4T~W) +0.18~10-~ ?&‘) b, +2.66Xl0-3

-l.z -0.6

t-o.025

-1.1

tCoBre1’”

am

a) IZrCDparameters from ref. 191. ‘) Value for (~~C/k~~~ at ambient temgernture

from&f.

and [CoBrG12- in the lattices studied are listed in table 1, together with the MCD parameters available [9,10] for the corresponding 4A, -+ *T1(P) transition.

2. Results and discussion

The 4T1(F) and 4T1(P) states of the tetrahedral cobalt(H) terrahalides derive from a common pair of. excited con~gurat~ons,

The form OEthe 4T, (P) function is the analogue of eq. (4) in which the coefficients are interchanged with a sign reversal, w=2)(E,

= -CC&,),,.

(5)

Values of the coefficients for the 4T1(F) state, obtained from the experimental dipole strengths of the two transitions, ~~~~~~

= (c2/C,12

(6)

are listed in table 2 for [CoCl4 1 2- and fCcBr4 f2- at ambient and at low temperature. For the simple two-system model of the cobaItfII) tetr~~ides, in which overlap between the metal-ion and the ligands is neglected, the overal! B/X) ratio for the 4A~ + 4T1(F) band system is given by [8] t (7) where 0 is the Bohr magneton and A is the interval between the ground 4A2(F) 2nd excited 4Tz(F) state, The overt&C/Dratio for the ~ansjtioR to the 4T1fF) 447

V&me

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CHEhiICAL PHYSICS LET?&RS

-Table 2. The e&mposition of the ‘TX d-electron states of [Co&]‘[eqs. (4) and (S)] from the ratio of the dipole strength D(p)@) of the transi:ions to the 4T1@) and 4Tr(F) states from the ground state

Complex

TiKI

“&+F>

cx

C?

[CoCI‘$I*-

298 80

2.69 2.36

0.52r 0.545

0.854 0.838

298 80

3.02 2.27

OS97 OS53

0.866 0.833

[CoBrq]=-

state in the &me appro~atio* pression f91,

follows from the ex-

where c is tf?e one-electron spin-orbital coupling parameter for the d-electrons of the metai ion. The substitution of eq. (5) into eqs. (7) and (8) gives the B/D and the C/D ratio, respectively, for the 4 AZ + 4T,p) transition. Eqs. (7), (S) and their anaiogues cannot account for the experimentai B/D and C/D ratios recorded (table 1) if the transition moment ratio 4 has a positive value, as crystal field and MO theory require,. If (I is positive the B/D and C/D parameters for the 4A, -+ 4T,(F) transition must be negative and larger %Imag nitude than the corresponding ratios for the transition to the 4T,CP) state, contrary to observation (table 1). If A is taken as 4000 cm-l and f as tiO0 cm-l , as the g-value (2.37) suggests f 1 If, the

observed C/D parameters for the transitions to the 4Tl(F) and 4T1(P) states of [CoC14f2- and [CoBr4]2give, through eq. (8) and its analogue, the transition moment ratio q values (table I) close to that required (-- 1.225) by the dynamic coupiing model [eq. <2)]. The experimental B/‘D parameters for the two transitions of the cobalt tetrahalides also require the ratio 4 to be negative, through eq. (7) and its analogue, although the q-values so derived disclay more scatter (table I)._The B/D ratio. is gene&y extracted with less

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precision than the C/D ratio from the di&ctiy-observed (B+C/EF)/D band-area quotient, and it is obtained on the assumption that the B-term is-invariant with respect to temperature. The temperature ciepen-

dence of the coefficients, C, and Cz (table 2), and eq. (7) shows that the B-terms of the transitions to the 4T, states of the cobalt(H) tetrahalides are not strictly temperature independent. At liquid-helium temperatures the MCD is dominated by the C-terms, and the more-certain C/D ratios provide substantial and selective support for the dynamic ligand-polarisation model

(8)

$48..

15 March 1976

of d-electron transition probabilities in tetrahedral metaf complexes.

Acknotiedgement

We thank the Science Research Council for support of the work reported_

Xeferences fi1 R. CWe, RX. GMJfrey and S-F. Mnson, Chem. Phys. Letters 38 (1976) 441. [ 21 S.F. hfason, R.D. Peacock and B. Stewart, Chem. Phys. Letters 29 (1974) 149. 131 R. Gale, RX. Godfrey, S.F. Mason, R.D. Peacock and 3. Stewart, 3. Chem. Sac. Chem. Commun. (1975) 329. f4] SF. Mason and R.R. Seal, J, Chem. Sot. Chem. Commun. (1975) 331. [S] J.S. Griffith, The theory of transition metal ions (Cambridge Univ. Press, L&don, 1961) p. 291 and appendices. [6] C.J. Ballheusen and A.D. Liehr, J. X101.Spectry. 2 (1958) 342;4 (1960) 190. I71 B-D. Bird, E.A. Cooke, P. Day and A.F. Qrchard, Phil. Trans. Roy. Sot. 276 (1974) 277. [S] P-J. Stephens, J. Chem. Phys. 43 (1965) 4444. [9] R.G. Denning and J-A. Spencer, Symp. Faraday SW. 3 (1969) 84. fl0) R.G. Denning, J. Chem. Phys. 45 (1966) 1307. 11 I] R.P. van Stapele, H.G. Belgers, P.F. Bangers and H. Zijlstra, J. Cbm. Phys. 44 (1966) 3719.