1809
NOTES
Paramagnetic Relaxation of Hexacoordinated Chromium(II1) Complexes with Anionic Ligands in Aqueous Solutions'"
by L. Burlamacchi, G. Mart,ini, and E. Tiezzi Institute of Physical Chemistry, University of Florence, Florence, Italy (Received August 16, 1969)
The analysis of the factors which affect the line width of an esr spectrum often provides useful kinetic and chemical information. Little work has been done as yet on the electron spin relaxation of Cr(II1) in water solution in the presence of anionic ligands. The electron spin resonance absorption of chromic ion consists of a single line, about 150 G wide a t points of maximum slope, with no hyperfine structure.lb The spectrum may be interpreted in terms of the general hamiltonian for a quartet spin state = gPHs
+ D[Xz2- '/3S(X + I ) ] + E[&2 -
fJu2I
(1)
in which the last two terms determine the relaxation. I n a perfectly cubic field, such would arise from a hexaaquo chromic complex [CT(H~O)B]~+, D and E should be zero and no relaxation should be induced. However, modulation of the quadratic zero field splitting parameter by changes in orientation or by collision with solvent particles may result in a mixing of different electronic spin states. The dominant mechanism of relaxation is indeed believed to be the modulation of the quadratic crystalline field splitting term SD(,,S, where D2 = 2/rD2 2E2 is the trace of the square of the zero-field splitting (zfs) hamiltonian. This mechanism was treated by RiIcGarvey2 and Bloembergen and Morgan3 and more recently by Carrington and L u c k h u r ~ t . ~Using the Redfield density matrix formalism, they found that for a d a configuration the spectrum consists of three lorentzian curves: one for the m, '/z e - '/z transition and two equivalent for the m, "2 F? + l / ~ and for - 1/2 S -3/z transitions. I n the limit of fast motion, when the correlation time T, for the time dependence of the zfs modulation is much shorter than the reciprocal of the Larmor frequency W O , the three lorentzians are exactly superimposed and have the same relaxation time
+
+ +
T2-l
=
('/6)(D2)2~,
(2)
At room temperature this condition is generally realized. I n addition to the fluctuating distortion, when anionic ligands are coordinated around the transition metal ion in solution, complexes of lower symmetry are formed and a static electric field distortion may arise. This induces larger zfs, and line broadening over that of the aquo ion is observed. Dealing with ionic association, two main possibilities must be examined: (a) the ligand enters an outer coordination sphere and only a slight distortion is induced, and (b) the ligand displaces one of the solvent molecules from the first coordination sphere. I n the latter case, an inner complex is formed, with large crystalline field distortion. Paramagnetic resonance has seldom been observed in these complexes because line width is usually so large as to escape detection. Sancier6 has studied the association of aqueous Cr(II1) with several inorganic anions and cations a t relatively high concentrations. He developed his theory in terms of relaxation induced by electric field anisotropy and by restricted rotation of the complex due to cations which enter a third coordination sphere. However, this study is confined to outer-sphere coordination. We wish to show that esr absorption intensity and line width variations as a function of ligand concentration are closely related to the inner- and outer-sphere equilibrium constants. We shall use the method previously outlined for Mn(II).6 Briefly, this method may be described as follows: the stepwise equilibrium reaction may be expressed as Cras3+
+ L-"
kab
kbs
Cr(aq)L(3-")+
kbc
kca
Cr~(3-n) + (3)
where the subscript aq means the hexaaquo coordination. Each species has a different line width which we define as A H i o n , AHout,and A H i n ) respectively. Under rapid exchange conditions, that is Tab = l / k a b [ L - " ]
