Photophysics of the gadolinium(III) ion in aqueous solution. Part 1.—Chemical relaxation of the excited states

Abstract

The study of the photoexcited octahydrated Gd^III ion in aqueous solution has shown its unusual reactivity, previously revealed by conventional and time-resolved emission spectra and further evidenced here by the influences of temperature, pH and ⁸S_7/2 Gd(OH₂)³⁺₈ concentration on the observed lifetime τ_obs of the ⁶P_7/2 level. The repeatedly reported τ_obs of ca. 2 ms, which is five times lower than the theoretically calculated radiative lifetime, is due to chemical relaxation of ^*Gd(OH₂)³⁺₈(G^*₂) involving the consecutive excited-state formation of the hexa-aquo ^*Gd(OH₂)³⁺₆(X^*), the hydrolysed ^*Gd(OH₂)₅OH²⁺(Y^*) and the exciplex ^*Gd₂(OH)(OH₂)²⁺_x(E^*)(x≈ 13). At 298 K, constants K^*, enthalpies ΔH^*/kJ mol^–1 and entropies ΔS^*/J mol^–1 K^–1 of formation are, respectively: 68 mol² dm^–6, 1.34, 39.7 (X^*); 2 × 10^–3, –9, –79 (Y^*) and 51 mol^–1 dm³, 6.3, 54 (E^*), whereas the probabilities of physical relaxation k/s^–1 are: 163 (G^*₂), ca. 160 (X^*), 185 (Y^*) and 380 (E^*). The experimentally determined radiative probability k^r_G2= 98 s^–1 for the Gd(OH₂)³⁺₈⁶P_7/2→⁸S_7/2 process is in excellent agreement with the theoretical value, whilst the non-radiative part, k^nr_G2= 65 s^–1, remains unexplained by current theories of multiphonon de-excitation. Water expulsion (G^*₂⇌ X^*+ 2H₂O) is explained in terms of ^*Gd³⁺ radius contraction by 4f-shell expansion and 5p-shell shrinkage, inducing inner-sphere water hindrances. The unique case for an aquo-metallic complex, of enthalpy loss in the X^*+ H₂O ⇌ Y^*+ H₃O⁺ hydrolysis (H) process is quantitatively rationalised by a Förster–Weller type of cycle, by ΔH_H and ΔS_H to cation charge (z)/metal–oxygen(d_M–O) distance correlations and by pK_Hversus nephelauxeticity β and βversus d_M–O relations. Nephelauxetic ratios β for ⁸S_7/2 Gd(OH₂)³⁺₈, ⁸S_7/2 Gd(OH₂)³⁺₆(hypothetical or actual), ⁶P_7/2 Gd(OH₂)³⁺₈ and ⁶P_7/2 Gd(OH₂)³⁺₆ have been evaluated and are: 0.988, 0.971, ⩽0.988 and 0.957, respectively. The fall in β from 0.988 to 0.971 or from ca. 0.988 to 0.957 is argued to be primarily the result of central field effects and, to a lesser extent, of change in coordination and symmetry. This latter effect is confirmed by MS-Xα m.o. calculations performed, in both spin-polarised (SP) and non-spin-polarised (NSP) formalisms by choosing a common Gd—O distance, on the two idealised square-antiprism and octahedral structures.