Kinetics of the Vanadium(II)-Vanadium(III) Isotopic Exchange Reaction¹

The self-exchange of a nonbonding electron via the outer-sphere pathway: reorganizational energy and electronic coupling matrix element for the V(OH2)62+/3+, Ru(OH2)62+/3+, V(OH2)63+/4+, and Ru(OH2)63+/4+ couples

“…The fact that, on one hand, this value is considerably larger than those for the Fe(OH 2 ) 6 2ϩ/3ϩ and Ru(OH 2 ) 6 2ϩ/3ϩ couples, and that, on the other hand, the ionic radii of the V(OH 2 ) 6 2ϩ and V(OH 2 ) 6 3ϩ ions lie between those of the corresponding hexaaqua ions of Fe and Ru, indicates that the experimental 9 value of 0.010 M Ϫ1 s Ϫ1 (25 ЊC and I = 2.0 M) is too low. A critical analysis of the experimental details 9 shows that this is indeed the case: the reaction has been investigated in perchlorate medium. It is known 12 that V(OH 2 ) 6 2ϩ reacts quite rapidly with ClO 4 Ϫ .…”

“…K A , ν el , and ∆E ‡ or λ [eqn. (9)], depend on the M ؒ ؒ ؒ M distance, r, and this data has been calculated for the V(OH 2 ) 6 2ϩ/3ϩ and Ru(OH 2 ) 6 2ϩ/3ϩ couples. K A [eqns.…”

“…∆E ‡ , the activation energy, is related to the total reorganizational energy λ via eqn. (9). whereby ν ou = 30 cm Ϫ1 7 (5) ν el = gH ab 2 /λ 1/2 , g = 1.75 × 10 13 kJ Ϫ3/2 s Ϫ1 (6)…”

A Critical Assessment of Classical and Semi-Classical Models for Electron Transfer Reactions in Solution

“…With the force constants given in Table 2, Eq. [21] yields ∆E ‡ = 14·2 kJ/mol. This is much less than the value given by the "equal bond-length" pathway.…”

“…A troubling question that arises from the above discussion is why do MT calculations agree within an order of magnitude with the experimental adiabatic, outer-sphere self-exchange rate constants of transition-metal complexes (with the exception of the Co (aq) 2+/3+ exchange), while they severely underestimate (by 3 to 8 orders of magnitude) the analogous rates for nonadiabatic processes and for Co(OH 2 ) 6 2+/3+ ? Considering that MT estimates the ET energy barriers in high ionic strength media as the sum of two dominant factors, ∆G out * and ∆G in *, it is possible Fe(CN) 6 4-/3-(π) 6 /(π) 5 138 f) 144 f) 188 188 880 6·8 × 10 3 1 10 13 2·1 0·38 294 0·01 1·9 × 10 1 [18] Cr(OH 2 ) 6 2+/3+ (π) 3 (σ*) 1 /(π) 3 96 153 215 198 650 9·6 × 10 -5 1 4·2 × 10 10 2·0 × 10 -3 -0·40 298 1.0 ≤ 2 × 10 -5 [19] Mn(OH 2 ) 6 2+/3+ (π) 3 (σ*) 2 /(π) 3 (σ*) 1 99 153 217·7 g) 199·1 650 6·1 × 10 -7 1 4·9 × 10 9 9·0 × 10 -5 1·52 298 0·5 <4 [20] V(OH 2 ) 6 2+/3+ (π) 6 /(π) 5 96 153 213.1 h) 199.2 i) 650 2·6 × 10 -1 1 10 13 5·0 × 10 -1 -0·255 298 2·0 1·0 × 10 -2 [21] Fe(OH 2 ) 6 2+/3+ (π) 4 (σ*) 2 /(π) 3 (σ*) 2 96 153 210 198 650 4·8 × 10 -1 1 10 13 9·9 × 10 -1 0·74 298 0·1 1·1 [22] Co(OH 2 ) 6 2+/3+ (π) 5 (σ*) 2 /(π) 6 96 153 208·1 187·3 650 1·2 × 10 -9 1 10 13 3·1 1·96 291 1·0 2·4 [23] Ru(OH 2 ) 6 2+/3+ (π) 6 /(π) 5 116 j) 182 j) 211 203 650 9·5 × 10 2 1·18 10 13 3·1 × 10 1 0·23 298 5·0 2·0 × 10 1 [24] Co(NH 3 ) 6 2+/3 (π) 5 (σ*) 2 /(π) 6 78 148 219 197 660 1·5 × 10 -7 1 2·4 × 10 7 5·0 × 10 -5 0·06 313 2·5 ≥ 8 × 10 -6 [25] Ru(NH 3 ) 6 2+/3+ (π) 6 /(π) 5 (π) 5 (σ*) 2 /(π) 6 83 k) 148 k) 216 l) 197 800 1·2 × 10 -4 1 1·0 × 10 7 4·4 × 10 -6 -0·24 298 0·98 7·7 × 10 -5 [27] Ru(en) 3…”