Kinetic and spectroscopic observations on the azidyl, N3{radical dot}, radical oxidation of fac-(Lspectator)ReI(CO)3(Lacceptor ) to fac-(Lspectator)ReII(CO)3(Laccepto r), Lspectator = 4,4′-bpy; Lacceptor ...

Article abstract of DOI:10.1016/j.ica.2007.02.049

Full title: Kinetic and spectroscopic observations on the azidyl, N3{radical dot}, radical oxidation of fac-(Lspectator)ReI(CO)3(Lacceptor ) to fac-(Lspectator)ReII(CO)3(Laccepto r), Lspectator = 4,4′-bpy; Lacceptor = dipyridyl[3,2-a:2′3′-c]phenazine or Lspectator = Cl-; Lacceptor = bathocuproindisulfonate: A revisitation to the self-exchange rate constants of the N3{radical dot} / N3- and Re(II)/Re(I) couples and to the redox potential of the N3{radical dot} radical The oxidation of two triscarbonyl fac-(Lspectator)ReI(CO)3(Lacceptor )z complexes (Lspectator = 4,4′-bpy; Lacceptor = dipyridyl[3,2-a:2′3′-c]phenazine (dppz) and z = + or Lspectator = Cl-; Lacceptor = bathocuproinedisulfonate (bcds2-) and z = 2-) by azidyl radicals, N3{radical dot}, was investigated by pulse radiolysis. Reaction rate constants were determined for the electron transfer reactions between the Re(II) products and reductants, Ru (bipy)33 + and Ni(Me6-[14]dieneN4)2+, and used for the calculation of the self-exchange rate constant of the Re(II)/Re(I) couples. The self-exchange rate constants, k ～ 107 M-1 s-1, were one order of magnitude larger than the constant, k ～ 106 M-1 s-1, communicated in the literature for the [Re(DMPE)3]+/2+ (DMPE = 1,2-bis(dimethylphosphine)ethane). The larger rate constants of the triscarbonyl complexes are in agreement with the smaller inner sphere reorganization energy of the complexes relative to [Re(DMPE)3]+/2+. Moreover, the study demonstrated that the redox potential of the azidyl radicals is EN3{radical dot} / N3-0 = 1.70 V versus NHE, a value larger than one communicated earlier, and that the self-exchange rate constant of the N3{radical dot} / N3- couple is kN3{radical dot} / N3- = 2.7 × 106 M- 1 s- 1. The small value of the N3{radical dot} / N3- self-exchange rate constant has been related to the large solvent reorganization energy of the reaction.

Full text of DOI:10.1016/j.ica.2007.02.049

Inorganica Chimica Acta 360 (2007) 3681–3687
www.elsevier.com/locate/ica
Kinetic and spectroscopic observations on the azidyl, NÅ3,
radical oxidation of fac-(Lspectator)ReI(CO)3(Lacceptor) to
fac-(Lspectator)ReII(CO)3(Lacceptor), Lspectator = 4,40-bpy;
Lacceptor = dipyridyl[3,2-a:2030-c]phenazine or Lspectator = Clꢀ;
L
acceptor = bathocuproindisulfonate: A revisitation to the
Å
ꢀ
self-exchange rate constants of the N3=N3 and Re(II)/Re(I)
couples and to the redox potential of the NÅ3 radical
b
a
a
b,
*
G.T. Ruiz , M.P. Juliarena , E. Wolcan , G. Ferraudi
a
INIFTA, Universidad Nacional de La Plata, C. C. 16, Suc. 4, 1900 La Plata, Argentina
Chemistry Department and Radiation Laboratory, University of Notre Dame, Notre Dame, IN 46556, USA
b
Received 3 November 2006; accepted 19 February 2007
Available online 6 May 2007
Abstract
The oxidation of two triscarbonyl fac-(Lspectator)ReI(CO)3(Lacceptor)z complexes (Lspectator = 4,40-bpy; Lacceptor = dipyridyl[3,2-a:2030-c]
phenazine (dppz) and z = + or Lspectator = Clꢀ; Lacceptor = bathocuproinedisulfonate (bcds2ꢀ) and z = 2-) by azidyl radicals, NÅ3, was
investigated by pulse radiolysis. Reaction rate constants were determined for the electron transfer reactions between the Re(II) products
and reductants, RuðbipyÞ3 and Ni(Me6-[14]dieneN4)2+, and used for the calculation of the self-exchange rate constant of the Re(II)/
3þ
Re(I) couples. The self-exchange rate constants, k ꢁ 107 Mꢀ1 sꢀ1, were one order of magnitude larger than the constant,
k ꢁ 106 Mꢀ1 sꢀ1, communicated in the literature for the [Re(DMPE)3]+/2+ (DMPE = 1,2-bis(dimethylphosphine)ethane). The larger rate
constants of the triscarbonyl complexes are in agreement with the smaller inner sphere reorganization energy of the complexes relative to
[Re(DMPE)3]+/2+. Moreover, the study demonstrated that the redox potential of the azidyl radicals is E0NÅ =N ¼ 1:70 V versus NHE, a
ꢀ
3
3
value larger than one communicated earlier, and that the self-exchange rate constant of the NÅ3=N3
couple is
ꢀ
kN =N ¼ 2:7 ꢂ 106 Mꢀ1
s
ꢀ1. The small value of the N3Å =N3ꢀself-exchange rate constant has been related to the large solvent reorganiza-
Å
ꢀ
3
3
tion energy of the reaction.
ꢀ 2007 Elsevier B.V. All rights reserved.
1. Introduction
Re(I) self-exchange redox reactions in this family and
other families of Re(I) complexes. Only one literature
report on this subject has shown that the self-exchange of
The photochemically induced redox reactions of fac-
(Lspectator)ReI(CO)3Lacceptor complexes, where Lspectator
=
[Re(DMPE)3]+/2+
, (DMPE = 1,2-bis(dimethylphosphine)
azine, halide, pseudo-halide, carboxylate and Lacceptor
= diazine, have been the matter of considerable interest
[1,2]. Little is known however on the rates of the Re(II)/
ethane) in aqueous solution (Eq. (1))
½ReðDMPEÞ3ꢃþ þ ½ReðDMPEÞ3ꢃ
2þ
! ½ReðDMPEÞ3ꢃ2þ þ ½ReðDMPEÞ3ꢃþ
ð1Þ
*
is relatively slow process occurring with a rate constant,
Corresponding author.
E-mail address: Ferraudi.1@ND.EDU (G. Ferraudi).
k = 4.0 · 106 Mꢀ1 sꢀ1 [3]. Since excited state redox
0020-1693/$ - see front matter ꢀ 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.ica.2007.02.049

3682
G.T. Ruiz et al. / Inorganica Chimica Acta 360 (2007) 3681–3687
radiolytic pulse
reactions mostly produce Re(I) species with a reduced
Lacceptor ligand, such as an azine or diazine compound,
the photochemical method has not been widely used for a
study of the Re(II)/Re(I) self-exchange. Radiolytically ini-
tiated redox reactions could offer better conditions for
these studies.
...
)
(eaq-; OH•
+ N2O, + H+
-
•
ð2Þ
OH + N3
OH•
N3
- N2
-
The title compounds proved to be enough soluble in
aqueous media where suitable oxidants of the Re(I)
complexes can be used for a study of the Re(II)/Re(I)
self-exchange reactions. One possible oxidant, the NÅ3 azi-
dyl radical, has been pulse radiolytically-generated in a
mixed-solvent, 20% v/v CH3CN in H2O [4]. In this
solvent, the NÅ3 radical oxidizes fac-(4,40-bpy)-
In order to radiolyze a fresh sample with each pulse, an
appropriate flow of the solution through the reaction cell
was maintained during the experiment. Other conditions
used for studies of the time-resolved spectroscopy of
the intermediates or a reaction kinetics are given in Sec-
tion 4.
Commercially available software, Mathcad 2001i – Vis-
Sim V5 and Microcal Origin 6, were used for the reaction
kinetic calculations and for analyzing time-resolved spec-
tra. A series solution of the rate equations for the reactions
described elsewhere in the text and literature extinction
coefficients of the reactants and reaction intermediates were
used in the calculation [14].
ReI(CO)3(dppz)+
to
fac-(4,40-bpy)ReII(CO)3(dppz)2+
(dppz = dipyridyl[3,2-a:2030-c]phenazine) without compli-
cations introduced by parallel reactions of the NÅ3 radical.
However, the broad spread of values communicated in
the literature for the reduction potential of the NÅ3=N3
ꢀ
couple [5–7] and the unknown rate constant of the cou-
ple’s self-exchange reaction make the NÅ3 radical reaction
with Re(I) complexes unsuitable for the study of the
Re(II)/Re(I) self-exchange.
2.2. Cyclic voltammetry
Rate constants for the self-exchange rꢀeactions of the
Re(II)/Re(I) complexes and the NÅ3=N3 couple have
been determinated from the rate constants of pulse-
radiolytically initiated cross reactions in this work. The
goodness of these self-exchange rate constants was estab-
lished by calculating experimentally determined rate
constants of cross reactions with a modified Marcus
equation.
The electrochemical experiments were conducted with a
BAS, CVS-1B cyclic voltammograph interfaced through a
Tektronix TDS 220 oscilloscope to a Micron PC. Triply
distilled H2O (ꢁ18.5 MX) was used for the preparation
of the solutions. A platinum disc, polished to a mirror fin-
ish, was used as a working electrode and a Pt wire was used
as an auxiliary electrode. Potentials were measured against
a BAS, KClsat, AgCl/Ag electrode.
2. Experimental
3. Materials
2.1. Pulse-radiolytic procedures
The sodium salt of the bathocuproinedisulfonate,
bcds2ꢀ, containing 3% H2O were purchased from Aldrich
and used as received. The [fac-(4,40-bpy)ReI(CO)3-
(dppz)](PF6), (I), [Ni(Me6[14]diene N4)(ClO4)2, (II), and
[Ru(2,20-bpy)3](ClO4)2 complexes were available from pre-
vious works.
Pulse radiolysis experiments were carried out with a
model TB-8/16-1S electron linear accelerator. The
instrument and computerized data collection for time-
resolved UV–Vis spectroscopy and reaction kinetics have
been described elsewhere in the literature [8–13].
Thiocyanate dosimetry was carried out at the beginning
of each experimental session. Details of the dosimetry
3.1. [fac-ClReI(CO)3(bcds)]Na2 Æ 5H2O, (III)
have been reported elsewhere [9,10]. This procedure is
ꢀ
based on the concentration of ðSCNÞ2
radicals
A solution made of 180 mg (0.5 mmol) of Re(CO)5Cl in
50 cc of ethanol was added to 50 cc of an aqueous solution
containing 280 mg (0.5 mmol) of bathocuproinedisulfonate
disodium salt. The mixture was refluxed overnight and rot-
ovaporated to a volume of about 5 cc. Recrystallization
from H2O by the addition of ethanol and drying the solid
under vacuum produced a pure product. Yield: 80%
(350 mg). Elemental Analysis: Anal. Calc. for ReC29H28
N2O14S2ClNa2: H, 2.94; C, 36.27; N, 2.92; S, 6.68. Found
H, 3.21; C, 36.23; N, 2.95; S, 6.78%.
generated by the electron pulse in a N2O saturated
10ꢀ2 M SCNꢀ solution. Calculations of the ðSCNÞ2
ꢀ
concentrations were made with G = 6.13 and an the rad-
ical’s extinction coefficient, e = 7.58 · 103 Mꢀ1 cmꢀ1 at
472 nm [10–13]. In general, the experiments were carried
out with doses that in N2 saturated aqueous solutions
resulted in (2.0 0ꢀ.1) · 10ꢀ6 M to (6.0 0.3) · 10ꢀ6 M
concentrations of eaq. Solutions were deaerated passing
streams of O2-free N2O before and during the experi-
ment. The reactiꢀon of the radiolytically generated OHÅ
radicals with N3 was used for the preparation of N3Å
radicals, Eq. (2).
The FTIR of the compound confirmed the presence of
H2O in the product. No water molecules were lost when
the compound was kept 24 h under vacuum at 45 ꢁC.

G.T. Ruiz et al. / Inorganica Chimica Acta 360 (2007) 3681–3687
3683
Aldrich, LC grade, CH3CN, and reagent grade NaClO4
and NaN3 were used as received.
1.5
1.0
0.5
0.0
-0.5
a
Delay: 90 μs
300 400 500 600 700
Delays:
1 μs
15 μs
70 μs
4.0
2.0
b
0.0
-2.0
400 500 600 700 800
λ, nm
Fig. 1. Difference spectrum of fac-(4,40-bpy)ReII(CO)3(dppz)2+, (a). The
spectrum was recorded 90 ls after the radiolytic generation of azidyl
radicals [4]. The transient spectra in (b) was recorded during the decay of
fac-ClReII(CO)3(bcds)ꢀ. The Re(II) complex was produced when
1.8 · 10ꢀ4 M fac-ClReI(CO)3(bcds)2ꢀ in N2O-saturated 0.05 M NaN3
Å
reacted with pulse radiolytically generated N3 radicals.
of the Re(II) complex produced by the oxidation of the
corresponding Re(I) complex is shown in Fig. 1a.
In order to compare the UV–Vis spectrum of the Re(II)
complexes, fac-(4,40-bpy)ReII(CO)3(dppz)2+ and fac-
ClReII(CO)3(bcds)ꢀ, a similar reaction of the NÅ radical
3
with fac-ClReI(CO)3(bcds)2ꢀ was investigated in this work.
The oxidation of 5.0 · 10ꢀ4 M fac-ClReI(CO)3(bcds)2ꢀ by
NÅ3 radicals, Eq. (4),
4. Results and discussion
2ꢀ
fac-Cl ReIðCOÞ3ðbcdsÞ þ Nꢄ3
In a previous work [4] it has been demonstrated that the
totality of the radiolytically generated OHÅ radical in N2O-
saturated 20% (v:v) CH3CN in H2O is scavenged by
0.1–0.05 M N3ꢀ. The reaction formed, therefore, a concen-
! fac-Cl ReIIðCOÞ3ðbcdsÞꢀ þ Nꢀ3
ð4Þ
was investigated in 0.1 or 0.05 M NaN3 dissolved in neat
H2O. The sulfonate groups of bcds2ꢀ increase the solubility
of fac-ClReI(CO)3(bcds)2ꢀ complex in neat H2O to make
the addition of CH3CN unnecessary. A complete trapping
Å
tration of N3 radical equivalent to the initial concentration
of OHÅ radical. It was also demonstrated that oxidation of
the fac-(4,40-bpy)ReI(CO)3(dppz)+ to fac-(4,40-bpy)ReII-
(CO)3(dppz)2+ by the radiolytically generated NÅ3 radicals,
Eq. (3),
of the NÅ radicals by fac-ClReI(CO)3(bcds)2ꢀ was achieved
3
when the doses used in the experiments produced 2 · 10ꢀ6
to 4 ꢂ 10ꢀ6 NÅ3 radicals per pulse and the concentration of
complex was equal to or larger than 5 · 10ꢀ4 M. Time-
resolved changes in the spectrum of the solution showed
the oxidation of the fac-ClReI(CO)3(bcds)2ꢀ to fac-
ClReII(CO)3(bcds)ꢀ, Fig. 1b. The formation of the Re(II)
product was kinetically of a pseudo-first order in the con-
centration of Re(I) complex. To calculate the second order
rate constant, k = 4.9 · 108 Mꢀ1 sꢀ1, the rate constant ob-
tained under the pseudo-first order regime was divided by
the fac-ClReI(CO)3(bcds)2ꢀ concentration.
k¼2:2ꢂ109 Mꢀ1 sꢀ1
fac-ð4; 40 ꢀ bpyÞReIðCOÞ3ðdppzÞþ þ N3Å
!
2þ
fac-ð4; 40 ꢀ bpyÞReIIðCOÞ3ðdppzÞ þ Nꢀ3
ð3Þ
in 20% (v:v) CH3CN in H2O solutions containing 10ꢀ4 M
complex and 0.1 or 0.05 M NaN3 resulted in a complete
Å
trapping of the N3 radicals by the complex. A second order
rate constant for Eq. (3), k = 2.2 · 109 Mꢀ1 sꢀ1, has been
communicated in the literature [4]. The difference spectrum

3684
G.T. Ruiz et al. / Inorganica Chimica Acta 360 (2007) 3681–3687
30
30.0
20.0
10.0
0.0
8.0
6.0
4.0
20
2.0
0.0
300
400
600
750
λ, nm
10
Fig. 2. Absorption spectrum of fac-ClReII(CO)3(bcds)ꢀ in aqueous
0.05 M NaN3, pH = 7, calculated on the basis of Eq. 5.
NÅ3 radicals reacted with themselves and with the Re(I)
complex when the doses were higher and/or the concentra-
tions of the Re(I) complex were smaller than 5 · 10ꢀ4 M.
In these conditions, the total concentration of Re(II) prod-
uct formed in the reaction is a fraction a of the concentra-
tion of radiolytically generated NÅ3 radicals, ½N3Å ꢃinitial. The
values of a were calculated on the basis of the integrated
rate equation with the rate constant of Eq. (4) communi-
cated above, the literature value of the rate constant for
the annihilation of NÅ3 radicals [7], and the concentration
of Re(I) complex. Extinction coefficients for the spectrum
of fac-ClReII(CO)3(bcds)ꢀ, Fig. 2, were calculated with
0
300
400
500
600
λ, nm
Fig. 3. Absorption spectrum of fac-(4,40-bpy)ReII(CO)3(dppz)2+ in aque-
ous 0.08 M NaN3, pH = 7.
(7.0 0.4) · 105 cm sꢀ1 for the decay of fac-(4,40-bpy)ReII-
(CO)3(dppz)2+ in 20% (v:v) CH3CN in H2O and k/e =
(2.2 0.5) · 107 cm sꢀ1 for the decay of fac-ClReII(CO)3-
(bcds)ꢀ in neat H2O, were calculated from oscillographic
DAfinal
a½Nꢄ3ꢃinitial
traces recorded respectively with kob = 410 nm and kob
=
ꢀ
eCl ReII
¼
þ eClReIðCOÞ ðbcdsÞ2ꢀ
ð5Þ
ðCOÞ3ðbcdsÞ
3
620 nm. The decay of the Re(II) species is probably reflect-
ing the disproportionation of the Re(II) species into Re(I)
and Re(III) complexes with the rate of the fac-ClReII(CO)3-
(bcds)ꢀ disproportionation being approximately 16 times
faster than the rate of the fac-(4,40-bpy)ReII(CO)3-
(dppz)2+disproportionation. The disproportion process
requires a Re(II)/Re(I) couple with a larger reduction
potential than the potential of the Re(III)/Re(II) couple.
While this condition appears to be satisfied by the couples
involving the triscarbonyl complexes, it is not the case with
the stable [ReII(DMPE)3]2+ complex where the reduction
potential of the Re(II)/Re(I) couple is less than 1/7 of the
carbonyl complexes reduction potentials, Table 1.
where the absorbance change, DAfinal, was measured after
the completion of Eq. (4), i.e., at times t > 30 ls. The calcu-
lated spectrum of fac-ClReII(CO)3(bcds)ꢀ showed a good
agreement in the position of the absorption bands with the
literature spectra of other Re(II) complexes [15]. Because
of the oxidizable chloride ligand, E0 ꢁ 2.6 V versus NHE
for the ClÅ/Clꢀ couple, in fac-ClReII(CO)3(bcds)ꢀ, the
absorption spectrum must show significant differences with
the spectrum of fac-(4,40-bpy)ReII(CO)3(dppz)2+. The spec-
trum of the latter, Fig. 3, was calculated from the difference
spectrum following the same procedure used in the calcula-
tion of the fac-ClReII(CO)3(bcds)ꢀ spectrum. A comparison
of the spectra in Fig. 2, 3 reveals that the spectrum of fac-
(4,40-bpy)ReII(CO)3(dppz)2+ below 500 nm is largely domi-
nated by intraligand electronic transitions centered in the
dppz ligand. Moreover, a 600 nm band in the spectrum of
fac-ClReII(CO)3(bcds)ꢀ is absent in the spectrum of fac-
(4,40-bpy)ReII(CO)3(dppz)2+. Based on the band position
and intensity, it can be attributed to a partially forbidden,
chloride-to-Re(II), charge transfer transition.
Neither the Eq. (3) nor the Eq. (4) could be used for a
calculation of the Re(I)/Re(II) self-exchange rate constant
because of the uncertainty in the reduction potential and
Å
ꢀ
unknown self-exchange rate constant of the N3 =N3 cou-
ple. Instead, the Re(II) products of the Eqs. (3) and (4)
were reduced after the radiolytic synthesis with
RuðbipyÞ3 (Eq. (6)) and Ni(Me6-[14]dieneN4)2+ (Eq. (7))
3þ
z
2þ
fac-ðLspectatorÞReIIðCOÞ3ðL acceptorÞ þRuIIðbpyÞ3
In contrast to other Re(II) complexes in the literature,
the Re(II) products of Eqs. (3),(4) were unstable. The rate
of the Re(II) complexes transformation, followed by means
of the decay of the Re(II) spectrum, was kinetically of a
second order on the Re(II) concentration. Ratios of the
rate constant to the extinction coefficient, k/e =
zꢀ1
3þ
! fac-ðLspectatorÞReIðCOÞ3ðLacceptor
Þ
þRuIIIðbpyÞ3
ð6Þ
z
2þ
fac-ðLspectatorÞReIIðCOÞ ðL acceptorÞ þNiIIðMe6 ꢀ½14ꢃdieneN4Þ
3
zꢀ1
! fac-ðLspectatorReIðCOÞ3ðLacceptor
Þ
3þ
þNiIIIðMe6 ꢀ½14ꢃdieneN4Þ
ð7Þ

G.T. Ruiz et al. / Inorganica Chimica Acta 360 (2007) 3681–3687
3685
Table 1
Rate constants of cross electron transfer reactions (kRe(II)/Red), self-exchange rate constants (kRe(II)/Re(I), kOx/Red) and reduction potentials ðER0 eðIIÞ=ReðIÞ
,
E0Ox=RedÞ of the complexes used in relevant reactions
kRe(II)/Red (Mꢀ1 sꢀ1
)
kRe(II)/Re(I) (Mꢀ1 sꢀ1
)
kOx/Red (Mꢀ1 sꢀ1
)
E0ReðIIÞ=ReðIÞ (V)
E0Ox=Red (V)
a
Red:
Re(II):
fac-(4,40-bpy) ReII(CO)3(dppz)2+
2þ
RuIIðbpyÞ3
1.7 · 107
1.2 · 107
8.0 · 106
2.0 · 103
1.65
1.65
1.5
1.2
NiII(Me6[14]dieneN4)2+
9.4 · 107
3.5 · 107
fac-ClReII(CO)3(bcds)ꢀ
8.3 · 108
2þ
RuIIðbpyÞ3
2.0 · 107
1.4 · 107
8.0 · 106
2.0 · 103
1.3b
1.3b
1.5
1.2
NiII(Me6[14]dieneN4)2+
1.9 · 109
[ReII(DMPE)3]2+c
[ReI(DMPE)3]+
4.0 · 106
0.21
a
Unless otherwise stated, the reversible redox potentials were determined in deaerated CH3CN vs a KClsat, AgCl/Ag reference electrode and referred to
the NHE by adding 0.197 V. Data from Ref. [4,23].
b
Quasi-reversible potentials determined in aqueous solutions of CH3CN containing 15% (v:v) of H2O and 0.01 M NaClO4 as supporting electrolyte. A
KClsat, AgCl/Ag was used as a reference electrode and the potentials were referred to the NHE by adding 0.197 V.
c
Data from Ref. [3].
where Lspectator = 4,40-bpy; Lacceptor = dppz and z = 2+ or
L
spectator = Clꢀ; Lacceptor = bcds2ꢀ and z = ꢀ. The concen-
2.0x105
1.5x105
trations of RuðbipyÞ3 and Ni(Me6-[14]dieneN4)2+ used in
the experiments were varied from 5 · 10ꢀ4 to 1 · 10ꢀ5 M in
order to prevent reactions of the NÅ3 radicals with either
Ru(II) or Ni(II) complexes.
2þ
The disproportionation of the Re(II) carbonyl com-
plexes, a reaction that is kinetically of a second order
on Re(II) concentration, occurred in competition with
reactions 6 and 7. Therefore, the reciprocal of the Re(II)
1/t1/2
decay half-life, tꢀ1=12, was plotted against the respective
2þ
concentrations of RuðbipyÞ3
and Ni(Me6-[14]die-
4.0x103
2.0x103
0.0
neN4)2+. Second order rate constants of the cross elec-
tron transfer reactions, Eqs. (6) and (7), were calculated
from the slope of the lines. Typical plots for the
Ni(Me6-[14]dieneN4)2+ reactions are shown in Fig. 4
and the calculated rate constants are communicated in
Table 1. The self-exchange rate constants of the Re(II)/
Re(I) couples, kRe(II)/Re(I), are shown in Table 1. They
0.0
2.0x10-5
4.0x10-5
were calculated with the rate constants of the cross reac-
[Ni(Me6[14]dieneN4)2+], M
3þ
tions and literature properties of the RuðbipyÞ3
=
RuðbipyÞ3 [16] and Ni(Me6-[14]dieneN4)3+/Ni(Me6-[14]
dieneN4)2+ [17]. A modified Marcus expression of the
rate constant of a cross reaction was used in the calcula-
tions, Eq. (8), [18,19],
2þ
Fig. 4. Typical linear dependencies of the reciprocal of the reaction half-
life on the concentration of NiII(Me6[14]dieneN4)2+
Data for the
j, and fac-ClReII(CO)3-
.
respective fac-(4,40-bpy)ReII(CO)3(dppz)2+
:
(bcds)ꢀ; d, reactions with NiII(Me6[14]dieneN4)2+
.
ꢀ
ꢁ
1=2
kReðIIÞnReðIÞkRednOxKf
jReðIIÞnReðIÞjOxnRed
W ReðIIÞnRed
jReðIIÞnRed
kReðIIÞnRed
¼
!
2
ðlnK þ ðwReðIIÞnRed ꢀ wOxnReðIÞÞ=RT Þ
f ¼ exp
ð8Þ
4ðlnðkReðIIÞnReðIÞ
k
RednOx=Z2jReðIIÞnReðIÞjOxnRedÞ þ ðwReðIIÞnReðIÞ ꢀ wOxnRedÞ=RTÞ
h
i
K ¼ exp 38:9ðE0ReðIIÞnReðIÞ ꢀ E0OxnRedÞÞ where E0i are the electrochemical reduction potentials;
ꢂ
ꢃ
W ReðIIÞnRed ¼ exp ꢀðwReðIIÞnRed þ wOxnReðIÞ ꢀ wReðIIÞnReðIÞ ꢀ wOxnRedÞ=2RT

3686
G.T. Ruiz et al. / Inorganica Chimica Acta 360 (2007) 3681–3687
Reorganization of Eq. (8) leads to a quadratic equation
on kRe(II)/Re(I). Values of the self-exchange rate constants
were obtained as a solution of the quadratic equation
under the assumption that the reactions were adiabatic,
jRe(II)/Red ꢁ jRe(II)/Re(I) ꢁ jOx/Red ꢁ 1. The work terms,
wRe(II)/Red, wRe(II)/Re(I) and wOx/Red, were evaluated with
literature equations [20]. While the values of kRe(II)/Re(I)
resulting from the calculation are close to those of low
communicated in this work were in good agreement con-
firming, in this manner, the correctness of the obtained
values.
It is now possible to account for the rather small reduction
potential of the N3Å radical, EN0 Å =N ¼ 1:33V versus NHE,
ꢀ
3
communicated in a literature repo3rt [6]. In the calculation
of this value, the redox potential was obtained from the
calculated equilibrium constant of Eq. (9). The latter was
calculated as a quotient, kf/kb, of the experimentally
obtained rate constants of the forward, kf, and backward,
kb, electron transfer reactions. No allowance was made
by the authors for the difference between the Coulombic
work terms, wf ꢀ wb, of the reactions. In accordance to
the Marcus theory, the relationship between the ratio of
the rate constants and the equilibrium constant is,
kf/kb = Keq · exp ꢀ (wf ꢀ wb)/RT. Using literature expres-
sions of the Coulombic terms [18,19] and estimated radius
of the reactants the values calculated for wf ꢀ wb are equal
to or larger than 10 kJ/mol resulting in kf/kb values that are
10ꢀ2 to 10ꢀ3 times smaller than Keq. The reduction poten-
tial of NÅ3 calculated in the literature on the kf/kb ꢁ Keq
assumption is, therefore, somewhere between 20% and
30% smaller than the correct thermochemical potential.
spin d5/d6 couples such as RuðbipyÞ33þ=RuðbipyÞ3 and
2þ
OsðbipyÞ33þ=OsðbipyÞ32þ, they are larger than one com-
municated for the couple [Re(DMPE)3]2+/+, Table 1.
To calculate the rate constants of electron transfer reac-
tions of NÅ3 radicals such as Eqs. (3) and (4), the reduction
0
ꢀ
potential, ENÅ =N ꢀ , and the N3 self-exchange rate constant,
3
3
Å
ꢀ
kN =N , must be known. A 0.6 V uncertainty in the reduc-
3
3
tion potential, EN0 Å =N ꢀ , of the NÅ3 radical is too large to
3
3
make and accurate calculation of the self-exchange rate
Å
ꢀ
constant, kN =N with the modified Marcus expression for
3
3
a cross reaction rate constant. To obtain the values of
E0NÅ =N and kN
, the literature values of the rate con-
ꢀ
Å=N3
ꢀ
3
3
sta3nts, Table 2, of two reactions, Eq. (9), (10), were used
in two different quadratic equations.
kN
ꢀnIrBr26ꢀ
3
Nꢀ3 þ IrBr62ꢀ ꢀꢀꢀꢀꢀ! N3ꢄ þ IrBr63ꢀ
ð9Þ
5. Conclusions
kNÅ
3nIrCl36ꢀ
Nꢄ3 þ IrCl63ꢀ ꢀꢀꢀꢀꢀ! N3ꢀ þ IrCl62ꢀ
ð10Þ
The self-exchange rate constants calculated for the fac-
z/zꢀ1
(Lspectator)ReII(CO)3(Lacceptor
)
are near one order of
The
solutions
of
the
quadratic
and kN
equations,
E0NÅ =N ¼ 1:70 V versus NHE
¼ 2:7ꢂ
ꢀ
magnitude larger than the self-exchange rate constant,
k = 4 · 106 Mꢀ1 sꢀ1, communicated for [Re(DMPE)3]2+/+
[3]. This difference between the values of kRe(II)/Re(I) is
Å=N3
ꢀ
3
3ꢀ1
3
106 M
s
ꢀ1, were calculated assuming that reactions 9
and 10 were adiabatic. Although this value of E0NÅ =N is
ꢀ
3
3
indicative of a smaller reorganization energy, k = kouter
+
close to those in the literature, it had to be validated
because redox potentials calculated from kinetic data not
always agree with thermochemical potentials. To verify
ꢀ
kinner [20,21], for the transfer of the electron from fac-
zꢀ1
(Lspectator)ReI(CO)3(Lacceptor
)
to fac-(Lspectator)ReII(CO)3-
z
(Lacceptor
)
than in the transfer from [Re(DMPE)3]+ to
the correctness of the E0NÅ =N and kN
values, they were
Å=N3
[Re(DMPE)3]2+. Relative to the phosphine complexes, a
smaller inner sphere reorganization energy, kinner, is
expected in the carbonyl complexes. The infrared frequen-
cies of the vibrational modes [22] making a contribution to
kinner show that force constants of the Re–C bonds are
smaller than the Re–P bonds of the phosphine complex.
On the other hand, differences between the outer-sphere
reorganization energies, kouter, of the Re(II)/Re(I) couples
must be a minor factor because all the studies were con-
ducted in aqueous media.
ꢀ
3
3
used in calculations of a 3number of cross reaction rate con-
stants including several of them in the literature, Table 2.
The rate constants derived from experimental data and
those calculated with the values of E0NÅ =N and kN
Å=N3
ꢀ
ꢀ
3
3
3
Table 2
Comparison between calculated and experimentally obtained valuꢀes of the
Å
rate constants of electron transfer reactions involving the N3 =N3 couple
Cross reaction rate constants for the oxidation of a
number of transition metal complexes by the NÅ3 radical
kcross (Mꢀ1 sꢀ1
Calculated value Experimental value
)
reflect the radical’s large reduction potential, EN0 Å =N
¼
ꢀ
Electron donor (to NÅ3)
fac-(4,40-
3
3
1:70 V versus NHE, and far from diffusion-controlled rate,
4.2 · 109
2.2 · 109
kN =N ¼ 2:7 ꢂ 106 Mꢀ1
s
ꢀ1, for the exchange of the elec-
Å
ꢀ
bpy)ReI(CO)3(dppz)+
3
3
tron between NÅ3 and N3ꢀ, Table 2. If the assumption made
on the adiabaticity of the cross reactions used in the calcu-
lations was partially valid, larger values of the rate constant
and/or redox potential would have resulted from the calcu-
4ꢀ
FeðCNÞ6
2.0 · 109
2.0 · 109
5.3 · 108
4.0 · 109a
5.5 · 108a
4.9 · 108
IrCl36ꢀ
fac-ClReI(CO)3(bcds)ꢀ
ꢀ
Electron acceptor (from N3
)
IrCl26ꢀ
IrBr26ꢀ
a
1.3 · 102
1.6 · 102a
lations. However, the calculations of various cross reaction
1.2 · 10ꢀ2
6.1 · 10ꢀ2a
0
Å
ꢀ
rate constants based on the values of ENÅ =N and, kN =N
ꢀ
3
3
communicated in this work agreed with 3the experimental
3
Rate constants from Ref. [5,6].

G.T. Ruiz et al. / Inorganica Chimica Acta 360 (2007) 3681–3687
3687
´
[4] G.T. Ruiz, M.P. Juliarena, R.O. Lezna, E. Wolcan, M.R. Feliz, G.
Ferraudi, J. Chem. Soc. Dalton Trans. 20 (2007) 2020.
[5] W.K. Wilmarth, D.M. Stanbury, J.E. Bird, H.N. Po, C-P. Chua,
Coord. Chem. Rev. 51 (1983) 155.
values of the rate constants. This fact supports the assump-
tion made on the adiabaticity of the various reactions.
Å
ꢀ
Moreover, the low value of kN =N signals a sizable reorga-
3
3
nization energy for the electron exchange between NÅ3 and
N3ꢀ. A reorganization energy, kN =N ¼ 104 kJ=mol, was
[6] M.S. Ram, D.M. Stanbury, Inorg. Chem. 24 (1985) 4233.
[7] J.F. Endicott, in: A.W. Adamsom, P.D. Fleischauer (Eds.), Concepts
in Inorganic Photochemistry, Wiley, New York, 1975, p. 88.
[8] J. Guerrero, O.E. Piro, E. Wolcan, M.R. Feliz, G. Ferraudi, S.A.
Moya, Organometallics 20 (2001) 2842.
Å
ꢀ
3
3
calculated with Eq. (11).
ꢀ
ꢁ
ꢄ
ꢀ
k
N3nN3
kN =N ¼ 1011 exp
ꢀ
ð11Þ
ꢄ
ꢀ
3
3
[9] G.L. Hugh, Y. Wang, C. Scho¨neich, P.-Y. Jiang, R.W. Fesenden,
Radiat. Phys. Chem. 54 (1999) 559.
4 RT
Based the vibrational frequency of the stretching mode in
azides, m ꢁ 2125 cmꢀ1 [22], and an average radius of
1.17 A, the inner-sphere reorganization energy appears to
[10] M.R. Feliz, G. Ferraudi, Inorg. Chem. 37 (1998) 2806.
[11] G.V. Buxton, C.L. Greenstock, W.P. Hellman, A.B. Ross, W. Tsang,
J. Phys. Chem. Ref. Data 17 (1988) 513.
[12] N. Getoff, A. Ritter, F. Schworer, Radiat. Phys. Chem 41 (1993) 797.
[13] S.K. Dutta, G. Ferraudi, J. Phys. Chem. A 105 (2001) 4241.
[14] H. Margenau, G.M. Murphy, The Mathematics of Physics and
Chemistry, 2nd edn., D. Van Nostrand Company Co., New York,
1956, Ch. 13.
Å
ꢀ
be making a small contribution, ꢁ4%, to kN =N while
the largest contribution, ꢁ96%, is made by the 3solvent-
3
reorganization.
[15] K. Dumbar, E.J. Schelter, A.V. Palii, S.M. Ostrovsky, V.Y. Miro-
vitskii, J.H. Hudson, M.A. Omary, S.I. Klokishner, B.S. Tsukerblat,
J. Phys. Chem. 107 (2003) 11102.
[16] M.S. Chan, A.C. Wahl, J. Phys. Chem. 82 (1978) 2542.
[17] K. Kumar, F.P. Rotzinger, J.F. Endicott, J. Am. Chem. Soc 105
(1983) 7064.
[18] D.J. Szalda, D.H. Macartney, N. Sutin, Inorg. Chem 23 (1984) 3473,
and references therein.
[19] D.H. Macartney, N. Sutin, Inorg. Chem 22 (1983) 3530, and
references therein.
[20] W.L. Reynolds, R.W. Lumry, in: B.C. Crawford, W.D. McElroy,
C.C. Price (Eds.), Mechanisms of Electron Transfer. Modern Con-
cepts in Chemistry, The Ronald Press Co, NewYork, 1966.
[21] For a summary of the kouter and kinner expressions see: R.G. Wilkins,
in: Kinetics and Mechanism of Reactions of Transition Metal
Complexes, 2nd edn., VCH, New York, 1991, p. 263, Ch. 5.
[22] K. Nakamoto, Infrared and Raman Spectra of Inorganic and
Coordination Compounds, Wiley–Interscience, New York, 1978.
[23] G. Ruiz, Thesis Disertation, Universidad Nacional de La Plata, 2003.
Acknowledgements
G.F and G.R. acknowledge support from the Office of
Basic Energy Sciences of the US department of Energy.
This is contribution No. NDRL-4693 from the Notre
Dame Radiation Laboratory. M.P.J. and E.W. acknowl-
edge support from CONICET. We are thankfull to Dr.
E. Carrasco Flores for his assistance with the FTIR
measurements.
References
[1] N. Winterton, Annu. Rep. Prog. Chem., Sect. A 96 (2000) 557.
[2] D.J. Stufkens, A. Vlcek Jr., Coord. Chem. Rev. 177 (1998) 127.
[3] K. Libson, M. Woods, J.C. Sullivan, J.W. Watkins II, R.C. Elder, E.
Deutsch, Inorg. Chem. 27 (1988) 999.