Molecular Electrochemistry of Coordination Compounds …
415
positive solv G°(Fc) in MeCN, which is obviously physically unrealistic, because
Fc is well soluble in this solvent.
Roma´ nczyk et al. [8] obtained reliable values of E°(Fc
+ /Fc) from computations at the SMD/B3LYP-D2/def2-QZVPPD//B3LYP/LanL2TZf/6-31G(d) level of
theory. This method provides virtually the same gas-phase energetics for ionisation
of Fc as does the G3(MP2)-RAD-Full-TZ level. Table 1 compares E
◦
(abs) of Fc
+ /Fc
couple, computed using the methodologies described above, for other non-aqueous
solvents commonly used in electrochemistry, and water, for which no such data were
available. Note that the values obtained by Namazian et al. [25] (numbers marked
with footnote c Table 1) include the correction for the Gibbs energy of free electrons (−0.038 eV) based on Fermi–Dirac statistics, whereas E°s computed by us
(footnotes a and b) follow the “ion convention” (see [3] for explanation of thermochemical conventions concerning the thermodynamics of the electron). We found
a linear dependence between ferrocene oxidation potentials and the reciprocal of
solvent dielectric constants only in the case of the SMD solvation; the obtained linear regression equation reads E
◦
abs 4.910 + 2.091/ε (for 8 solvents), which may
be employed in the estimation of this potential in other solvents. Obviously, in the
case of solvation models for which the bulk electrostatic contribution to solv G° is
calculated from the Poisson equation (like SMD) or the generalised Born approximation (e.g. SM12 [26]), a linear relationship between the difference solv G°(Red)
– solv G°(Ox) (and E°) with respect to 1/ε is expected. It should be noted that the
E
◦
(abs) (Fc
+ /Fc) values based on the SMD and COSMO-RS solvation energies are very
similar only for polar solvents, whereas for non-polar ones they differ appreciably
(even by 0.25 V). The COSMO-RS derived E
◦
(abs) s in DCE and DMSO solvents are
not consistent with experimental data: higher E
◦
(abs) s in solvents of lower polarity
(see Table 1) and the measured formal potential in DCE (or CH 2 Cl 2 ) being of an
order of 0.1 V higher than that in DMSO [27, 28]. Moreover, Krishtalik [29] has
demonstrated that for metallocenes, like ferrocene and cobaltocene, the dielectric
response energy contribution to the solvation energy can be calculated with the Born
equation applying the same effective radii for all the aprotic solvents.
Knowing the absolute potentials of the Fc
+ /Fc pair in a given solvent makes it
possible to present the computed redox potentials for other redox processes in the
ferrocenium/ferrocene scale, i.e. versus Fc
+ /Fc, and compare them with the experimentally determined values in the same scale. It is also possible, to convert thus
computed potentials to the commonly applied SCE scale by using the experimental
formal potential of Fc
+ /Fc in a given solvent measured versus SCE [31], by simply
adding it to the value calculated versus Fc
+ /Fc.
E comp (vs. SCE) E comp
vs. Fc
+
/Fc
+ E
◦
Fc
+
/Fc vs. SCE
(3)
Please note that the potential versus SCE also depends on the type and concentration of supporting electrolyte used. Reference [31] cites a couple of examples of
this variation. The differences due to using different base electrolytes in the same
solvents may reach ca. 40 mV, but we know from our own experience that changing the concentration of the base electrolyte in dichloromethane from 0.1 to 0.2 M
415
positive solv G°(Fc) in MeCN, which is obviously physically unrealistic, because
Fc is well soluble in this solvent.
Roma´ nczyk et al. [8] obtained reliable values of E°(Fc
+ /Fc) from computations at the SMD/B3LYP-D2/def2-QZVPPD//B3LYP/LanL2TZf/6-31G(d) level of
theory. This method provides virtually the same gas-phase energetics for ionisation
of Fc as does the G3(MP2)-RAD-Full-TZ level. Table 1 compares E
◦
(abs) of Fc
+ /Fc
couple, computed using the methodologies described above, for other non-aqueous
solvents commonly used in electrochemistry, and water, for which no such data were
available. Note that the values obtained by Namazian et al. [25] (numbers marked
with footnote c Table 1) include the correction for the Gibbs energy of free electrons (−0.038 eV) based on Fermi–Dirac statistics, whereas E°s computed by us
(footnotes a and b) follow the “ion convention” (see [3] for explanation of thermochemical conventions concerning the thermodynamics of the electron). We found
a linear dependence between ferrocene oxidation potentials and the reciprocal of
solvent dielectric constants only in the case of the SMD solvation; the obtained linear regression equation reads E
◦
abs 4.910 + 2.091/ε (for 8 solvents), which may
be employed in the estimation of this potential in other solvents. Obviously, in the
case of solvation models for which the bulk electrostatic contribution to solv G° is
calculated from the Poisson equation (like SMD) or the generalised Born approximation (e.g. SM12 [26]), a linear relationship between the difference solv G°(Red)
– solv G°(Ox) (and E°) with respect to 1/ε is expected. It should be noted that the
E
◦
(abs) (Fc
+ /Fc) values based on the SMD and COSMO-RS solvation energies are very
similar only for polar solvents, whereas for non-polar ones they differ appreciably
(even by 0.25 V). The COSMO-RS derived E
◦
(abs) s in DCE and DMSO solvents are
not consistent with experimental data: higher E
◦
(abs) s in solvents of lower polarity
(see Table 1) and the measured formal potential in DCE (or CH 2 Cl 2 ) being of an
order of 0.1 V higher than that in DMSO [27, 28]. Moreover, Krishtalik [29] has
demonstrated that for metallocenes, like ferrocene and cobaltocene, the dielectric
response energy contribution to the solvation energy can be calculated with the Born
equation applying the same effective radii for all the aprotic solvents.
Knowing the absolute potentials of the Fc
+ /Fc pair in a given solvent makes it
possible to present the computed redox potentials for other redox processes in the
ferrocenium/ferrocene scale, i.e. versus Fc
+ /Fc, and compare them with the experimentally determined values in the same scale. It is also possible, to convert thus
computed potentials to the commonly applied SCE scale by using the experimental
formal potential of Fc
+ /Fc in a given solvent measured versus SCE [31], by simply
adding it to the value calculated versus Fc
+ /Fc.
E comp (vs. SCE) E comp
vs. Fc
+
/Fc
+ E
◦
Fc
+
/Fc vs. SCE
(3)
Please note that the potential versus SCE also depends on the type and concentration of supporting electrolyte used. Reference [31] cites a couple of examples of
this variation. The differences due to using different base electrolytes in the same
solvents may reach ca. 40 mV, but we know from our own experience that changing the concentration of the base electrolyte in dichloromethane from 0.1 to 0.2 M