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P. P. Roma´ nczyk and S. S. Kurek
frequency calculation commonly done in the harmonic approximation (for the gasphase or solution-optimised structure),
2 and solv G°. The solvation free energies
can be received at a low computational cost employing an implicit solvent model
(ISM), when specific interactions, i.e. hydrogen bonding, solvent molecule coordination, can be neglected. Otherwise, there is a need for taking into account one
or a few explicit solvent molecules to form a solvent–solute cluster embedded in
a continuous environment [8], in water; however, explicit solvation, e.g. within a
QM/MM framework, may be required [9]. The commonly used continuum solvation
models are polarisable continuum models (PCMs) [10], the solvation model based
on solute density (SMD) [11] (which uses the IEF-PCM algorithm for bulk electrostatics), the conductor-like screening model (COSMO), and COSMO for realistic
solvation COSMO-RS (statistical thermodynamics for the molecular surface interactions, COSMO polarisation charge densities used) [12]. solv G° may be computed
using, e.g. B3LYP/6-31+G(d,p) (COSMO-RS requires the use of BP/TZP), in accordance with the level of theory applied in parametrisation of the solvation model;
nevertheless, the results are not largely dependent on the model chemistry, which
delivers a reasonably accurate electronic density for a solute [3]. Nowadays, continuum solvation models allow obtaining reliable redox potentials with mean unsigned
error (MUE) even of ca. 0.1 V; for organic solutes in acetonitrile using SMD Guerard and Arey [13] obtained MUE equal to 0.13 V, in water it is higher. Note that we
frequently take advantage of error compensation between E ea,gas and solv G° (and
other effects). In case structural changes upon solvation are not very large, using
gas-phase optimised geometries in both phases is justified and recommended [2].
2.1 Problems with Calibration Based on Comparison
with Experimental Data
Potentials calculated with DFT/ISM can be directly compared with voltammetrically
determined E 1/2 potentials
3 for reversible or quasi-reversible processes, however, provided well-calibrated
4 computational protocols (method/basis set, solvation model)
2 If the liquid and gas-phase solute structures differ appreciably, using partition functions computed
in solution is a correct approach, see [83].
3 E 1/2 denotes a mean of voltammetric anodic and cathodic peak potentials. E 1/2 E f (E f is formal
potential) if the diffusion coefficients of the oxidised (Ox) and reduced (Red) forms are equal.
E f potential refers to the situation, when the concentration ratio of [Ox] to [Red] at the electrode
surface is equal to one, which obviously is not true in the case of more complex systems, like, e.g.
proton-coupled reactions. Then, knowing the electrode reaction, and the concentration of that other
participating species, like protons, the relation between the E f and E ° (based on concentrations)
can easily be found.
4 Calibrated against the best available experimental data or highly accurate QM methods, such as
G3(MP2)-RAD or explicitly correlated coupled cluster theory CCSD(T)-F12 calculations, which
could now be applied even for midsized metal complexes, if only single reference quantum methods
are applicable.
P. P. Roma´ nczyk and S. S. Kurek
frequency calculation commonly done in the harmonic approximation (for the gasphase or solution-optimised structure),
2 and solv G°. The solvation free energies
can be received at a low computational cost employing an implicit solvent model
(ISM), when specific interactions, i.e. hydrogen bonding, solvent molecule coordination, can be neglected. Otherwise, there is a need for taking into account one
or a few explicit solvent molecules to form a solvent–solute cluster embedded in
a continuous environment [8], in water; however, explicit solvation, e.g. within a
QM/MM framework, may be required [9]. The commonly used continuum solvation
models are polarisable continuum models (PCMs) [10], the solvation model based
on solute density (SMD) [11] (which uses the IEF-PCM algorithm for bulk electrostatics), the conductor-like screening model (COSMO), and COSMO for realistic
solvation COSMO-RS (statistical thermodynamics for the molecular surface interactions, COSMO polarisation charge densities used) [12]. solv G° may be computed
using, e.g. B3LYP/6-31+G(d,p) (COSMO-RS requires the use of BP/TZP), in accordance with the level of theory applied in parametrisation of the solvation model;
nevertheless, the results are not largely dependent on the model chemistry, which
delivers a reasonably accurate electronic density for a solute [3]. Nowadays, continuum solvation models allow obtaining reliable redox potentials with mean unsigned
error (MUE) even of ca. 0.1 V; for organic solutes in acetonitrile using SMD Guerard and Arey [13] obtained MUE equal to 0.13 V, in water it is higher. Note that we
frequently take advantage of error compensation between E ea,gas and solv G° (and
other effects). In case structural changes upon solvation are not very large, using
gas-phase optimised geometries in both phases is justified and recommended [2].
2.1 Problems with Calibration Based on Comparison
with Experimental Data
Potentials calculated with DFT/ISM can be directly compared with voltammetrically
determined E 1/2 potentials
3 for reversible or quasi-reversible processes, however, provided well-calibrated
4 computational protocols (method/basis set, solvation model)
2 If the liquid and gas-phase solute structures differ appreciably, using partition functions computed
in solution is a correct approach, see [83].
3 E 1/2 denotes a mean of voltammetric anodic and cathodic peak potentials. E 1/2 E f (E f is formal
potential) if the diffusion coefficients of the oxidised (Ox) and reduced (Red) forms are equal.
E f potential refers to the situation, when the concentration ratio of [Ox] to [Red] at the electrode
surface is equal to one, which obviously is not true in the case of more complex systems, like, e.g.
proton-coupled reactions. Then, knowing the electrode reaction, and the concentration of that other
participating species, like protons, the relation between the E f and E ° (based on concentrations)
can easily be found.
4 Calibrated against the best available experimental data or highly accurate QM methods, such as
G3(MP2)-RAD or explicitly correlated coupled cluster theory CCSD(T)-F12 calculations, which
could now be applied even for midsized metal complexes, if only single reference quantum methods
are applicable.