268
D. Escudero
evaluating the performance of the different exchange-correlation (xc) functionals are
common in the literature, systematic TD-DFT studies on TMCs are more scattered
and less common, as the attainment of reliable benchmark data is more complicated
in these systems. This makes difficult to develop general recommendations. In general, difficulties at describing on the same footing the ESs of different character have
been described for TD-DFT [3]. In addition, TD-DFT results are often functional
dependent, particularly in the description of long-range CT states and MLCT states.
Among the different xc functionals, it is generally observed that hybrid functionals, and especially those bearing intermediate amounts of exact exchange (such as
B3LYP and PBE0), outperform the rest of pure and range-separated functionals,
which tend to under- and over-estimate, respectively, the excitation energies. This
trend is overall observed for the singlet ESs of positively charged Ru(II), Pt(II),
Os(II), Ir(III), Re(I), Au(I) TMCs (to mention some relevant examples) [3, 63–67].
In contrast, pure functionals might be more suited to treat the ESs of negatively
charged TMCs (bearing, e.g., a Fe(II) and Cr central atom) [63, 68], but also to
generally provide more accurate singlet–triplet gaps, as recently shown in the case
of [Ru(bpy) 3 ]
2+ [69, 70]. Note that if one aims to study the ISC processes, attaining
accurate estimations of singlet–triplet gaps might be more crucial than describing the
UV-Vis is absorption bands with a higher accuracy (this is the reason that the pure
PBE functional is recommended for [Ru(bpy) 3 ]
2+ in [69]). As the inclusion of exact
exchange usually exacerbates the triplet instability problems, and thereto impairing
the accurate calculation of singlet–triplet gaps, an alternative approach is the use
of the Tamm–Dancoff approximation within TD-DFT, which avoids problems with
spurious low-lying triplet ES. In a nutshell, future work should be devoted to evaluate statistical errors and extract further conclusions regarding the performance of
TD-DFT for TMCs.
With the final goal of an effective recovery of correlation effects at a reduced
computational cost, other alternative methods are those combining wave function theory with DFT. Among these methods, three different approaches are highlighted, namely (i) the multi-configuration pair-density DFT (MC-pDFT) method
[71], which it may be considered as a multi-configurational analog of Kohn-Sham
(KS)-DFT, (ii) the MC-srDFT approach [72] of Jensen and coworkers, and (iii)
the DFT/MRCI approach [73]. The latter approach is a DFT-based method for electronically ES that makes use of KS orbitals in a multi-reference configuration interaction (MRCI) framework. Hence, non-dynamic (long-range) correlation effects are
ensured at the MRCI level while KS-DFT captures the dynamic (short-range) electron correlation. While the performance of the MC-pDFT method should still be
explored for describing the ES of TMCs, the DFT/MRCI method appears to be superior as compared with TD-DFT for these types of systems, especially in providing the
correct ordering of their ES and in attaining a balanced description of all type of ES
[62]. A redesigned spin-invariant DFT/MRCI Hamiltonian was recently developed
[74].
SOCs importantly impact the photophysical and photochemical properties of
TMCs. Indeed, without SOCs, the electronically ES of different spin angular moment
would not couple, and thus, the ISC probability in classical terms would be zero [75].
D. Escudero
evaluating the performance of the different exchange-correlation (xc) functionals are
common in the literature, systematic TD-DFT studies on TMCs are more scattered
and less common, as the attainment of reliable benchmark data is more complicated
in these systems. This makes difficult to develop general recommendations. In general, difficulties at describing on the same footing the ESs of different character have
been described for TD-DFT [3]. In addition, TD-DFT results are often functional
dependent, particularly in the description of long-range CT states and MLCT states.
Among the different xc functionals, it is generally observed that hybrid functionals, and especially those bearing intermediate amounts of exact exchange (such as
B3LYP and PBE0), outperform the rest of pure and range-separated functionals,
which tend to under- and over-estimate, respectively, the excitation energies. This
trend is overall observed for the singlet ESs of positively charged Ru(II), Pt(II),
Os(II), Ir(III), Re(I), Au(I) TMCs (to mention some relevant examples) [3, 63–67].
In contrast, pure functionals might be more suited to treat the ESs of negatively
charged TMCs (bearing, e.g., a Fe(II) and Cr central atom) [63, 68], but also to
generally provide more accurate singlet–triplet gaps, as recently shown in the case
of [Ru(bpy) 3 ]
2+ [69, 70]. Note that if one aims to study the ISC processes, attaining
accurate estimations of singlet–triplet gaps might be more crucial than describing the
UV-Vis is absorption bands with a higher accuracy (this is the reason that the pure
PBE functional is recommended for [Ru(bpy) 3 ]
2+ in [69]). As the inclusion of exact
exchange usually exacerbates the triplet instability problems, and thereto impairing
the accurate calculation of singlet–triplet gaps, an alternative approach is the use
of the Tamm–Dancoff approximation within TD-DFT, which avoids problems with
spurious low-lying triplet ES. In a nutshell, future work should be devoted to evaluate statistical errors and extract further conclusions regarding the performance of
TD-DFT for TMCs.
With the final goal of an effective recovery of correlation effects at a reduced
computational cost, other alternative methods are those combining wave function theory with DFT. Among these methods, three different approaches are highlighted, namely (i) the multi-configuration pair-density DFT (MC-pDFT) method
[71], which it may be considered as a multi-configurational analog of Kohn-Sham
(KS)-DFT, (ii) the MC-srDFT approach [72] of Jensen and coworkers, and (iii)
the DFT/MRCI approach [73]. The latter approach is a DFT-based method for electronically ES that makes use of KS orbitals in a multi-reference configuration interaction (MRCI) framework. Hence, non-dynamic (long-range) correlation effects are
ensured at the MRCI level while KS-DFT captures the dynamic (short-range) electron correlation. While the performance of the MC-pDFT method should still be
explored for describing the ES of TMCs, the DFT/MRCI method appears to be superior as compared with TD-DFT for these types of systems, especially in providing the
correct ordering of their ES and in attaining a balanced description of all type of ES
[62]. A redesigned spin-invariant DFT/MRCI Hamiltonian was recently developed
[74].
SOCs importantly impact the photophysical and photochemical properties of
TMCs. Indeed, without SOCs, the electronically ES of different spin angular moment
would not couple, and thus, the ISC probability in classical terms would be zero [75].