Photodeactivation Channels of Transition Metal Complexes …
267
regime (Sect. 3.2) but also longer timescales including long-lived phosphorescence
(Sects. 3.1 and 3.3). Finally, Sect. 4 is devoted for conclusions and outlook.
2 State-of-the-Art Theoretical and Computational Methods
for the Study of the ES Deactivation Channels of TMCs
This section is split into three subsections, and it covers in the following order the
state-of-the-art quantum chemical methods for the ES and computational techniques
to study the ES PES (Sect. 2.1), ES decay rate theories (Sect. 2.2), and ES reaction dynamic methods (Sect. 2.3). The objective of this section is not to present an
exhaustive description of these methods, as this topic has extensively been covered
elsewhere [3, 9, 40], but to present a concise overview that focuses on the recent
advances in theoretical and computational methods to describe the ES of TMCs.
2.1 Quantum Chemical Methods for the ES
As highlighted in Sect. 1, the accurate description of the ESs of TMCs poses significant challenges, as these systems concentrate multiple complexities inherent to their
theoretical study (e.g., relativistic effects, near degeneracies, high density of ESs
of various spins and characters). Due to their capability to recover large amounts
of dynamic and non-dynamic electron correlation, multi-configurational wave function approaches, such as the complete-active-space second-order perturbation theory
(CASPT2) [49] and the restricted-active-space PT2 (RASPT2) [50] methods, are
capable to deal with all kinds of electronic structures, including the complex ESs of
TMCs. In fact, the errors of these methods for vertical excitation energies are generally well below 0.3 eV for TMCs, and within 0.15 eV for most of the cases [51, 52].
However, these methods have not yet acquired a black-box status, since (i) the selection of a chemically sound active space is not always straightforward, and (ii) their
computational cost still restricts their use for medium- and large-size TMCs, which
require the use of very large active spaces. To alleviate the first problem, general rules
and even automatic approaches have been developed to choose a chemically sound
active space for TMCs [53–55]. The second problem has a less likely solution within
these approaches. However, recent advances on the use of matrix renormalization
group (DMRG) [56, 57] and quantum Monte Carlo [58] linked to CASPT2 permit
the study in practical terms of large TMCs with 30–50 active orbitals [59, 60].
Methods based on DFT, such as constricted variational DFT (CV-DFT) [61],
spin-flip and/or SCF-DFT [62], and TD-DFT in its linear response version [29],
appear as computationally cheaper alternatives to treat the ES of TMCs, but they are
generally less accurate than multi-configurational methods. In opposition to organic
molecules, for which abundant benchmark data, and systematic TD-DFT studies
267
regime (Sect. 3.2) but also longer timescales including long-lived phosphorescence
(Sects. 3.1 and 3.3). Finally, Sect. 4 is devoted for conclusions and outlook.
2 State-of-the-Art Theoretical and Computational Methods
for the Study of the ES Deactivation Channels of TMCs
This section is split into three subsections, and it covers in the following order the
state-of-the-art quantum chemical methods for the ES and computational techniques
to study the ES PES (Sect. 2.1), ES decay rate theories (Sect. 2.2), and ES reaction dynamic methods (Sect. 2.3). The objective of this section is not to present an
exhaustive description of these methods, as this topic has extensively been covered
elsewhere [3, 9, 40], but to present a concise overview that focuses on the recent
advances in theoretical and computational methods to describe the ES of TMCs.
2.1 Quantum Chemical Methods for the ES
As highlighted in Sect. 1, the accurate description of the ESs of TMCs poses significant challenges, as these systems concentrate multiple complexities inherent to their
theoretical study (e.g., relativistic effects, near degeneracies, high density of ESs
of various spins and characters). Due to their capability to recover large amounts
of dynamic and non-dynamic electron correlation, multi-configurational wave function approaches, such as the complete-active-space second-order perturbation theory
(CASPT2) [49] and the restricted-active-space PT2 (RASPT2) [50] methods, are
capable to deal with all kinds of electronic structures, including the complex ESs of
TMCs. In fact, the errors of these methods for vertical excitation energies are generally well below 0.3 eV for TMCs, and within 0.15 eV for most of the cases [51, 52].
However, these methods have not yet acquired a black-box status, since (i) the selection of a chemically sound active space is not always straightforward, and (ii) their
computational cost still restricts their use for medium- and large-size TMCs, which
require the use of very large active spaces. To alleviate the first problem, general rules
and even automatic approaches have been developed to choose a chemically sound
active space for TMCs [53–55]. The second problem has a less likely solution within
these approaches. However, recent advances on the use of matrix renormalization
group (DMRG) [56, 57] and quantum Monte Carlo [58] linked to CASPT2 permit
the study in practical terms of large TMCs with 30–50 active orbitals [59, 60].
Methods based on DFT, such as constricted variational DFT (CV-DFT) [61],
spin-flip and/or SCF-DFT [62], and TD-DFT in its linear response version [29],
appear as computationally cheaper alternatives to treat the ES of TMCs, but they are
generally less accurate than multi-configurational methods. In opposition to organic
molecules, for which abundant benchmark data, and systematic TD-DFT studies