multiconfiguration quasi-degenerate perturbation theory (MCQDPT) and used with
success for transition metal complexes [70, 71].
Whereas in nonrelativistic theory the eigenstates form a basis for an irreducible
representation of the molecular point group, the eigenstates of the spin-orbit
operator form a basis for an irreducible representation of the molecular point double
group [72].
When introducing spin-orbit interaction, spin eigenfunctions are affected by
symmetry operations and cannot be described in general by any of the symmetry
operations permitted by the point group of the molecule. The extension of molecular point group to molecular point double group representation by additional
symmetry elements associated with spin eigenfunctions allows the description of
multiplet non-degenerate eigenstates, so-called fine structure, generated by spinorbit splitting. For a discussion on the calculation of spin-orbit splitting in transition
metal atoms at various levels of approximation, one can refer to [73, 74].
Two ingredients are particularly important when discussing transition metal
complexes’ optical properties, namely the SOC terms and the spin-orbit splitting
of the triplet states. Whereas splitting is usually small and can appear as a perturbation, the SOC values may vary from a few tens of cm
À1 to 1,000 cm
À1 . However,
the heavy atom effect is not always operating simply because of the molecular
character of the electronic states that are delocalized over the ligands. This has
important consequences on the absorption spectroscopy and photophysics of transition metal complexes as illustrated in recent applications [26, 75–83] and examples discussed in Sects. 3–5.
2.2 Vibronic Couplings
An additional difficulty in transition metal complexes is the simultaneous treatment
of vibronic and spin-orbit couplings, sometimes together with Jahn–Teller
(JT) effects. Indeed, the interplay between these effects contributes to the structural
characteristics of the electronic spectra and cannot be neglected for a meaningful
comparison between experimental and computed absorption spectra [84, 85]. Of
course this is true for all kind of molecules but more crucial for transition metal
complexes as shown by the vibronic structure of the well-resolved experimental
spectrum of the permanganate anion MnO 4
À already available in the 1960s, but
hardly assigned by the most accurate methods of quantum chemistry [86]. Another
illustration is given by the combined effects of Jahn–Teller (JT) and SOC on the
adiabatic PES and electronic spectra of a series of first-row transition metal halides
MF 3 (M ¼ Mn, Co, Ti, Cr, and Ni) recently investigated from first-principles
methods based on the derivation of a Hamiltonian expanded up to linear, quadratic,
and higher order in normal modes displacements active for JT distortions and
including spin-orbits up to first order in these modes [87]. This original work has
put in evidence spin-orbit-induced JT distortions not detectable by the standard
382
C. Daniel
success for transition metal complexes [70, 71].
Whereas in nonrelativistic theory the eigenstates form a basis for an irreducible
representation of the molecular point group, the eigenstates of the spin-orbit
operator form a basis for an irreducible representation of the molecular point double
group [72].
When introducing spin-orbit interaction, spin eigenfunctions are affected by
symmetry operations and cannot be described in general by any of the symmetry
operations permitted by the point group of the molecule. The extension of molecular point group to molecular point double group representation by additional
symmetry elements associated with spin eigenfunctions allows the description of
multiplet non-degenerate eigenstates, so-called fine structure, generated by spinorbit splitting. For a discussion on the calculation of spin-orbit splitting in transition
metal atoms at various levels of approximation, one can refer to [73, 74].
Two ingredients are particularly important when discussing transition metal
complexes’ optical properties, namely the SOC terms and the spin-orbit splitting
of the triplet states. Whereas splitting is usually small and can appear as a perturbation, the SOC values may vary from a few tens of cm
À1 to 1,000 cm
À1 . However,
the heavy atom effect is not always operating simply because of the molecular
character of the electronic states that are delocalized over the ligands. This has
important consequences on the absorption spectroscopy and photophysics of transition metal complexes as illustrated in recent applications [26, 75–83] and examples discussed in Sects. 3–5.
2.2 Vibronic Couplings
An additional difficulty in transition metal complexes is the simultaneous treatment
of vibronic and spin-orbit couplings, sometimes together with Jahn–Teller
(JT) effects. Indeed, the interplay between these effects contributes to the structural
characteristics of the electronic spectra and cannot be neglected for a meaningful
comparison between experimental and computed absorption spectra [84, 85]. Of
course this is true for all kind of molecules but more crucial for transition metal
complexes as shown by the vibronic structure of the well-resolved experimental
spectrum of the permanganate anion MnO 4
À already available in the 1960s, but
hardly assigned by the most accurate methods of quantum chemistry [86]. Another
illustration is given by the combined effects of Jahn–Teller (JT) and SOC on the
adiabatic PES and electronic spectra of a series of first-row transition metal halides
MF 3 (M ¼ Mn, Co, Ti, Cr, and Ni) recently investigated from first-principles
methods based on the derivation of a Hamiltonian expanded up to linear, quadratic,
and higher order in normal modes displacements active for JT distortions and
including spin-orbits up to first order in these modes [87]. This original work has
put in evidence spin-orbit-induced JT distortions not detectable by the standard
382
C. Daniel