metal trifluorides [88] and to ultra-fast excited states dynamics in Cu
(I) phenanthroline complexes [89] illustrate the potential of the (spin)-vibronic
coupling multimode quantum dynamics in this field of research.
2.3 Intersystem Crossings
Ultrafast intersystem crossing (ISC) processes coupled to nuclear relaxation and
solvation dynamics play a central role in the photophysics and photochemistry of a
wide range of transition metal complexes [27–32, 89–97]. These phenomena are
investigated experimentally by ultrafast picosecond (ps) and femtosecond
(fs) transient absorption or luminescence spectroscopies, and optical laser pumpX-ray probe techniques using ps and fs X-ray pulses. Again, we are facing the
determination of multi-dimensional PES associated with various multiplet electronic excited states and with simultaneous treatment of vibronic and spin-orbit
couplings which control ultrafast intramolecular relaxation and photophysical
decays.
The qualitative rules such as El-Sayed [98] or energy gap law [99, 100] are of no
help for the determination of the kinetics of ISC in this context. The golden rule
approximation is adapted to organic systems with a limited number of interacting
states, typically S 1 /T 1 where the SOC is small compared to their adiabatic energy
difference [56] (and references therein). Alternatively, ISC rates can be determined
assuming direct spin-orbit coupling with separation of electronic and vibrational
contributions within the Condon approximation based on harmonic potentials. In
contrast to the time-independent approach which requires the computation of the
Franck–Condon integrals, the recently developed time-dependent formalism [101,
102] is especially adapted to the treatment of ISC in large molecules with a high
number of degrees of freedom and large adiabatic electronic energy differences.
This is illustrated by recent applications, both in organic and inorganic systems [90,
103].
The determination of ultra-fast ISC kinetics by means of direct quantum dynamical simulation of a cascade of transitions via several electronic states of different
multiplicities is based on wavepacket propagations on spin-vibronic coupled multidimensional PES. Various methods of electronic structure theory available for
transition metal complexes, among them the most popular TD-DFT approach, are
able to compute electronic excited states and associated nuclear forces with reasonable accuracy. The bottleneck is the computation of accurate multi-dimensional
PES, seat of the ultra-fast dynamics observed in time-resolved experiments. To
bypass these difficulties two strategies can be considered: (1) ab initio molecular
dynamics where efficient electronic structure methods are coupled to classical
trajectory-based approaches [104] (and reference therein); and (2) quantum dynamics where both electronic and nuclear wave functions are treated exactly within a
given level of approximation [84, 105–107].
Molecular dynamics, usually coupled with DFT methods and extended recently
to the non-adiabatic regime [104, 108, 109] is adapted to large systems involving a
384
C. Daniel
(I) phenanthroline complexes [89] illustrate the potential of the (spin)-vibronic
coupling multimode quantum dynamics in this field of research.
2.3 Intersystem Crossings
Ultrafast intersystem crossing (ISC) processes coupled to nuclear relaxation and
solvation dynamics play a central role in the photophysics and photochemistry of a
wide range of transition metal complexes [27–32, 89–97]. These phenomena are
investigated experimentally by ultrafast picosecond (ps) and femtosecond
(fs) transient absorption or luminescence spectroscopies, and optical laser pumpX-ray probe techniques using ps and fs X-ray pulses. Again, we are facing the
determination of multi-dimensional PES associated with various multiplet electronic excited states and with simultaneous treatment of vibronic and spin-orbit
couplings which control ultrafast intramolecular relaxation and photophysical
decays.
The qualitative rules such as El-Sayed [98] or energy gap law [99, 100] are of no
help for the determination of the kinetics of ISC in this context. The golden rule
approximation is adapted to organic systems with a limited number of interacting
states, typically S 1 /T 1 where the SOC is small compared to their adiabatic energy
difference [56] (and references therein). Alternatively, ISC rates can be determined
assuming direct spin-orbit coupling with separation of electronic and vibrational
contributions within the Condon approximation based on harmonic potentials. In
contrast to the time-independent approach which requires the computation of the
Franck–Condon integrals, the recently developed time-dependent formalism [101,
102] is especially adapted to the treatment of ISC in large molecules with a high
number of degrees of freedom and large adiabatic electronic energy differences.
This is illustrated by recent applications, both in organic and inorganic systems [90,
103].
The determination of ultra-fast ISC kinetics by means of direct quantum dynamical simulation of a cascade of transitions via several electronic states of different
multiplicities is based on wavepacket propagations on spin-vibronic coupled multidimensional PES. Various methods of electronic structure theory available for
transition metal complexes, among them the most popular TD-DFT approach, are
able to compute electronic excited states and associated nuclear forces with reasonable accuracy. The bottleneck is the computation of accurate multi-dimensional
PES, seat of the ultra-fast dynamics observed in time-resolved experiments. To
bypass these difficulties two strategies can be considered: (1) ab initio molecular
dynamics where efficient electronic structure methods are coupled to classical
trajectory-based approaches [104] (and reference therein); and (2) quantum dynamics where both electronic and nuclear wave functions are treated exactly within a
given level of approximation [84, 105–107].
Molecular dynamics, usually coupled with DFT methods and extended recently
to the non-adiabatic regime [104, 108, 109] is adapted to large systems involving a
384
C. Daniel