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D. Escudero
the ES dynamics, and in principle, more accurate rates calculations can be derived
from these simulations. Two suites of reaction dynamic methods are generally used
to follow the fate of ES, namely quantum wavepacket dynamics and on-the-fly nonadiabatic molecular dynamics. For an exhaustive description of these methods, the
readers are referred to exceptional reviews on the field [9, 40].
Let us start the discussion with quantum dynamics. The multi-configuration timedependent Hartree (MCTDH) method [92] belongs to this class of methods and it is
especially well suited to treat cases where strong vibronic and/or SOCs applies. This
is because the equations of motion in the MCTDH method are purely derived from
quantum mechanics. In addition, purely quantum effects like tunneling are inherently
described. In MCTDH, one should build model PES before running the dynamic simulations, and thus, these methods require a prior evaluation of the important electronic
and nuclear degrees of freedom. Although these simulations have not yet acquired
a routine status, MCTDH simulations have already provided important insights into
the photodeactivation dynamics of TMCs. Notably, a MCTDH study of Daniel and
coworkers in the [Re(bpy)(CO) 3 (X)] (where X Br, I) series [83, 93], highlighted
that a spin-vibronic mechanism involving several intermediate singlet and triplet
states of different characters is responsible for the counterintuitive heavy atom effect
measured experimentally, namely a faster decay for the bromine substituted complex
as compared to the iodine substituted one. The computed lifetimes for the ultrafast
decay to T 1 agree well with the measured evidence. Regarding its future prospects,
the biggest challenge for MCTDH is to calculate the multidimensional PES, as there
is a limitation in the number of nuclear degrees of freedom (DOFs) to account for,
and importantly, these DOFs are often approximated as harmonic potentials. These
approximations might be insufficient to treat large TMCs and especially, to treat
large geometrical deformations (e.g., ligand dissociation), which are not uncommon
in TMCs photochemistry. Additionally, it is challenging to propagate these dynamic
beyond the picosecond regime.
Conversely, nonadiabatic on-the-fly molecular dynamics offer the possibility
to perform simulations on full-dimensional PES. This is so because these mixed
classical-quantum approaches are based on trajectories (which can be easily parallelized, as each trajectory is independent of the ensemble), where the nuclei are
propagated classically following Newton’s equations of motion and the electronic
properties (e.g., energies, gradients, SOCs, and nonadiabatic couplings) are computed on-the-fly at each time step and only when it is required, and hence reducing
the computational efforts as compared to quantum dynamic approaches. Among such
methods, fewest switches Tully’s trajectory surface hopping (TSH) [94] is one of the
most commonly used approaches. The initial formulation of the TSH algorithm has
been recently expanded to treat both SOCs and nonadiabatic dynamical effects, such
as in the SHARC suite of programs developed by González and coworkers [95, 96],
and hence giving access to model ISC processes. In TSH approaches, the nonadiabatic population transfer occurring between the PES, and which is strictly forbidden
within a classical dynamics framework, is conducted using an stochastical algorithm
which is controlled by the nonadiabatic couplings and SOCs. The main drawbacks
of these methods are that purely quantum effects such as quantum tunneling and/or
D. Escudero
the ES dynamics, and in principle, more accurate rates calculations can be derived
from these simulations. Two suites of reaction dynamic methods are generally used
to follow the fate of ES, namely quantum wavepacket dynamics and on-the-fly nonadiabatic molecular dynamics. For an exhaustive description of these methods, the
readers are referred to exceptional reviews on the field [9, 40].
Let us start the discussion with quantum dynamics. The multi-configuration timedependent Hartree (MCTDH) method [92] belongs to this class of methods and it is
especially well suited to treat cases where strong vibronic and/or SOCs applies. This
is because the equations of motion in the MCTDH method are purely derived from
quantum mechanics. In addition, purely quantum effects like tunneling are inherently
described. In MCTDH, one should build model PES before running the dynamic simulations, and thus, these methods require a prior evaluation of the important electronic
and nuclear degrees of freedom. Although these simulations have not yet acquired
a routine status, MCTDH simulations have already provided important insights into
the photodeactivation dynamics of TMCs. Notably, a MCTDH study of Daniel and
coworkers in the [Re(bpy)(CO) 3 (X)] (where X Br, I) series [83, 93], highlighted
that a spin-vibronic mechanism involving several intermediate singlet and triplet
states of different characters is responsible for the counterintuitive heavy atom effect
measured experimentally, namely a faster decay for the bromine substituted complex
as compared to the iodine substituted one. The computed lifetimes for the ultrafast
decay to T 1 agree well with the measured evidence. Regarding its future prospects,
the biggest challenge for MCTDH is to calculate the multidimensional PES, as there
is a limitation in the number of nuclear degrees of freedom (DOFs) to account for,
and importantly, these DOFs are often approximated as harmonic potentials. These
approximations might be insufficient to treat large TMCs and especially, to treat
large geometrical deformations (e.g., ligand dissociation), which are not uncommon
in TMCs photochemistry. Additionally, it is challenging to propagate these dynamic
beyond the picosecond regime.
Conversely, nonadiabatic on-the-fly molecular dynamics offer the possibility
to perform simulations on full-dimensional PES. This is so because these mixed
classical-quantum approaches are based on trajectories (which can be easily parallelized, as each trajectory is independent of the ensemble), where the nuclei are
propagated classically following Newton’s equations of motion and the electronic
properties (e.g., energies, gradients, SOCs, and nonadiabatic couplings) are computed on-the-fly at each time step and only when it is required, and hence reducing
the computational efforts as compared to quantum dynamic approaches. Among such
methods, fewest switches Tully’s trajectory surface hopping (TSH) [94] is one of the
most commonly used approaches. The initial formulation of the TSH algorithm has
been recently expanded to treat both SOCs and nonadiabatic dynamical effects, such
as in the SHARC suite of programs developed by González and coworkers [95, 96],
and hence giving access to model ISC processes. In TSH approaches, the nonadiabatic population transfer occurring between the PES, and which is strictly forbidden
within a classical dynamics framework, is conducted using an stochastical algorithm
which is controlled by the nonadiabatic couplings and SOCs. The main drawbacks
of these methods are that purely quantum effects such as quantum tunneling and/or