146
L. González et al.
7.1 Introduction
Progress in monitoring and controlling the dynamics of molecules by means of ultrashort femtosecond pulses, and particularly photochemical reactions, has been spectacular over the last thirty years [1–16]. Moreover, the advent of strong pulses [17]
has given access to highly excited states of molecules, increasing the complexity of
the competing photochemical and photophysical processes [18–21] and thus making difficult to interpret the main mechanisms governing the dynamics based on
simple models. Computational photochemistry is indispensable to unravel photoinduced phenomena, since predictions are put forward regarding the paths that are
likely to be followed in a molecule under light irradiation, based on calculated potential energy curves (PES) with the corresponding couplings. However, and despite the inherent difficulties in calculating electronic excited states [22], averaged
kinetic calculations based on the approximate evaluation and counting of the energy
eigenstates of the molecule do not suffice to understand the dynamics driven by ultrashort pulses. In order to predict or understand the outcome of experiments, it is
becoming indispensable to solve the time-dependent Schrödinger equation (TDSE)
for all the electronic and nuclear degrees of freedom in the presence of an external
field, beyond the usual Born-Oppenheimer approximation and weak-field perturbation regime. Unfortunately, an “exact” solution of the TDSE is computationally
intractable except for the simplest systems [23]. The key to achieve successful numerical simulations depends then on the nature and extension of the approximations
that are undertaken to solve this equation. Naturally, these approximations will condition the expected dynamics that is subject to the molecular Hamiltonian and the
laser field.
Several methods, such as the multiconfigurational time-dependent Hartree
method (MCTDH) [24], the multiple spawning approach [25–27] and other techniques [28–36] have emerged in the last years to describe multidimensional dynamics. Not all these methods are able to incorporate the laser field into the dynamics,
but many efforts are being made in this direction [37–44]. An alternative to the
full quantum mechanical solution of the TDSE is the use of semiclassical methods.
A particularly extended approach is ab initio molecular dynamics [45–47] (MD),
where an ensemble of independent semiclassical trajectories is used to describe the
nuclear positions while the electronic structure is treated quantum mechanically,
i.e. with ab initio methods. The most accurate version of this method is indeed the
use of ab initio methods, but it is also possible to couple MD with time-dependent
density functional theory (TD-DFT) or even semiempirical methods. Semiclassical
strategies are particularly popular since they allow a complete full dimensional description of the system under study with by far much less computational effort than
calculating PES and performing wavepacket propagations on them. The electronic
structure calculations in MD are computed on-the-fly. Thus, the cost of such simulations is mainly related to the cost of the level of theory employed for the electronic
structure and of course to the fact that a sufficiently large number of trajectories
is required to obtain reliable quantum yields in the case of competing processes.
In photochemistry, due to non-adiabatic and/or spin-orbit couplings, it is common
L. González et al.
7.1 Introduction
Progress in monitoring and controlling the dynamics of molecules by means of ultrashort femtosecond pulses, and particularly photochemical reactions, has been spectacular over the last thirty years [1–16]. Moreover, the advent of strong pulses [17]
has given access to highly excited states of molecules, increasing the complexity of
the competing photochemical and photophysical processes [18–21] and thus making difficult to interpret the main mechanisms governing the dynamics based on
simple models. Computational photochemistry is indispensable to unravel photoinduced phenomena, since predictions are put forward regarding the paths that are
likely to be followed in a molecule under light irradiation, based on calculated potential energy curves (PES) with the corresponding couplings. However, and despite the inherent difficulties in calculating electronic excited states [22], averaged
kinetic calculations based on the approximate evaluation and counting of the energy
eigenstates of the molecule do not suffice to understand the dynamics driven by ultrashort pulses. In order to predict or understand the outcome of experiments, it is
becoming indispensable to solve the time-dependent Schrödinger equation (TDSE)
for all the electronic and nuclear degrees of freedom in the presence of an external
field, beyond the usual Born-Oppenheimer approximation and weak-field perturbation regime. Unfortunately, an “exact” solution of the TDSE is computationally
intractable except for the simplest systems [23]. The key to achieve successful numerical simulations depends then on the nature and extension of the approximations
that are undertaken to solve this equation. Naturally, these approximations will condition the expected dynamics that is subject to the molecular Hamiltonian and the
laser field.
Several methods, such as the multiconfigurational time-dependent Hartree
method (MCTDH) [24], the multiple spawning approach [25–27] and other techniques [28–36] have emerged in the last years to describe multidimensional dynamics. Not all these methods are able to incorporate the laser field into the dynamics,
but many efforts are being made in this direction [37–44]. An alternative to the
full quantum mechanical solution of the TDSE is the use of semiclassical methods.
A particularly extended approach is ab initio molecular dynamics [45–47] (MD),
where an ensemble of independent semiclassical trajectories is used to describe the
nuclear positions while the electronic structure is treated quantum mechanically,
i.e. with ab initio methods. The most accurate version of this method is indeed the
use of ab initio methods, but it is also possible to couple MD with time-dependent
density functional theory (TD-DFT) or even semiempirical methods. Semiclassical
strategies are particularly popular since they allow a complete full dimensional description of the system under study with by far much less computational effort than
calculating PES and performing wavepacket propagations on them. The electronic
structure calculations in MD are computed on-the-fly. Thus, the cost of such simulations is mainly related to the cost of the level of theory employed for the electronic
structure and of course to the fact that a sufficiently large number of trajectories
is required to obtain reliable quantum yields in the case of competing processes.
In photochemistry, due to non-adiabatic and/or spin-orbit couplings, it is common