semiclassical approximations, which reduce the wavefunction propagation to
ensembles of independent trajectories based only on local properties [11]. In
particular, the independent-trajectory approximation, essential to the surface hopping approach, cannot predict nonlocal quantum effects, such as tunneling, quantum phases, or decoherence [8, 12, 13]. Moreover, the statistical ensembles are
often of too reduced size to comply with the computational capabilities, leading to
high statistical uncertainties [14]. (For recent discussions on nonadiabatic dynamics
beyond the independent-trajectories approach, see [15–17].)
From the point of view of semiclassical nonadiabatic excited-state dynamics
simulations, the ideal method for electronic structure calculations should satisfy the
following criteria:
1. Be computationally fast
2. Provide energies for excited states of different natures with similar accuracy
3. Provide reliable (preferentially analytical) gradients for excited states
4. Allow the computation of electronic structures near intersection seams with the
ground state
5. Allow the computation of electronic structures near intersection seams between
excited states
6. Be independent of human intervention for running large ensembles of different
geometries
With different accuracies, methods for excited-states computation based on DFT
comply with most of these criteria, especially computational efficiency. These
methods, however, usually fail criterion 4, the description of the crossing seam
with the ground state. Nevertheless, still considering the pros and cons, surface
hopping based on DFT excitations (SH/DFT) is a good alternative for nonadiabatic
simulations, on condition that it is applied critically, bearing in mind all these
restrictions and limitations.
In this contribution, we examine the current situation of the SH/DFT methods,
starting with a review of surface hopping in Sect. 2. In Sect. 3 we address the
methods for computing the excited state in the DFT framework, especially focusing
on the linear-response time-dependent methodology and its relation to lower-level
methods (Sect. 3.1). In Sect. 3.2 we review the computation of nonadiabatic
couplings in DFT. In Sect. 3.3 the limitations of the method in the context of
dynamics simulations are critically addressed. In Sect. 4 the elements from Sects. 2
and 3 are put together to discuss the different SH/DFT implementations. Finally, in
Sect. 5 we present a series of case studies showing the potentials and limitations of
using SH/DFT in diverse fields.
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M. Barbatti and R. Crespo-Otero
ensembles of independent trajectories based only on local properties [11]. In
particular, the independent-trajectory approximation, essential to the surface hopping approach, cannot predict nonlocal quantum effects, such as tunneling, quantum phases, or decoherence [8, 12, 13]. Moreover, the statistical ensembles are
often of too reduced size to comply with the computational capabilities, leading to
high statistical uncertainties [14]. (For recent discussions on nonadiabatic dynamics
beyond the independent-trajectories approach, see [15–17].)
From the point of view of semiclassical nonadiabatic excited-state dynamics
simulations, the ideal method for electronic structure calculations should satisfy the
following criteria:
1. Be computationally fast
2. Provide energies for excited states of different natures with similar accuracy
3. Provide reliable (preferentially analytical) gradients for excited states
4. Allow the computation of electronic structures near intersection seams with the
ground state
5. Allow the computation of electronic structures near intersection seams between
excited states
6. Be independent of human intervention for running large ensembles of different
geometries
With different accuracies, methods for excited-states computation based on DFT
comply with most of these criteria, especially computational efficiency. These
methods, however, usually fail criterion 4, the description of the crossing seam
with the ground state. Nevertheless, still considering the pros and cons, surface
hopping based on DFT excitations (SH/DFT) is a good alternative for nonadiabatic
simulations, on condition that it is applied critically, bearing in mind all these
restrictions and limitations.
In this contribution, we examine the current situation of the SH/DFT methods,
starting with a review of surface hopping in Sect. 2. In Sect. 3 we address the
methods for computing the excited state in the DFT framework, especially focusing
on the linear-response time-dependent methodology and its relation to lower-level
methods (Sect. 3.1). In Sect. 3.2 we review the computation of nonadiabatic
couplings in DFT. In Sect. 3.3 the limitations of the method in the context of
dynamics simulations are critically addressed. In Sect. 4 the elements from Sects. 2
and 3 are put together to discuss the different SH/DFT implementations. Finally, in
Sect. 5 we present a series of case studies showing the potentials and limitations of
using SH/DFT in diverse fields.
418
M. Barbatti and R. Crespo-Otero