in different fields, and to predict new properties with potential technological
applications.
There are a relatively large number of methods for excited-state calculations
available. They include wavefunction-based and density-functional-based methods
derived from different approaches, such as configuration interaction, perturbation
theory, and coupled cluster; and providing different approximation levels, from
semiempirical to fully first principles, from single-reference to multireference, from
short truncated spaces to complete configurational expansions. Each of these
methods and their hybrid combinations has its own domain of applicability
depending on the nature and size of the molecular system. For this very reason,
none of them can be expected to perform equally well for every problem without
exception.
Extensive benchmarks of excitation energies have shown that most of methods
present mean deviation errors of about 0.2–0.3 eV for vertical excitation energies
[1–5]. Not only are such values of the order of magnitude of many reaction barriers,
but also these errors are unevenly distributed among several states for the same
method and tend to grow bigger out of the Franck–Condon region. Well known
examples are the relatively large errors of the energy of ionic states predicted by
truncated ab initio configuration interaction [6] or of the energy of charge-transfer
states of time-dependent density functional theory with conventional
functionals [7].
The root of this problem rests on the very nature of electronic excitations.
Electronically-excited states lie close to each other in the energy spectrum and
relatively small variations in the molecular geometry may lead to their reordering.
Moreover, the characters of these states may be extremely different: from diffuse
Rydberg, through charge-transfer, to spatially localized densities.
Given these features, a basic requirement for a proper computational description
of an excited-state phenomenon is that the theoretical model should describe
different types of states for different nuclear geometries on the same footing. At
this moment, this is a requirement that no single method can fully and affordably
satisfy. The consequence is that the simulations often deliver an unbalanced
description of the electronic states, with deep implications on the reliability of
predictions.
This problem is under relative control in static simulation of reaction pathways,
where only a few degrees of freedom are considered. In dynamics simulations,
however, it may grow out of control because of the much greater number of degrees
of freedom and variables (now, time among them) to tackle.
Besides the question of the accuracy of the potential energy surfaces, dynamics
simulations add two new layers of potential complications to the simulations: first,
nonadiabatic phenomena [8, 9], originated by the coupling of nuclear and electronic
degrees of freedom during the dynamics propagation, must be taken into account;
second, the dynamics propagation itself multiplies the computational costs.
Again, several methods are available for nonadiabatic excited-state dynamics
simulations, from full propagation of the electronic wavefunctions [10], which
requires predefinition of multidimensional potential energy surfaces, to
Surface Hopping Dynamics with DFT Excited States
417
applications.
There are a relatively large number of methods for excited-state calculations
available. They include wavefunction-based and density-functional-based methods
derived from different approaches, such as configuration interaction, perturbation
theory, and coupled cluster; and providing different approximation levels, from
semiempirical to fully first principles, from single-reference to multireference, from
short truncated spaces to complete configurational expansions. Each of these
methods and their hybrid combinations has its own domain of applicability
depending on the nature and size of the molecular system. For this very reason,
none of them can be expected to perform equally well for every problem without
exception.
Extensive benchmarks of excitation energies have shown that most of methods
present mean deviation errors of about 0.2–0.3 eV for vertical excitation energies
[1–5]. Not only are such values of the order of magnitude of many reaction barriers,
but also these errors are unevenly distributed among several states for the same
method and tend to grow bigger out of the Franck–Condon region. Well known
examples are the relatively large errors of the energy of ionic states predicted by
truncated ab initio configuration interaction [6] or of the energy of charge-transfer
states of time-dependent density functional theory with conventional
functionals [7].
The root of this problem rests on the very nature of electronic excitations.
Electronically-excited states lie close to each other in the energy spectrum and
relatively small variations in the molecular geometry may lead to their reordering.
Moreover, the characters of these states may be extremely different: from diffuse
Rydberg, through charge-transfer, to spatially localized densities.
Given these features, a basic requirement for a proper computational description
of an excited-state phenomenon is that the theoretical model should describe
different types of states for different nuclear geometries on the same footing. At
this moment, this is a requirement that no single method can fully and affordably
satisfy. The consequence is that the simulations often deliver an unbalanced
description of the electronic states, with deep implications on the reliability of
predictions.
This problem is under relative control in static simulation of reaction pathways,
where only a few degrees of freedom are considered. In dynamics simulations,
however, it may grow out of control because of the much greater number of degrees
of freedom and variables (now, time among them) to tackle.
Besides the question of the accuracy of the potential energy surfaces, dynamics
simulations add two new layers of potential complications to the simulations: first,
nonadiabatic phenomena [8, 9], originated by the coupling of nuclear and electronic
degrees of freedom during the dynamics propagation, must be taken into account;
second, the dynamics propagation itself multiplies the computational costs.
Again, several methods are available for nonadiabatic excited-state dynamics
simulations, from full propagation of the electronic wavefunctions [10], which
requires predefinition of multidimensional potential energy surfaces, to
Surface Hopping Dynamics with DFT Excited States
417