Top Curr Chem (Z) (2018) 376:24
1 3
computations and non-adiabatic quantum dynamics simulations to resolve the
elaborate nonlinear response equations. On one hand, the practical use of quantum
dynamics makes it possible to accurately model spectral dynamics while relying
only on approximate electronic potentials, capturing just the essence of the electronic structure complexity, which is reflected in the absence of ESA contributions.
On the other hand, the electronic structure complexity can be straightforwardly
incorporated within a static approach, recovering ESA contributions. However, as
dynamics are neglected, this approach is not able to provide realistic spectral line
shapes. Trajectory-based approaches offer a compromise by permitting us to adjust
the level of precision applied to molecular dynamics and PES sampling. In the following section, we begin our discussion by utilizing the static approach to outline
a protocol for the accurate computation of transition energies and dipole moments
(Sect. 3.1), as well as for benchmarking low-cost methods. Sections 3.2 and 3.3
demonstrate how the latter can be employed to study GS conformational dynamics
of oligopeptides and DNA nucleobase dimers within the framework of the SOS//
QM/MM protocol. We then go beyond the static approximation and re-introduce
dynamic features in Eqs. 14 and 15 within the CGF framework for the study of
excited states. Specifically, coherent intramolecular vibrational dynamics is discussed in Sect. 3.3, while Sect. 3.4 covers population transfer.
4.1 Benchmarking the Excited‑State Manifolds
Accurate prediction of the basic spectroscopic parameters that define the space of
electronic transitions (i.e. TEs and TDMs) accessible by 2DES experiments is the
first computational challenge. The excited-state manifolds of UV-active chromophores in the 2DUV energy range (from ca. 3.5 to 11 eV) comprise various types of
electronic transitions, generally including single and double excitations with local
or (inter- and intramolecular) charge-transfer character, and thus involving covalent as well as ionic (valence bond-like) excited states. Wave function approaches
introduced in the 1980s, based on the combination of CASSCF multi-configurational wave functions [64] and PT2 perturbative energy corrections [65] (CASSCF//
CASPT2), currently represent the most widely used methodology for handling such
a variety of excited states on equal footing [66], generally providing good quantitative predictions of TEs and TDMs, with expected error of around 0.2 eV (ca.
1600 cm
−1
). Application of the CASSCF//CASPT2 methodology to larger and larger
molecules has become possible through many developments over the years, including the implementation of the restricted active space self-consistent field (RASSCF)
methodology [67], efficient approximations for two-electron integral estimates [68]
and large-scale parallelization [69], to cite some of those most widely used in the
results reported here. The single-state PT2 treatment (hereafter “PT2”) has likely
been preferred to the more expensive (and in most cases infeasible) multistate PT2
approach. However, the accuracy of CASSCF//PT2 predictions strongly depends
on the choice of active spaces and basis sets, two parameters that involve a critical
increase in computational cost. Moreover, the number of excited states present in
76
Reprinted from the journal
1 3
computations and non-adiabatic quantum dynamics simulations to resolve the
elaborate nonlinear response equations. On one hand, the practical use of quantum
dynamics makes it possible to accurately model spectral dynamics while relying
only on approximate electronic potentials, capturing just the essence of the electronic structure complexity, which is reflected in the absence of ESA contributions.
On the other hand, the electronic structure complexity can be straightforwardly
incorporated within a static approach, recovering ESA contributions. However, as
dynamics are neglected, this approach is not able to provide realistic spectral line
shapes. Trajectory-based approaches offer a compromise by permitting us to adjust
the level of precision applied to molecular dynamics and PES sampling. In the following section, we begin our discussion by utilizing the static approach to outline
a protocol for the accurate computation of transition energies and dipole moments
(Sect. 3.1), as well as for benchmarking low-cost methods. Sections 3.2 and 3.3
demonstrate how the latter can be employed to study GS conformational dynamics
of oligopeptides and DNA nucleobase dimers within the framework of the SOS//
QM/MM protocol. We then go beyond the static approximation and re-introduce
dynamic features in Eqs. 14 and 15 within the CGF framework for the study of
excited states. Specifically, coherent intramolecular vibrational dynamics is discussed in Sect. 3.3, while Sect. 3.4 covers population transfer.
4.1 Benchmarking the Excited‑State Manifolds
Accurate prediction of the basic spectroscopic parameters that define the space of
electronic transitions (i.e. TEs and TDMs) accessible by 2DES experiments is the
first computational challenge. The excited-state manifolds of UV-active chromophores in the 2DUV energy range (from ca. 3.5 to 11 eV) comprise various types of
electronic transitions, generally including single and double excitations with local
or (inter- and intramolecular) charge-transfer character, and thus involving covalent as well as ionic (valence bond-like) excited states. Wave function approaches
introduced in the 1980s, based on the combination of CASSCF multi-configurational wave functions [64] and PT2 perturbative energy corrections [65] (CASSCF//
CASPT2), currently represent the most widely used methodology for handling such
a variety of excited states on equal footing [66], generally providing good quantitative predictions of TEs and TDMs, with expected error of around 0.2 eV (ca.
1600 cm
−1
). Application of the CASSCF//CASPT2 methodology to larger and larger
molecules has become possible through many developments over the years, including the implementation of the restricted active space self-consistent field (RASSCF)
methodology [67], efficient approximations for two-electron integral estimates [68]
and large-scale parallelization [69], to cite some of those most widely used in the
results reported here. The single-state PT2 treatment (hereafter “PT2”) has likely
been preferred to the more expensive (and in most cases infeasible) multistate PT2
approach. However, the accuracy of CASSCF//PT2 predictions strongly depends
on the choice of active spaces and basis sets, two parameters that involve a critical
increase in computational cost. Moreover, the number of excited states present in
76
Reprinted from the journal