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Top Curr Chem (Z) (2018) 376:24
Thus far, we have reviewed the benchmark studies of the aromatic protein
chromophores and the canonical nucleobases of DNA and RNA (with the exception
of Gua, which is a work in progress), aimed at obtaining converged results among
the highest (still computationally feasible) levels of multi-configurational treatment
for each chromophore so that reference theoretical data are made available. These
reference transition energies and dipole moments could indeed be used both as
ab initio parameters in exciton Hamiltonians and as target values for benchmarking
computationally cheaper approaches, in order to tackle 2DUV spectra simulation of
larger (multi)chromophoric systems and/or several of their structural conformations.
To this end, we have used computational recipes to account for the σ-π polarization
effects when dealing with reduced active spaces [71, 72] (as necessary for increased
system size). In the benchmark study reported above, we observed that reduced
active space schemes (i.e. lacking virtual orbitals with higher orbital momenta) can
dramatically underestimate transition energies, as they overestimate the dynamic
correlation of ionic (in valence bond terms) states. In the search for cost-effective
protocols to counteract or at least damp this effect, we came up with two semiempirical procedures. On the one hand we observed that by deleting a number of
virtual extravalence π*-orbitals with higher angular momentum in the perturbation
treatment, the number of dynamic correlations is reduced, producing a state-dependent blue-shift of the excitation energies, thus minimizing the mean deviation from
the reference values in the whole excited-state manifold. On the other hand, we realized that real and imaginary shift parameters (originally introduced to cure intruder
state problems) [80, 81] invoke a non-uniform decrease in the correlation contribution, much more pronounced for ionic than for covalent states. This makes their use
well suited for our purposes, even if we need to resort to larger values than suggested
in the literature (a detailed argumentation can be found in Ref. [82]). However, the
choice of shift parameter is chromophore-dependent, and its application, while simpler with respect to orbital removal procedure, is limited to systems where transition
energies of different chromophores can be corrected with a similar shift parameter,
such as homodimeric systems. We must stress that the application of either of the
two protocols makes sense only in the framework of semi-empirical parameterization against a reliable reference data set, and their use is otherwise discouraged.
As an example case study, here we report a benchmark for benzene and phenol
and their dimer in the gas phase and for their corresponding amino acid side chains
(Phe and Tyr, respectively) in a model tetrapeptide in water solution [58].
As shown in Fig. 8, the reference TEs computed for benzene and phenol (see Fig. 4),
i.e. those at RAS(6,6|2,12) and RAS(8,7|2,12) levels with ANO-L(432,21)-aug basis
set, respectively, can be used as target values for determining computationally cheaper
approaches that could accurately simulate 2DES spectroscopy of related multi-chromophoric systems. In fact, reference computations with large RAS schemes are unaffordable even for the smallest multimeric system comprising benzene and phenol monomers,
i.e. the benzene–phenol dimer. The first step towards reducing the computational costs
is thus to develop a recipe that at least allows the use of minimal (still full-valence)
active spaces (mAS), i.e. CAS(6,6) and CAS(8,7) for benzene and phenol, respectively,
and relatively small basis sets, without compromising TEs and TDMs estimates. As
shown in Figs. 4 and 8, the full-valence mAS in combination with the large basis set,
83
Reprinted from the journal
Top Curr Chem (Z) (2018) 376:24
Thus far, we have reviewed the benchmark studies of the aromatic protein
chromophores and the canonical nucleobases of DNA and RNA (with the exception
of Gua, which is a work in progress), aimed at obtaining converged results among
the highest (still computationally feasible) levels of multi-configurational treatment
for each chromophore so that reference theoretical data are made available. These
reference transition energies and dipole moments could indeed be used both as
ab initio parameters in exciton Hamiltonians and as target values for benchmarking
computationally cheaper approaches, in order to tackle 2DUV spectra simulation of
larger (multi)chromophoric systems and/or several of their structural conformations.
To this end, we have used computational recipes to account for the σ-π polarization
effects when dealing with reduced active spaces [71, 72] (as necessary for increased
system size). In the benchmark study reported above, we observed that reduced
active space schemes (i.e. lacking virtual orbitals with higher orbital momenta) can
dramatically underestimate transition energies, as they overestimate the dynamic
correlation of ionic (in valence bond terms) states. In the search for cost-effective
protocols to counteract or at least damp this effect, we came up with two semiempirical procedures. On the one hand we observed that by deleting a number of
virtual extravalence π*-orbitals with higher angular momentum in the perturbation
treatment, the number of dynamic correlations is reduced, producing a state-dependent blue-shift of the excitation energies, thus minimizing the mean deviation from
the reference values in the whole excited-state manifold. On the other hand, we realized that real and imaginary shift parameters (originally introduced to cure intruder
state problems) [80, 81] invoke a non-uniform decrease in the correlation contribution, much more pronounced for ionic than for covalent states. This makes their use
well suited for our purposes, even if we need to resort to larger values than suggested
in the literature (a detailed argumentation can be found in Ref. [82]). However, the
choice of shift parameter is chromophore-dependent, and its application, while simpler with respect to orbital removal procedure, is limited to systems where transition
energies of different chromophores can be corrected with a similar shift parameter,
such as homodimeric systems. We must stress that the application of either of the
two protocols makes sense only in the framework of semi-empirical parameterization against a reliable reference data set, and their use is otherwise discouraged.
As an example case study, here we report a benchmark for benzene and phenol
and their dimer in the gas phase and for their corresponding amino acid side chains
(Phe and Tyr, respectively) in a model tetrapeptide in water solution [58].
As shown in Fig. 8, the reference TEs computed for benzene and phenol (see Fig. 4),
i.e. those at RAS(6,6|2,12) and RAS(8,7|2,12) levels with ANO-L(432,21)-aug basis
set, respectively, can be used as target values for determining computationally cheaper
approaches that could accurately simulate 2DES spectroscopy of related multi-chromophoric systems. In fact, reference computations with large RAS schemes are unaffordable even for the smallest multimeric system comprising benzene and phenol monomers,
i.e. the benzene–phenol dimer. The first step towards reducing the computational costs
is thus to develop a recipe that at least allows the use of minimal (still full-valence)
active spaces (mAS), i.e. CAS(6,6) and CAS(8,7) for benzene and phenol, respectively,
and relatively small basis sets, without compromising TEs and TDMs estimates. As
shown in Figs. 4 and 8, the full-valence mAS in combination with the large basis set,
83
Reprinted from the journal