Top Curr Chem (Z) (2018) 376:24
1 3
scheme to reduce the computational cost. In fact, a small (or even empty) RAS2
space could be adopted, while including the remaining valence orbitals in the RAS1/
RAS3 active spaces, where a restricted number of holes are allowed in the RAS1
space and the corresponding electrons are promoted to the RAS3 orbitals. This type
of RAS1|RAS2|RAS3 scheme has been tested to minimize the active space and the
computational cost for simulation of the non-interacting benzene and phenol dimer.
Thus, here, we apply the RASSCF protocol to reduce the active space (and consequently the computational cost) by limiting the number of excitations, opposite to
what is done for the reference computations, where the number of excitations has
been increased for improving the accuracy.
Figure 9 shows the comparison of simulated one-color 2DUV–UV spectra of
benzene–phenol dimers obtained with different refined active spaces, including the
refined-mAS, i.e. CAS(14,13)
δ
, and the computationally cheaper RAS(2,3|8,8|2,2)
δ
and
RAS(4,7|0,0|4,6)
δ
schemes, while using the relatively small ANO-L(321,21) basis set.
As compared to the dimer refined-mAS, the RAS spaces involve much less CSF, with
the RAS(2,3|8,8|2,2) and the RAS(4,7|0,0|4,6) spaces corresponding to 219’048 and
52’641 CSF, respectively. As shown in Fig. 9, the former RAS scheme provides a reliable one-color spectrum when compared to that of the CAS(14,13)
δ
, while the latter cannot not properly describe some of the states located in the UV probing region (e.g. phenol signals related to the S 0 → S 7–9 transitions, namely 7P, 8P and 9P in Fig. 9a), as well
as mixed doubly excited states that give rise to off-diagonal signals (1B/1P or 1P/1B in
Fig. 9a). In fact, the electronic structure of the dimer involve several of these mixed double excitations, given by the collective one-electron excitations on both monomers and
appearing at the energy sum of the localized single excitations. The electronic coupling
between two interacting monomers, denoted as “quartic” coupling (Δ) [2, 83], shifts
the energies of mixed states relative to the sum of the corresponding single excitations,
yielding off-diagonal cross-peaks in the 2DUV–UV maps. Thus, quartic coupling and
corresponding off-diagonal 2D signals are expected to be absent (or negligible) in the
non-interacting benzene–phenol dimer. This is correctly observed in the CAS(14,13)
δ
and RAS(2,3|8,8|2,2)
δ
spectra, but it is broken in the RAS(4,7|0,0|4,6)
δ
simulations,
indicating that too great a reduction of the active space degrades the description of the
excited-state manifold and the corresponding 2D maps.
In order to validate the benchmark study on the gas-phase non-interaction and to
establish an efficient protocol for 2DUV spectra simulations of realistic systems, the
cysteine-phenylalanine-tyrosine-cysteine (CFYC) tetrapeptide (Fig. 9b, c), solvated
in water solution, was considered as a model protein system [54]. As will be shown in
the next section, the folding/unfolding dynamics of this tetrapeptide involve configurations with interacting and non-interacting benzene and phenol chromophores, occurring
as aromatic side chains of the phenylalanine (Phe, F) and tyrosine (Tyr, Y) amino acid
residues, respectively. In Fig. 9, we report two representative structures of these configurations and their corresponding 2DUV–UV spectra, simulated with our SOS//QM/MM
approach [52]. Notably, the comparison of various levels of theory shown for the noninteracting dimer in the gas phase (Fig. 9a) is completely preserved for the non-interacting aromatic side chains in the realistic solvated tetrapeptide model, with the computed
RAS(2,3|8,8|2,2)
δ
spectrum showing the same accuracy as that of the CAS(14,13)
δ
,
while a cheaper RAS scheme yields artificial quartic coupling. When considering a
86
Reprinted from the journal
1 3
scheme to reduce the computational cost. In fact, a small (or even empty) RAS2
space could be adopted, while including the remaining valence orbitals in the RAS1/
RAS3 active spaces, where a restricted number of holes are allowed in the RAS1
space and the corresponding electrons are promoted to the RAS3 orbitals. This type
of RAS1|RAS2|RAS3 scheme has been tested to minimize the active space and the
computational cost for simulation of the non-interacting benzene and phenol dimer.
Thus, here, we apply the RASSCF protocol to reduce the active space (and consequently the computational cost) by limiting the number of excitations, opposite to
what is done for the reference computations, where the number of excitations has
been increased for improving the accuracy.
Figure 9 shows the comparison of simulated one-color 2DUV–UV spectra of
benzene–phenol dimers obtained with different refined active spaces, including the
refined-mAS, i.e. CAS(14,13)
δ
, and the computationally cheaper RAS(2,3|8,8|2,2)
δ
and
RAS(4,7|0,0|4,6)
δ
schemes, while using the relatively small ANO-L(321,21) basis set.
As compared to the dimer refined-mAS, the RAS spaces involve much less CSF, with
the RAS(2,3|8,8|2,2) and the RAS(4,7|0,0|4,6) spaces corresponding to 219’048 and
52’641 CSF, respectively. As shown in Fig. 9, the former RAS scheme provides a reliable one-color spectrum when compared to that of the CAS(14,13)
δ
, while the latter cannot not properly describe some of the states located in the UV probing region (e.g. phenol signals related to the S 0 → S 7–9 transitions, namely 7P, 8P and 9P in Fig. 9a), as well
as mixed doubly excited states that give rise to off-diagonal signals (1B/1P or 1P/1B in
Fig. 9a). In fact, the electronic structure of the dimer involve several of these mixed double excitations, given by the collective one-electron excitations on both monomers and
appearing at the energy sum of the localized single excitations. The electronic coupling
between two interacting monomers, denoted as “quartic” coupling (Δ) [2, 83], shifts
the energies of mixed states relative to the sum of the corresponding single excitations,
yielding off-diagonal cross-peaks in the 2DUV–UV maps. Thus, quartic coupling and
corresponding off-diagonal 2D signals are expected to be absent (or negligible) in the
non-interacting benzene–phenol dimer. This is correctly observed in the CAS(14,13)
δ
and RAS(2,3|8,8|2,2)
δ
spectra, but it is broken in the RAS(4,7|0,0|4,6)
δ
simulations,
indicating that too great a reduction of the active space degrades the description of the
excited-state manifold and the corresponding 2D maps.
In order to validate the benchmark study on the gas-phase non-interaction and to
establish an efficient protocol for 2DUV spectra simulations of realistic systems, the
cysteine-phenylalanine-tyrosine-cysteine (CFYC) tetrapeptide (Fig. 9b, c), solvated
in water solution, was considered as a model protein system [54]. As will be shown in
the next section, the folding/unfolding dynamics of this tetrapeptide involve configurations with interacting and non-interacting benzene and phenol chromophores, occurring
as aromatic side chains of the phenylalanine (Phe, F) and tyrosine (Tyr, Y) amino acid
residues, respectively. In Fig. 9, we report two representative structures of these configurations and their corresponding 2DUV–UV spectra, simulated with our SOS//QM/MM
approach [52]. Notably, the comparison of various levels of theory shown for the noninteracting dimer in the gas phase (Fig. 9a) is completely preserved for the non-interacting aromatic side chains in the realistic solvated tetrapeptide model, with the computed
RAS(2,3|8,8|2,2)
δ
spectrum showing the same accuracy as that of the CAS(14,13)
δ
,
while a cheaper RAS scheme yields artificial quartic coupling. When considering a
86
Reprinted from the journal