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Fig. 5 Isodensity surfaces of HOMO, LUMO, and their difference for three chromophore
structures, from Nifos` et al. [ 71 ]. In the third column, pink ( cyan ) regions indicate charge
depletion (increase) upon HOMO
LUMO excitation
The picture emerging from the comparison between gas-phase experimental and
theoretical results on p -HBDI would highlight the good performance of highly
correlated methods (CASPT2, many-body Green function, see Table 3 ), time-
dependent density functional theory (TD-DFT) methods predicting too blueshifted
values. A recent investigation by Filippi and coworkers showed how using a more
accurate zero-order Hamiltonian for CASPT2 (with the IPEA shift) leads to a
significantly blueshifted value [ 66 ]. For in-depth discussion of these discrepancies,
the interest reader is referred to [ 66 , 74 ].
The case of RFP model chromophores (i.e., p -HBMPI , p -HBMPDI , and the
RFP chromophore itself) shows similar trends, with TD-DFT predicting blueshifted
values with respect to CASPT2 (Table 4 ). In contrast to the case of GFP model
chromophores, the experimental photo destruction value lies midway between the
values predicted by the two classes of methods. A better agreement between TD-
DFT and experiment is found for the larger p -HBMPDI model. Likewise, for the
RFP chromophore (not stable in solution) CASPT2 and TD-DFT predictions are in
rather good agreement. CASPT2 prediction for different isomers yields blueshifted
values for the trans chromophore (180 rotation around
, defined in Table 2 )of
around 0.10-0.15 eV, rather uniformly for the various models used [ 72 , 79 ].
TD-DFT low computational cost makes it an affordable method for a systematic
and homogeneous investigation of the large set of chromophore structures [ 71 ].
Using this technique, the trends among the various FPs are reproduced. As already
mentioned, chromophore structure is the principal determinant of the excitation
energy. In term of the computed gas-phase vertical excitation energies, the most
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