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include solvent effects were performed using implicit solvent methods [ 71 ]orby
considering solvent-solute electronic interactions using liquid-structure simula-
tions [ 72 , 77 ]. Despite being relatively small molecules (though not so small for
the most sophisticated quantum chemistry methods), there are subtle issues to be
considered when trying to reproduce FPs chromophore optical spectra [ 66 ]. What is
usually reported in computational analyses is the vertical excitation energy. This
value is compared with the peak of the experimental spectrum either in the solution
or in the gas phase. Such comparison neglects vibronic and other broadening
effects, which influence the shape and the location of the absorption band. As
long as photon absorption is well described by the vertical excitation picture, the
comparison between the mentioned values is justified. It should be kept in mind,
however, that a complete description requires taking into account vibronic and
inhomogeneous broadening effects.
Starting from the most studied p -HBDI , excitation energies in the gas phase
were evaluated with a broad range of methods summarized in Table 3 . All studies
agree that the absorption band is due to excitation from the ground to the first bright
excited state, with a prevalently HOMO
LUMO character, where the HOMO
and the LUMO are
* orbital, respectively. The excitation involves a limited
(0.1e) charge displacement from the phenolate ring to the imidazolinone, and to the
bridging carbon [ 70 ] (see Fig. 5 ). As discussed in [ 74 ], this
* excitation is
embedded in the photodetachment continuum. The interaction with the ionization
continuum might affect the broadening of the gas-phase spectrum and the photo-
dynamics of the chromophore.
Table 3 Theoretical predictions for GFP chromophore excitation energy, in eV (nm)
p -HBDI eV (nm)
p -HBI a eV (nm)
2.59 (479) b
Expt. (gas)
2.84 (437) c
Expt. (sol. ext.)
2.52 (491) d
2.67 (464) e
2.67 (464) f
2.63 (471) g
2.92 (425) h
2.96 (419) h
2.93 (423) i
2.99 (415) i
3.04 (408) j
3.06 (405) j
3.05 (407) k
a p -HBI stands for 4-( p -hydroxybenzylidene)imidazolinone, with two hydrogen atoms replacing
the methyl groups of p -HBDI
b Photodestruction experiments [ 56 ]
c Extrapolation from Kamel-Taft fit [ 57 ]
d MRMP2 based on sa-CASSCF(14/12)/cc-pVDZ, DFT (PBE0/cc-pVDZ) geometry [ 74 ]
Many-body Green's function theory, DFT(PBE) geometry [ 75 ]
CASPT2/CASSCF(12/11)/6-31 G(d), CASSCF geometry [ 74 ]
CASPT2/CASSCF(12/11)/6-31 G(d), CASSCF geometry [ 70 ]
CASPT2/CASSCF(14/14)/6-31 G(d) with IPEA Hamiltonian, DFT/BLYP geometry [ 66 ]
TD-DFT/SAOP/ETpVQZ, DFT/BLYP geometry [ 66 ]
Diffusion Monte Carlo/CASSCF(14/14), DFT/BLYP geometry [ 66 ]
TD-DFT/B3LYP/6-31++G(D), DFT/B3LYP geometry [ 78 ]
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