Performance of DFT functionals with different percentages of exact Hartree–Fock exchange energy (EX) is assessed for recovery of the CC2 reference one- (OPA) and two-photon absorption (TPA) spectra of fluorescent proteins chromophores in vacuo. The investigated DFT functionals, together with their EX contributions are BLYP (0%), B3LYP (20%), B1LYP (25%), BHandHLYP (50%), and CAM-B3LYP (19% at short range and 65% at long range). Our test set consists of anionic and neutral chromophores as naturally occurring in the fluorescent proteins. For the first time, we compare TDDFT and CC2 methods for higher excited states than the S 1 state, exhibiting relatively large TPA intensity. Our TDDFT results for neutral chromophores reveal an increase in excitation energies as well as TPA and OPA intensities errors, compared to CC2-derived results, as the DFT functional contains less exact exchange. The long-range-corrected CAM-B3LYP functional performs the best, closely followed by BHandHLYP, while BLYP usually significantly underestimates all investigated spectral properties, hence being the worst in reproducing the reference CC2 results. The hybrid B3LYP and B1LYP functionals can be roughly placed in between. We propose that TDDFT may underestimate the TPA intensities for neutral chromophores of fluorescent proteins due to underestimated oscillator strengths between some excited states. In the case of anionic chromophores, we find that B3LYP and B1LYP functionals overcome others in terms of reproducing CC2 excitation energies. On the other hand, however, TPA intensity is usually significantly underestimated, and in this respect, CAM-B3LYP functional seems to be again superior. In contrast to the case of neutral chromophores, it seems that a large magnitude of excited-state dipole moments or changes in dipole moments upon excitation may be the driving force behind high TPA transition moments.

We systematically investigate an impact of the size and content of a quantum (QM) region, treated at the density functional theory level, in embedding calculations on one- (OPA) and two-photon absorption (TPA) spectra of the following fluorescent proteins (FPs) models: Aequorea victoria green FP (avGFP) with neutral (avGFP-n) and anionic (avGFP-a) chromophore as well as Citrine FP. We find that amino acid (a.a.) residues as well as water molecules hydrogen-bonded (h-bonded) to the chromophore usually boost both OPA and TPA processes intensity. The presence of hydrophobic a.a. residues in the quantum region also non-negligibly affects both absorption spectra but decreases absorption intensity. We conclude that to reach a quantitative description of OPA and TPA spectra in multiscale modeling of FPs, the quantum region should consist of a chromophore and most of a.a. residues and water molecules in a radius of 0.30–0.35 nm ( ca. 200–230 atoms) when the remaining part of the system is approximated by the electrostatic point-charges. The optimal size of the QM region can be reduced to 80–100 atoms by utilizing a more advanced polarizable embedding model. We also find components of the QM region that are specific to a FP under study. We propose that the F165 a.a. residue is important in tuning the TPA spectrum of avGFP-n but not other investigated FPs. In the case of Citrine, Y203 and M69 a.a. residues must definitely be part of the QM subsystem. Furthermore, we find that long-range electrostatic interactions between the QM region and the rest of the protein cannot be neglected even for the most extensive QM regions ( ca. 350 atoms).

The spectral properties of fluorescent proteins (FPs) depend on the protein environment of the chromophore (CRO). A deeper understanding of the CRO -environment interactions in terms of FPs' spectral characteristics will allow for a rational design of novel markers with desired properties. Here, we are taking a step towards achieving this important goal. With the timedependent density functional theory (TDDFT), we calculate oneand two-photon absorption (OPA and TPA) spectra for 5 green FPs (GFPs) and 3 yellow FPs (YFPs) differing in amino acid sequence. The goal is to reveal the roles of: (i) electrostatic interactions, (ii) hydrogen-bonds (h-bonds) and (iii) h-bonds together with distant electrostatic field in absorption spectra tuning. Our results point to design hypothesis towards FPs optimised for TPA-based applications. Both h-bonds and electrostatic interactions co-operate in enhancing TPA crosssection (s TPA ) for the S 0 ! S 1 transition in GFPs. Furthermore, it seems that details of h-bonds network in the CRO's vicinity influences s TPA response to CRO -environment electrostatic interactions in YFPs. We postulate that engineering FPs with more hydrophilic CRO's environment can lead to greater s TPA . We also find that removing h-bonds formed with the CRO's phenolate leads to TPA enhancement for transition to higher excited states than S 1 . Particularly Y145 and T203 residues are important in this regard.