Excitation of rhodamine 800 in aqueous media: a theoretical investigation

Abstract

The main goal of this work was to obtain a calculated absorption spectrum of rhodamine 800 in an aqueous solution, which most accurately reproduces the experimental one. To achieve this result, I used the hybrid functionals supported by Gaussian 16 software package. In this case, the basis set (6-31++G(d,p)) and the solvent model (IEFPCM) were not varied. The B3PW91 functional gave the best agreement with the experimental absorption spectrum of the dye in an aqueous medium. B3P86, B971, B972, B98, X3LYP, APF, HSE06, and N12SX functionals also give good absorption energy coincidence. The B3PW91/6-31++G(d,p)/IEFPCM theory level chosen in this way made it possible to calculate the various characteristics of rhodamine 800 in the ground and excited states. An important result of this work was the establishment of the vibronic nature of the short-wavelength smaller maximum of the absorption spectrum. The influence of the strong H-bond of the exocyclic nitrogen atom with the water molecule on the dye excitation was analyzed.

Graphical abstract

Appendix. R800 dimer

As mentioned above, the main absorption maximum of the R800 dimer coincides with the short-wavelength vibronic absorption peak of the dimer (see Fig. 4). This interesting feature prompts the calculation of absorbance for the dye dimer as well. Detailed structural information about it is absent in the literature. Only in Ref. [9], it was suggested that this should be a non-parallel H-dimer. Therefore, in this work, its structure was chosen for reasons of steric correspondence and geometry optimization by minimizing the potential energy. First of all, it should be noted that the mutual steric constraints of the hydrogen atoms of the aliphatic rings exclude the parallel (ring over the ring) arrangement of the monomers. The cruciform structure of the dimeric complex turned out to be stable (Fig. 11).

Fig. 11

Optimized structure of the R800 dimer. Cartesian coordinate axes are directed along principal axes of inertia

Fig. 1

Molecular structure of rhodamine 800

Fig. 2

Diagram of vibronic absorption transition

Fig. 3

Calculated maxima E_vibron (eV) of R800 vibronic absorption spectra in aqueous solution. The functionals are arranged in ascending order of the X percentage of exact Hartree-Fock exchange in them (X values are indicated in parentheses). For functionals with long-range correction, X values for small and large distances are indicated, for the HISS functional — for small, medium, and long distances, respectively. The bold horizontal line is the experimental maximum of the R800 dilute aqueous solution (λ_max = 690 nm, E_max = 1.80 eV [9])

Fig. 4

The calculated vibronic absorption spectrum of R800 in aqueous media (thin line) and the corresponding experimental spectrum (1.3 μM) (thick line, adapted with permission from Ref. [9]). Inset: spectrophotometrically resolved monomer (solid line) and dimer (dashed line) spectra adapted with permission from Ref. [9]. Copyright 2006 American Chemical Society. The vertical sticks are the dipole strength of the vibronic transitions from Table S2 (see Supplementary Material)

Fig. 5

Calculated IR spectra of R800 in an aqueous media. The vibration frequencies involved in vibronic transitions (see Table S2 in Supplementary Material) are indicated by red arrows

Fig. 6

HOMO (left) and LUMO (right). Positive lobes are shown in red and negative lobes in blue

Fig. 7

The electron density difference between Franck-Condon point and the ground state of R800 cation in an aqueous media. Regions of positive values are shown in red and negative values in blue

Fig. 8

Structure of the R800 hydrated complex. A strong hydrogen bond is shown by a dotted line. Its length in Å (distance between heavy atoms) is given for the ground and equilibrium excited (in parentheses) states

Fig. 9

Calculated vibronic absorption spectrum of the “R800+H₂O” complex (thin line) and the experimental spectrum (1.3 μM of R800 in water) from Ref. [9] (thick line)

Fig. 10

The electron density difference between Franck-Condon point and the ground state of the “R800+H₂O” system in an aqueous media

In addition, optimization of the geometry using the B3PW91 functional, which gave the best coincidence of the calculated spectrum of the monomer with the experimental one (see above), led to its destruction. This result is not unexpected, since the correct accounting of dispersion interactions requires the use of specialized functionals [42,43,44]. From the set of author’s hybrid functionals supported by Gaussian16 and including dispersion, the APFD [45] was chosen, since it gave the absorption energy for the monomer closest to the experiment compared with PW6B95D3 and ωB97XD (see Fig. 3). Indeed, optimization at the APFD/6-31++G(d,p)/IEFPCM theory level gave a stable structure of a dimeric complex with a distance between chromophores of 3.3 Å (see Fig. 11). However, in the IR spectrum of vibrations of the ground state of the dimeric complex (Fig. S11), one imaginary frequency was still present (synchronous vibrations of C3 and C22 atoms perpendicular to the chromophore plane, see Supplementary Material). This prevented the calculation of vibronic transitions, as was done for the dye monomer. The optimization of the excited state of the R800 dimer due to computational complexity could not be performed in a reasonable time using the available computing power. Therefore, we will be content with the analysis of vertical transitions in the dimer (Table 3). For correct comparative analysis, Table 3 also shows the corresponding data for the monomer, calculated at the same theory level.

Table 3 Calculated parameters of three lowest transitions in the R800 dimer and monomer (APFD/6-31++G(d,p)/IEFPCM theory level)

It can be seen from it that the three lowest absorption transitions are due to the same four transitions between MOs participating in each of them in different ratios. Of these, only the S₀ → S₃ transition has a significant oscillator strength f; therefore, the main absorption peak of the dimer corresponds to it (see the inset in Fig. 4). From Table 3, it can be seen that the S₀ → S₃ excitation energy of the dimer (2.14 eV) is very close to the S₀ → S₁ excitation energy of the monomer (2.17 eV). This almost equality of the excitation energies of the monomer and dimer, found experimentally in Ref. [9], prompted its authors to conclude that the S₁ dimer dissociates to produce the S₁ and S₀ monomers or relaxes to the S₀ dimer. However, the theoretical calculation performed in the present work refined this result: the excitation of the dimer is due to the electronic S₀ → S₃ transition.