Organic Electronics from Nature: Computational Investigation of the Electronic and Optical Properties of the Isomers of Bixin and Norbixin Present in the Achiote Seeds

Organic compounds have been employed in developing new green energy solutions with good cost-efficiency compromise, such as photovoltaics. The light-harvesting process in these applications is a crucial feature that still needs improvements. Here, we studied natural dyes to propose an alternative for enhancing the light-harvesting capability of photovoltaics. We performed density functional theory calculations to investigate the electronic and optical properties of the four natural dyes found in achiote seeds (Bixa orellana L.). Different DFT functionals, and basis sets, were used to calculate the electronic and optical properties of the bixin, norbixin, and their trans-isomers (molecules present in Bixa orellana L.). We observed that the planarity of the molecules and their similar extension for the conjugation pathways provide substantially delocalized wavefunctions of the frontier orbitals and similar values for their energies. Our findings also revealed a strong absorption peak in the blue region and an absorption band over the visible spectrum. These results indicate that Bixa orellana L. molecules can be good candidates for improving light-harvesting in photovoltaics.

One of the critical materials in DSSC is the sensitizer. Ruthenium-based DSSC complexes show high efficiency and excellent stability, implying potential practical applications [1,16]. However, ruthenium dyes are not suitable for environmentally friendly photovoltaic systems. Ruthenium is expensive and environmentally hazardous, and rutheniumbased compounds are highly toxic and carcinogenic. When these compounds are heated

Computational Details
DFT is a widely used tool for electronic structure calculations as it provides reliable information without a high computational cost. In the literature, there are several forms of development for the exchange and correlation functional, which seeks a real potential value of the interaction between the electrons of a system, for example, the generalized gradient approximation (GGA), a very popular approximation which, depending on the electron density and its gradient, describes the exchange and correlation energies [31]. The introduction of a term of a second-order derivative of density and/or kinetic energy density as additional degrees of freedom gives rise to another approximation, the meta-GGA [32]. Furthermore, there are also hybrid functionals, a combination of formulations of the Hartree-Fock exchange functional with exchange approximations and correlations used in DFT, such as GGA and meta-GGA. This form of blending improves the performance of energies in some situations and the different forms of this approach are related to the parameter used in the formulations. The Lee-Yang-Parr three-parameter Becke exchange and correlation functional (B3LYP) is a GGA hybrid, composed of the Hartree-Fock exchange functional (HF) and the GGA exchange and correlation approximation [33]. In addition, B3LYP has a version that includes a long-range fix, which addresses the Coulomb attenuating (CAM) method. This functional is known as CAM-B3LYP [34]. Another highlighted functional is Minnesota 2006 (M06), consisting of a meta-GGA hybrid type exchange and correlation functional. It is reasonable in evaluations of proton affinity in conjugated polyene chain and a good description of the π − π stacking interaction [35].
To obtain the optimized molecular geometries, we employed DFT calculations considering three different functionals, i.e., B3LYP, M06, and CAMB3LYP, with the 6-31+G(d,p) basis set [33][34][35][36]. We also performed the geometry optimization of the molecules presented in Figure 1 using these functionals and the 6-31G and 6-31G(d,p) basis sets. All the calculations considered molecules in the gas phase. The polarized continuum model (PCM) was used to include molecules in solution with chloroform.
Low-lying singlet excited states were evaluated at the optimized geometries using time-dependent density functional theory (TDDFT) [37]. The optical absorption profiles were simulated through convolution of the vertical transition energies with the Gaussian functions by a full width at half maximum (FWHM) equal to 0.37 eV (3000 cm −1 ). We adopted FWHM = 0.37 eV for all peaks since it is the standard value used in the literature, presenting a good track record [38,39]. All calculations were performed using the Gaussian 09 (Revision D.01) suite [40].

Structural and Electronic Properties
We begin our discussion by presenting the geometric properties of the molecular dyes studied here. Figure 2 illustrates their optimized structures. As a general trend, we observed that the molecules, in both chloroform solution and gas-phase cases, present nearly planar lattice configurations with small torsion angles (about 1-2 degrees) in the edges. Such a signature for the lattice arrangement allows for the wavefunction delocalization on the π-conjugated backbone. All the molecules showed similar extensions of conjugation, i.e., nine carbon double bonds C = C on the π-conjugated backbone. According to the earlier studies [41,42], these findings indicate that the electronic and optical properties of the dyes in Figure 1 tend to present similar behavior.
As mentioned above, BLA is a crucial geometric parameter related to the electronic energy gap [43,44]. BLA is defined as (R single − R double )/N, where R single , R double , and N denote single bond length, double bonds length, and the number of the single-double bond pairs in a π-delocalized system, respectively [44]. Here, we used the BLA values to realize possible changes in the bond length configuration of the dyes. In this way, Figure 3 shows the examined bonds, and Tables 1 and A1-A6 (Appendix A) show bond lengths and BLA values of the π-conjugated backbone for the dyes in gas phase and chloroform solution. For each DFT functional, we observed that both bond lengths and BLA values are similar among the dyes, and the solvent effect can be observed on the reduction of the BLA values when contrasted with the gas phase molecules. CAM-B3LYP provides higher single-bond lengths and lower double-bond lengths concerning the results obtained by employing B3LYP and M06. Consequently, results from CAM-B3LYP present higher BLA values. The total BLA values increased, in sequence, from B3LYP, M06, to CAM-B3LYP, indicating that the higher Hartree-Fock (HF) contribution on the DFT functional leads to higher BLA values. This behavior also impacted the HOMO-LUMO energy gap, as shown later.
Figures 4 and A1-A3 (see Appendix A) illustrate the HOMO and LUMO wavefunctions of the dyes in the chloroform solution and gas-phase cases. One can note that the frontier molecular orbitals widely delocalized on the π-conjugated backbone. Moreover, no impediment to electronic mobility along the π-conjugated chain was realized. This feature aggregates a metallic character to the polyenic systems since π-electrons of the conjugated chains are not part of a particular bond between atoms, which allows the charge to move along the chain freely [45].    According to Koopman's theorem, the HOMO energy is the first approximation to the potential of molecular ionization [46]. By analogy, the LUMO energy is an approximation for the electron affinity. In this context, Tables 2 and A7-A12 (see Appendix A) show the energies of the frontier molecular orbitals (MOs) and HOMO-LUMO gap energies of the dyes in the gas phase and chloroform solution. One can note a slight variation of the frontier MOs energies and gap energy for the same functional. We observed differences in the gap energy values for each DFT functional, which increased from B3LYP, M06, to CAM-B3LYP in sequence. These differences are related to the HF contribution since high HF contributions to the DFT functionals induce higher gap energy values. We also note an interplay between BLA and the electronic gap, where an increase in the BLA values leads to an increase in gap energy values. In general, for all DFT functionals and basis sets used, the cis conformation presented gap energy values higher than the trans conformation, i.e., the trans conformation is energetically more stable than its cis analog.

Nonlinear Optical Properties
The nonlinear optical (NLO) response in conjugated organic molecules can be optimized by varying the BLA values as proposed by Marder et al. [47]. It is essential to choose an appropriate basis set for the accurate description of NLO properties [48][49][50]. In this context, we investigate the electric properties of the isomers both in the gas-phase and chloroform solution to see how these properties were impacted both by the BLA behavior and by the choice of basis set. The analyzed quantities were the normal experimentally measured values, i.e., the dipole moment magnitude µ = µ 2 x + µ 2 y + µ 2 z , the average linear polarizability α = α xx +α yy +α zz 3 , and the vector component of the first hyperpolarizability . Tables 3 and A13-A16 (see Appendix A) show the absolute values of obtained electric quantities for different DFT functionals and basis sets. Here, we observed that the values of the µ, α, and β vec obtained with the CAM-B3LYP functional are smaller than B3LYP and M06. The exception occurred in isonorbixin with B3LYP that presented smaller values of µ and β vec compared to CAM-B3LYP and M06. As CAM-BLYP provided the highest values of BLA (see Table 1), the findings indicate that higher values of BLA had lower values of µ, α, and β vec . This relationship is in agreement with the work of Labidi et al. for transhexatriene [51]. In addition, the isobixin presented the highest values of µ and α, and bixin presented the highest values of β vec .
Furthermore, the 6-31+G(d,p) basis set provided the highest values of α followed in descending order by 6-31G and 6-31G(d,p) basis sets, so the inclusion of the diffuse function on the basis set induced increasing α values. On the other hand, this behavior was not observed in µ and β vec . The highest values of µ and β vec of isomers in the gasphase were provided by the 6-31G basis set. However, there were some cases where the 6-31+G(d,p) basis set provided the highest values of µ and β vec of isomers in chloroform solution. Furthermore, the findings of µ and β vec with the 6-31G(d,p) basis set were the lowest compared to the 6-31G and 6-31+G(d,p) basis set. We concluded the analysis of the NLO properties of isomers by observing that the solvent effect caused an increase of µ, α, and β vec . Table 3. Dipole moment (µ), average linear polarizability (α), and vector component of the first (β vec ) hyperpolarizability of the dyes in gas phase and chloroform solution. These results were obtained by employing the 6-31+G(d,p) basis set.

Excited States Properties
We now turn to the description of the low-lying excited states and optical properties of the molecular dyes. Here, we used Gaussian convolution of the wavelength to obtain the absorption spectra of these molecules and then compare the theoretical results of the UV-Vis absorption peak position with the experimental values. Figures 5, A4 and A5 (see Appendix A) show the absorption spectra of the molecules obtained by the Gaussian convolution of the vertical transitions with the FWHM = 0.37 eV (3000 cm −1 ). One can see that the solvent induces a slight shift in the absorption spectra to higher wavelengths considering the absorption bands. For each case, i.e., gas phase or chloroform solution with the same DFT functional and basis set, all molecules presented maximum absorption peaks in the same region, which can be associated with the same extension of backbone conjugation and close gap energies. Calculations with different DFT functionals revealed a shift in the absorption band positions to higher wavelengths from CAM-B3LYP, M06, to B3LYP, in sequence. We associate the increase of the gap energy with the decrease of the wavelength (analogously, an increase in the vertical energy). The relationship between the BLA values and the position of the absorption bands can be understood as follows: an increase in the average BLA value implies a decrease in the overlap between atomic orbitals, consequently leading the absorption bands to shift to higher energies (lower wavelengths).
Finally, Tables 4, A17 and A18 (see Appendix A) show the values of the vertical transition energy (E 01 ), the wavelength of the maximum absorption peak (λ 01 ), oscillator strength ( f ), and transition dipole moment (µ 01 ). In all cases, we observed that the transition dipole moment was mainly on the conjugated backbone, i.e., along the x-direction, and isobixin and isonorbixin presented higher values about µ 01 . The experimental data showed that the maximum peaks of bixin, isobixin, norbixin, and isonorbixin were in the blue region, i.e., 470, 476, 468, and 475 nm, respectively [52]. From these data, we conclude that the results obtained with the CAM-B3LYP functional and 6-31+G(d,p) basis set presented a better description of the optical properties. We can attribute this result to the higher HF contribution on the CAM-B3LYP functional compared to the others, combined with the inclusion of the diffuse and polarization functions on the basis set that is generally more appropriate to describe polyene systems.

Conclusions
In summary, we employed DFT and TD-DFT calculations to study the geometrical and optoelectronic properties of bixin and norbixin isomers. These molecules are present in the achiote seeds, a plant found in tropical America. Since they present a clear UV-Vis absorption spectrum, they can be good candidates for developing novel DSSCs. The DFT and TD-DFT calculations were conducted within the framework of three different functionals (B3LYP, CAM-B3LYP, and M06) and basis sets (6-31+G(d,p), 6-31G(d,p), and 6-31G).
As a general trend, we observed that these molecules in chloroform solution and gas-phase presented almost planar lattice configurations with small torsion angles in the edges. Such a lattice arrangement allows wavefunction delocalization on the π-conjugated backbone. Moreover, their similar extension in the conjugation pathway leads to close values for their MO energies. The HOMO-LUMO gap energy values increased from the B3LYP, M06, to CAM-B3LYP levels of theory, in the sequence as a response for increasing HF contribution to the DFT functional.
In the optical properties study, we observed that the increase of the HF contribution is reflected in the shift of the bands to lower wavelengths (or higher energies). The absorption bands of the molecules in the chloroform solution were slightly shifted to a higher wavelength concerning the gas phase. We also obtained the vertical transition energies, wavelengths, oscillator strengths, and transition dipole moments. Here, we observed that the transition dipole moments for all the molecular dyes were aligned with the molecular axis, and the comparison with the experimental data showed that the CAM-B3LYP functional, with the 6-31+G(d,p) basis set, provided a better description of the optical properties.
It is important to stress that bixin represents the main carotenoid found in the achiote seeds. In addition, the absorption peak position was comparable for both Z-isomer (bixin) and E-isomer (isobixin), which indicates that light capture and exciton formation tend to be similar in the two isomers.
This work provided a benchmark on the computational methodologies for the electronic and optical characterization of natural dyes, which is absent in the literature. Although bixin and norbixin do not perform better than other molecules recently reported in the literature for some photovoltaic applications, they are still worth investigating. These molecules are abundant in Tropical America (composed only of developing countries) and have easy extraction. These crucial features can aggregate in the final product a good costbenefit relationship, which is attractive when it comes to manufacturing of organic-based optoelectronic devices and their possible commercialization in developing countries.

Conflicts of Interest:
The authors declare no conclict of interest.