3.4.1. Mulliken, ESP, and Natural Charge Distribution

The Mulliken atomic charges of our molecule calculated at all the levels in gas phase and chloroform show positive charge for all the hydrogen atoms. The net charge on all the atoms varies from -1.109653e to 1.980512e, from -1.164916e to 1.904034e, and from -0.891775e to 1.524787e, respectively, in gas phase at the RHF, B3PW91, and B3LYP levels. In a solution of chloroform, the charges varied from -1.064962e to 1.826589e, from -1.206706e to 1.904292e, and from -0.945041e to 1.550492e with some oxygen atoms charges being positive and can be explained by the fact that the oxygen is related to extremely negative carbon atoms. The most positive charge atoms are C₆₃, C₅, C₈ and the most negative charge atoms are C₇₁, C₆₂, C₆₇.

The electrostatic charges were evaluated in this work using the CHelpG scheme of Breneman model. We found from our results that the most positive charges atom is C₄ followed by C₆₂ and C₂ and the most negative charge atom is C₁₂ followed by C₅ and C₇. The observation made at all levels and basis set in gas phase and in a solution of chloroform is that the most positive charge atoms are directly related to the most negative charge atoms.

The natural atomic charges, obtained using the natural bonding orbital method, were also used to evaluate the atomic charge of Rubescin E. Positive and negative charges were found for all hydrogen and oxygen atoms, respectively. In this case, all carbon atoms directly linked to hydrogen atoms were found to have negative charges except for those linked to oxygen atoms. The most negative charge atom was calculated using HF method and was observed for O₆₅ (-0.69456e) and O₆₀ (-0.68330e), respectively, in chloroform and gas phase. The most positive charge atom was found to be C₆₂ in both gas (0.97067e, 0.80601e, and 0.81407e, respectively, at the RHF, B3PW91, and B3LYP levels) and solvent (0.98887e, 0.81804e, and 0.82650e, respectively, at the RHF, B3PW91, and B3LYP levels); this is due to the fact that C₆₂ is related to negative charge atoms (O₆₅, O₆₀, and C₆₃). Mulliken, electrostatic, and natural atomic charge distributions are graphically shown in Figure 2. From Figure 2, one can observe that, for almost all the methods used for charge description, the most positive and negative charge atoms were calculated at the RHF level in both gas and chloroform and this is due to the fact that the effect of electron correlation is not well described in HF method.

3.4.2. Global Reactivity Descriptors

The calculated vertical IP values in gas phase are bigger than their corresponding values in solvent. From Table 3, we also found that putting the molecule in solvent increases its electron affinity. From the calculated IP and EA values, one can conclude that solvent effect increases the capacity of molecule of gaining an electron compared to donating it. It also reduces the harness of our molecule and increases the softness. Hence, the presence of solvent increases the reactivity of the molecule Rubescin.

3.4.3. Frontier Molecular Orbitals

The frontier molecular orbitals of Rubescin E were evaluated using the ab initio and DFT methods. The 6-311G(d,p) and 6-311++G(d,p) basis sets were used for this purpose in gas phase and in chloroform solution. The results show that the energy gap of our molecule decreases when diffuse functions are added onto all the atoms. We also found that whenever the basis set and methods used, the energy gap is greater than 4, showing that our molecule is hard and can be used as insulator in many electronic devices. In Figure 3, the 3D plots of the HOMO and LUMO orbitals computed at the RHF, B3PW91, and B3LYP levels with the 6-311G(d,p) basis set are illustrated in gas phase. We observed that the HOMO of Rubescin E is located over the furan ring at the three levels and also at the C-C of cyclohexane ring and C-O of oxiran ring. By contrast, the LUMO orbital is located over the cyclohex-2-enone ring, C-C and C-O bond of tetrahydrofuran ring. We can therefore conclude that electron can easily be transferred from furan ring to tetrahydrofuran ring.

The total density of states (DOS) spectrum of Rubescin E at the gas phase and in chloroform is given in Figure 4 for each level at the 6-311++G(d,p) basis set. These DOSs spectra presented in Figure 4 were obtained from Gauss-Sum 3.0 program [18] which was used in order to show the contributions of different group to molecular orbital (HOMO and LUMO). From Figure 4, we observe that the HOMO-LUMO energy gap is smaller when we move from RHF to B3PW91 and from B3PW91 to B3LYP level, respectively, for both gas and chloroform phases, with larger values obtained in chloroform.

3.4.4. UV-Vis Spectra Analysis

Time dependent density functional theory (TD-DFT) was used in gas phase at the two levels B3PW91 and B3LYP with the 6-311++G(d,p) basis set in order to determine the first six excited states to investigate the UV-vis absorption spectra of the molecule. The excitation energy (E), wavelength (λ), and oscillator strength (f) along with their major contributions are given in Table 4 and their results are compared to experiment.

Two intense electronic transitions were predicted at 4.4934 eV (275.92 nm) and 3.4415 eV (360.27 nm) with oscillator strengths of 0.0043 and 0.0014, respectively, at the B3PW91 level and 4.5123 eV (274.77 nm) and 3.4603 eV (358.31 nm) with oscillator strengths of 0.0041 and 0.0014, respectively, at the B3LYP level. We observed from the spectra that the maximum absorption wavelength corresponds to the electronic transition from HOMO to LUMO+1 with 100% contribution followed by the electronic transition from HOMO to LUMO with 99% contribution at the two levels. The experimental absorption spectra of the title molecule predict two bands at 254 nm and 365 nm. The error between the theoretical and experimental results range from - 4.73 nm to 21.92 nm at the B3PW91 and from - 6.69 nm to 20.77 nm at the B3LYP level. These errors are due to the fact that only one molecule was considered for simulation. The theoretical UV-vis absorption spectra of Rubescin E in gas phase are shown in Figure 5.

3.4.5. Dipole Moment (μ_DM), Average Polarizability (α), First Static Hyperpolarizability (β), and Anisotropy of Polarization

3.4.6. Optoelectronic Properties

In order to recognize the optoelectronic nature of Rubescin E for different devices applications, some parameters such as electric field (E), electric polarization (P), electric susceptibility (χ), permittivity (ℰ), refractive index (η), and electric displacement (D) were calculated using equations given in the literature [23–25]. We observed from Table 6 that the results of the calculated parameters are slightly different when we move from one level to another and also when the medium changes. The value of electric field is greater in a solution of chloroform than its corresponding value in gas phase. This is because the polarizability increases in presence of a solvent. The values of electric susceptibility, dielectric constant, and refractive index are greater at B3LYP level compared to their corresponding value at the RHF. All the calculated parameters of optoelectronic properties obtained at the B3LYP level are similar to those obtained at the B3PW91 level. None of these parameters have been determined before either theoretically or experimentally.

One of the central goals of this study is to understand the underlying structure–property relationships which might form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics. The molar refractivity of our molecule, known to be an important parameter in quantitative structure–property relationship analysis was calculated for this purpose. The value of the molar refractivity was calculated at the three levels, in both gas and chloroform using the 6-311++G(d,p) basis set. The Lorenz-Lorentz equation was used for this calculation [26, 27] and its results are listed in Table 6.

The high values of molar refractivity, polarizability, anisotropy of polarizability, and first static hyperpolarizability of Rubescin E molecule show that the molecule has good quantitative structure–property relationship analysis and might therefore form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics.