# Substitution Effects on the Optoelectronic Properties of Coumarin Derivatives
## 3 Results and Discussion
### Molecular Orbitals and Electrostatic Potentials  
The frontier orbitals (FOs) of the investigated compounds are depicted in Figure 4. For each molecule, both the HOMO and LUMO, are \(\pi\)-type and delocalized over-all the molecule. In particular, all the LUMOs are quite similar and mainly composed by the atomic orbitals of the coumarin moiety, with only small contributions from those of the substituents.  
As far as the HOMOs are concerned, the contributions from the substituents are much more relevant and consequently, these orbitals are more different between them in comparison with the LUMOs case. Therefore, larger differences between the energies of the HOMOs of the molecules **A**-**D** and that of the parent compound are expected in comparison with those of the LUMOs. Indeed, HOMO-LUMO gaps are smaller for the coumarin derivatives with respect to the parent compound.  
Figure 5 reports, for each compound, the electrostatic potential (EP) mapped onto the density surface. As expected on the base of the electronegativity, the parts of surfaces with the highest negative charge are those in the correspondence with the oxygen atoms, especially those doubly bound in the pyrone rings. Taking into account the effects of the substituents at the parent molecule, the hydroxide groups regardless the position, present negative EPs at the oxygen atoms, whereas the hydrogen involved in OH bonds are in the correspondence with the regions of the surfaces with the more positive potentials (molecules **B**, **C** and **D**). The phenyl rings show electronic density delocalized over the carbon atoms skeleton and positive EPs at the hydrogen ones (molecules **A**, **B** and **C**).  
Figure 4: Frontier molecular orbitals of coumarin and molecules **A**–**D** calculated by density functional theory (DFT) at B3 LYP/6-31G\({}^{*}\) level of theory (contour plot 0.04).  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Compound** & **Coumarin** & **A** & & **B** & & **C** & & **D** & \\ \hline Properties & PBE & \(\Delta\) & PBE & \(\Delta\) & PBE & \(\Delta\) & PBE & \(\Delta\) & PBE & \(\Delta\) \\ E\({}_{\text{HOMO}}\) (eV) & \(-5.72\) & \(-0.78\) & \(-5.39\) & \(-0.68\) & \(-5.51\) & \(-0.75\) & \(-5.01\) & \(-0.6\) & \(-4.88\) & \(-0.7\) \\ E\({}_{\text{LUMO}}\) (eV) & \(-2.60\) & \(0.72\) & \(-2.66\) & \(0.62\) & \(-2.89\) & \(0.66\) & \(-2.53\) & \(0.82\) & \(-2.63\) & \(0.59\) \\ (E\({}_{\text{LUMO}}-{}_{\text{HOMO}}\))/2 (eV) & 1.56 & 0.75 & 1.37 & 0.64 & 1.31 & 0.7 & 1.24 & 0.71 & 1.13 & 0.64 \\ CP = (E\({}_{\text{LUMO}}\) + E\({}_{\text{HOMO}}\))/2 (eV) & \(-4.16\) & \(-0.03\) & \(-4.03\) & \(-0.02\) & \(-4.2\) & \(-0.05\) & \(-3.77\) & \(0.11\) & \(-3.76\) & \(-0.05\) \\ Ionization energy IEV (eV) & 8.28 & 0.13 & 7.47 & 0.17 & 7.42 & 0.3 & 6.98 & 0.13 & 6.93 & 0.21 \\ Electron affinity EA\({}_{\text{V}}\) (eV) & 0.07 & \(-0.11\) & 0.51 & \(-0.16\) & 0.80 & \(-0.13\) & 0.41 & \(-0.26\) & 0.54 & \(-0.06\) \\ Quasi particle gap E\({}_{\text{QP}}\) (eV) & 8.21 & 0.24 & 6.96 & 0.33 & 6.62 & 0.43 & 6.57 & 0.39 & 6.39 & 0.27 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Electronic properties of the Coumarin and derived compounds **A**, **B**, **C** and **D**, employing PBE XC in combination with basis set 6-31G\({}^{*}\), and difference between two functionals (\(\Delta\) = B3 LYP–PBE).  
The thiophene ring exhibits similar properties with an important negative contribution at the sulphur atom (compound **D**). Interestingly, the bromine atom in the molecule **B** presents an anisotropic EP with negative values around the C-Br bond and a \(\sigma\)-hole at the tip of the halogen atom.