# Substitution Effects on the Optoelectronic Properties of Coumarin Derivatives
## 3 Results and Discussion
### Electronic Properties of the Compounds Using B3 LYP XC Functional  
The calculated electronic properties of the compounds are summarized in Table 2. The chemical reactivity of the molecule can be described by the energy of the lowest unoccupied molecular orbital (E\({}_{\text{LUMO}}\)) that defines the electron accepting ability, while the energy of the highest occupied molecular \begin{table}
\begin{tabular}{c c c c c c} \hline
**Atom 1** & **Atom 2** & **Exp.*** & **B3 LYP/6-31G* & **B3 LYP/6-311+G* & **PBE/6-31G* \\ \hline
1 O & 2 C & 1.371 & 1.398 (1.97\%) & 1.396 (1.82\%) & 1.419 (3.5\%) \\
1 O & 9 C & 1.372 & 1.365 (\(-\)0.5\%) & 1.365 (\(-\)0.5\%) & 1.367 (\(-\)0.36\%) \\
2 C & 11 O & 1.216 & 1.208 (\(-\)0.65\%) & 1.202 (\(-\)1.15\%) & 1.217 (0.08\%) \\
2 C & 3 C & 1.454 & 1.460 (0.4\%) & 1.459 (0.34\%) & 1.459 (0.34\%) \\
3 C & 4 C & 1.352 & 1.352 (0\%) & 1.349 (\(-\)0.22\%) & 1.363 (0.81\%) \\
4 C & 10 C & 1.440 & 1.442 (0.13\%) & 1.440 (0.0\%) & 1.441 (0.07\%) \\
5 C & 10 C & 1.406 & 1.407 (0.07\%) & 1.406 (0\%) & 1.414 (0.57\%) \\
5 C & 6 C & 1.388 & 1.388 (0\%) & 1.385 (\(-\)0.22\%) & 1.394 (0.432\%) \\
6 C & 7 C & 1.402 & 1.403 (0.07\%) & 1.402 (0\%) & 1.402 (0\%) \\
7 C & 8 C & 1.390 & 1.391 (\(-\)0.07\%) & 1.389 (\(-\)0.07\%) & 1.397 (0.50\%) \\
8 C & 9 C & 1.394 & 1.396 (0.14\%) & 1.394 (0\%) & 1.404 (0.72\%) \\
9 C & 10 C & 1.400 & 1.408 (0.57\%) & 1.405 (0.36\%) & 1.419 (1.36\%) \\ \hline \end{tabular} * Reference [65].  
\end{table} 
Table 1: Comparison of optimized bond length distances for coumarin with corresponding experimental data. Variation in the bond lengths is reported in %. The numbering scheme of coumarin molecule is same as shown in Figure 3. The bond lengths are reported in angstrom (Å), and up to four significant figures. Figure 3: Infrared spectrum of coumarin experimental and calculated (B3 LYP/6-31+G*) is shown here. orbital (E\({}_{\text{HOMO}}\)) is the one that defines the electron donating ability. The combination of the two parameters (E\({}_{\text{LUMO}}\), E\({}_{\text{HOMO}}\)) can then be used to estimate the electronic chemical potential (Equation (1), methods) and chemical hardness (Equation (2)) of the molecules. The higher the value of E\({}_{\text{HOMO}}\), the easier it becomes to donate an electron, while lower the value of E\({}_{\text{LUMO}}\) easier it becomes to accept an electron. Among the investigated coumarin derivatives, compound **D** displays the most favorable electron donating (E\({}_{\text{HOMO}}\)), and compound **B** the most favorable electron accepting (E\({}_{\text{LUMO}}\)) ability. It is worth mentioning that the electron donating capability of molecule **C** is quite close to that of compound **D**. The smaller the difference energy between the E\({}_{\text{LUMO}}\) and E\({}_{\text{HOMO}}\) values, the higher the reactivity of the molecule. Compound **D** represents highest reactivity, while the other three derivatives displayed very similar values. The E\({}_{\text{LUMO}}\)-E\({}_{\text{HOMO}}\) (\(\Delta\)E) gap also provides a measure of the chemical hardness of the molecule. A smaller value of \(\Delta\)E corresponds to a soft molecule. Substitution of sulfur atom in a molecule has been suggested to decrease the global hardness of the molecule. Indeed, compound **D**, which contains sulfur atoms, displays the lowest value of \(\Delta\)E (Figure 1). For the chemical potential, compound **B** displays the lowest value, thus best electron acceptor (higher electronegativity) among the other coumarin derivatives. Subsequently, the vertical ionization energies (IE\({}_{\text{V}}\), see Equation (3)) and the electron affinities (EA\({}_{\text{V}}\), see Equation (4)) values were calculated on the fixed geometries of the molecules in their ground state configuration. With respect to the coumarin molecule, all the coumarin derivatives displayed lower IE\({}_{\text{V}}\) values while higher EA\({}_{\text{V}}\) values.