*3.7. DFT/TD-DFT Calculations*

#### 3.7.1. Optimized Geometrical Structures

The DFT interaction energy (ΔIE) values were calculated by using Equations (9) and (10) in the acetonitrile solvent system for the hypothetical modeled complexes (Figure 11, and the calculated values are summarized in Table 4.

$$
\Delta \text{IE}\_{\text{int}} = \text{E}\_{\text{[PA]} \supset} \bigcap \text{[DDQ]} \quad \text{-} \left( \text{E}\_{\text{[PA]}} + \text{E}\_{\text{[DDQ]}} \right) \tag{9}
$$

$$
\Delta \text{IE} = \text{E}\_{\text{[PA]} \supset \bigcap \{ \text{ChA} \}} \text{ - (E\_{\text{[PA]}} + E\_{\text{[ChA]}}) \tag{10}
$$

where E[PA]<sup>⊃</sup> [DDQ] and E[PA]<sup>⊃</sup> [ChA] represent the electronic energy of the optimized structures of PA-DDQ and PA-ChA complexes, respectively, and E[PA], E[ChA], and E[ChA] represent the optimized energy of free PA, ChA, and DDQ, respectively.

**Figure 11.** Optimized structures of PA, ChA, DDQ, and their complexes: (**a**) PA; (**b**) ChA; (**c**) DDQ; (**d**) face-to-face I fashion complex of PA with ChA; (**e**) face-to-face II fashion complex of PA complex with ChA; (**f**) edge-to-edge fashion complex of PA with ChA; (**g**) face-to-face I fashion complex of PA with DDQ; (**h**) face-to-face II fashion complex of PA complex with DDQ; and (**i**) edge-to-edge fashion complex of PA with DDQ at the ωB97XD/6-311++G(2d,p) level of theory in acetonitrile solvent system. Close nonbonded contact distances are highlighted in Å.

On the other hand, the Gibbs interaction energy (ΔGint) values were obtained by using Equations (11) and (12) in the acetonitrile solvent system.

$$
\Delta \mathbf{G}\_{\rm int} = \mathbf{E}\_{\rm [PA]} \supset \bigcap \mathbf{[DDQ]} \mathbf{ - \ (G\_{\rm [PA]} + G\_{\rm [DDQ]})} \tag{11}
$$

$$
\Delta \mathbf{G}\_{\rm int} = \mathbf{G}\_{\rm [PA]} \supset \bigcap \mathbf{[ChA]} \tag{12}
$$

where G[PA]<sup>⊃</sup> [DDQ] and G[PA]<sup>⊃</sup> [ChA] represent the Gibbs free energy of the optimized molecular complex of PA with DDQ and ChA, respectively, and G[PA] and G[ChA] represent the Gibbs free energy of the optimized free PA and ChA, respectively.

The calculated ΔIE and ΔG values are represented in the following order: face-toface I fashion > face-to-face II fashion > edge-to-edge fashion. Negative ΔIE and ΔG values correlate with favorable interactions. These results strongly suggest that the π−π\* interactions between the two aromatic rings and the hydrogen bond play an important role in the interaction of the PA with ChA and DDQ, in agreement with the findings of others and also strongly supporting the results of our experimental free energies changes (ΔG) ([PA]⊃ [ChA] = −4.3 × 10<sup>3</sup> and [PA]⊃ [DDQ] = −4.08 × 10<sup>3</sup> kJ mol<sup>−</sup>1). The face-to-face I fashion of the PA-ChA and PA-DDQ complexes are thus considered to be stable structures based on the experimental and theoretical findings.

**Table 4.** DFT-calculated electronic binding interaction energies (ΔIE kJ/mole) and ΔG (kJ/mole) for the PA complex with ChA and DDQ compounds at the ωB97XD/6-311++G(d,2p) level of theory in acetonitrile solvent.


## 3.7.2. HOMO–LUMO Analysis

The structures were drawn in *GaussView 6.0.16* program. The highest occupied molecular orbitals (HOMOs) in which electrons are located and the lowest unoccupied molecular orbitals (LUMOs) were calculated based on the most stable geometry of the complexes. The HOMO of a chemical species is therefore nucleophilic or electron-donating, and the LUMO is electrophilic or electron-accepting. According to Koopmans' theorem [28], the energy of the HOMO (EHOMO), which is indicative of nucleophilic components, is correlated with the ionization potential's negative value (IP = −EHOMO).

The energy of the LUMO (ELUMO) is related to the electron affinity's negative value (EA = −ELUMO) and is a measure of the susceptibility of the molecule or species toward the reaction with nucleophiles. A large HOMO-LUMO gap signifies that the chemical species is extremely stable and has low reactivity. The HOMO-LUMO energy values shown in Table 5 can be used to calculate a number of other significant and valuable quantum chemical properties. These include global hardness (η), global softness (S), electrophilicity index (ω), electronegativity (χ), and chemical potential (μ), all of which give a measure of chemical reactivity. The hardness value (η) is a qualitative indication of its low polarizability and can be computed using Equation (13):

$$
\eta = \left[\frac{\text{E}\_{\text{LUMO}} - \text{E}\_{\text{HOMO}}}{2}\right] = \left[\frac{\text{IP} - \text{EA}}{2}\right] \tag{13}
$$

On the other hand, "soft" molecules are highly polarizable, have modest HOMO-LUMO energy gaps, and can be calculated by using Equation (14):

$$\mathbf{S} = \left[ \frac{2}{\mathbf{E}\_{\text{LUMO}} - \mathbf{E}\_{\text{HOMO}}} \right] = \left[ \frac{2}{\mathbf{IP} - \mathbf{E}\mathbf{A}} \right] = \frac{1}{\eta} \tag{14}$$

Electronegativity

The ability to attract electrons is a characteristic of a chemical's electronegativity (χ) and determines how chemically reactive it is, which can be computed using Equation (15):

$$\chi = \left[\frac{\text{E}\_{\text{LUMO}} - \text{E}\_{\text{HOMO}}}{2}\right] = \left[\frac{\text{IP} + \text{EA}}{2}\right] \tag{15}$$

Chemical Potential

The chemical potential (μ) is the ability for an electron to be taken out of a molecule, and it can be determined using Equation (16):

$$
\mu = \left[\frac{\text{E}\_{\text{HOMO}} - \text{E}\_{\text{LUMO}}}{2}\right] = -\left[\frac{\text{IP} + \text{EA}}{2}\right] \tag{16}
$$

Electrophilicity Index

The electrophilicity index (ω) measures the strength of the electron flow between a donor and an acceptor in a substance's electron acceptors. The mathematical expression for *ω* is as follows in Equation (17).

$$
\omega = \frac{\chi^2}{2\eta} = \left[\frac{\left(\frac{\text{E}\_{\text{HMOO}} - \text{E}\_{\text{LUMO}}}{2}\right)^2}{\left(\text{E}\_{\text{LUMO}} \text{E}\_{\text{HOMO}}\right)}\right] = \left[\frac{\left(\frac{\text{IP}}{2} + \text{EA}\right)^2}{\text{IP} - \text{EA}}\right] \tag{17}
$$

**Table 5.** HOMO-LUMO gap (ΔEgap), ionization potential (IP), electron affinity (EA), electronegativity (χ), chemical potential (μ), hardness (η), softness (S), electrophilicity index (ω), dipole moments (dm), and polarizability (α) of the PA, ChA, DDQ, and their complexes at the ωB97XD/6−311++G(d,2p) level of theory in acetonitrile solvent.


The molecular electrostatic surface potentials [29] of PA, ChA, DDQ, and PA complexes with ChA and DDQ are shown in Figures 12 and 13. The relative polarities and reactive sites of the species-negative ESP are shown in red, and the order of increasing electrostatic potential (i.e., highest negative value) is red > orange > yellow > green > blue. The carbonyl oxygen (-C=O) atom of PA, which is illustrated in red in Figures 12 and 13, has a high electron density and is the preferred site for electrophilic attack and interaction with the nucleophilic partly positive charged hydrogen atoms (blue color). The yellow color indicates the slightly rich electron regions, and the green reflects more neutral zones. The HOMO and LUMO properties and the quantum chemical properties of PA, ChA, DDQ, and PA complexes with ChA and DDQ are summarized in Table 5.

**Figure 12.** Molecular electrostatic potential (MEP) maps of HOMO and LUMO structures of PA, ChA, and their 1:1 complex: (**a**) PA; (**b**) ChA; (**c**) face-to-face I fashion complex of PA with ChA; (**d**) face-to-face II fashion complex of PA complex with ChA; and (**e**) edge-to-edge fashion complex of PA with ChA at the ωB97XD/6-311++G(2d,p) level of theory in acetonitrile solvent system.

**Figure 13.** Molecular electrostatic potential (MEP) maps of HOMO and LUMO structures of PA, DDQ, and their 1:1 complex: (**a**) PA; (**b**) DDQ; (**c**) face-to-face I fashion complex of PA with DDQ; (**d**) face-to-face II fashion complex of PA complex with DDQ; and (**e**) edge-to-edge fashion complex of PA with DDQ at the ωB97XD/6-311++G(2d,p) level of theory in acetonitrile solvent system.

As shown in Table 5, the electronegativity (*χ*) for ChA is 6.68 eV and for DDQ is 5.52 eV, which indicates that ChA and DDQ have the ability to form CT complexes with PA. In addition, the electrophilicity index (ω) of ChA is 6.37 eV and for DDQ is 6.11 eV, which also suggests the formation of CT complexes with PA. The stability between the PA-ChA and PA-DDQ complexes was measured using their HOMO-LUMO gaps (ΔEgap), and the face-to-face I fashion for PA⊃ ChA complex was found to be 6.09 eV, while the Face-to-face II fashion for PA⊃ DDQ complex was found to be 5.12 eV.
