The frontier molecular orbitals comprising the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) with the energy gap between HOMO and LUMO (ΔE) of the complexes are calculated and displayed in Table 1. Frontier orbital highlights the reactive property of complexes. The HOMO is the first orbital provider of the electron and the LUMO is the first orbital acceptor of the electron, and the gap between HOMO and LUMO characterizes the molecular chemical stability. The energy gap between the HOMO and the LUMO molecular orbitals is a critical parameter in determining molecular electrical transport properties though it is a measure of electron conductivity [14] . The chemical activity of the molecule is also observed from Eigen values of LUMO and HOMO and from the energy gap value calculated from them. Thus, ΔE is the result of a significant degree of intermolecular charge transfer (ICT) from the electron donor to the efficient electron acceptor group. Besides, from HOMO and LUMO which are admitted to be respectively the ionization potential and the affinity energy, the chemical hardness was determined according to Koopman’s theory given by:

where I_p = −E_HOMO is ionization potential (Kcal・mol⁻¹), E_A = −E_LUMO is electronic affinity (Kcal・mol⁻¹).

The hardness emphasizes the reactivity of the complex. Therefore, the larger the gap between HOMO and LUMO is, the harder the molecule is and the worse its reactivity is. In contrary, the chemical softness that is defined as the inverse of hardness highlights the capacity of an atom or group of atoms to receive electrons. Therefore, the soft molecule needs small energy to liberate an electron from HOMO since the gap ΔE is narrow. Besides, the chemical potential was calculated to account for the capability for

^aDE = LUMO-HOMO.

electron to leave from the molecule through Equation (3) as:

In Table 1, we can well see with each complex that the most reactive isomer represents δ-Cl for which energy gap is small. This can certainly be explained by the fact that both ligands are in Trans position where the repulsion brought about by the steric effect between them is minimized. Moreover, and specifically, δ-RuCl₂(Azpy)₂ is the most reactive complex with 41.5 Kcal・mol⁻¹. In consequence, it is assumed to be the soft molecule though it displays the low value of hardness [15] . However, the reactive RuCl₃・3H₂O presents the highest energy gap with 57.5 Kcal・mol⁻¹. Therefore, it is admitted to be the hardest molecule.

The natural bond orbital was performed on complexes using the pseudo-potential LANL2DZ basis set whose particularity is to freeze the core electrons [16] within the ruthenium atom. Therefore, Table 2 displays the electronic structure of ruthenium for each of the complexes. The calculations were made on the complexes, the reactive RuCl₃・3H₂O and also on ruthenium atom.

According to NBO analysis, Table 2 shows up that the structure of the valence orbital of Ru is characterized by 4d5s. Regarding the core electrons, Table 3 shows that LANL2DZ provides approximately 36 electrons regardless the structure of the ligand. Whereas the Rydberg orbitals (5p5d6p), they account for the more extended bits of the bases functions used including polarization functions electrons. Their occupancies within the complexes are low and constant with 0.06 electrons except Ru atom that does not display any value. We can assume that the Rydberg electrons are certainly related to the presence of ligands. Almost the same remark concerns the valence electrons where only Ru atom displays 8 electrons while all complexes show almost 7.40 electrons. Regarding the total electrons in ruthenium atom that is 44 when it is isolated, RuCl₂(L)₂ complexes display almost a constant value of 43.44 electrons while RuCl₃・3H₂O displays 43.1 electrons. Consequently, we can admit that these results tend to highlight the electron donor’s strength of azopyridine ligands to Ru. In reality, the nominal

charge of Ru in RuCl₂(L)₂ is +2. So, the natural atomic charge that corresponds to the difference between the nuclear charge of Ru (44) and its total electron population in Table 3 within each complex is very low (lower than +2) confirming a significant transfer of electron density from the ligands to Ru [17] . However, regarding RuCl₃・3H₂O, the nominal charge of Ru is +3 due to the presence of three chloride atoms while the natural charge is +0.9. This discrepancy of charge is attributed to the presence of water molecules that are known to be strong electrons donors.

Table 4 displays the atomic charges for each atom involved in the formation of Ru- Ligand bonds. It shows that the charge of Ru in the complex is almost the same regardless both the nature of the ligand and the configuration of the complex’s isomer [2] [18] . Thus, we can admit that azopyridine ligands behave seemingly and the hindrance that they provide should have no electronic influence on the charge of Ru. However, it must certainly induce a steric effect necessary for selective reactions [6] and for the symmetry. For instance, while the three complexes δ-RuCl₂(Azpy)₂, δ-RuCl₂(Dazpy)₂ and δ-RuCl₂(Mazpy)₂ are C₂-symmetrical with different chloride atomes, δ-RuCl₂ (Nazpy)₂ presents a C_i symmetry indicating an inversion center [19] . Herein, all ligands are consequently identical by pairs and thus, symmetric atoms display the same charge. Regarding the charges of nitrogen atoms both on ligands (Table 5) and on ruthenium complexes (Table 4), the lowest charges are located on both N₁ and N_py. Therefore, since the azopyridine ligands are known to be bidentate structures [5] , we can believe that the electrons density on N₁ should be delocalized either on N_py or on N₂ that leads to the formation of Ru-N_py and Ru-N₂ bonds. This process will give then rise to a five-ring stable shape of complex [5] [20] . Table 6, displays the interaction between N₁, N₂ and N_py atoms through NLMO delocalization of N₁ electrons within the four azopyridine ligands.

Through Table 6, we can see that the four ligands delocalize the occupancies of the lone pair LP(N₁) in the same natural atomic orbitals NAOs. Principally, LP(N₁) delocalizes greatly onto the C₁-N_py antibond. This fact confirms the identical electronic behavior of the azopyridine ligands.

All azopyridine complexes studied herein are admitted to show a C₂ axis [19] . So, both azopyridine ligands (ref. Figure 1) are identical and nitrogen atoms involved in the formation of Ru-ligand bonds are assumed to be in the same environment by pair. Regarding both chlorine atoms, they covalently bind to Ru atom since its nominal charge is +II. Here, the occupancy of NBO was performed at B3LYP/Lanl2dz level. So, Table 7 and Table 8 list the calculated occupancies of natural orbitals and natural hybrids of several atoms involved in the formation of Ru-N bonds in RuCl₂(L)₂ comprising electron delocalization. L stands for 2-phenylazopyridine (Azpy), 2-phenylazo-4,6-dime- thylpyridine (Dazpy), 2,6-dimethylphenylazo-2-pyridine (Mazpy) and 2-pyridylazo- naphtol (Nazpy). In these aforementioned Tables, only the AOs that occupancies are far lower than the ideal occupancy (2.0e) and the MOs involved in electronic transition are presented. It is assumed that the low occupancies of an AO disclose the orbital to be involved in MO formation [21] .

With azopyridine ligands and according to the reactive RuCl₃・3H₂O, ruthenium is involved in an octahedral structure with six single bonds. Regarding RuCl₂(L)₂, Cl atoms that are responsible for the nominal charge +II of Ru are involved in an ionic

^aLP represents Lone Pair Orbital; ^bHybrid concerns the first atom of the bond; ^cLinear combination of NAOs of the atom concerned in the NBO hybrid; ^dPercentage contribution of each NAO in the NBO hybrid.

^aStared label (*) indicates anti-bonding, LP (A) is a valence lone pair orbital on atom A.

bonding. Therefore, σ(Ru-Cl) is a strong bond. Whereas Ru-N bonds, they are actually formed of electron transfer from lone pair LP(N) to Ru atom. Table 7 displays the structures of LP(N) orbital expected to bind to Ru atomic orbital owing to their low occupancies. We can see that LP(N_py) and LP(N₂) have almost identical populations indicating their equal ability to form Ru-N bond and confirming therefore the bidentate state of the ligands. These interactions are highlighted through Table 8 by the second order perturbation theory where higher energies reflect the stability of the donor-ac- ceptor interactions. Here, Table 8 displays in fact the electron delocalization (ED) from filled donor orbital to empty acceptor orbital.

Besides, both transitions LP(N₂)?LP*(Ru) and LP(N_py)?LP*(Ru) show that only N_py and N₂ are involved in bonding with the same LP*(Ru) orbital.

Moreover, Table 7 shows LP(N₁) with 1.94e as occupancy. This carries out its non involvement in Ru-N bondings. However, it delocalizes its electrons in the C₁-N_py bonding as confirmed by Table 6 and Table 8.

Whereas LP(Ru)?p*(N₁-N₂), it indicates the electron delocalization regarding the metal to ligand charge transfer (MLCT) transition. This result is consistent with literature where Azopyridine ligands are admitted to be π-acceptor and σ-donor [11] . This transition is also consistent with the ability for δ-Cl complexes to better behave as photo-sensitizer though the structure of their donor LP(Ru) is exclusively made of combination of d_xz and d_yz as indicated in Table 7.

TD-DFT is performed to understand the electronic absorption and find out the ability for the complex to behave as sensitizer [22] . Since an efficient photosensitizer shows a strong absorption band in the visible region (400 - 800 nm) [23] , Figure 3 shows up the electronic spectra of azopyridine ruthenium complexes. We can see here that δ-Cl isomers present the highest and the widest wavelengths. Therefore, Table 9 lists the calculated wavelengths of the complexes.

Table 9 displays the main wavelengths (λ_max) calculated for each complex, their excited energy, the frontier orbital’s composition and the main transitions regarding the

visible region. Through this table we can see that γ-RuCl₂(Nazpy)₂ presents the highest wavelength with the important extinction coefficient (λ_max = 748.1 nm and f = 0.106). We can assume that it should be the most sensitive complex. Moreover, all except one of them show that from the HOMO orbital until HOMO-4, molecular orbitals MOs are made principally of Ru orbital. Therefore, the regarding transitions are assumed to be metal to ligand charge transfer (MLCT) types. However, with γ-RuCl₂(Nazpy)₂, although maximum wavelength and extinction coefficient are also slightly important, HOMO is mainly made of ligand Nazpy orbital indicating that this transition is a ligand to ligand charge transfer (LLCT) type, which is not suitable for photochemical caracterisation since azopyridine ligands are reportedly insulator [6] . However, HOMO-1 is made of 63% Ru orbital and the second most important transition which wavelength is 538.2 nm with excited energy that is 2.3 ev is from H-6 to L. In consequence, we can assume that γ-RuCl₂(Nazpy)₂ is not sufficiently active as sensitizer. Besides, regarding LUMO and LUMO + 1 orbitals, they are exclusively made of Ligand orbitals in all complexes. Whereas the reactive RuCl₃・3H₂O, its HOMO and LUMO are both made of Ru orbitals and the maximum wavelength and oscillation strength f regarding transitions are low (λ_max = 515.3 nm and f = 0.061). Since ΔE = 57.5 kcal・mol⁻¹, we can see here the importance of ligands that improve the sensitivity of the ruthenium. Regarding excitation energy, we observe that δ-RuCl₂(Azpy)₂ presents the lowest value confirming its softness. Whereas the δ-RuCl₂(Nazpy)₂ it displays many metallic orbitals involved in the transition such as H-1, H-2 and H-4 with a large band of absorption. This strength can be attributed to the larger conjugate system that the ligand Nazpy provides [24] .