After full optimization, the structural parameters such as bond distances and angles of the [tris(bdt)M]³⁻ (M = V³⁺, Cr³⁺, Mn³⁺, Fe³⁺ and Co³⁺) complexes are calculated. The calculated geometrical parameters as depicted in Figure 2 and Table 1. The metal and the sulfur atoms are 2.51 Å apart for V, 2.48 Å for Cr, 2.55 Å for Mn, 2.54 Å for Fe and 2.60 Å for Co. The DFT and X-ray analysis of the tris-dithiolate complexes reported V-S distances of 2.337 Å and 2.350 Å respectively [15], for Cr-S distances were 2.283 Å and 2.299 Å [19]. The experimental average Cr-S distance in the monoanion of the tris complexes at 2.299 ± 0.003 Å, is shorter by 0.086 Å than the calculated one. The experimental average Cr-S distance in monoanion of the tris complex is 0.175 Å shorter than that for our DFT calculation of the [tris(bdt)Cr]³⁻ complex. The Mn-S distances are 2.383 Å and 2.347 Å respectively in the [Mn^IV(Cl₂-bdt)₃] [Net₄]₂. CH₂Cl₂ complex and 2.331 Å for the [Mn(bdt)₃]²⁻ complex [13]. The DFT calculated [tris(bdt)Mn]³⁻ complex is 2.55 (±0.17) and 0.17 Å higher than experiment one [13]. The calculated Fe-S bond distance of the tris complex is 2.54 Å which is 0.29 Å higher than the experimental value of the complex of [Fe^III(cyclam)(tdt)] (PF₆) where the Fe-S distance is 2.25Å [23]. The experimental value deviates due to present

bulky substitute group cyclam. The theoretically calculated average Co-S bond lengths is 2.60 Å for the tris complex whereas experimentally measured value was found 2.25 Å [30] of the complex [Co^III(tren)(bdt)](PF_6)1/2(Cl)_1/2∙H₂O. This deviation was due to present bulky groups tren and bdt in the complex [Co^III(tren)(bdt)](PF_6)1/2(Cl)_1/2∙H₂O.

The present S-M-S angles were significantly larger than the previous X-ray crystal structures. The average angle is nearly octahedral angle 90˚. The angles formed by the metal ion and the two sulfur atoms of the dithiolate ligands are within 90.30˚ to 90.80˚ on an average indicating almost octahedral geometry in the coordination. The average S-Cr-S angle of the complex [N(n-Bu)₄] [Cr^III(^3,5L_S,_S)₂(^3,5L_S,S)] is 84.22˚ [19] whereas theoretically calculated value of the present tris complex of [Cr(bdt)₃]³⁻ is 90.80˚. The experimental S-Mn-S angles of the [Mn^IV(Cl₂-bdt)₃] [NEt₄]₂∙CH₂Cl₂ and [Mn(S,S-C₆H₄)₃]²⁻ complexes was 85.2˚ and 92.28˚ respectively [13] The present DFT calculation estimates 90.30˚ (±6.66) which are within the experimental range. The theoretical S-Fe-S angles in our calculation was 90.47˚, in good agreement with experimentally measured value (90.72˚) in the [(n-Bu)₄N]₂ [Fe(bdt)₂]² complex [37]. The DFT calculated average bond angle S-Co-S was found 90.51˚. Figure 2 shows the average M-S bond distance’s d_MS’s and the angles of S-M-S triplets, θ_SMS’s. The fluctuation in d_MS was significant. All the, θ_SMS’s however fluctuate significantly from their average values.

In this study we have investigated the metal-ligand binding energies, ΔE, of the trivalent metal ions considered and are presented in Figure 3 and Table 2. The ΔE values have greatly exceeded the physiorption energy of benzene-1,2-dithiol adsorbed on metallic surface. Lee et al. reported that a single benzene-1,2-dithiol molecule binds to a gold (111) surface with a binding energy of 6.0 kcal/mol [38]. A similar energy was reported in a DFT study of the adsorption of benzene-1, 2-dithiol to silver (111) surface (3.30 kcal/mol) [38]. The present ΔE

values (467.19 - 497.20 kcal/mol) are an order of magnitude larger than these. Interestingly, the previous study also reported that trivalent 1^st row transition metal coordination produced a 1 (one) order of magnitude increase in the cross-linking strength [39]. Figure 3 shows that the overall ΔE increases with increasing nuclear charge due to the increased electrostatic interaction with increasing nuclear charge. The decreasing ΔE with changing Cr to Mn arises from the Jahn-Teller distortion of the metal complex. The dip in ΔE observed for Fe is ascribed to the d⁵ configuration of Fe (III). In this case, as all of the d orbitals are occupied, the ligand-to-metal charge transfer is inefficient resulting in a reduced ΔE. The peak at Cr can be understood by noting that the ligand field stabilization should be largest for the d³ configurations of a high-spin complex. We have calculated the binding energies by including the zero-point energies (ZPEs), thermal energies, enthalpies and Gibbs free energies as summarized in Table 2. The vibrational, thermal, and entropic contributions to ΔE values turned out to be small, presumably due to the covalent nature of the metal ligand binding. Regardless of the metal ion, the ZPE-, thermal-energy-, enthalpy-, Gibbs free energy corrected ΔE value were all within 6% of the uncorrected binding energies.

In order to assign the electronic absorption bands of the complexes, TD-DFT calculations have been carried out on these complexes in gas phase optimized geometries at the CAM-B3LYP [34] /6-311 + G(d,p) level of theory. TD-DFT is a useful method for studying excitation energies, and its application has increased in the recent years. The electronic absorption spectra of complexes formed by V, Cr, Mn, Fe and Co have been calculated. The calculated electronic absorption spectra of the tris complexes formed by V to Co are presented in Figure 4 and Table 3. Transition metal complexes generally show three types of electronic excitation bands which cover a wide wavelength range: d-d (crystal-field) transitions (300 - 1500 nm); metal-to-ligand charge-transfer (MLCT) and ligand-to-metal charge transfer (LMCT) transitions (200 - 500 nm) [40]. The LMCT transitions localized on the ligands commonly known as intra-ligand charge transfer (ILCT) transitions, which regularly occur in the ultraviolet region. ILCT results

from n → π and n → π* transitions and is affected by the type of coordination. The calculated spectra of the model compound [V(bdt)₃]³⁻ are 431, 448, 522 and 691 respectively whereas in [PPh₄]₂ [V(bdt)₃] where vanadium has (IV) oxidation state showed the absorption maxima at 878, 681, 553, 426 and 327 respectively [15]. The calculated spectra of the model compound [Cr(bdt)₃]³⁻ are 442 nm and two d-d transitions with relatively low intensities in the visible region at 565 and 687 nm, as typical for chromium (III) octahedral complex. The electronic structure of this complex is best described as [Cr^III(^3,5L_S,S)₃]³⁻ with a chromium (III) central ion (d³, S = 3/2) and three closed-shell dithiolate-(2-) ligands [19]. The electronic spectra of these tris(dithiolene)chromium complexes resemble closely those reported previously for the corresponding tris(dioxolene) chromium complexes [19].

For the trianion manganese [tris(bdt)Mn]³⁻ complex, the absorption spectra were obtained at 453, 488 and 559 nm. These are in the range of experimentally measured absorption spectra (363, 508, 582 and 741 nm) of the [Mn(S,S-C₆H₄)₃]²⁻ complex (where Mn is d³) in CH₃CN solution [22]. Our DFT calculated absorption spectra of the tris complex of iron [Fe(bdt)₃]³⁻ was found at 394, 546 and 650 nm respectively. The experimentally measured values of the complex of toluene-3,4-Dithiolate(tdt), [Fe^III(cyclam)(tdt)](PF₆) complex, the monocation, shows absorption bands above 400 nm with maximum at 580 nm and 825 nm respectively [23]. The calculated absorption spectra of the Co tris complex [tris(bdt)Co]³⁻ was found at 687, 731 and 863 nm which are overestimated compared to the measured spectra of the [Co(III)(tren)(bdt)](PF₆)_1/2(Cl)_1/2∙H₂O complex at 463 nm and 646 nm respectively [30]. This discrepancies due to present bulky groups tren and bdt of the complex [Co(III)(tren)(bdt)](PF₆)_1/2(Cl)_1/2∙H₂O.

The electronic structure parameters are very important for understanding the molecular interactions with other species. We have calculated the electronic energy gap Eg, electron affinity A, electronegativity χ, chemical hardness η and chemical softness S for all the considered complexes. The results are presented in Table 4. The energetics of frontier molecular orbitals (FMOs), i.e., the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies are calculated. HOMO, which can be considered of as the outermost orbital containing electrons, tends to give these electrons and acts as an electron donor. On the other hand LUMO can be considered as the innermost orbital containing free places and accepts electrons. The difference between HOMO and LUMO provides the electronic gap Eg as depicted in Figure 5. Our investigation shows that Eg for the considered complexes increases in the following direction Mn³⁺ > V³⁺ > Cr³⁺ > Co³⁺ > Fe³⁺. The electron affinity and electro negativity values also follow the same trend (Table 4). From MOs plots (Figure 5), it can be concluded that the HOMO is mainly centered on metal coordinated sulfur atoms (which acts as a donor atoms) whereas LUMO is mainly located on the metal surface.

The Energy gap characterizes the molecular chemical stability, and it is a critical parameter in determining molecular electrical transport properties because it is a measure of electron conductivity. The energy gap between HOMO and LUMO (E_g) also plays important role in predicting the polarizability of a molecule. Smaller the energy gap, the more polarizable the molecule is. The chemical stability of molecule can be also studied by the calculation of the chemical hardness η and chemical softness S as shown in Table 4. Large energy gap is an indication of hard molecule and small energy gap is the sign of soft molecule. Therefore, among the [tris(bdt)M]³⁻ (M = V, Cr, Mn, Fe and Co) complexes, the

[tris(benzene-1,2-dithiolato)Fe]³⁻ complex is the hardest, followed by those of Co³⁺, Cr³⁺, V³⁺ and Mn³⁺ respectively. The soft molecules are more polarizable than the hard ones as they need small energy for excitation.

The atomic charge on the metal ion has been calculated and summarized in Table 5. Four different schemes were used to calculate the charges: Natural Population Analysis (NPA) [41], MK [42] (Merz-Singh-Kollman), CHelpG [43] (Charges from ELectrostatic Potentials using a Grid based method), and CHelp [44] methods. The atomic charges vary according to the schemes. For example, according to NPA method, the charge is 1.513 for Fe, but the charge is 2.038 if the MK scheme was used. The atomic charge decreased with increasing nuclear charge. The present drift of the atomic charge deviated considerably from a uniform decrease with increasing nuclear charge. The uniform decrease was attributed to the increased covalent nature of the metal-sulfur bond (hence, the charge transfer increased from the ligand to metal). For the present complexes, however, the atomic charge was a minimum for Co³⁺, regardless of the charge scheme. The charge also decreased as the metal atom was changed from Cr to Mn and Fe, according to the MK, CHelpG and CHelp schemes.

In the natural bond orbital (NBO) [45] analysis, electronic wave function is explained in terms of occupied Lewis and unoccupied Lewis localized orbitals. The delocalization of electron density(ED) between occupied Lewis-type and unoccupied non-Lewis NBOs correspond to stabilizing donor-acceptor interactions that contribute predominantly to the stabilization of the entire molecular system. The strength of donor-acceptor interactions, E i j ( 2 ) , are evaluated by second-order perturbation theory. For each donor (i) and acceptor (j) in the complexes, the stabilization energy or second-order perturbation energy, E i j ( 2 ) associated with the delocalization from i → j was estimated using Equation (2).

Δ E i j ( 2 ) = − q ( F ^ i j ) 2 ε j − ε i (2)

In Equation (2), q is the donor orbital occupancy, ε i and ε j are diagonal elements (orbital energies) of donor and acceptor NBOs respectively and F ^ i j is the off-diagonal NBO Fock matrix element. Values of this energy are proportional to the intensities of NBO interactions or to the extent of intramolecular charge transfer (ICT) within a molecular entity. The greater the electron donating tendency from donor to acceptor NBOs is, the larger the E i j ( 2 ) values and the more intense the interaction between the electron donors and the electron acceptors are. Table 6 summarizes the E i j ( 2 ) values of the tris(benzene-1,2-dithiol) complexes of trivalent V, Cr, Mn, Fe and Co complexes in gas phase for the important NBO interactions. The most important interaction energies of these complexes are due to interactions between the lone pair electron of the S atom(LP₀) and antibonding orbital of the M³⁺( LP M * ) (M³⁺ = V, Cr, Mn, Fe and Co). According to Table 6, E i j ( 2 ) values decrease with a decrease in the ionic sizes. Therefore, donor-acceptor interaction energies are the greatest values in the tris(benzene-1,2-dithiol) complex of trivalent V ion except Mn. The donor-acceptor interaction value of Mn complex is higher due to Jahn-Teller

^aNatural Population Analysis (NPA) [41]. ^bMK(Merz-Singh-Kollman) [42]. ^cCHelpG (CHarges from ELectrostatic Potentials using a Grid based method) [43]. ^dCHelp methods to fit the electrostatic potential method [44].

effect. The strongest interaction in V-complex is LP_S12 → LP_V, in Cr-complex is LP_S37 → LP_Cr, in Mn-complex is LP_S12 → LP_Mn. In Fe-complex the strongest interaction is LP_S37 → LP_Fe and in Co-complex is LP_S36 → LP_Co. The results of NBO analysis reflect generally charge transfer from lone pair orbitals located on the donor atoms S to the central metal ions. NBO analysis provides the most accurate possible “natural Lewis structure”.