2.1. Structural Aspects
As a first step of the work, we have optimized the initial [Cr(III)(n-TMC)O2
= 12, 13, 14 and 15) complexes starting from the crystallographic structures where available [10
]. The availability of crystallographic structures contributes to decrease the calculation time and allows comparison between experimental and theoretical parameters. Different spin multiplicities values (2S + 1 = 3, 5, 7) deriving from the two side-on (η2) and end-on (η1) binding modes of O2
molecule (Scheme 1
b), which as mentioned before, determine the oxidation state of metal center in the complexes, have been considered.
In the [Cr(III)(12-TMC)(O2
complex, the η2 side-on coordination of oxygen to the metal center is the preferred one, regardless of the electronic spin state. All the attempts to obtain the end-on η1 isomer failed since the structure collapses into the η2 one during the optimization. Support to these findings arises from the second-order perturbative analysis that reveals the presence of electronic delocalization in the Cr-O2
region involving the O-O bonding orbitals with the empty orbitals of the metal ion. The most stable spin configuration for the complex is the triplet electronic state followed by the quintet at 4.4 kcal mol−1
. As expected, the state with multiplicity seven appears to be unstable since the oxygen molecule lies out from the metal coordination shell (Cr-O distances are 4.484 and 4.925 Å). The geometrical features of the minimum well match with the X-ray structure of a similar complex in which the chlorine atom is replaced by an aqua ligand [10
global minima, our computations indicate the η1 coordination for oxygen and the triplet spin state. The excited quintet state lies at 5.5 and 6.2 kcal mol−1
, respectively, above the absolute one. The end-on coordination of O2
as preferred binding mode in the [Cr(III)(14-TMC)(O2
complex, has already been suggested by the previous theoretical calculations performed at DFT/ B3LYP level of theory and by crystallographic studies [5
]. The situation is different for the [Cr(III)(13-TMC)(O2
complex for which we still find the η1 as O2
preferred coordination mode but a ground state of quintet followed by the triplet lying at only 2.4 kcal mol−1
The main geometrical parameters for the obtained minima of the considered species, in the most stable spin state and binding modes of O2
, are summarized in Table 1
As can be seen from Table 1
, the Cr-Oa distance and the O-O-Cr valence angle increases in going from the complex involving 12-TMC to that with 14-TMC, but decreases with the 15-TMC.
This behavior can be explained by the different conformational flexibility of the ligands imposed by different rearrangements. In fact, in the complex [Cr(III)(15-TMC)(O2)(Cl)]+, the four methyl groups attached to the nitrogen atoms are equally distributed up and down the ring plane, while in the [Cr(III)(14-TMC)(O2)(Cl)]+, the four N-CH3 groups present a syn-type orientation with respect to the oxygen. This means that the end-on coordinated O2 suffers minor steric hindrance.
In the complex involving 12-TMC ligand, the topology is different and the axial positions are occupied by the peroxo ligand and one nitrogen atom, while the four pseudo-equatorial positions include three nitrogen and the chlorine atoms.
2.2. NO Conversion Mechanism
In the considered reaction mechanism, depicted in Scheme 1
, the first step of the reaction is the nucleophilic attack of the end-on [Cr(III)(n-TMC)(O2
= 13, 14 and 15) superoxo or side-on [Cr(IV)(n-TMC)(O2
= 12) peroxo complexes on NO to form the peroxynitrite (ES) species. Since the peroxynitrite complexes can assume cis and trans isomeric forms, we have explored both these possibilities. We specify that, after the intermediate species (INT), the stationary point can assume only the cis arrangement. Combining the lowest lying electronic state of the peroxo or superoxo complexes with that of NO substrate, the ES complex can assume a spin multiplicity of doublet or quartet. For all the considered species, the quartet results to be the ground state, with the doublet being one that lies at higher energy (22.8, 23.2, 33.3, 24.2 kcal mol−1
for the peroxynitrite complexes with 12-TMC, 13-TMC, 14-TMC and 15-TMC ligands, respectively). Peroxynitrite species prefer the cis arrangement (Figure 1
) and the trans isomers lie at about 4–5 kcal mol−1
above the cis ones. It is important to note that the formation of ES complexes occur without an energy barrier. The most stable species (ES cis peroxynitrite for 12-TMC, 13-TMC, 14-TMC and 15-TMC ligands) have been selected for its next conversion in NO3−
Following the proposed reaction mechanism of Scheme 1
, for both the spin multiplicities, we have characterized all the minima and the transition states, whose cartesian coordinates are reported in the Supplementary Materials
. The relative potential energy surfaces (PES) are reported in Figure 2
. In the same figure, we also report the relative energies for the trans isomers in parenthesis.
From the peroxynitrite complex (ES) the formation of the NO2 species is obtained throughout the transition state TS1, in which the homolytic O-O cleavage and the N-O bond formation occur simultaneously. The potential energy surfaces concerning the doublet state lie at very higher energy with respect to those of quartet, therefore, we will discuss in detail only the second ones.
IRC computations clearly indicated that this transition state connects the ES with the intermediate INT. As it can be seen from Figure 2
, the energy amount necessary to convert ES into INT is considerably small: 4.6 (12-TMC), 4.3 (13-TMC), 5.2 (14-TMC), and 4.1 (15-TMC) kcal mol−1
. This means that with these activation energies (TS1), the first reaction step results to be very fast at laboratory temperature.
As it can be evinced from the Figure 3
, where are depicted the TS1 optimized geometries in cis and in trans conformation of all complexes, the O-O distance reveals the breaking of the bond with the consequent formation of the O-N one that gives rise to the NO2
As mentioned before, the quartet PESs wind below the doublet ones, but spin crossing at the first intermediate (INT) level are present on the PES describing the catalytic activity of complexes with 12-TMC, 13-TMC and 15-TMC. However, the energy values of intermediate in the two different multiplicities are very similar, therefore the inter-surface crossings should not introduce significant effects in the energetic behaviors.
For the formation of the final product (EP), which implies the definitive conversion of NO2
in nitrate ion, the NO2
must approach the Cr=O moiety. In the PESs, it clearly shows that this event requires a small amount of energy. The highest barrier is found for the complex having 15-TMC (7.2 kcal mol−1
, 10 kcal if the spin crossing is considered), while the lowest one is obtained for the complex with 12-TMC (1.0 kcal mol−1
). Figure 4
shows, as in TS2, the NO2
is coordinated to Cr=O moiety and the new N-O bond is forming (N-O = 2.212, 2.036, 1.980 and 2.037 Å in 12, 13, 14 and 15-TMC, respectively).
In the final products (EP), the formed NO3−
is linked to the chromium ion throughout one oxygen (the distance is about 1.9 Å for all the considered cases), giving rise to a complex with a six-coordinated metal center (Figure 5
). For the complex with 12-TMC ligand, our result concerning the Cr-O bond length (1.961 Å) can be compared with previous crystallographic X-ray data (2.003 Å).
The energetic potential energy surfaces we have determined allow to extrapolate some important information: (i) the formation of the peroxynitrite species occurs without an energy barrier and with a considerable energy stabilization; (ii) the nitrate ion formation process is strongly exothermic; (iii) the potential energy surfaces for the complex with different ligands are similar, indicating that all the starting complexes are able to easily oxidize NO in NO3−; and (iv) the spin inversion occurring along some reaction paths does not significantly affect the process.
The NBO charges computed for the atoms for every stationary point along the PESs are reported in Figure 6
. A common aspect to all examined cases is that the net charge of nitrogen atom increases in going from ES to EP indicating its activation. The negative charge of oxygen atom Oa linked to the metal center in the initial complex increases until the TS2 is reached, then it decreases in the nitrate final product due to the electronic delocalization on the NO3−