DFT Quantum-Chemical Modeling Molecular Structures of Cobalt Macrocyclic Complexes with Porphyrazine or Its Benzo-Derivatives and Two Oxygen Acido Ligands

Based on the results of a quantum chemical calculation using the DFT method with the OPBE/TZVP and B3PW91/TZVP levels, the possibility of the existence of three cobalt heteroligand complexes containing in the inner coordination sphere porphyrazine, di[benzo]- and tetra[benzo]porphyrazine, and two oxygen (O2−) ions with probable oxidation state VI of Co, which is unknown for this element at the present time, was shown. Data on the structural parameters are presented. It was shown that CoN4 chelate nodes as well as all metal-chelate and non-chelate cycles in each of these complexes, were strictly planar. Besides, the bond angles formed by two donor nitrogen atoms and a Co atom were close or equal to 90°, while the bond angles formed by donor atoms N, Co, and O, in most cases, albeit insignificantly, differed from this value. Good agreement between the calculated data obtained using the above two versions of the DFT method was found. Standard thermodynamic parameters of formation (standard enthalpy ΔH0f, 298, entropy S0f, 298 and Gibbs’s energy ΔG0f, 298) for the indicated complexes were presented too.


Introduction
As is known, cobalt in its currently known chemical compounds can be in oxidation states from 0 up to V, wherein its highest oxidation state, namely IV and V, are uncharacteristic for the given element [1][2][3].
In particular, such compounds as CoO 2 dioxide and cesium hexafluorocobaltate(IV) Cs 2 CoF 6 [4,5], have been known for Co(IV) for a long time and for Co(V), sodium tetraoxocobaltates(V) Na 3 CoO 4 and potassium K 3 CoO 4 [6,7], and also a number of organometallic complexes [3,[8][9][10]]. An availability of Co(VI) was supposed in the matrix of cesium tetraoxoferrate(VI) (Cs 2 FeO 4 ) as isomorphically replacing Fe(VI), and its identification was carried out by Mössbauer spectroscopy [11]; however, any compound with a stoichiometric chemical composition for a given oxidation state of cobalt was described neither in this work nor in other publications. By taking into account the theoretical considerations expressed in the introduction to the articles [12,13] devoted to Cu(IV) and Zn(IV) complexes with porphyrazine and its benzo-derivatives (in particular, trans-di[benzo]porphyrazine and tetra[benzo]porphyrazine) and one oxo ligand, we have every reason to believe that the given macrocyclic ligands in combination with two oxo ligands will also be able to form complexes with structural formulas [CoL1  [benzo]porphyrazine H2L2 and tetra[benzo]porphyrazine H2L3). These complexes are interesting in that, as it is easy to see from these formulas, in any of these complexes the cobalt atom is bonded to other atoms by eight chemical bonds, six of which are formed by the exchange mechanism (namely, two with each of two oxygen atoms and one with the each of two nitrogen atoms), and according to the generally accepted definition, the concept of "oxidation state", the value of this parameter for a given atom of a 3d-element should be accepted equal to (+6). It should be specially noted that no mention of complexes of type I-III in the special literature devoted to (NNNN)-donor atomic macrocyclic ligandsporphyrins, porphyrazines and their derivatives [14][15][16][17][18][19][20][21][22], or anywhere else, could not be found. In this connection, the given article will be devoted to a theoretical analysis regarding the possibility of the existence in principle of such complexes with the use of modern methods of quantum chemistry, namely, the density functional theory (DFT) method.

Results
The chemical bond lengths between atoms and bond angles for the [CoL1 ( The pictures of spin density distribution in the complexes under study are shown in Figure 4.      Table 2. For complete NBO analysis data, see Supplementary Materials, too.        Table 3. As may be seen, all these parameters are positive for each of the complexes under consideration.

Discussion
As can be seen from the data presented in Table 1, both versions of DFT methods used by us, on the whole, give similar values of key parameters of molecular structures for the chemical compounds under study. According to these data, all four 5-membered and 6-membered metal chelate rings as well as chelate nodes CoN 4 and N 4 groupings in them, are a strong plane or, at least, are practically plane because the sum of the bond angles in each of these structural fragments are exactly 540.0 • , 720.0 • , 360.0 • , and 360.0 • , respectively, or very close to these values (deviation from planarity is not more than 0.2 • ). Besides, all chelate and non-chelate rings are completely identical to each other in the sum of bond angles in them, but are slightly different between themselves in the lengths of bonds between the corresponding atoms and in the assortment of bond angles in them. In [CoL1(O) 2 ] and [CoL2(O) 2 ] complexes, however, both 5-membered and 6-membered rings are identical only in pairs because the assortment of bond angles in these pairs differ among themselves. This difference becomes quite understandable if we take into account only the pairwise equality of (NCoN) bond angles formed by the central metal atom Co with neighboring donor nitrogen atoms (  2 ] are quite typical for coordination compounds of 3d-elements containing L1 2− , L2 2− , and L3 2− as ligands (see, e.g., Supplementary Materials). It should be noted in this connection that within the framework of any of these structures, there are bonds between cobalt and oxygen atoms, the lengths of which (169-179 pm) correspond to double Co=O bonds, and bonds between cobalt and nitrogen atoms, the lengths of which (192-196 pm) correspond to a single Co-N bond. Note in this regard that the lengths of cobalt-nitrogen, carbon-nitrogen, and carbon-carbon bonds, as well as bond angles in the CoN 4 chelate node and in metal chelate rings in the most bulky structures of these three complexes, namely [CoL3(O) 2 ], are very close to the experimental values of the corresponding parameters for the complex of cobalt(II) with tetra [benzo]porphyrazine (phthalocyanine) [CoL3] found in [23,24].
As mentioned above, both the independent DFT methods used by us give rather close values of the key structural parameters for these complexes, but there are very significant differences on two points. On the one hand, according to the DFT OPBE/TZVP data, the bond angles formed by two oxygen and cobalt atoms (O1Co1O2) differ quite noticeably from 180 • , while according to the DFT B3PW91/TZVP data, on the contrary, they are exactly 180 • . On the other hand, that is interestingly the   2 ] complexes under examination, respectively, does not seem possible.
As may be seen from Table 2, values of effective charges on Co atoms are considerably less than +6.000ē which would be the case if all chemical bonds between Co, N, and O atoms would be ionic; the similar situation occurs for N donor atoms and O atoms, the values of charges on which are very different from −3.000 and −2.000ē, respectively, too. This is evidence that a very high degree of electron density delocalization takes place in the each of the given coordination compounds.
According to the data of our calculations, the ground state of the  2 ] one is spin quartet; the nearest excited state is located higher than ground one, on 17.6, 48.3 and 55.9 kJ/mol, respectively. The difference in the values of the "energetic distances" in the ground and the nearest excited states given by these methods turns out to be very significant, but in any case, in our opinion, they allow us to make a conclusion that a spin crossover for such complexes should not have occurred. By taking into consideration the important fact that, as will be indicated further (see Section 4), the DFT OPBE/TZVP method in the case of 3d elements more adequately predicts the relative energy stabilities of high-spin and low-spin states than the DFT B3PW91/TZVP one, we consider it more correct to conclude that the ground state of [CoL1(O) 2 ] and [CoL2(O) 2 ] is namely a spin doublet, the ground state of [CoL3(O) 2 ] is namely a spin quartet. An additional argument in favor of this conclusion is the values of <S**2> for these complexes ( Table 2) On the other hand, testing the wave functions of the ground state for stability within of this method using the STABLE = OPT procedure showed that, in all cases, the wave function did not show any attributes of instability.

Materials and Methods
As in our articles [12,13], and also in earlier ones, in particular [26][27][28][29][30], quantum-chemical calculations were performed by the DFT method with OPBE/TZVP level combining the common TZVP extended triple zeta split-valence basis set [31,32] and the OPBE non-hybrid functional [33,34]. As shown in [34][35][36][37][38], 3d elements more adequately predict the relative energy stabilities of high-spin and low-spin states, and reliably characterize the key geometric parameters of corresponding molecular structures. Moreover, for comparison, the other variant of the DFT method, namely with the B3PW91/TZVP level, which combining the TZVP and B3PW91 functional [39,40], was used in the given work; according to data [41], this has a minimal value of so-called "normal error" in comparison with other variants of the DFT method. This conclusion is in full harmony with the data of structural parameters of macrocyclic complexes of various 3d-elements with phthalocyanine obtained as a result of various DFT quantum-chemical calculations and in experiment (see Supplementary Materials). For comparison, the Supplementary Materials also presents the calculation data for the known complex of cobalt with phthalocyanine [CoL3], carried out using the DFTD wB97XD/TZVP method described in [42] and taking into account dispersion (Van der Waals) interactions; as it turned out, this method gives structural data close to those obtained by the DFT OPBE/TZVP and DFT B3PW91/TZVP methods. However, in comparison with them, it is much more costly in terms of the calculation time. Calculations were performed with the Gaussian09 program package [43]. The correspondence of the found stationary points to energy minima was proved in all cases by the calculation of second derivatives of energy with respect to atom coordinates; all equilibrium structures corresponding to minima of the potential energy surfaces had only real positive frequency values. When carrying out calculations within the framework of any of the above two variants of the DFT method (OPBE/TZVP as well as D3PW91/TZVP), we did not impose any symmetry restrictions; the structure with the C 1 symmetry group was initially specified. Theoretically, Co(VI) must have 3d 3 electronic configuration, and spin multiplicities 2 and 4 were considered for it. Among the structures optimized at these multiplicities, the lowest-lying structure was selected. Parameters of molecular structures with the given multiplicities were always calculated by unrestricted methods (UOPBE and UB3PW91, correspondingly). In addition, in all cases, the wave functions at the minimum point were checked for stability according to procedure STABLE = OPT in Gaussian. The standard thermodynamic parameters of formation (∆H 0 f, 298 , S 0 f, 298 and ∆G 0 f, 298 ) for the given macrocyclic metal chelates under examination were calculated using the method described in [44].

Conclusions
The data obtained using two various DFT methods, namely with OPBE/TZVP and B3PW91/TZVP levels and presented above in the given paper, unambiguously predicted the possibility of the existence of three novel cobalt complexes having [CoL1(O) 2 ], [CoL2(O) 2 ], and [CoL3(O) 2 ] compositions where L1 2− , L2 2− , and L3 2− is a double deprotonated form of porphyrazine, trans-di[benzo]porphyrazine and tetra[benzo]porphyrazine, respectively. In each of them, there are six bonds formed by cobalt atoms with atoms having greater electronegativity in comparison with it, according to the exchange mechanism-two chemical bonds with nitrogen atoms, and four with oxygen atoms. The generally accepted definition of the term "oxidation degree" is as follows: "the oxidation degree is the charge in units of electron charge that would occur on the atom of a given element in a given chemical compound under the assumption that within the framework of each of the conditionally existing in this compound two-center two-electron chemical bonds formed by the exchange mechanism, there would be a complete transfer of electrons from the atom with less electronegativity to the atom with more electronegativity". The oxidation degree of the each of central atoms in the metal complexes (i.e., Co) may be postulated equal to + 6. But since the oxidation state of any chemical element with a positive oxidation degree is determined as the modulus of oxidation degree and is displayed by the corresponding Roman numeral, in each of these compounds, the oxidation state of cobalt may be considered equal to VI. Naturally, the real charge on the Co atoms in the complexes under consideration differ significantly from the value of +6.00ē, but given that the parameter is not connected with the above definition, in principle it cannot be used as a definition of the oxidation state [2]. Be that as it may, the results of our quantum-chemical calculation completely fit into the idea of a fairly high stability of those chemical compounds with a high oxidation state of the central atom, where the coordination polyhedron is formed from the most durable and difficult-to-oxidize acid ligands having atoms with the highest electronegativity (in our case, O 2− ). Note in this regard that, upon the introduction of the second oxo ligand into the inner coordination sphere of the square pyramidal complex [CoL1(O)] described in [25], the molecular structure of the resulting complex [CoL1(O) 2 ] remains practically unchanged in comparison with that for [CoL1(O) 2 ], both qualitatively and quantitatively.
As can be seen from the data presented in Table 3, the values of standard thermodynamic parameters of formation ∆H 0 f, 298 , S 0 f, 298 and ∆G 0 f, 298 for the cobalt complexes of types I-III are positive and this is an indirect indication of their relatively low stability. This circumstance, however, is in no way a contraindication to attempts to obtain them, since it is known that there are a number of chemical compounds for which there is a similar situation with respect to standard thermodynamic characteristics, but which, nevertheless, were obtained experimentally in one way or another (f.e., boranes having general formula B n H n+2 , dicarbon dinitride (cyanogen) C 2 N 2 et al.) Moreover, according to the above data of a quantum-chemical calculation by the two independent DFT methods indicated above, the molecular structures of these complexes presented in Figures 1-3 are quite stable). As for the possible synthesis of these chemical compounds, then, in principle, any of them could be obtained by exposure to very strong oxidizing agents, for example F 2 , KrF 2 , or of such an exotic oxidizer as difluoride dioxygen O 2 F 2 , on cobalt(II) complexes with the macrocyclic ligands L1, L2 and L3. In particular, in the case of [CoL3(O) 2 ], such a synthesis may be realized according to the general schemes (1-3). [ It can be assumed that these macrocyclic compounds, if they will be obtained in experiment, will gain not only purely academic, but also very substantial practical interest and may be promising in a number of industry areas, in particular in catalysis, photonic, electronic, and electrochemical technologies. On the other hand, the complexes under study may be used as "precursors" in the various reactions of synthesis coordination compounds and, also, in the reactions of coordinated ligands owing to which, in principle, novel macrocyclic compounds may be obtained.