Theoretical investigation of paramagnetic group 13 diazabutadiene radicals: Insights into the prediction and interpretation of EPR spectroscopy parameters†

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Introduction
During the past quarter of a century, 1,4-diaza-1,3-butadiene (DAB) ligands (1) have attracted considerable attention as useful reagents in organometallic chemistry due to their coordination and redox properties. The lone pairs of the nitrogen atoms and the electrons of the C=N bonds allow these molecules to act both as n-and -electron donors, which allows coordination to metals using 2, 4, 6, or 8 electrons. In addition, the identities of the four substituents on the N=CC=N backbone can be easily varied, allowing for the steric and electronic properties of the ligand to be fine-tuned; the ligand substituted at the nitrogen atoms with the bulky t Bu group has been widely employed in research.
At present, DAB ligands have been coordinated to nearly all the transition metal elements, 1 to lanthanoids such as europium and gadolinium 2 , as well as to a range of main group elements including silicon 3 and germanium. 4 A number of the synthesized metal complexes are catalytically active and can effect a broad spectrum of chemical reactions. 5 In recent years, a growing interest in complexes of the DAB ligand which contain group 13 elements has emerged and many novel systems have arisen from this work. 6 Of especial importance have been the anionic species [(DAB)M:]  (M = Al, Ga) 6d,e which are isoelectronic with the stable N-heterocyclic Arduengo-type carbenes [(DAB)C:]. 7 More closely aligned with our research interests are the vast number of metal complexes which formally contain the DAB ligand as a monoanion radical (2), formed from the one-electron reduction of the parent species 1. Paramagnetic DAB complexes of alkaline earth metals, 8,9 lithium, 9 and zinc 8b,9,10 have been known for a number of years, while more recent work in this area has resulted in the isolation of variety of group 13 complexes containing the DAB anion radical. 6f,11 Very recently the first complexes of group 13 elements with two paramagnetic DAB ligands were reported. 11eh All these species have been characterized primarily by EPR spectroscopy and X-ray crystallography, though other experimental techniques including cyclic voltammetry and photoelectron spectroscopy have also been employed. Despite the wealth of experimental data available for these systems, significantly less is known regarding their electronic structure and, especially, their spin density distributions. Although EPR spectroscopy offers a unique experimental means of acquiring much of this information, the majority of the spectra obtained for the paramagnetic group 13 DAB complexes are poorly resolved due to hyperfine couplings to a number of spin-active nuclei. In consequence, it is difficult to extract accurate values of the hyperfine coupling constants (HFCCs) and, thus, the spin densities, from these spectra. In many cases, this has led to spectral assignments that are tentative at best. 11 The spirocyclic systems [( t Bu-DAB)2M]  (3-M tBu , M = Al, Ga) offer an extreme example of the controversies reported for these systems; 11a,b inadequate spectral analysis initially lead to an incorrect assignment of different oxidation states for the group 13 elements in 3-Al tBu (M III ) and 3-Ga tBu (M II ) whereas more detailed spectral 12 and theoretical 12b,13 analyses have demonstrated that both systems contain a group 13 atom in the M III oxidation state.
While information regarding the electronic structures and spin densities of radical systems can also be obtained through high-level theoretical calculations, only two computational studies of the DAB complexes of p-block elements have been reported to date. 13 Both studies have been confined to the investigation of spirocyclic complexes of the type 3-M R , and only one reports the calculated spin densities for the group 13 metal derivatives. 13b This is somewhat surprising considering the vast number of paramagnetic group 13 DAB complexes reported recently and the unexpected, and at times conflicting, spectroscopic data that they have yielded. 11ch A high-level theoretical study of these systems is expected to give valuable information about their spin densities which would facilitate a re-interpretation of the experimental data and perhaps clarify some of the controversy which surrounds these radicals.

Results and discussion
Spirocyclic group 13 diazabutadiene monoradicals The first paramagnetic spirocyclic diazabutadiene complexes of aluminium 11a and gallium [( t BuDAB)]2Ga]  (3-Ga tBu ) 11b were reported a number of years ago. These compounds were characterized both in solution by EPR spectroscopy, and in the solid state by X-ray crystallography and photoelectron spectroscopy. The structural analyses of 3-Al tBu and 3-Ga tBu revealed the presence of two inequivalent DAB ligands in each molecule, with distinctly different metrical parameters observed throughout the two DAB moieties. Interpretation of the solution EPR spectra of these species led to the rather curious assignment of oxidation states +3 and +2 for the group 13 elements in 3-Al tBu and 3-Ga tBu , respectively, indicating that 3-Al tBu is a ligandcentred radical with one singly and one doubly reduced ligand, while 3-Ga tBu would be a gallium-centred radical. This controversial claim was later refuted by a re-interpretation of the poorly resolved EPR spectrum of 3-Ga tBu , combined with theoretical calculations which suggested that 3-Ga tBu is a ligand-centred radical like 3-Al tBu . 12b,13 Recently, the first derivatives of 3-Ga R which contain aromatic substituents on the DAB nitrogen atoms have been isolated and both structurally and spectroscopically characterized. 11d,h The EPR spectrum the complex [(DippDAB)2Ga]  (3-Ga Dipp , Dipp = 2,6-diisopropylphenyl) 11h is considerably better resolved than that of 3-Ga tBu , allowing for a definitive interpretation of the observed hyperfine couplings and confirming that the unpaired electron is ligand-centred and interacts primarily with only one of the DAB units. Because systems of type 3 have been well-characterized in the past, they will provide a useful benchmark in determining the accuracy of our calculated metrical parameters and hyperfine coupling constants (HFCCs).
Calculations were carried out on a series of compounds of types 3-M R , varying the identities of the substituents on the DAB nitrogen atoms. Calculated metrical parameters for selected compounds are compiled in Table 1 along with experimental data; calculated hyperfine coupling constants for all relevant spin-active nuclei are listed in Table 2. As a whole, the calculated bond lengths and bond angles accurately reproduce those obtained from X-ray structural analyses, 11a,b,d,h indicating that the chosen level of theory is sufficient for these systems. In complexes of types 3-Al R and 3-Ga R , the central group 13 element has a tetrahedral coordination environment and the molecules display C2v symmetry, with the exception of 3-Al Ph and 3-Ga Ph , which are C2 symmetric due to the orientation of the phenyl groups. Previous theoretical work 13b has shown that the global energy minimum for the indium analogues 3-In R has C2 symmetry, where the indium atom is slightly pyramidalized: however, for ease of comparison with 3-Al R and 3-Ga R , the geometries of the calculated species 3-In R have been constrained such that the coordination sphere of the indium atom is tetrahedral. The singly occupied molecular orbital (SOMO) of 3-Al tBu is depicted in Figure 1, and is bonding along the CC bond and anti-bonding between the carbon and nitrogen atoms. Varying the substituents on the DAB nitrogen atoms does not result in significant changes to the SOMO; similarly, changing the identity of the central group 13 element from aluminium to gallium to indium does not affect its general features. Composed primarily of carbon and nitrogen p-orbitals of one DAB ligand, the SOMO has no scontribution from the central metal and only minute contributions from the second DAB moiety. In consequence, relatively small hyperfine couplings to the group 13 atom and the nitrogen atoms of one DAB ligand are expected. The SOMO also has no contribution from the DAB hydrogen atoms which suggests that any observed 1 H coupling is entirely due to spin polarization effects.
Mulliken population analysis indicated that the spin densities in 3-M R are nearly equally distributed throughout the carbon and nitrogen atoms of one DAB unit. The lack of variation in the calculated HFCCs (Table 2)  These same trends in 14 N and 1 H hyperfine coupling constants are observed for the gallium and indium systems 3-Ga R and 3-In R , and no significant variation in their magnitudes over those in the aluminium congeners is predicted. The close agreement between the 1 H and 14 N HFCCs of 3-Al R , 3-Ga R , and 3-In R is not unexpected based on the strong similarities between the SOMOs of these three radical systems. As was seen for the aluminium nucleus of 3-Al R , the 69 Ga and 115 In HFCCs are essentially static at 22 G and 33 G, respectively, regardless of the substituents on the DAB ligands. The ratios of the calculated 27 Al: 69 Ga and 27 Al: 115 In HFCCs are consistent with the relative values of the isotropic hyperfine constants of the free nuclei demonstrating again the similarity between the electronic structures of 3-M R . 16 The EPR spectra of the hitherto uncharacterized spirocyclic systems 3-In R are predicted to have a width of around 350 G, with a 30 G hyperfine coupling to indium resulting in a dectet signal which will be further split into overlapping heptets due to coupling of the unpaired electron to two magnetically equivalent 14 N and two equivalent 1 H atoms.
The calculated HFCCs compare favourably with the experimental values that have been determined for 3-Al tBu , 12a 3-Ga tBu , 12a and 3-Ga Dipp . 11h It should be noted that the experimental EPR spectra of both 3-Al tBu and 3-Ga tBu are very poorly resolved, and that the HFCCs for these species have only been estimated; a reasonable simulation of the experimental spectrum of 3-Al tBu has been reported by assuming identical HFCCs of 5 G to the five spin-active nuclei (1  1 H, 2  14 N, 1  27 Al). 12a EPR spectra of both 3-Ga tBu 11b and 3-Ga Dipp 11h have been reported in the literature; however, the extreme linebroadening observed for 3-Ga tBu has prevented the determination of accurate HFCCs for this radical and only the magnitudes of the 69,71 Ga HFCCs have been determined. 12a In contrast, a good simulation of the experimental EPR spectrum of 3-Ga Dipp has been obtained using HFCCs to 69,71 Ga (17.0 G, 20.5 G), two equivalent 14 N atoms (6.00 G), and two equivalent 1 H nuclei (5.80 G). 11h These values are in good agreement with the calculated values for the closely related species 3-Ga Ph ( Table 2). The most notable discrepancies between the experimental and calculated values are the underestimation of the 14 N HFCCs, which was also observed in our previous investigation of the related boraamidinate 14 complexes 4, and the slight overestimation of the 1 H HFCCs. As the hyperfine couplings to the hydrogen atoms of the DAB backbone arise due to spin-polarization, this behaviour is to be expected since unrestricted calculations are known to overestimate the amount of the effect. 17 Though no hyperfine couplings to the second DAB unit in 3-Al tBu , 3-Ga tBu , or 3-Ga Dipp have been detected experimentally, the experimental spectra all have relatively broad line shapes and display an S-curve, indicative of the presence of small unresolved HFCCs. 11b,h;12a ENDOR analysis of 3-Ga Dipp has confirmed the presence of small (ca. 1 G) 1 H couplings which the authors assigned to the hydrogen atoms of the isopropylmethyl groups. 11h However, the computational results suggest an alternative assignment of these HFCCs, as 1 H hyperfine couplings of this magnitude are predicted to the two CH hydrogen atoms of the second DAB unit of 3-Ga Ph .
The good correlation between the experimental and calculated HFCCs for systems 3-Al R and 3-Ga R indicates that calculations at this level are appropriate for both of these systems and thus should provide useful insights and semi-quantitative results regarding the spin density distributions of the related radicals 6-M R X and 7-M R X.

Monocyclic group 13 diazabutadiene monoradicals
The paramagnetic gallium diazabutadiene complexes [(RDAB)GaI2]  (R = Dipp, 6-Ga Dipp I; R = Mes, 6-Ga Mes I; R = Xyl, 6-Ga Xyl I) have been synthesized by the reduction of the corresponding neutral RDAB ligands with Green's "GaI"; 11d,e,h the alkyl derivative [( t BuDAB)GaI2]  (6-Ga tBu I) has also been reported as the minor product from the analogous reaction involving the t BuDAB ligand. 11e All four of these compounds have been characterized in the solid state, but EPR spectra have only been reported for 6-Ga tBu I and 6-Ga Dipp I.
The experimental EPR spectrum of 6-Ga Dipp I is very poorly resolved, and the number and magnitude of the HFCCs present could only be estimated. 11d,h The initial spectral simulation of 6-Ga Dipp I employed a 27 G coupling to the 69,71 Ga metal, 4 G and 7 G couplings to the imine hydrogen and nitrogen atoms, respectively, and a 8 G coupling to each of the two 127 I nuclei. 11d Table 3) contrast sharply with the estimated HFCCs for 6-Ga Dipp I, 11d,h for which a significantly larger gallium coupling ( 25 G) is thought to exist; the magnitude of the gallium hyperfine coupling in 6-Ga Dipp I has recently been confirmed with ENDOR measurements. 11h The estimated 1 H couplings (1.4 G) in 6-Ga tBu I are also anomalously low and well out of the range typically observed for DAB centred radicals (5-7 G) 711 .
At the same time as 6-Ga tBu I, the aluminium analogue [(DippDAB)AlI2]  (6-Al Dipp I) was also reported and characterized by both X-ray crystallography and EPR spectroscopy (Table 3). 11e The width of the poorly resolved EPR spectrum of 6-Al Dipp I is similar to that of 6-Ga tBu I, but a significantly larger 1 H coupling (5.95 G) is believed to be present in 6-Al Dipp I, which is comparable to those observed in other paramagnetic DAB complexes. Extremely small couplings to both the 27 Al (2.85 G) and 127 I (0.4 G) nuclei were also detected in the EPR spectrum of 6-Al Dipp I; the large 3.5 G line width observed for 6-Al Dipp I renders these assignments somewhat speculative. However, the simple general appearance of the spectrum (nine lines) and the relatively small spectral width clearly rule out the possibility of large couplings to any high-spin nuclei such as 27 Al and 127 I.  Table 3; the values for other derivatives of 6-M R X are included as supplementary information. Focusing on the aluminium systems 6-Al R X, it is noted that the halogen HFCCs exhibit only a small dependence on the identity of the R-group, and that the magnitudes of the 1 H and 14 N HFCCs remain essentially unchanged throughout this series (see supplementary information). The absolute value of the aluminium HFCC for these monocycles is predicted to be slightly larger (8 G) than the corresponding coupling in the spirocycles 3-Al R , while the ranges of 1 H (67 G) and 14 N (34 G) HFCCs for 6-Al R X are comparable to those of 3-Al R . Though the halogen atoms make only a minor contribution to the SOMO, relatively large (610 G) hyperfine couplings are predicted to 19 F, 79,81 Br, and 127 I nuclei due their large gyromagnetic ratios. 16 The sizes of these HFCCs are predicted to increase slightly with increasing size of the alkyl substituent; intermediate values were calculated for the aromatic derivatives 6-Al Ph X due to the more electron-withdrawing nature of their phenyl rings. In the light of controversy surrounding the assignment of a 127 I HFCC in compounds 6-Al Dipp I, 6-Ga tBu I, and 6-Ga Dipp I, 11d,h these results are of especial import.
The calculated 1 H, 14 N, and halogen HFCCs for the gallium 6-Ga R X and indium 6-In R X systems are consistent with those predicted and discussed for 6-Al R X above. The couplings to the central metals gallium ( 25 G) and indium ( 35 G) are larger than the HFCCs predicted for the aluminium compounds partially due to the larger gyromagnetic ratios of these heavier isotopes. 16 The calculated data for 6-M R  Interestingly, the ENDOR spectra reported for 6-Ga tBu I and 7-Ga tBu I are also virtually identical. 11h It is possible that compounds 6-Ga tBu I and 7-Ga tBu I, which are the minor and major products, respectively, of the same reaction, undergo various processes (such as disproportionation) in solution which equilibrate to yield significant amounts of the paramagnetic species that has been detected by EPR spectroscopy. We will resume to this topic in more detail in the next section discussing the dimeric diradicals 7-M R X.
In the case of the aluminium systems 6-Al R I, the HFCCs estimated based on the experimental EPR spectrum of 6-Al Dipp I 11e are not entirely consistent with those calculated for 6-Al Ph I (Table 3). While reasonable agreement is found for the 1 H and 14 N couplings, the observed 27 Al and 127 I HFCCs are again considerably smaller than the predicted values. As 6-Al Dipp I is expected to display a significant 127 I coupling, it seems reasonable to suggest that the species characterized in solution by EPR spectroscopy is not the same radical 6-Al Dipp I that was identified in the solid state by X-ray crystallography. This conclusion is further supported by the experimental observation that  (Table 3). In consequence, the accuracy of the experimentally derived 1 H and 14 N HFCCs should not be overestimated. However, as the 115 In coupling can readily be extracted from the experimental EPR spectrum of 6-In Dipp Cl, a comparison of this value (27 G) with the calculated HFCC (33.7 G) is much more valid: though the agreement is not exact, the fit is reasonable.

Dimeric group 13 diazabutadiene diradicals
The first complex of a group 13 element with not one but two paramagnetic DAB ligands HFCCs is markedly smaller and generally on the order of half a Gauss.
Looking more closely at a specific diradical system, no correlation between the HFCCs inferred from the experimental EPR spectrum of 7-Ga Dipp I and the calculated values for anti-7-Ga Ph I exists (see Table 4). In solution, 7-Ga Dipp I gives rise to a wellresolved EPR spectrum such that it is possible to extract accurate values for not only the 69 Ga HFCC, but also the 1 H and 14 N HFCCs. 11h However, very poor agreement is observed between the calculated and experimentally determined HFCCs: the predicted 69 Ga HFCC is 3.6 G, while the experimental value is 17.0 G, and both the 1 H and 14 N HFCCs are approximately 3 G higher than the calculated values. Though the predicted 127 I HFCC is 6.6 G  a value which should be clearly visible in the EPR spectrum  the available experimental data shows no indication of such a large iodine coupling. In fact, a closer look to the experimental data reveals that both the EPR and ENDOR spectra of 7-Ga Dipp I are virtually identical to that reported for the spirocyclic radical 3-Ga Dipp for which the calculations reproduced the experimental HFCCs well; 11h the reported g-values of the radicals 7-Ga Dipp I and 3-Ga Dipp are also the same (2.0032). Thus, the experimental and computational evidence suggest that the gallium diradical 7-Ga Dipp I, which is obtained as a minor product from the reaction between a Dipp-DAB ligand and "GaI", undergoes a rearrangement (disproportionation) in solution to yield the well-known, stable, spirocyclic radical 3-Ga Dipp .
Additional evidence which supports the above hypothesis is obtained from the crystal structure of 7-Ga Dipp I. 11h As noted earlier, the experimental GaGa bond length is but becomes more favourable as the size of the substituent R increases; for the R = Ph derivative, the reaction is essentially thermoneutral (G = 8 kJ mol 1 ). Although we did not repeat the calculations using the experimental Dipp substituted systems due to their large computational cost, it feels reasonable to expect that the energy for that reaction is close to, or possibly even less than, the value calculated utilizing the Ph derivatives. We also note that the above disproportionation reaction can be further driven to the exergonic side by subsequent transformations of Ga2I4 to a mixture of gallium sub-iodides having the Ga metal in either +3 or +1 oxidation state c.f. Green's "GaI". 19 Thus, it seems more than plausible that the diradical 7-Ga Dipp I undergoes a variety of reactions in solution, yielding the spirocyclic radical 3-Ga Dipp that has been observed by EPR and ENDOR spectroscopies. 11h Unfortunately, no UV-vis data has been reported for either 7-Ga Dipp I or 3-Ga Dipp which could be used to either confirm or refute this hypothesis.
The lone bromine-containing derivative 7-Ga Dipp Br gives rise to a solution EPR spectrum consisting of a broad resonance ( 200 G) with unresolved hyperfine couplings. 11h Due to the poor resolution of the spectrum, the experimentally derived HFCCs (Table 4) are only estimated values: in fact, attempts to simulate the experimental EPR spectrum using the reported HFCCs do not accurately reproduce the shape or width of the experimental spectrum (see Figure 2a). 20 Similarly, when the calculated HFCCs are employed, the simulated EPR spectrum is also considerable narrower than the experimental (not shown). The broad EPR spectrum observed for 7-Ga Dipp Br clearly indicates a large 69,71 Ga coupling of approximately 2025 G in size. Thus, the experimentally obtained solution EPR spectrum is not, in fact, produced by 7-Ga Dipp Br, as its calculated HFCCs show only a very minute coupling to the group 13 metal (see Table   4). Based on the above analysis for 7-Ga Dipp I, it is tempting to propose that the bromine derivative, like its iodine analogue, undergoes disproportionation in solution. The end product cannot, however, be the spirocyclic monoradical 3-Ga Dipp as it produces an EPR spectrum which is markedly different than that observed for 7-Ga Dipp Br.
To shed light upon this matter, the reported EPR spectrum of 7-Ga Dipp Br was reanalysed. 11h The spectrum displays a broad singlet signal with a plethora of fine structure.
Upon closer inspection, it was found that the peak distances within the fine structure are approximately constant throughout the whole spectrum. This implies that the paramagnetic species in question displays a  6 G HFCC to a high-spin nucleus or to a several nuclei with lower spins (possibly 1 H and 14 N). The broad nature of the signal also implies that more than one large (> 10 G) coupling is present. In addition to the large  Table 4). For example, the reported indium HFCC is 26.2 G, while the predicted value is 4.3 G; the expected 1 H (2.6 G) and 14 N (2.2 G) HFCCs are both considerable smaller than those cited in the literature. 11f As noted above, the reported EPR spectrum of 7-In Dipp Cl, including its width, g-value, 115 In HFCC, and line width, is essentially identical to that reported for the monocyclic monoradical 6-  Table 4). 11e The experimental EPR spectrum of 7-Ga tBu I is very poorly resolved, and has not allowed for accurate determination of the 1 H and 14 N HFCCs. As the general features of this spectrum are quite similar to those of the better-resolved spectrum of 6-Ga tBu I described earlier, the spectrum of 7-Ga tBu I was simulated using the same HFCCs, but a larger line width. 11e Since the g-values of the experimental EPR spectra of 6-Ga tBu I (2.0038) and 7-Ga tBu I (2.00385) are nearly identical and their EPR (and also ENDOR) spectra can be adequately simulated using the same HFCCs, 11e,h it seems probable that the species contributing to the experimental EPR spectrum of 7-Ga tBu I is the same species observed in the EPR spectrum of 6-Ga tBu I. However, the theoretical calculations reported herein clearly exclude the possibility that this unknown species would be of any of the types observed earlier i.e. a spirocyclic, monocyclic, or a dimeric gallium DAB radical. Thus, we are unable to provide a definite identification for this species. Detailed theoretical investigations of this system, as well as the aluminium monocycle 6-Al tBu I, are currently being pursued.

Conclusions
The electronic structures and the spin density distributions of the group 13 DAB radicals to the experimental EPR spectrum of 7-Ga tBu I is the same species observed in the EPR spectrum of 6-Ga Dipp I; definite identification of this paramagnetic system could not, however, be given.
The present study clearly demonstrates the ability of theoretical methods to produce realistic spin densities and, hence, accurate EPR hyperfine coupling constants.
Such data is indispensable in the analysis of EPR spectra of inorganic compounds which are often complicated by the presence of a number of nuclei with several magnetically active isotopes, and are thus readily misinterpreted.

Computational Details
The geometries of all compounds were optimized in their ground states using DFT. The calculations utilized the hybrid PBE0 exchange-correlation functional 21 and Ahlrichs' triple-zeta valence basis sets augmented by one set of polarization functions (TZVP). 22 For iodine and indium, the corresponding ECP basis sets were used. 22 The PBE0 hybrid density functional was chosen on the grounds of several published benchmarks that have shown it to perform well in calculating molecular properties for a wide variety of chemical systems. 23 The way in which the PBE0 functional is constructed and the lack of empirical parameters fitted to specific physical properties also make it appealing from a purely theoretical standpoint. Appropriate molecular point groups were used to improve the efficiency of the calculations. All geometry optimizations were done with the Turbomole 5.7.1 24 and Gaussian 03 25 program packages.
Hyperfine coupling constants were calculated for all paramagnetic systems in their geometry optimized structures by using both non-relativistic and fully relativistic methods and the unrestricted Kohn-Sham formalism. The non-relativistic calculations utilized the same basis sets and density functional as the geometry optimizations; several benchmarks have recently been published which demonstrate the suitability of TZVP basis set for the calculation of EPR parameters. 26 For the heavier nuclei indium and iodine, the use of ECPs prevents the direct determination of HFCCs using the same method. In addition, relativistic calculations are essential in order to obtain more than a qualitative accuracy. Thus, relativistic calculations for all systems with In and I atoms were carried out. The calculations utilized the large QZ4P STO basis set, the PBEPBE GGA functional 21ac as well as the scalar-relativistic ZORA formalism. The hyperfine coupling constant calculations were done with the Gaussian 03 25 (non-relativistic) and ADF 2004.01 27 program packages (relativistic). The values reported in Tables 2, 3, and 4 are non-relativistic for the lighter nuclei and scalar-relativistic for the heavier atoms indium and iodine.