Conformations and Energetics of Sulfur and Selenium Diimides

The geometries and energetics of different conformations of sulfur and selenium diimides E(NR) 2 (E = S, Se; R = H, Me, t Bu, C 6 H 3 Me 2 -2,6, SiMe 3 ) have been studied by using various ab initio and DFT molecular orbital techniques. The syn,syn conformation is found to be most stable for parent E(NH) 2 but in general the preferred molecular conformation for substituted chalcogen diimides is syn,anti . In the case of E(NH) 2 the present calculations further confirm that syn,syn and syn,anti conformations lie energetically close to each other. From the three different theoretical methods used, B3PW91/6-31G* proved to be the most suitable method for predicting the geometries of chalcogen diimides. The optimized geometrical parameters are in a good agreement with all available experimental data. While qualitative energy ordering of the different conformations is independent of the level of theory, the quantitative energy differences are dependent on the method used. The performance and reliability of higher-level ab initio calculations and DFT methods using large basis sets were tested and compared with experimental information where available. All of the higher-level ab inito methods give very similar results but the use of large basis sets with the B3PW91 method does not increase the reliability of the results. The combination of CCSD(T)/cc-pVDZ with the B3PW91/6-31G* optimized geometries is found to be the method of choice to study energetic properties of chalcogen diimides.


Introduction
The structure and isomerism of sulfur diimides S(NR)2 have attracted considerable interest in view of their utility as ligands in transition metal complexes 1-3 and as reagents in organic syntheses. 4 S(NSiMe3)2, in particular, is a convenient source for the NSN fragment in a variety of cyclic and acyclic main-group compounds. 5 Three different conformations are possible for chalcogen diimides, as shown in Figure 1.
Variable temperature NMR spectroscopic studies have indicated that the syn,anti conformation of S(NR)2 is most stable in solution in the case of small organic groups (R = Me, t Bu). 7 With bulkier organic substituents, small amounts of the anti,anti conformation was inferred to be in equilibrium with the syn,anti conformation. [8][9][10] Recently, however, the existence of syn,syn conformations has been reported in the solutions of S(NC6H2Br3-2,4,6)2, S(NC6H3Me2-2,6)2, and S(NC6F5)2. 11,12 Structural determinations of a variety of S(NR)2 molecules by X-ray diffraction in the solid state and electron diffraction in the gas phase have shown the presence of syn,anti and syn,syn conformations depending on the organic substituent R. [11][12][13][14][15][16][17][18][19][20][21][22][23] There are a few semiempirical, 11,12,24,25 ab initio, 26,27 and DFT 28 calculations on sulfur diimides that have established that while syn,anti and syn,syn conformations lie close to each other in energy, the anti,anti conformation lies at a higher relative energy.
In contrast to stable sulfur diimides, selenium diimides Se(NR)2 are thermally unstable. [29][30][31][32] The only known X-ray structure is that of N,N'-diadamantyl selenium diimide, which expectedly shows a syn,anti conformation in the solid state. 33 It has also been inferred from the 1 H and 13 C NMR spectra that Se(N t Bu)2 exists in solution in the syn,anti conformation. 31 The analogous tellurium diimides have been observed to undergo a facile [2+2] cycloaddition with the formation of thermally stable dimers RNTe(µ-NR)2TeNR. [34][35][36] A similar [2+2] cycloaddition has also been observed between Se(N t Bu)2 and t BuNSeO. 37 Sandblom et al. 28 have reported a DFT study of the conformations and dimerization energies of E(NMe)2 (E = S, Se, Te). 38 These calculations have verified the facile [2+2] cycloaddition of Te(NMe)2. The cycloaddition of methyl sulfur diimide was found to be strongly endothermic and that of methyl selenium diimide was concluded to be approximately thermochemically neutral.
The present ab initio and DFT study was undertaken in order to compare the geometries and energetics of a number of sulfur and selenium diimides at different levels of theory. The scope is to establish the level of reliability in the prediction of geometries and relative energies of different conformations of the monomeric diimides and establish the relevant structural trends.
Comparison to experimental information is carried out where possible.

Computational Methods
All calculations were carried out with the Gaussian 98 program. 39 Geometries of all different conformations of E(NR)2 (E = S, Se; R = H, Me, t Bu, C6H3Me2-2,6, SiMe3) were fully optimized at the RHF, 40 MP2, 41 and B3PW91 42,43 levels of theory. The standard 6-31G* basis set was used as implemented in Gaussian 98. The hybrid B3PW91 functional was chosen, since it has been shown to perform well for molecules containing third-row elements. 44 A standard pruned (75,302) grid was used for B3PW91 optimizations but a denser pruned (99, 590) grid was chosen for the single point energy calculations in order to minimize inaccuracies arising from the use of numerical integration. The fundamental frequencies were calculated at the RHF and DFT levels of theory in order to assess the nature of stationary points and estimate the zero-point energy (ZPE) corrections.
Two different high-level methods were used to calculate the relative energies of different conformations more accurately. Single point calculations for all optimized geometries were performed at the coupled-cluster 45 level of theory using Dunning's correlation consistent cc-pVDZ basis set as implemented in Gaussian 98. In addition, single point energies were also calculated with the B3PW91 method using basis sets of increasing size on B3PW91/6-31G* optimized geometries. Two Pople-type basis sets (6-31G* and 6-311G**) and two correlation consistent basis sets (cc-pVDZ and cc-pVTZ) were used as internally available in Gaussian 98.

Results and Discussion
Geometries: The optimized geometries of sulfur diimides are given in Table 1 and those of   selenium diimides in Table 2. In the case of each sulfur diimide studied in this work, the calculated values can be compared with molecular parameters that have been determined by Xray or electron diffraction (see Table 1). The comparison of calculated and experimental geometries indicates that the bond parameters can be predicted reasonably well at all levels of theory. 46 The RHF/6-31G* calculations underestimate the S=N bond lengths by 0.01-0.03 Å, whereas at the MP2/6-31G* level they are overestimated by approximately 0.06 Å. The S=N bond lengths yielded by the B3PW91/6-31G* calculations seem to be in best overall agreement with the experimental values. The experimental H-N, C-N, and Si-N bond lengths are accurately reproduced at every level of theory. Calculated RMS deviations between the experimental and calculated bond lengths are 0.022, 0.041, and 0.018 Å at the RHF/6-31G*, MP2/6-31G*, and B3PW91/6-31iG* levels of theory, respectively.
With the exception of S(NH2)2 and S(NC6H3Me2-2,6)2 that appear as syn,syn conformers, the experimental molecular structures of all other sulfur diimides shown in Table 1 exhibit syn,anti conformations. 47 It can also be noted that the two NSN fragments in S(NSNSiMe3)2 49 and Se(NSNSiMe3)2 6 also lie in syn,anti conformations. As seen in Table 1, in most cases the S=N bond of the syn-S=N-R fragment is shorter than that corresponding to the anti-S=N-R orientation. This can be rationalized in terms of the bonding description discussed by Sandblom et al. 28 While the S=N bond lengths generally seem to be independent of the identity of the organic group, those in S(NSiMe3)2 are shorter in every conformation. This can be explained by charge delocalization due to the hyperconjugative interaction between the nitrogen 2p lone pair and the SiMe3 fragment. Results from the preliminary ELF 50,51 calculations for S(N t Bu)2 and S(NSiMe3)2 seem to support this conclusion, as they show that the electron population in lone pairs is much smaller in S(NSiMe3)2 than in S(N t Bu)2.
Of the selenium diimides, the X-ray structure is known only for N,N'-diadamantyl selenium diimide Se(NC10H15)2, 33 which shows a syn,anti conformation consistent with most sulfur diimides. The experimental Se=N bond lengths are 1.679(8) Å (syn-Se=N-R) and 1.732(7) Å (anti-Se=N-R) displaying a similar trend as syn,anti sulfur diimides. Other estimates for the Se=N double bond length can be obtained from the X-ray structures of t BuNSe(-N t Bu)2SO2 and t BuNSe(-N t Bu)2SeO. 37 The exocyclic Se=N bonds in these two compounds show lengths of 1.665(2) and 1.687(4) Å, respectively. The optimized syn-Se=N bond lengths for the different syn,anti conformations of Se(NR)2 lie in the range 1.633-1.650, 1.708-1.743, and 1.678-1.702 Å at RHF/6-31G*, MP2/6-31G*, and B3PW91/6-31G* levels of theory, respectively (see Table 2). Although the calculations reproduce the bond lengths relatively accurately, the calculated bond angles show a larger deviation from the experimental values. It can be seen from Table 1 that the NSN bond angles are in good agreement with experimental values (deviations ca. 1) at each level of theory, but the RHF/6-31G* and MP2/6-31G* optimized SNA (A = H, C, Si) angles deviate from the experimental values. The RHF/6-31G* calculations overestimate the SNA angles, whereas MP2/6-31G* calculations lead to a small underestimation. By contrast, the B3PW91/6-31G* calculations seem to provide a good prediction also for the experimental SNA The present calculations seem to yield a better agreement between the calculated and experimental bond parameters than the previous theoretical approaches. Semi-empirical CNDO and MNDO calculations 11,12,24,25 should only be considered as qualitative and the early ab initio calculations 26,27 have suffered from the use of small, inflexible minimal STO-3G* basis sets that limit the accuracy in the predictions of both molecular geometry and energetics. Sandblom et al. 28 have recently reported a DFT study of the conformations and dimerization of E(NMe)2 (E = S, Se, Te). These calculations agree well with the present B3PW91/6-31G* results in the case of N,N'-dimethyl sulfur diimide with somewhat more pronounced differences in the case of N,N'dimethyl selenium diimide. The DFT prediction of Sandblom et al. 28 yields Se=N bond lengths that are ca. 0.070 Å longer and bond angles that are 2-4° smaller than the corresponding B3PW91/6-31G* values. It seems that generally the B3PW91/6-31G* geometries are in better agreement with experiment than those yielded by the earlier DFT calculations. 38

Energetics:
The total energies and ZPE corrections calculated for sulfur and selenium diimides at RHF/6-31G*, MP2/6-31G*, and B3PW91/6-31G* levels of theory are presented in Supporting Information (Table S1). The relative energies of the different conformations are depicted in conformation is most stable, the syn,anti conformation is predicted to be most stable for substituted sulfur and selenium diimides regardless of the level of theory. 52 In the case of parent E(NH)2, our calculations further confirm the earlier deductions that syn,syn and syn,anti conformations of the parent molecule lie close to each other in energy. These results are expectedly in agreement with the previous experimental 11-23 and computational 11,12,24-28 findings. The qualitative energy ordering of the different conformations is found to be independent of the level of theory. Results in Figure 3 also show that the anti,anti conformer is more unstable than could be expected on the basis of steric factors alone. Sandblom et al. 28 have recently suggested that the antibonding interaction between the in-plane nitrogen lone pair and the p orbital on sulfur destabilizes the sterically favorable anti,anti conformation.
Since no accurate experimental energetics data are available for chalcogen diimides, the reliability of the results lies solely on the grounds of theory. This was evaluated by high-level CCSD/cc-pVDZ and CCSD(T)/cc-pVDZ calculations. It was not, however, possible to carry out full geometry optimizations at coupled cluster levels of theory. Therefore single point calculations utilizing optimized geometries that were calculated at RHF/6-31G*, MP2/6-31G*, and B3PW91/6-31G* levels of theory (see Tables 1 and 2) were carried out for all sulfur and selenium diimides. The total energies yielded by these calculations are presented in Supporting Information (Table S2). Relative energies are presented at Table 3. The CCSD(T)/cc-pVDZ//B3PW91/6-31G* relative energies are shown in Figure 4. The CCSD(T)/cc-pVDZ single point calculations were chosen to utilize B3PW91/6-31G* optimized geometries, since they were in closest agreement with experimental geometries, where available. Furthermore, in most cases, the B3PW91/6-31G* geometries yielded lowest total energies at the CCSD/cc-pVDZ level and could therefore be considered as best geometries at coupled cluster levels of theory. The energetics of the three conformations of the different chalcogen diimides will therefore be discussed below at CCSD(T)/cc-pVDZ//B3PW91/6-31G* level of theory.
It can be seen from Figures 3 and 4 that the terminal R-group in E(NR)2 seems to have a greater influence on the relative energies of the conformations than the identity of the chalcogen atom. The relative energies for molecules with same substituents but different chalcogen atoms deviate only in the case of tert-butyl diimides, whereas the relative energies for different substituents vary substantially. For example, syn,syn-S(NMe)2 lies 12.2 kJ mol -1 and syn,syn-S(N t Bu)2 lies 46.8 kJ mol -1 above their respective syn,anti conformations, and the syn,syn conformations of Se(NMe)2 and Se(N t Bu)2 lie at 8.3 and 29.9 kJ mol -1 above the most stable syn,anti-conformations, respectively (see Figure 4). In the cases of S(NSiMe3)2 and Se (NSiMe3) Table 4. These values can be compared to the CCSD(T)/cc-pVDZ//B3PW91/6-31G* relative energies that represent the highest level of reliability in the present ab initio calculations (see Table 3). It can clearly be seen from Table 4 that as the size of the basis set is increased, the B3PW91 relative energies show variation, the mutual differences between the basis sets often being above 10 kJ mol -1 . In the case of the most flexible basis set, cc-pVTZ, the B3PW91 calculations in fact yield relative energies that are furthest away from those obtained by the CCSD(T)/cc-pVDZ//B3PW91/6-31G* level calculations. The smallest Pople-type basis sets seem to reproduce best the high level ab initio relative energies in the case of all sulfur and selenium diimides.
By contrast, it is well-known that the relative energies calculated using ab initio methods converge and become more accurate, when the level of sophistication is increased (See Tables S1 and S2 in Supporting Information). In most cases, the relative energies calculated at MP2/cc-pVDZ level of theory can already be considered reasonably reliable.
These findings seem to contradict the one-dimensionality of the DFT methods i.e. the increase in the size of a basis set should result in a better description of the energy. 56 It has been stated earlier that "...it is rather plausible that the many honors density functional theory has earned in this field in the past are due to massive error compensation effects arising from the use of a small basis sets". 57 Large basis sets should therefore not be kept as a definite measure of the quality of DFT results. This has not been explored to its full extent in computational chemistry. It can be very tempting in individual situations to select a basis set that will best reproduce the observed property and hold the method superior, though the agreement between calculated and experimental property might only be fortuitous. Current hybrid density functional methods are fast and valuable means to study structures and chemical properties of molecules. However, as there seems to be no systematic way to improve the accuracy of the DFT calculations, the comparison of the calculated parameters with experimental or sufficiently high-level ab initio data is necessary to evaluate the level of reliability of the results.

Conclusion
The geometries and energetics of the different conformations of a number of sulfur and selenium diimides E(NR)2 (E = S, Se; R = H, Me, t Bu, C6H3Me2-2,6, SiMe3) have been studied by using ab initio and DFT molecular orbital techniques. With the exception of parent E(NH)2, for which the syn,syn conformation is most stable, the syn,anti conformation is predicted to be most stable for substituted sulfur and selenium diimides regardless of the level of theory. In the case of parent E(NH)2, the present calculations further confirm that syn,syn and syn,anti conformations lie close to each other.
The geometry optimizations were carried out at RHF/6-31G*, MP2/6-31G*, and B3PW91/6-31G* levels of theory. B3PW91/6-31G* proved to be the most suitable method for reproducing the experimental geometries of chalcogen diimides. It has a speed advantage compared to ab initio methods and provides results of at least the same accuracy as computationally much more demanding MP2/6-31G*.
The total and relative energies of the different conformations of S(NR)2 and Se(NR)2 molecules have been calculated at RHF/6-31G*, MP2/6-31G*, and B3PW91/6-31G* levels of theory and compared with those yielded by higher-level CCSD(T) and B3PW91 calculations.
The qualitative energy ordering of the different conformations is found to be independent of the level of theory. By contrast, the quantitative energy differences are found to be dependent on the method. Whereas ab initio methods yield increasingly accurate relative energies with increasing level of theory, B3PW91 results show divergence, as the size of the basis set is increased. The B3PW91 involving small Pople-type basis sets seem to reproduce best the energetics of chalcogen diimides from high-level ab initio calculations. Since the B3PW91/6-31G* calculations predict well the optimum geometries, reliable relative energies of the chalcogen diimide conformers can conveniently be computed at CCSD(T)/cc-pVDZ//B3PW91/6-31G* level of theory.
It is well established experimentally that, whereas sulfur diimides S(NR)2 exist as monomeric species in solution, the corresponding tellurium diimides Te(NR)2 undergo a facile [2+2] cycloaddition reaction to form dimeric RNTe(µ-NR)2TeNR. 34-36 It is not quite clear whether selenium diimides are preferentially monomeric or dimeric. The NMR spectroscopic evidence of selenium diimides in solution 31 as well as the X-ray structure of N,N'-diadamantyl selenium diimide 33 indicate a preference for monomeric structures, but [2+2] cycloaddition reactions have been inferred for the dimerization of t BuNSeO to OSe(µ-t BuN)2SeO 33 and for the reaction of t BuNSeO and Se(N t Bu)2 that affords t BuNSe(N t Bu)2SeO. 37 The DFT calculations of Sandblom et al. 28 (Tables S1 and S2). This material is available free of charge via the Internet at http://pubs.acs.org.