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The isotropic shielding calculations for the ground state of S2N2, as well as for

other electronic states in this chapter, were performed at the CASSCF(22,16)/cc-pVTZ level of theory. The semi-experimental D2h

geometry of S2N2, which was obtained by Perrin et al.[151], was used during all

the isotropic shielding calculations.

As it can be seen from table (5-1), both the sulfur and nitrogen nuclei are deshielded but the deshielding of the latter is significantly higher. A different shielding profile at 1 Å above the nuclei can be observed. The shielding values decreased to about one-tenth of the nuclear shieldings. If the absolute difference values of |𝛥𝜎_{𝑖𝑠𝑜(𝑆−𝑁)}0 Å | and |𝛥𝜎_{𝑖𝑠𝑜(𝑆−𝑁)}1 Å | are compared, one can notice that the value of the latter is much lower than the former.

Table 5-1: CASSCF(22,16)/cc-pVTZ isotropic shielding data (σiso) (in ppm) of ground state

of S2N2 for sulfur and nitrogen nuclei and for points placed 1 Å above them as

well as absolute shielding difference values of the S-N bond nuclei,

|𝛥𝜎_{𝑖𝑠𝑜(𝑆−𝑁)}0 Å |, and of points located 1 Å above the nuclei, |𝛥𝜎𝑖𝑠𝑜(𝑆−𝑁)1 Å |.

Nuclear σiso (ppm) σiso 1 Å above nuclei |𝛥𝜎𝑖𝑠𝑜(𝑆−N) 0 Å _{| |𝛥𝜎} 𝑖𝑠𝑜(S−𝑁)1 Å | S -77.79 9.50 42.50 2.57 N -120.29 12.07

More shielding details are displayed by the 2D shielding maps, see figure (5- 2). In general, the shielding assigns aromatic features to S2N2. The S-N bond

domains are obviously well-shielded. Interestingly, although the sulfur nuclei are deshielded, see table (5-1), they are surrounded by very highly shielded- spheres. In contrast to this, the nitrogens are also surrounded by deshielded- spheres. Both types of sphere have radii of around 0.5 Å, see maps (a,b). Three other shielding features can also be observed from figure (5-2). The first regards the shielding cloud corresponding to π-electron delocalisation which correspond to contour level of 1-5 (ppm) shaped as a hollowed-centre four-pointed star, see maps (a-e). However, at 0.75 Å, see map (d), another star-shaped cloud of 10 (ppm) represents the maximum activity of the π- electron delocalisation at that height, which decreases to 7.5 (ppm) at 1 Å, see map (e).

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Figure 5-2: Five contour maps of isotropic shieldings (σiso) (in ppm) obtained at the

CASSCF(22,16)/cc-pVTZ level of theory for the ground state of disulfur dinitride. (a-e): grids parallelly placed at 0.00, 0.25, 0.50, 0.75 and 1.00 Å heights above the molecular plane, respectively.

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The second point shown by figure (5-2) relates to the shielding clouds of the lone pairs. The shielding islands located at the corners of above-mentioned star shapes in maps (a-c) besides two shielding islands above the nitrogens in maps (d,e) represent the shielding activity of the lone pairs of the nitrogens and sulfurs. When comparing these shielding activities of the lone pairs, it is obvious that higher contributions come from the nitrogens rather than the sulfurs.

Both points mentioned above can also partially be noticed in figure (5-3) showing the vertical component of the isotropic shielding σiso(zz).

Figure 5-3: Contribution of the vertical-component of the isotropic shielding (σiso(zz)) (in

ppm) in the total isotropic shielding σiso of ground state S2N2, obtained at the

CASSCF(22,16)/cc-pVTZ level of theory for a grid placed parallelly at 1.00 Å above the molecular plane.

The third point is that the less shielded core, LSC, of S2N2 becomes not only

“lower in shielding” but also becomes “deshielded”. This most probably belongs to the small size of the ring of S2N2 which makes the σ-bonds closer,

which, in turn, affects the shielding activity of the ring centre.

A clearer shielding profile above the ring centre is shown in figure (5-4). The maximum deshielding value is found at the ring centre, -0.99 (ppm). Above this point, the deshielding activity gradually fades away till 0.32 Å at which there is a switch to shielding which increases till reaching a maximum value of +2.65 (ppm) at 1.02 Å above the ring centre. Figure (5-5) shows cross- sectionally an ovoid LSC centred on the S2N2 ring.

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Figure 5-4: Variation in the CASSCF(22,16)/cc-pVTZ isotropic shielding σiso (in ppm) of the

ground state of S2N2 obtained from 71 ghost atoms placed perpendicularly

from the ring centre to a 2 Å height above it.

By comparing the close surroundings of the nuclei in maps (a) and (b) in figure (5-5), one can notice strongly shielded and deshielded spheres that surround sulfur and nitrogen, respectively. Outside these spheres, shielding activity about the nitrogen exceeds that about sulfur. In other words, there are higher contributions from nitrogen in S-N bonding and π-delocalisation than from sulfur. Also, the presence of two islands above and below each nitrogen in map (b) corresponds to the shielded-triangles of nitrogen lone pairs that are shown in figure (5-2 (c)). The reason for the shielding variation of both nuclei most probably belongs to the electronegativity difference and to other possible reasons mentioned in the introduction of this chapter (see section (5-1)). Inspecting the two outer shielding borders at 1 and 2 (ppm) of the three maps in the figure (5-5) clearly highlights the shielding combination above and below the ring centre which can be considered as a characteristic feature of π-electron delocalisation at these places. The maps show no sign of diagonal shieldings along S-S or N-N bonds which can be seen in figure (5-1 (i) and (iii)). The conclusion is that such bonds do not exist.

Cross-sections of the S-N bond shielding are shown in figure (5-6). Map (a) indicates a shift of the shielding cloud from the midpoint towards nitrogen. Several factors may cause this, the delocalisation as well as the lone pair above and below the nitrogen atom promote such shifting towards nitrogen, see figure (5-2 (c-e)). The maximum shielding at the midpoint of the S-N bond

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in figure (5-6 (b)) is around 40 (ppm), centred in a less-shielded triangular cloud. However, the map shows a slight shift of the above cloud towards the space outside the ring. The existence of deshielding of LSC at the ring centre, which counteracts with nearby shielding activities, is the cause of this shift. Interestingly, an example of shielding/deshielding avoidance can be observed in the shielded/deshielded spheres around sulfur represented by curve (a) in figure (5-7). The very strongly shielded-sphere, located at the sulfur with maximum shielding of +169.5 (ppm) shows a tendency to enforce the shrinkage of the inner-deshielded sphere to occupy the smallest volume possible, see also map (a) in figures (5-5) and (5-6).

Figure 5-5: Ground state CASSCF(22,16)/cc-pVTZ isotropic shielding map obtained by utilising 2D grids placed perpendicularly to the S2N2 molecular plane,

diagonally passing through sulfurs (a) and nitrogens (b) as YZ and XZ planes, respectively, evenly bisecting the ring and opposite S-N bonds (c).

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Figure 5-6: CASSCF(22,16)/cc-pVTZ isotropic shielding contour maps (in ppm) of ground state S2N2 obtained byutilising2Dghost-atoms grids located perpendicularly

to and passing along an S-N bond, (a), or bisecting and crossing the bond at its midpoint (b). The (0,0) X,Y point is located at the bond midpoint.

The above shielding behaviours of sulfur and nitrogen, as well as of the S-N bond, can be analysed numerically via figure (5-7). The maximum shielding value of the S-N bond AMBL is 42.6 (ppm) which is located about 0.1 Å away from the bond midpoint towards nitrogen. Also, both shielded/deshielded- spheres can be observed as shielded/deshielded peaks near the nuclei. However, the shielded-sphere of sulfur surrounds a smaller deshielded- sphere of around 0.07 Å radius. Curve (b) shows a more homogenous shielding trend than curve (a). However, the points above and near nitrogen are higher in shielding than those around sulfur.

Figure 5-7: Variation in the CASSCF(22,16)/cc-pVTZ isotropic shielding (σiso) (in ppm) of

the S-N bond of ground state S2N2 obtained from 71 ghost atoms: (a)

positioned along the S-N bond, and (b) placed 1Å parallelly above the bond.

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Clearly, the blue isosurface in figure (5-8), which corresponds to +16 (ppm), indicates that S2N2, in general, shares the shielding behaviour of aromatic

molecules. However, the shrinking of this isosurface in regions near S-N bonds indicates lower shielding and aromatic content than aromatic molecules. The transparent isosurface at +7 (ppm) serves as a comparative tool which shows how much S2N2 is lower in shielding and aromaticity than

aromatic molecules. The expansion trend of this isosurface is similar to that of +16 (ppm) in aromatic molecules. Thus, the ratio of +7 to +16 isosurface extents may reflect aromaticity content of S2N2 relative to strongly aromatic

molecules.

Finally, unlike the sulfurs, the nitrogens behave like the atoms in aromatic rings because of the deshielded-spheres presence about the nitrogens. This is shown by the red isosurface of -16 (ppm) in figure (5-8).

Figure 5-8: CASSCF(22,16)/cc-pVTZ isotropic shielding (σiso) isosurfaces of ground state

S2N2, (a) front view, (b) and (c) side views along the X- and Y-axis,

respectively, (d) horizontal (in-plane) cross-section. The isosurfaces colour/shielding value are defined as transparent/+7; blue/+16; and red/-16.

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