Una interpretación simbólica del mito bíblico

The results of the previous section provide us with the necessary information to make predictions about the formation of the triatomic species, NSF and FNS, based on the electronic structure of the parent diatomic molecule, NS. In this section we describe the formation of a recoupled pair bond dyad in NSF. Although this is a 2c-2e interaction involving the singly occupied orbital resulting from the formation of the initial recoupled pair π bond in NS and a singly occupied orbital on the incoming ligand, it results in the formation of a recoupled pair bond dyad.

5.4.1 The NSF(X¹A′) Isomer

The GVB orbital diagram for F addition to NS is shown in Figure 5.6 and the four GVB orbitals involved in the recoupled pair bond dyad at the equilibrium geometry, (R_e, θe), of NSF are plotted in Figure 5.7. For clarity, the orbital labels in Figures 5.6 and 5.7 are consistent with those in Figures 5.2 and 5.3. Since we are primarily interested in the relative description of the two F(NS) isomers, the GVB calculations on the triatomic species considered only the four active a′ orbitals needed to describe bond formation in the two isomers species, rather than the eight active a′ and a″ orbitals for the full GVB wave function. Leaving the NS σ and π(a″) orbitals doubly occupied in the GVB wave function is not expected to significantly affect the relative energetics of the two isomers, although it will impact the NS dissociation energies. The NS bond energies for both a 3-

measure of the error introduced by requiring the orbitals describing these two bonds to be doubly occupied (as they would be in a HF wave function).

At (Re, θe), the PP spin-coupling weight for the four-electron GVB wave function is 0.99 for the NSF(X¹A′) state; so this state is well described by a set of four covalent bonds—a σ and two π-type bonds connecting NS and the σ bond connecting SF (recall that NS is well described as having a σ and πx bond). In MO terms the NS π (a′) and SF σ bonds would be considered to be a variation of a (3c-4e) bond. However, as can be seen by the nature of the orbitals in Figure 5.7 and the fact that the PP spin coupling weight is so large, these bonds are simply two polar covalent bonds.

Apart from a slight polarization due to the presence of the F atom, the bond pair making up the NS recoupled pair p bond, (φ5, φ6), remains singlet coupled and the orbitals are very similar to the NS orbitals plotted in Figure 5.2. Examining the newly formed bond pair, (φ7, φ8), the F-centered 2p-like orbital, φ8, is almost unperturbed by bond formation. On the other hand, there are significant changes in φ7: this orbital has localized in the SF bonding region and delocalized onto the F atom, displaying the expected S^δ+F^δ– polarity of a σ bond between S and F.

The polarity of the NS–F bond has an additional benefit—it reduces the ‘bad’

overlaps of φ7 with the NS bond pair, (φ5, φ6), from S67 = 0.63 and S57 = 0.12 in NS to S67 = 0.37 and S57 = 0.10, respectively, in NSF. The resulting decrease in the Pauli repulsion has a stabilizing effect and leads to an increase in the strength of the NS–F bond as well as that of the N–SF bond compared to their covalent counterparts:

D(NS–F) = 87.88 kcal/mol D(S–F) = 83.32 kcal/mol

A larger increase might have been expected from completing the dyad. However, because of the spatial arrangement of the two bond pairs, the repulsive interaction between the two pairs, especially that related to S67, is still significant, and this, along with increases in the repulsions between the other electron pairs, reduces the strengths of these bonds. The calculated NS–F bond length is slightly longer than that in the covalent SF bond, Re(NS–F) = 1.651 Å versus 1.601 Å in the SF(X²Π) state, which is also most likely due to repulsion between the new bond and the N–SF recoupled pair π bond as well as that between the F lone pairs and the other σ and π bonds. Completion of the recoupled pair bond dyad in NSF does shorten the N–SF bond as a result of the reduced ‘bad’

overlaps. The N–SF bond is 0.050 Å shorter than the NS bond at 1.497 Å, see Table 5.2.

It is also possible to form NSF though the addition of a nitrogen atom to the recoupled pair σ bonded a⁴Σ^- state of SF; this is shown in Figure 5.8. In this configuration orbitals (φ7, φ8) make up the SF recoupled pair σ bond while the incoming nitrogen orbital, φ5, forms a bond with φ6, the singly occupied orbital left over from formation of the recoupled pair σ bond in the SF(a⁴Σ^–) state (orbitals that complete the dyad are shaded yellow in both Figures 5.6 and 5.8). Note that, although the sulfur lobes, (φ6, φ7), in Figure 5.8 are drawn on either side (top and bottom) of the atom, representing recoupled pair σ bond formation, the orbitals have significant density on both sides of the sulfur atom, see Figure 2.10. Mixing of the configurations represented in Figures 5.6 and 5.8 may make a contribution to the stability of NSF, although the similarity of the orbitals of NS (Figure 5.2) and NSF (Figure 5.7) suggests that the contribution associated with the configuration in Figure 5.8 is likely to be small.

5.4.2. The FNS(X¹A′) Isomer

The calculated geometries for NSF along with FNS are listed in Table 5.3.

Formation of an F–NS bond will disrupt the NS recoupled pair p bond and would be expected to weaken and lengthen the FN–S bond. That is, in fact, what is observed:

Re(FN–S) = 1.550 Å whereas Re(N–SF) = 1.447 Å, and De(FN–S) = 83.37 kcal/mol whereas D_e(N–SF) = 114.93 kcal/mol (Tables 5.3 and 5.4). The GVB diagram describing the PP spin-coupling pattern is shown in Figure 5.9. The stabilizing effect of the recoupled pair bond dyad in NSF and the destabilization of the FN–S bond as a result of the formation of the F–NS bond together provide an explanation for the NSF isomer being lower in energy than the FNS isomer by 39.42 kcal/mol, the only isomer pair in the X(NY); X = H, F and Y = O, S series to exhibit this behavior. Our work on the oxygen-substituted species will be reported in Chapter 6.

The relative stabilities of the isomers calculated at the HF, and GVB levels of theory, at the RCCSD(T) geometries, are also included in Table 5.3 (basis set: AVQZ).

The GVB isomerization energy is only 1.24 kcal/mol greater than that from the RCCSD(T) calculations, but is 4.12 kcal/mol less than the HF energy.