Use of d orbitals

The foregoing discussion indicates that while there are difficulties in the way of a bonding role for 3d orbitals, for certain situations at least it is possible to conceive of ways in which these difficulties may be overcome. However, it is necessary to say that even for hypervalent molecules such as SF6 which seem to require the use of d orbitals, there are molecular orbital treatments not involving the use of d orbitals. In fact, as shown by Bent in an elegant exposition12, the MO model of SF6 involving the use of d orbitals is only one of several possibilities. The octahedral stereochemistry of SF6, traditionally explained in... 

A hybridization scheme is adopted to match the electron arrangement of the molecule. Valence-shell expansion requires the use of d-orbitals. 

However, there are some cases when an unpaired electron is localized not on the n, but on the o orbital of an anion-radical. Of course, in such a case, a simple molecular orbital consideration that is based on the n approach does not coincide with experimental data. Chlorobenzothiadiazole may serve as a representative example (Gul maliev et al. 1975). Although the thiadiazole ring is a weaker acceptor than the nitro group, the elimination of the chloride ion from the 5-chlorobenzothiadiazole anion-radical does not take place (Solodovnikov and Todres 1968). At the same time, the anion-radical of 7-chloroquinoline readily loses the chlorine anion (Fujinaga et al. 1968). Notably, 7-chloroquinoline is very close to 5-chlorobenzothiadiazole in the sense of structure and electrophilicity of the heterocycle. To explain the mentioned difference, calculations are needed to clearly take into account the o electron framework of the molecules compared. It would also be interesting to exploit the concept of an increased valency in the consideration of anion-radical electronic structures, especially of those anion-radicals that contain atoms (fragments) with available d orbitals. This concept is traditionally derived from valence-shell expansion through the use of d orbital, but it is also understandable in terms of simple (and cheaper for calculations) MO theory, without t(-orbital participation. For a comparative analysis refer the paper by ElSolhy et al. (2005). Solvation of intermediary states on the way to a final product should be involved in the calculations as well (Parker 1981). 

A somewhat different problem occurs in the question of the structure of, say, the phosphine oxides, the phosphine methylenes or the sul-phoxides. Again in a 3s3p framework the structure of triphenyl phosphine oxide must be written with the oxygen attached by a conventional coordinate link. On the other hand the use of d-orbitals allows the removal of the excess negative charge on the oxygen atom by the formation of a t-bond (Fig. 3). 

These calculations indicate that, for both the aluminum derivatives and for those formed by the Group II metals, one must consider metal-metal bonding interactions particularly through the use of d orbitals, but also take into account repulsion between these centers. A parameter related to these interactions is the metal-metal distance which on comparison with the sum of the metal covalent radii gives an indication of the relative magnitudes of these terms. Also, we must consider the metal-to-bridging atom distance, which must be related to the stability of the bond and should be compared with normal 2-electron bond distances between these same elements. Further, we should consider the electro-... 

Three-centre bonding is invoked in situations where the o framework cannot be described in terms of two-centre, electron-pair bonds, although it can often be accommodated by postulating resonance of a different type from that usually encountered. Two types of three-centre bond can be distinguished. The first is often postulated in hypervalent molecules/polyatomic ions AB where the central atom exceeds the octet in its Lewis formulation, as an alternative to the use of d orbitals which many chemists find objectionable. The second type occurs where there appear to be insufficient electrons - regardless of the supply of orbitals -to form the requisite number of bonds in a Lewis/VB description. In other words, the first type is postulated where we have an insufficiency of orbitals, and the second where there is a deficiency of electrons compounds containing the latter type are often described as electron-deficient . 

FHF-) formed by hydrogen bonding in F- and HF. It leads to 3c4e model which are an alternative to use of d-orbitals in hypervalent compounds with octet expansion, e.g. XeF2... 

Use of d Orbitals. The S—Po elements employ d orbitals together with their s and p orbitals to form more than four form multiple bonds. Thus, for example, in the sulfate ion, where the s and p orbitals are used in o bonding, the shortness of the S—O bonds suggests that there must be considerable multiple-bond character. The usual explanation for this is that empty dir orbitals of sulfur accept electrons from filled pn orbitals of oxygen. Similar dir—pn bonding occurs in some phosphorus compounds, but it seems to be more prominent with sulfur. 

Once again, however, ab initio calculations reproduced both bond angles and lengths without the use of d orbitals. It was concluded that, evidently, the Si-O bond is much more polar than estimated from electronegativities. Thus, both angles and lengths can be explained by coulombic repulsions. 

The isolobal approach was used in the previous section to describe the formation of metal-metal bonds. These bonds differ from others only in the use of d orbitals on both atoms. In addition to the usual ct and n bonds, quadruple bonds are possible in transition metal compounds. Furthermore, bridging by ligands and the ability to form cluster compounds make for great variety in structures containing metal-metal bonds. 

The studies described in sec. 2.3 on of die orbitals in conjugated systems went along with another line of enquiry, on the question of the tendency of second row elements to display their higher covalencies, five in the case of phosphorus, six in sulphur, towards the more electronegative first row elements. Pauling had proposed the use of d-orbitals in bonds in his classic 1931 paper [240],... 

Benzoselenadiazole (128) behaves as a heterodiene toward dimethyl acetylenedicarboxylate, with which it gives the quinoxaline 124 and selenium. But 128 reacts differently with benzyne (generated from 4 or from 9) to give the 1,2-benzisoselenazole derivative 132 (88%) and a small amount of a cis,trans stereoisomer of 132.82 The analogous adduct 131 is obtained in lower yield from benzyne and 2,1,3-benzothiadiazole (127). The structure of these benzyne adducts is strikingly reminiscent of 135, which is obtained from a photochemical addition of dimethyl acetylenedicarboxylate to 126 via a nitrile oxide intermediate.84 However, for reasons given elsewhere,82 a nitrile selenide is unlikely to be an intermediate in the formation of 132, which is better explained by the mechanism outlined in Scheme 16. As in the case of thiophen (Section V,B), this is a 1,3-cycloaddition (in one or two steps) of benzyne to the heterocycle, enabled by the use of d orbitals on the sulfur or selenium atom. 

The six S—F bonds are formed by the overlap of the hybrid orbitals of the S atom and the 2p orbitals of the F atoms. Since there are 12 electrons around the S atom, the octet rule is violated. The use of d orbitals in addition to s and p orbitals to form an expanded octet (see Section 9.9) is an example of valence-shell expansion. Second-period elements, unlike third-period elements, do not have 2d energy levels, so they can never expand their valence shells. Hence atoms of second-period elements can never be surrounded by more than eight electrons in any of their compounds. 

Table 2 presents an abstract of Table 1 in ref. 12. In general, all three methods MNDO, AMI, and PM3 give rather remarkable results. In many cases, however, PM3 is more accurate than AMI, and both are more accurate than MNDO. MNDO predicts sterically crowded molecules to be too unstable and favors, in contrast, small rings, a shortcoming in most ZDO methods largely corrected in AMI and PM3. Of special interest is the observation that PM3 successfully reproduces the heats of formation of hypervalent compounds without the use of d orbitals. 

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