Nodal properties p orbitals

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All in all our work implies that the highest filled orbitals are of a symmetry. To anyone reflecting on the electronic structure of carbon dioxide it is extraordinary to find the a orbital above the tt orbital, implying that the latter forms he stronger bond. Nevertheless this state of affairs was anticipated many years ago in the overlap calculations of Belford and Belford (4). They pointed out that the angular nodal properties of the f and f orbitals are such that at short distances the f -p overlap may actually be less than the f -p overlap a result con irmed in a calculation by Newman (5). 

Note, as mentioned above that all terms are included in these two-electron calculations over the Gaussian primitives, which is in conflict with the nodal properties of actual p orbitals. 

So far the nodal structure of the valence s- and p-orbitals themselves has been in our focus, allowing us to explain the special role of the 2p-elements compared to their heavier homologues. The further modulations of chemical and physical properties as we descend to a given group from period 3 on are often summarized under the term secondary periodicity [65, 66]. The main influences here are incomplete screening of nuclear charge by fllled core or semi-core shells and the effects of special relativity. The former reflect shell structure of the atom as a whole and are already important for differences and similarities of the homologous third and fourth period elements, whereas the latter become crucial mainly for the chemistry of the sixth period elements. These aspects have been discussed in detail in various review articles (see, e.g.. Refs [16, 28, 67]), and we, thus, touch them only briefly. 

Figures 2.7a and 2.7b show the in-phase and out-of-phase combinations of two atomic orbitals. In terms of the region between the nuclei, the Pz Pz interaction is similar to that of two s atomic orbitals (Fig. 2.5) and the symmetries of the resultant MOs are consistent with the and (t labels. Thus, the direct interaction of two p atomic orbitals (i.e. when the orbitals lie along a common axis) leads to (Tg(2p) and o- (2p) MOs. The p orbitals of the two atoms X can overlap only in a sideways manner, an interaction which has a smaller overlap integral than the direct overlap of the P2 atomic orbitals. The in-phase and out-of-phase combinations of two 2p atomic orbitals are shown in Figs. 2.7c and 2.7d. The bonding MO is called a rr-orbital pi-orbitaV), and its antibonding counterpart is a 7r -orbital Cpi-star-orbitaV). Note the positions of the nodal planes in each MO. A tt molecular orbital is asymmetrical with respect to rotation about the intemuclear axis, i.e. if you rotate the orbital about the intemuclear axis (the z axis in Fig. 2.7), there is a phase change. A tt -orbital must exhibit two properties ...

The mixing of AOs into MOs is restricted only by the nodal properties of the orbitals and by symmetry the 3s orbital of a chlorine atom may not contain contributions from any of the p gaussians, because the s—p overlap between AO s centered on the same atom is zero. This can be easily checked by mentally overlapping the two spherical harmonics in Fig. 3.2, where the (-1—1-) overlap is equal and of opposite sign to the (H—) overlap. In the same way, the pz AOs of the ethylene carbon atoms do not overlap with any of the s-type orbitals in the rest of the molecule, and mix as a separate subset of AO s into the n-MOs [5]. These restrictions ultimately stem from the angular momentum of electrons. 

The third set of solutions furnishes the 3 and 3p atomic orbitals. They are similar in shape to, but more diffuse than, their lower-energy counterparts and have two nodes. Still higher-energy orbitals (3d, 4, 4p, etc.) are characterized by an increasing number of nodes and a variety of shapes. They are of much less importance in organic chemistry than are tbe lower orbitals. To a first approximation, the shapes and nodal properties of the atomic orbitals of other elements are very similar to those of hydrogen. Therefore, we may use s and p orbitals in a description of the electronic configurations of helium, lithium, and so forth. 

L in Scheme 11.3) departs. Nucleophilic addition to the intermediate benzyne (step D) is readily explained by perturbative MO arguments. The extra and orbitals of benzyne are compared to those of ethylene in Figure 11.7. The aromatic n system is not involved in the special properties of benzyne. The third benzyne n bond is due to the overlap in fashion of the two sp2 hybrid orbitals which lie in the nodal plane of the intact 6 electron system. Two factors contribute to a very low LUMO for benzyne. First, the sp2 hybrid orbitals are lower in energy than the 2p orbitals from which the ethylene orbitals are constructed. Second, the intrinsic interaction between the two sp2 orbitals is less than the normal / cc since the orbitals have less p character and are tipped away from each other. The low LUMO of benzyne makes the molecule a strong Lewis acid, susceptible to attack by bases, and a reactive dienophile in Diels-Alder reactions, as we shall see later. 

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