P atomic orbitals

As another example, the 2s and 2p orbitals on the two N atoms of N2 can be formed into pairs of sp hybrids on each N atom plus a pair of p atomic orbitals on each N atom. The sp hybrids directed... 

Fig. A. Molecular-orbital representation of the 1-centrc F-Xe-F bond, (a) The possible combinations of colinear p, atomic orbitals, and (b) the energies of the resulting MOs (schematic).

What is wrong with the following sentence "The it bonding molecular orbital in ethylene results from sideways overlap of two p atomic orbitals."... 

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

Although the hybrid orbitals discussed in this section satisfactorily account for most of the physical and chemical properties of the molecules involved, it is necessary to point out that the sp orbitals, for example, stem from only one possible approximate solution of the Schrddinger equation. The i and the three p atomic orbitals can also be combined in many other equally valid ways. As we shall see on page 12, the four C—H bonds of methane do not always behave as if they are equivalent. 

Evaluated from ionization potentials of dimethyl derivatives. STO-3G. picis the component of p-atomic orbital at the reaction center. 

A pair of sp hybrid orbitais forms by interacting an s atomic orbital and one p atomic orbital. The two hybrids point in opposite directions. 

The bonding and antibonding cr orbitals are more stable than any of the six molecular orbitals derived from the 2 p orbitals. This is because the 2. S orbitals that generate the cr and cr orbitals are more stable than the 2 p atomic orbitals. 

The Lewis structure shows that methyl methaciylate has the formula C5 Hg O2, with 40 valence electrons. You should be able to verily that the two CH3 groups have. s -hybridized carbons, the inner oxygen atom is s hybridized, the outer oxygen atom uses 2 p atomic orbitals, and the three double-bonded carbons are s p hybridized. These assignments lead to the following inventory of a bonds and inner-atom lone pairs ... 

Isolated F-atom Molecular orbitals Isolated P-atom orbitals of three-center bond p orbitals... 

With both (la) and (2a) above, lateral overlap of the p atomic orbitals on adjacent carbon atoms could lead to the formation of two localised n bonds as shown, and the compounds would thus be expected to resemble ethene, only twice as it were This is indeed found to be the case with (2), but (1) is found to behave differently in terms of its slightly greater stability (referred to above), in spectroscopic behaviour (see below), and in undergoing addition reactions more readily than does an isolated diene (p. 194). On looking more closely, however, it is seen that with (la), but not with (2a), lateral overlap could take place between all four p atomic orbitals on adjacent carbon atoms. Such overlap will result in the formation of four molecular orbitals (Fig. 1.2), two bonding ( and 2) and two anti-bonding (i//3 and 4)—the overlap of n atomic orbitals always gives rise to n molecular orbitals ... 

One of the major problems of elementary organic chemistry is the detailed structure of benzene. The known planar structure of the molecule implies sp2 hybridisation with p atomic orbitals, at right angles to the plane of the nucleus, on each of the six carbon atoms (4) ... 

Molecular orbitals are obtained by the linear combination of atomic orbitals, and the question of phase will, of course, arise with them too. Thus we can write the two MOs (it and it, cf. p. 12) arising from the two p atomic orbitals in ethene,... 

Table 1 Electronegativity, covalent and van der Waals radii of group 16 elements, together with outermost maximum values and energies of s- and p-atomic orbitals...

At the present, the most straightforward mechanism for the formation of J5 from 1 is via insertion of CO into the Th-C(acyl) bond to form a ketene (H, (eq. (4)) which subsequently dimerizes. Presumably, initial CO interaction could involve coordination either to the metal ion as shown or to the electrophilic vacant "carbene p atomic orbital. Considering the affinity of the Th(IV) ion for oxygenated ligands, interaction of the ketene oxygen atom with the metal ion seems reason-... 

The hydrogen atom migration observed on thermolysis of is reminiscent of 1,2-hydrogen atom migrations in carbene chemistry (45,46,47). The stereochemistry of such processes is now relatively well-understood and involves initial hyperconjugative interaction between a gauche C-H bond and the carbene unoccupied p atomic orbital, followed by a low activation energy 1,2 shift (eq.(6)) ( 7,48,49,50). 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

Figure 11.13 Hybridization of 5- and p- atomic orbitals, (a) Linear sp hybrid, from one s- and one p-orbital. (b) sp2 hybrid, from one s- and two p-orbitals, with a plane triangular shape, (c) sp3 hybrid, from one 5-orbital and the three p-orbitals, which has a tetrahedral shape in three dimensions.

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