Fig. 12.12 JcH for hydrocarbons and s-character of C hybrid orbitals defined by the maximum overlap criterion (see also ref. 156). |

Suppose you use Po,p-y and p+, along with s orbitals to construct hybrid orbitals. Will they be the same hybrid orbitals defined by thep ,pj and p orbitals Justify your answer. [Pg.473]

The significance of term A was defined in section 1.17.1. Factor f is analogous (ratio A/ defines the polarity of the bond) and parameters e and s describe the hybridization state of the orbitals. Because cos e = 0.093 (Duncan and Pople, 1953), molecular hybrid orbitals ) and are composed essentially of the wave functions of atomic orbitals 2p of oxygen and D of hydrogen. The value 0.578 obtained for cos s also indicates that orbitals (0 and are essentially of type sp. Figure 8.1C shows the formation of hybrid MOs [Pg.481]

To confirm that hi, hi, and hs are equivalent to each other, we can calculate their hybridization indices and see that they are identical. The hybridization index n of a hybrid orbital is defined as [Pg.105]

The two nonbonding electron pairs may be described in two ways. We may choose to accommodate two electrons in a third hybrid orbital h3 with maximum electron density in the plane of the molecule corresponding to the /i3 hybrid orbital defined by equation (13.5) and the last two electrons in an uhybridized p orbital perpendicular to the molecular plane. The other possibility is to combine hs and p to form two new equivalent hybrids, and hs pointing in approximately tetrahedral directions [Pg.260]

Hybrid Orbitals. Orbitals, as one-electron energy levels, and corresponding wavefunctions are mathematical concepts only states are physically observable. Nevertheless, the simple picture of orbitals as the rungs of an energy ladder is very helpful, and is in many cases sufficient to account for the photophysical and photochemical properties of molecules. In more accurate pictures of orbitals it is necessary to consider their interactions, as they are not really totally independent. In this respect the concept of hydrid orbitals is important such hybrid orbitals are formed from a combination of elementary orbitals defined by their quantum numbers n, /, and m. The best [Pg.32]

For more complex molecules, the v.b. wavefimctions are defined using functions describing each formal covalent bond which are similar to Eq. (8.10) (eventually mixed with ionic contributions). In this process, it is often necessary to consider, not the pure s and p (or s, p, and d) atomic orbitals, but linear combinations of them hybrid atomic orbitals. We have already briefly encountered hybrid orbitals in the study of excited H atoms (for n = 2, for example) and in the m.o. study of BeH2. For instance, in the case of CH4, the 2s atomic orbital and the three 2p a.o.s are replaced by four linear combinations four sp hybrid orbitals. They are equivalent and have symmetry axes that conform to the actual tetrahedral geometry of the molecule, as is illustrated in Fig. 8.5. [Pg.182]

There exists no uniformity as regards the relations between localized orbitals and molecular symmetry. Consider for example an atomic system consisting of two electrons in an (s) orbital and two electrons in a (2px) orbital, both of which are self-consistent-field orbitals. Since they belong to irreducible representations of the atomic symmetry group, they are in fact the canonical orbitals of this system. Let these two self-consistent-field orbitals be denoted by Cs) and (2p), and let (ft+) and (ft ) denote the two digonal hybrid orbitals defined by [Pg.46]

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