Figure 3.7. Common representations of the s, p, d and atomic orbitals, sp3 hybridized orbitals, and some representations of how they overlap to form bonds between atoms. |

Figure Schematic representation of the two components of the ij -Hi-metal bond (a) donation from the filled (hatched) CT-H2 bonding orbital into a vacant hybrid orbital on M (b) jr-back donation from a filled d orbital (or hybrid) on M into the vacant a antibonding orbital of Hj. |

Fig. 5.4 Other ways of representing hybrid orbitals (a) orbital shape shown by a single contour, (b) clcnd representation, (c) simplified r resemaiicr. The small back lobes have been omitted and the shape streamlined to make it easier to draw molecules containing several hybrid orbitals. |

No matter whether calculated within the perfect pairing VB approach or by the spin-coupled VB approach, in both cases the CC hybrid orbital extends outside the three-membered ring as expected by the schematic representations in Figure 7, but also inside [Pg.58]

FIGURE 17. Schematic representation of the symmetry-unique spin-coupling patterns in cyclopropane (above) and benzene (below). In the case of cyclopropane, carbon hybrid orbitals and, in the case of benzene, carbon p n orbitals are shown. For each structure, Gallup-Norbeck occupation numbers as determined by spin-coupled valence bond theory are given. All data from Reference 51 [Pg.83]

Problem 7.13 (a) Give an orbital representation for an S 2 reaction with (S)-RCHDX and Nu, if in the transition state the C on which displacement occurs uses sp hybrid orbitals, (b) How does this representation explain (i) inversion, (ii) the order of reactivity 3 >2°> 1° [Pg.124]

Recalling our earlier discussion, this equation means that the four AOs which are combined to make the set of four hybrid orbitals must be chosen so as to include one orbital which belongs to the P 1 representation and a set of three orbitals which belong to the rT representation. Reference to Table 11-2.2 shows that the AOs fall into the categories below for the "d point group. So we can combine an s-orbital [Pg.227]

In carrying out the procedure for a tetrahedral species, it is convenient to let four vectors on the central atom represent the hybrid orbitals we wish to construct (Fig. 3.26). Derivation of the reducible representation for these vectors involves performing on them, in turn, one symmetry operation from each class in the Td point group. As in the analysis of vibrational modes presented earlier, only those vectors that do not move will contribute to the representation. Thus we can determine the character for each symmetry operation we apply by simply counting the number of vectors that remain stationary. The result for AB4 is the reducible representation, I",. [Pg.585]

Figure 3.15 An sp hybrid orbital, (a) left, radial functions for the 2s and 2p atomic orbitals right, radial function for the sp hybrid orbital (b) left, the shapes of the 2s and 2p atomic orbitals as indicated by a single contour value right, the shape of the sp hybrid orbital as indicated by the same contour, (c) The shape of a surface of constant electron density for the sp hybrid orbital, (d) Simplified representation of (c). (Reproduced with permission from R. J. Gillespie, D. A. Humphreys, N. C. Baird, and E. A. Robinson, Chemistry, 2nd Ed., 1989, Allyn and Bacon, Boston.) |

As a second example, let us consider a molecule with the formula AB6 having the symmetry of a trigonal bipyramid Ih. The vector system is shown in Fig. 11-3.2. The set of five hybrid orbitals (or vectors) on A form a basis for a reducible representation of the point group, with the following character [Pg.228]

First then, for methane, we must obtain I 71. To do this let us associate with each carbon hybrid orbital a vector pointing in the appropriate direction and let us label these vectors vv vs, v , v4 (see Fig. 11-3.1). All of the symmetry properties of the four hybrid orbitals will be identical to those of the four vectors. The reducible representation using these vectors (or hybrids) as a basis can be obtained from 4 [Pg.226]

We therefore conclude that, for a combination of model, numerical and conceptual reasons the OHAO basis is well-adapted to a theory of valence. The hybrid orbital basis (for simple molecules) has a distinctive symmetry property it carries a permutation representation of the molecular symmetry group the equivalent orbitals are always sent into each other, never into linear combinations of each other. This simple fact enables the hybrid orbital basis to be studied in a way which is physically more transparent than the conventional AO basis. [Pg.64]

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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