This proof relied on the atomic orbitals used to create the hybrid orbitals being themselves normalized and orthogonal. Other combinations, such as the three sp or the four sp hybrid orbitals, are also orthogonal sets. [Pg.228]

Each set can be shown to be orthonormalized, provided that the s- and p-functions are normalized and orthogonal. Fig. 10.5 shows a contour plot of a tetrahedral sp hybrid. The strong directional character of this and other hybrid orbitals enhances the overlap with neighboring orbitals, thus contributing to stronger bonds. [Pg.243]

FIGURE 13.26 Operation of the symmetry classes of T on the sp orbitals. The a, b, c, and ti labels are used only to keep track of the individual hybrid orbitals. The nrnnber of hybrid orbitals that do not move when a symmetry operation occurs is listed in the final coliunn. This set of mrmbers is the reducible representation F of the sp orbitals. The great orthogonality theorem is used to reduce F into its irreducible representation labels. [Pg.468]

Natural bond orbital (NBO) analysis The NBO analysis transforms the canonical delocalized Hartree-Fock (HF) MOs and non-orthogonal atomic orbitals (AOs) into the sets of localized natural atomic orbitals (NAOs), hybrid orbitals (NHOs), and bond orbital (NBOs). Each of these localized basis sets is complete, orthonormal, and describes the wavefunction with the minimal amount of filled orbitals in the most rapidly convergent fashion. Filled NBOs describe the hypothetical, strictly localized Lewis structure. NPA charge assignments based on NBO analysis correlate well with empirical charge measures. [Pg.56]

A second condition, which does not apply generally to orbitals but which does apply to different atomic orbitals on the same atom is that they do not overlap with each other. The correct terminology for orbitals that have zero overlap is that they are orthogonal. We have seen that the overlap of two orbitals is found by integrating over space the product 951952- Since our s and p orbitals, and also the resulting hybrids, are on the same atom, we require for any pair in the s, p set and also for any pair in the hybrid set that Equation A1.2 be satisfied [Pg.43]

See also in sourсe #XX -- [ Pg.64 , Pg.70 , Pg.86 , Pg.96 , Pg.109 ]

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