Linear shape hybrid orbitals

FIGURE 3.16 Three common hybridization schemes shown as outlines of the amplitude of the wavefunction and in terms of the orientations of the hybrid orbitals, (a) An s-orbital and a p-orbital hybridize into two sp hybrid orbitals that >oint in opposite direc tions, forming a linear molecular shape, (b) An s-orbital and two p-orbitals can blend together to give three ip hybrid orbitals that point to the corners of an equilateral triangle, (c) An s-orbital and three p-orbitals can blend together to give four sp hybrid orbitals that point to the corners of a tetrahedron. 

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.

The hybridisation between one s orbital and one p orbital results in two sp hybrid orbitals, which form a linear shape. In this scenario, the second and third p orbitals are left unhybridised, and are orthogonal to each other, but co-linear with the axis described by the sp orbitals. Examples of this geometry include BeCl2, RC=N, RC=CR and R-N+=C. They all have in common that there are two... 

The directional properties of the hybrid orbitals are better appreciated with the BeClj molecule, which is linear in shape, Cl-Be-Cl 180°, and in which Be has an configuration which can be promoted to an s p configuration. 

Now the two axial hybrid orbitals, each of which has one electron, overlaps with the 3px orbital (singly-filled) of two Cl-atoms to form two IC1 s-bonds. Due to the presence of Ips, IC12- ion assumes linear (symmetrical) shape... 

Figure 10.9 shows the shape and orientation of the sp orbitals. These two hybrid orbitals lie on the same line, the x-axis, so that the angle between them is 180°. Each of the BeCl bonds is then formed by the overlap of a Be sp hybrid orbital and a Cl 3p orbital, and the resulting BeCl2 molecule has a linear geometry (Figure 10.10). 

Figure 7.1 presents contour diagrams for the Lewis-type NBOs of formaldehyde (panels a, c, e, g, h), calculated at the B3LYP/6-311-H-G""" level of hybrid density functional theory (DFT). As is immediately apparent, the bonding Gch, and Kcq NBOs exhibit the familiar sigma and pi shapes of idealized textbook depictions. The resemblance to expected textbook forms is further emphasized when each A-B bond is written as a linear combination (LC) of its constituent natural hybrid orbitals (NHOs) and with polarization coefficients and Cg, namely. 

For the trigonal bipyramidal shape of the PCI5 molecule, for example, the VB model proposes that the one 35, the three 3p, and one of the five 3d orbitals of the central P atom mix and form five sp d hybrid orbitals, which point to the vertices of a trigonal bipyramid (Figure 11.6). Seesaw, T-shaped, and linear molecules have this electron-group arrangement with lone pairs in one, two, or three of the central atom s sp d orbitals, respectively. 

As you review each type of hybrid orbital in the following subsections, take note of (1) the number and types of atomic orbitals that were combined to make the hybrid orbitals, (2) the number of orbitals that remain uncombined, and (3) the three-dimensional arrangement in space of the hybrid orbitals and any uncombined p orbitals. In particular, you will find that these three-dimensional arrangements will retain the names (tetrahedral, trigonal planar, linear) and bond angles (109.5°, 120°, and 180°) used to describe the shapes of molecules in our section on VSEPR (Section 1.3). 

Orbitals mixed and orbitals formed. VB theory explains the linear orientation by proposing that two nonequivalent orbitals of a central atom, one s and one p, mix and form two equivalent sp hybrid orbitals that are oriented 180° apart (Figure 11.2A). The shape of these hybrid orbitals, with one large and one small lobe, differs markedly from the shapes of the atomic orbitals that were mixed. The orbital orientations increase electron density in the bonding direction and minimize repulsions between electrons that occupy them. Thus, both shape and orientation maximize overlap with the orbital of the other atom in the bond. 

Each set of hybrid orbitals is associated with a particular shape, although this may not coincide with the molecular shape if lone pairs also have to be accommodated linear... 

A linear shape indicates that each C uses sp hybrid AO s (Table 19.1). The energy levels of an sp hybridized C are shown in Fig. 19.7d. Figure 19,9 shows the assembly of 2 H atoms, each with a Is atomic orbital, and 2 C atoms, each with two sp hybrid orbitals and a p and p orbital. Each C atom forms two cr bonds, one by overlapping an sp hybrid orbital with the other C atom, and one by overlapping an sp orbital with the s orbital of a H atom. The p orbitals overlap laterally to form a ir... 

Hybridization and symmetry are intimately connected because of the relationships seen above Atomic centers in molecules that have certain hybridization have specific shape. Atoms that make sp hybrid orbitals impart a linear shape about that atomic center (which might suggest Coov or D h point groups, for simple molecules). Atoms that have sp hybrid orbitals make bonds in a threefold, or trigonal, shape. 

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