Orbital, atomic orientation

There is another possible consequence of a collision between two fluorine atoms. The two atoms can remain together to form a molecule. Each atom has a valence electron in a half-filled orbital. We can imagine these two atoms orienting so that these half-filled" orbitals overlap in space. Then the half-filled" valence orbital of... 

Using Valence Bond (VB) theory, the central atoms of the molecules with formulas AB2U2 and AB3U should undergo sp3 hybridized with predicted bond angles of 109.5°. If no hybridization occurs, bonds would be formed by the use of p orbitals. Since the p orbitals are oriented at 90° from each other, the bond angles would be 90°. Note that hybridization is only invoked if the actual molecular geometry data indicate that it is necessary. 

Orbitals have a variety of different possible shapes. Therefore, scientists use three quantum numbers to describe an atomic orbital. One quantum number, n, describes an orbital s energy level and size. A second quantum number, I, describes an orbital s shape. A third quantum number, mi, describes an orbital s orientation in space. These three quantum numbers are described further below. The Concept Organizer that follows afterward summarizes this information. (In section 3.3, you will learn about a fourth quantum number, mg, which is used to describe the electron inside an orbital.)... 

A second common type of orbital hybridization involves the 2s orbital and only two of the three 2p orbitals (2a). This process is therefore referred to as sp hybridization. The result is three equivalent sp hybrid orbitals lying in one plane at an angle of 120° to one another. The remaining 2px orbital is oriented perpendicular to this plane. In contrast to their sp counterparts, sp -hybridized atoms form two different types of bond when they combine into molecular orbitals (2b). The three sp orbitals enter into a bonds, as described above. In addition, the electrons in the two 2px orbitals, known as n electrons, combine to give an additional, elongated n molecular orbital, which is located above and below the plane of the a bonds. Bonds of this type are called double bonds. They consist of a a bond and a n bond, and arise only when both of the atoms involved are capable of sp hybridization. In contrast to single bonds, double bonds are not freely ro-... 

In the chemical deformation densities introduced by Schwarz and collaborators, the density and the orientation of the atoms is quantitatively defined by variation of the atomic orientation and orbital population such as to minimize the space integral over the squared deformation density (Schwarz et al. 1989, Mensching et al. 1989). 

A p orbital on the central atom, oriented perpendicular to the molecular plane. 

Fig. 5.30 The atomic orbitals of ihe nitrite ion when viewed along the z axis, which is the principal twofold axis of the anoin. (a) the p, and py atomic orbitals on nitrogen The plane of the anion is the yz plane, and the x axis is perpendicular to that plane, (b) The atomic p orbitals of the left-hand oxygen atom. Note ihJl the z axis has been redefined along the 0—N bond axis. The x axis is still perpendicular to the plane of the molecule, and the y axis most be mutually perpendicular to x and z. (c) The atomic p orbitals of the nghl-hiind oxygen atom. Again, the z axis has been redefined along the N—O bond axis, and x and y art mutually perpendicular, (d) Group orbitals for the oxygen atoms in NOJ, derived (ram the 2s and 2p atomic orbitals. The orientations are as shown in parts (b) and (c).

FIG. 1. Orientation of the orbitals. The orientation of the oxygen orbitals relative to the axes oh the central atom is shown in this figure. The direction cosines of the Oi orbitals are 01 —1/3, —1/31, —1/3 nr. 1/6, -273, 1/6 mu 1/2, 0, —1/2. The direction cosines of the other oxygen orbitals may be obtained from these by the action of the twofold axes of Ta, winch coincide with the x, y, and z axes shown. The central atom orbitals are defined with respect to the axes on the central atom. 

Suppose that wc make a molecular orbital by combining p orbitals on two atoms. We can do this in one of two ways. If we choose the p orbitals that are oriented toward each other (Figure 1.7), we get MO s with the same Cx symmetry we had before. But if the p orbitals are oriented as shown in Figure 1.8, we get a new type of molecular orbital. 

Several forms of the superoxide 02 radical ion formed on the surface of ZnO, MgO, CoO/MgO and Si02 have been reported in [40, 83]. The species were differed by the orientation of the 0-0 residue relatively the surface and the metal ion Mn+. The correlation between distances and angles in the most probable structures with the experimentally measured gz values was found, and the dynamic behaviour observed in some cases was also discussed [83], Calculated EPR spectra of the adsorbed 02 for different charges of the metal ion Mn+ (2 < n < 6) showed that gz values are sensitive to the ionic charge and the increase of n+ causes the decrease of gz [83]. The z-axis of the tensor is usually in the direction of the internuclear axis and the x- direction is that of the mole-cular orbital hosting the unpaired electron. The data in Table 8.3 show that the dependen-ce of gz on n+ is, however, valid quantitatively not always because of rather many factors affecting the gz value (distances to the neighbouring atoms, orientation, local fields, etc.). Additional detailed information can be found in references cited in this section. 

The substrates preferentially bind each other with those atoms that exhibit the largest LCAO coefficients (absolute values) in the closest pair of frontier orbitals. The orientation selectivity generally increases, the larger the relative significance of one HOMO/LUMO interaction compared to the other and the greater in each of the two crucial frontier orbitals the difference in magnitude of the LCAO coefficients (absolute values) at one terminus, compared to the other. 

In addition to the 2s orbital, the second shell also contains three 2p atomic orbitals, one oriented in each of the three spatial directions. These orbitals are called the 2px, the 2py, and the 2pz, according to their direction along the x, y, or z axis. The 2p orbitals... 

The d orbitals have orientations as shown in Figure 19.2, and atomic orbitals must have the appropriate orientations (symmetry) for hybrid orbitals to form. For example, no hybrid orbitals are formed between the px and dyz orbital (those orbitals are orthogonal). A few of the common types of hybrid orbitals involved in bonding in complexes are shown in Table 19.4. 

In BeH2, the Be atom is sp hybridized because it is surrounded by two groups (two H atoms). Eiach Be- H bond is formed by overlap of an sp hybrid orbital from Be and a Is orbital from H. The sp hybrid orbitals are oriented 180° away from each other. 

As mentioned in Chapter 3, the octahedral models used to describe the active sites on metal surfaces are not compatible with the presence of three different types of saturation sites on a catalyst surface so another model must be developed. On consideration of the fee crystal structure, which is that of most catalytically active metals, it can be seen that the bulk atoms in these metals are bound to twelve nearest neighbor atoms using the lobes of the t2g d orbitals. The octahedraily oriented eg orbitals are directed toward but not bonded to the next nearest neighbors in the crystal lattice as shown in Fig. 4.1.1 This atomic orientation precludes the presence of any octahedral arrangement involving M-M bonds. 

Four ijf hybrid orbitals (green), oriented to the corners of a regular tetrahedron, are formed by combination of an atomic s orbital (red) and three atomic p orbitals (blue). The sp hybrids are unsymmetrical about the nucleus, giving them a directionality and allowing them to form strong bonds when they overlap an orbital from another atom. 

Atomic orbitals represent the electron probability clouds of an atom s electrons. Q The spherical 1s and 2s orbitals are shown here. All s orbitals are spherical in shape and increase in size with increasing principal quantum number. The three dumbbell-shaped p orbitals are oriented along the three perpendicular X, y, and z axes. Each of the p orbitals related to an energy sublevel has equal energy. 

As stated, atomic orbitals on two atoms may interact if they are oriented appropriately with respect to each other.2 In general, if atomic orbitals point toward each other and interact directly between the nuclei, they participate in a a interaction if atomic orbitals are oriented such that they interact in two regions off to the side, they participate in a n interaction. Examples of these interactions follow. 

Consider first a matrix element Hc k), from Eq. (3-22), where both Bloch sums are taken over a p orbital on the metallic atom, oriented in the x-direction. In zincblende, since all nearest neighbors are nonmetallic atoms, no nearest-neighbor matrix elements enter the calculation the matrix element Hp cp c k) of Eq. (3-22) becomes simply a sum over Np p orbitals oriented in the x-direction, divided by A/, which is simply a, with c denoting cation. Similarly, every other diagonal matrix element is simply the corresponding atomic term value. Furthermore, no off-diagonal matrix elements H p k) couple Bloch sums of cation states with those of other cation states, or Bloch sums of anion states with those of other anion slates. 

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