Orbitals hybridization of atomic

The AO s of carbon can hybridize in ways other than sp as shown in Fig. 2-7. Repulsion between pairs of electrons causes these HO s to have the maximum bond angles and geometries summarized in Table 2-2. The sp and sp HO s induce geometries about the C s as shown in Fig. 2-8. Only a bonds, not v bonds, determine molecular shapes. 

Type Bond Angle Geometry Number of Remaining p s Type of Bond Formed 

Problem 2.7 The H O molecule has a bond angle of 105°. ( j) What type of AO s does O use to form the two equivalent a bonds with H (b) Why is this bond angle less than 109.5°  

O has two degenerate orbitals, the and p., with which to form two equivalent bonds to H. However, if O used these AO s, the bond angle would be 90°, which is the angle between the y- and e-axes. Since the angle is actually 105°, which is close to lt)9.5°. O is presumed to use sp HO s. 

Problem 2.8 Each H—N—H bond angle in NH, is 107°. What type of AO s does N use  

Each of the 2p orbitals points to a pair of opposite faces of the cube. Once more aU four hydrogen Is orbitals can combine with each p orbital, provided the hydrogen AOs on the opposite faces of the cube are of opposite phases. 

Using this approach, it is possible to construct a complete MO picture of methane—and indeed for very much more complex molecules than methane. There is experimental evidence too that these pictures are correct. But the problem is this the four filled, bonding orbitals of methane are not all the same (one came from the interaction with the C 2s orbital and three from the C 2p orbitals). But we also know from experimental observations all four C—H bonds in methane are the same. 

That would be using physics to do chemistry. It might be accurate but it would kill creativity and invention. So here is an alternative we keep our tried and tested practical picture of molecules made from discrete bonds, each containing a pair of electrons, but we make it compatible with MO theory. To do this we need a concept known as hybridization. 

To get a picture of methane with four equivalent pairs of electrons we need to start with four equivalent AOs on C, which we don t have. But we can get them if we combine the carbon 2s and 2p orbitals first to make four new orbitals, each composed of one-quarter of the 2s orbital and three-quarters of one of the p orbitals. The new orbitals are called sp (that s said s-p-three, not s-p-cuhed) hybrid orbitals to show the proportions of the AOs in each. This process of mixing is called hybridization. The hybrid orbitals are mathematically equivalent to the 2s and 2p orbitals we started with, and they have the advantage that when we use them to make MOs the orbitals correspond to bonding pairs of electrons. 

What do the four hybrid orbitals look like Each sp orbital takes three-quarters of its character from a p orbital and one-quarter from an s orbital. It has a planar node through the nucleus like a p orbital but one lobe is larger than the other because of the extra contribution of the 2s orbital the symmetry of the 2s orbital means that adding it to a 2p orbital will increase the size of the wavefunction in one lobe, but decrease it in the other. 

The four sp3 orbitals on one carbon atom point to the corners of a tetrahedron and methane can be formed by overlapping the large lobe of each sp3 orbital with 

The great advantage of this method is that it can be used to build up structures of much larger molecules quickly and without having to imagine that the molecule is made up from isolated atoms. So it is easy to work out the structure of ethene (ethylene) the simplest alkene. Ethene is a planar molecule with bond angles dose to 120°. Our approach will be to hybridize all the orbitals needed for the C-H framework and see what is left over. In this case we need three bonds from each carbon atom (one to make a C-C bond and two to make C-H bonds). 

Therefore we need to combine the 2s orbital on each carbon atom with two p orbitals to make the three bonds. We could hybridize the 2s, 2px, and 2py orbitals (that is, all the AOs in the plane) to form three equal sp2 hybrid atomic orbitals, leaving the 2p7 orbital unchanged. These sp2 hybrid orbitals will have one-third s character and only two-thirds p character. 

The three sp2 hybrid atomic orbitals on each carbon atom can overlap with three other orbitals (two hydrogen Is AOs and one sp2 AO from the other carbon) to form three G MOs. This leaves the two 2pz orbitals, one on each carbon, which combine to form the jc MO. The skeleton of the molecule has five o bonds (one C-C and four C-H) in the plane and the central n bond is formed by two 2pz orbitals above and below the plane. 

The three sp hybrid atomic orbitals on each carbon atom can overlap with three 

Chemical Bonding II Molecular Geometry and Hybridization of Atomic Orbitals 

The concept of atomic orbital overlap should apply also to polyatomic molecules. However, a satisfactory bonding scheme must account for molecular geometry. We will discuss three examples of VB treatment of bonding in polyatomic molecules. 

Media Piayer Molecular Shape and Orbital Hybridization 

Consider the CH4 molecule. Focusing only on the valence electrons, we can represent the orbital diagram of C as 

Because the carbou atom has two unpaired electrons (one in each of the two 2p orbitals), it can form only two bonds with hydrogen in its ground state. Although the species CH2 is known, it is very unstable. To account for the four C—H bonds in methane, we can try to promote (that is, energetically excite) an electron from the 2s orbital to the 2p orbital  

Interactivty Determining Orbitai Hybridization ARiS, interactives 

Now there are four unpaired electrons on C that could form four C—H bonds. However, the geometiy is wrong, because three of the HCH bond angles would have to be 90° (remember that the three 2p orbitals on carbon are mutually perpendicular), and yet all HCH angles are 109.5°. 

If we try to extend the unmodified valence bond method of Section 11-2 to a greater number of molecules, we are quickly disappointed. In most cases, our descriptions of molecular geometry based on the simple overlap of unmodified atomic orbitals do not conform to observed measurements. For example, based on the ground-state electron configuration of the valence shell of carbon 

The simplest hydrocarbon observed imder normal laboratory conditions is methane, CH4. This is a stable, unreactive molecule with a molecular formula consistent with the octet rule of the Lewis theory. To obtain this molecular formula by the valence bond method, we need an orbital diagram for carbon in which there are four unpaired electrons so that orbital overlap leads to four C—H bonds. To get such a diagram, imagine that one of the 2s electrons in a ground-state C atom absorbs energy and is promoted to the empty 2p orbital. The resulting electron configuration is that of an excited state. 

The problem is not with the theory but with the way the situation has been defined. We have been describing bonded atoms as though they have the same kinds of orbitals (that is, s, p, and so on) as isolated, nonbonded atoms. This assumption worked rather well for H2S and PH3, but we have no reason to expect these unmodified pure atomic orbitals to work equally well in all cases. 

The transformation described involves replacing four atomic orbitals with four new orbitals, each of which points toward the vertex of a tetrahedron. Because atomic orbitals are mathematical expressions, this transformation can be represented mathematically by taking appropriate algebraic combinations of the wave functions representing the 2s and three 2p orbitals. To obtain four new 

The four carbon orbitals are sp hybrid orbitals (purple). Those of the hydrogen atoms (yellow) are Is. The structure is tetrahedral, with H — C—H bond angles of 109.5° (more precisely, 109.471°). Remember that the hydrogen orbitals and the carbon hybrid orbitals have the same phase, but we have colored the hydrogen orbitals yellow for clarity. 

In order to explain these and other observations, we need to extend our discussion of orbital overlap to include the concept of hybridization or mixing of atomic orbitals. 

With one of its valence electrons promoted to the 2p subshell, the Be atom now has two unpaired electrons and therefore can form two bonds. However, the orbitals in which the two unpaired electrons reside are different from each other, so we would expect bonds formed as a result of the overlap of these two orbitals (each with a 3p orbital on a Cl atom) to be different  

MPEG Content Hybrid orbitals—orbital hybridization and valence bond theory. 

Remember that Be is one of the atoms that does not obey the octet rule [Mt Section 8.1]. The Lewis structure of BeCt is 

Experimentally, though, the bonds in BeCl are identical in length and strength. 

The Lewis bonding model may be rationalized using quantum mechanics if the ordinary C2s and C2p orbitals, for example, are mixed in such a way that they point into the comers of a tetrahedron with the carbon atom at its center. Generally, AOs on the same atom mix to form directed orbitals. This is referred to as (atomic) hybridization. Hybridization is important for the interpretation of the wave function, but of little interest computationally, since it just amounts to a unitary transformation of the orbitals, and Slater determinants are invariant under unitary transformations. 

If one s orbital and one p orbital (or Py or p J from the same shell are superposed, two new asymmetric AOs are formed, which point along the x-axis in the positive and negative directions. One s and two p orbitals from the same shell (p, and Py, for example) form three new, asymmetric orbitals in the xy plane, directed with 120° between them. Finally, if one s orbital and all three p orbitals are combined, four new AOs are formed, pointing into the comers of a tetrahedron. 

The AOs, X2s Xipx X2py nd %2pz to e nonoverlapping and normalized. The directed AOs are formed as 

It is easily seen that X2s + Xipz is an AO that has large positive values on the positive z-axis (0 = 0), where both 2s and 2p are positive, but close to zero on the negative z-axis (0 = 180). This type of hybridization is called sp-hybridization. The linear combination X2s Z2pz on the other hand, is directed toward the negative z-axis. 

In planar organic molecules, each carbon atom binds to three other atoms. One may combine 2s, 2p,, and 2py orbitals to form hybridized orbitals  

Sample Problem 9.4 shows how to use valence bond theoiy to explain the bonding in a molecule. 

Hydrogen selenide (H2Se) is a foul-smelling gas that can cause eye and respiratory tract inflammation. The H—Se—H bond angle in H2Se is approximately 92°. Use valence bond theory to describe the bonding in this molecule. 

Strategy Consider the central atom s ground-state electron configuration, and determine what orbitals are available for bond formation. 

Setup The ground-state electron configuration of Se is [Ar As 3d °Ap. Its orbital diagram (showing only the Ap orbitals) is 

Solution Two of the Ap orbitals are singly occupied and therefore available for bonding. The bonds in H2Se form as the result of the overlap of a hydrogen Is orbital with each of these orbitals on the Se atom. 

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Of particular importance in structural chemistry is the concept of hybridization, that is, the construction of linear combinations of atomic orbitals that transform according to the symmetry of the structure. For the present, a simple illustration is provided by the hybridization of atomic orbitals in a molecule or complex ion of trigonal structure. 

Soon after the quantum revolution of the mid 1920s, Linus Pauling and John C. Slater expanded Lewis s localized electronic-structural concepts with the introduction of directed covalency in which bond directionality was achieved by the hybridization of atomic orbitals.1 For normal and hypovalent molecules, Pauling and Slater proposed that sp" hybrid orbitals are involved in forming shared-electron-pair bonds. Time has proven this proposal to be remarkably robust, as has been demonstrated by many examples in Chapter 3. 

Energy of Chemical Bond and Spatial-Energy Principles of Hybridization of Atom Orbitals... 

Key words spatial-energy parameter, hybridization of atom orbitals, bond energy. 

In this research the attempt is made to estimate the energy of chemical bonds based on initial spatial-energy characteristics of free atoms with the help of the concept on spatial-energy parameter (P-parameter), taking into consideration their changes during the hybridization of atom orbitals. 

In [1] there is a conclusion based on the analysis of multiple computational and experimental data that the most valence-active are the orbitals with minimum values of P0-parameters. Let us apply this principle to the hybridization of atom orbitals on the example of carbon and nitrogen atoms. 

Table 2. Computation of bond energy taking into account the hybridization of atom orbitals... 

True or False Hybridization of atomic orbitals is best used for rationalizing known molecular geometries rather than for predicting molecular geometries. 

One rather satisfactory way is to introduce all valence electrons in the molecular orbital approach without a hypothesis on the hybridization of atomic orbitals. Population analysis using the CNDO/2-SCF-MO showed the electronic configuration of the nitrogen atom of aromatic nitrogen cation systems (1, 40, 41, 42, 43, 44) in the ground state to be as follows (69G1078) ... 

The concept of hybridization of atomic orbitals was subsequently introduced, in an attempt to interpret the difference between the actual bond angle for the water molecule and the value of 90° considered in the previous model. This concept had already been introduced to interpret, for example, the tetrahedral geometry of the methane molecule. We shall come back to this subject later in the chapter, to conclude that, although it is possible to establish a correlation between molecular geometry and hybrid orbitals, it is not correct to take the latter as the basis of an explanation of the former. This distinction is very important in teaching. 

Valence Shell Electron Pair Repulsion (VSEPR) Theory Hybridization of Atomic Orbitals, sp, sp, sp Single Bonds Conformational Isomers Pi Bonds Pi Barrier to Rotation C/s and Trans, 2p-3p Triple Bonds Cumulenes... 

For the following species, draw (i) diagrams that show the hybridization of atomic orbitals and (ii) three-dimensional structures that show all hybridized orbitak and outermost electrons, (iii) Determine the oxidation state of the Group VIA element (other than oxygen) in each species, (a) H2S (b) SFg (c) SF4 (d) SO2 (e) SO3. 

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