Combining Valence Bond (VB) and Molecular Orbital- 123docz.net

Theories: The Creation of s and p Bonding and Antibonding Orbitals

At the beginning of this section (1.7A), we noted that the molecular orbitals of H2 are created by adding and subtracting wave functions for the atomic 1s orbitals on the individual hydrogen atoms. We also noted that the exercise of adding and subtracting atomic orbitals such as 1s, 2s, and 2p to create molecular orbitals is one principle of MO theory, where the resulting molecular orbitals are spread across atoms in the entire molecule. Yet, orbitals spread across many atoms in a molecule are often diffi cult to visualize. Therefore, it is convenient to consider orbitals to be localized between adjacent atoms as in valence bond theory, or slightly delocalized over three or more atoms (as is done in Section 1.9). The most common model for bonding in organic compounds uses the MO theory notions of addition and subtraction to create the molecular orbitals, but also includes some principles from valence bond theory.

Valence bond theory views bonding as arising from electron pairs localized between adjacent atoms. These pairs of electrons create bonds. Further, organic chemists commonly use the atomic orbitals involved in the three hybridization states of atoms (sp3, sp2, and sp) to create the orbitals that hold these electrons because doing so allows the resulting orbitals to match the experimentally deter- mined geometries around the atoms. Therefore, hybridization is also a VB theory concept. But how do we make the orbitals that contain the electrons and that re- side between adjacent atoms? This is where we turn back to MO theory.

To create orbitals that are localized between adjacent atoms we add and subtract (also called in and out of phase addition) the atomic orbitals on the adjacent atoms, which are aligned to overlap with each other. For example, let’s consider methane, CH4 (Figure 1.17). The sp3 hybrid orbitals point at the 1s hydrogen orbitals, and therefore we add and subtract these atomic orbitals to create the molecular orbitals. As with H2, one resulting molecular orbital is lower in energy than the two separate atomic orbitals, and is called the bonding s orbital. The other resulting

Connections to

Biological Chemistry Phosphoesters

Many biochemical structures, including DNA, are in part made up of derivatives of phosphoric acid. These derivatives are re- ferred to as phosphoesters. The P atoms in these structures are nearly always depicted with fi ve bonds. However, as just described, the modern view of such structures involves charge separation and sp3 hybridization at P. Because the fi ve-bond representation is historically the most widely spread depiction, this depiction is how we render such structures throughout this book. Yet, you should keep in mind that the alternative is now considered more correct.

3'-Adenine monophosphate Common depiction

O O–

N NH2

O O

N N

O– OH

N NH2

O O

N N

More correct

–O +

O HO

HO OH P O– O

Common depiction

Glucose 6-phosphate

More correct O HO

HO OH P O– O–

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38 Chapter 1 Covalent Bonding and Shapes of Molecules

molecular orbital is higher in energy than the two atomic orbitals and is antibonding. Only the lower-energy orbital is populated with electrons in methane. Popula- tion of the s bonding orbital results in what we call a s bond between the C and the H. Each of the four C!H bonds in methane is created in the manner discussed here. Also, although we created this picture for the C!H bonds in methane, we will view all C!H bonds in other organic structures in the same way. In other words, even with sp2 and sp hybridized carbons, we think of their C!H bonds as looking similar to those in Figure 1.17.

It is important to note in Figures 1.17 and 1.10, as well as in the orbital mixing diagrams (Figures 1.18, 1.21, and 1.25), that the energy of the antibonding orbital goes up further than the drop experienced by the bonding orbital. This is the rea- son that population of the antibonding orbital with electrons leads to cleavage of the bond. Early, less accurate theoretical methods for modeling bonding found the increase and decrease in energy of these respective orbitals to be identical, but the bonding approach described here correctly predicts the relative energies.

An identical approach used to create C!H s bonds is used to create C!C s bonds. For example, whenever a C!C bond exists in an organic structure we consider the overlap of hybrid orbitals on the two carbons. As shown in Figure 1.18, the overlap of two sp3 hybrid orbitals on the individual carbons creates s bonding and antibonding molecular orbitals. Only the bonding orbital is populated with electrons, thereby creating a carbon-carbon s bond. We consider all C!C s bonds to consist of orbitals similar to those given in Figure 1.18.

Two common cartoon representations

Computed

Common cartoon representations

Computed

C H

or (b) Out-of-phase

addition

(a) In-phase addition

Energy

C H

H C

Figure 1.17

Molecular orbital mixing diagram for the creation of any C!H s bond. (a) In-phase addition of a C hybrid orbital (albeit sp 3, sp 2, or sp) with a H 1s orbital forms a s orbital that is lower in energy than the two starting orbitals.

When the resulting orbital is populated with two electrons, a s bond results. (b) Addition of the orbitals in an out- of-phase manner (meaning reversing the phasing of one of the starting orbitals) leads to an antibonding s* orbital.

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1.7 A Combined Valence Bond and Molecular Orbital Theory Approach to Covalent Bonding 39 For example, the simplest two-carbon compound ethane (CH3CH3) contains

one C!C s bond and six C!H s bonds. As shown in Figure 1.19, we consider these bonds to arise from overlap of H 1s and C sp3 orbitals, while the actual bonding orbitals appear as shown in Figures 1.17 and 1.18.

Let’s now examine compounds with a double bond. Anytime there is a double bond, sp2 hybridization should be considered for the atoms involved. For example, second-period elements use a combination of an sp 2 hybrid orbital and the unhybridized 2p atomic orbital to form double bonds. Consider ethylene, C2H4, whose Lewis structure is shown in Figure 1.20(a). A s bond between the carbons in ethylene is formed by overlapping sp2 hybrid orbitals along a common axis as

Two common cartoon representations

Computed

Common cartoon representation

Computed (b) Out-of-phase

addition

(a) In-phase addition

Energy

C C

Figure 1.18

Molecular orbital mixing diagram for the creation of any C!C s bond. (a) In-phase addition of two C hybrid orbitals (albeit sp3, sp2, or sp orbital) forms a s orbital that is lower in energy than the two starting orbitals. When the resulting orbital is populated with two electrons, a s bond results. (b) Addition of the orbitals in an out-of-phase manner (meaning reversing the phasing of one of the starting orbitals) leads to an antibonding s* orbital.

Figure 1.19

(a) Lewis structure for ethane (CH3CH3). (b) Overlap of sp 3 hybrid orbitals on adjacent carbons forms a C!C s bond (see Figure 1.18), and overlap of carbon sp 3 hybrid orbitals with hydrogen 1s orbitals gives C!H s bonds (see Figure 1.17).

H C

H H

H C

H H

H C H

H H

H C

6 C—H s bonds form from overlap of a C sp3 with H 1s orbitals on hydrogen atoms A C—C s bond forms

from overlap of two sp3 orbitals

(a) (b)

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40 Chapter 1 Covalent Bonding and Shapes of Molecules

seen in Figure 1.18(b). Each carbon also forms s bonds with two hydrogens (as in Figure 1.17).

The combination of parallel 2p atomic orbitals by in phase and out of phase addition of their wave functions to give a pi (p) bonding molecular orbital and a pi antibonding molecular orbital (p*) is shown in Figure 1.21. A p bonding molecular orbital has a nodal plane that cuts through both atomic nuclei, with electron density above and below the nodal plane concentrated between the nuclei. We picture all isolated p bonds between carbons to have orbitals such as those of Figure 1.21.

Lastly, let’s examine triple bonds. Anytime there is a triple bond, sp hybridization is appropriate for the atoms involved. Figure 1.22 shows an orbital overlap diagram for acetylene, C2H2. A carbon-carbon triple bond consists of one s bond formed by overlapping sp hybrid orbitals and two p bonds. Overlapping a pair of parallel 2p atomic orbitals gives one p bond. Overlapping the other pair of parallel 2p atomic orbitals (perpendicular to the fi rst pair) gives the second p bond.

The relationship among the number of atoms bonded to carbon, orbital hybridization, and types of bonds involved is summarized in Table 1.10.

Pi (p) molecular orbital A molecular orbital with a nodal plane that cuts through both atomic nuclei, with electron density concentrated above and below the nodal plane.

A p bond forms between these two 2p orbitals.

C C H

H H H

(a) H (b)

C H H C

Four C — H s bonds form from overlap of a C sp2 and a H 1s orbital. See one here.

A C — C s bond forms from overlap of two sp2 orbitals

Figure 1.20

Covalent bond formation in ethylene (CH2CH2). (a) Lewis structure. (b) Overlap of sp 2 hybrid orbitals on adjacent carbons forms a C!C s bond (see Figure 1.18), and overlap of carbon sp 2 hybrid orbitals on carbons with 1s orbitals on hydrogens gives C!H s bonds (see Figure 1.17). Further, overlap of parallel 2p orbitals on the adjacent carbons gives a p bond (see Figure 1.21).

Cartoon

Computed

Cartoon Computed

(b) Out-of-phase addition of two 2p atomic orbitals

(a) In-phase addition of two 2p atomic orbitals

Energy

C C

C C Figure 1.21

Molecular orbital mixing diagram for the creation of any C!C p bond.

(a) Addition of two p atomic orbitals in phase leads to a p orbital that is lower in energy than the two separate starting orbitals.

When populated with two electrons the p orbital gives a p bond. (b) Addition of the p orbitals in an out-of-phase manner (meaning a reversal of phasing in one of the starting orbitals) leads to a p* orbital.

Population of this orbital with one or two electrons leads to weakening or cleavage of the p bond respectively.

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1.7 A Combined Valence Bond and Molecular Orbital Theory Approach to Covalent Bonding 41 A bond

forms between these two 2p orbitals

A bond forms between these two 2p orbitals

H C

C Two C — H bonds form

from overlap of a C sp and a H 1s orbital. See one here.

(a) (b)

A C—C bond forms from overlap of two sp orbitals

C H

H Figure 1.22

Covalent bond formation in acetylene. (a) Lewis structure.

(b) Overlap of sp hybrid orbitals on adjacent carbons forms a C!C s bond (see Figure 1.18), and overlap of carbon sp hybrid orbitals with hydrogen 1s orbitals gives C!H s bonds (see Figure 1.17). Further, overlap of parallel 2p orbitals on the adjacent carbons gives a C!C p bond (see Figure 1.21). Two such p bonds exist in acetylene.

Table 1.10 Covalent Bonding of Carbon Groups

Bonded to Carbon

Orbital Hybridization

Predicted Bond Angles

Types of Bonds

to Carbon Example Name

4 sp3 109.5° Four s bonds Ethane

3 sp2 120° Three s bonds

and one p bond

Ethylene

2 sp 180° Two s bonds

and two p bonds

Acetylene C C

H H H

H C H

H C C H H

H C H H

Example 1.15

Describe the bonding in 1-methoxypropanone (CH3OCH2COCH3) in terms of (a) hybridization of C and O, (b) type of bonds between C and O, and (c) type of orbitals that hold the lone electron pairs on O.

Solution

H H H H H

H H

C C C

O O O

H H H H H

H H

C C C

O H

H H H H H

H H

C C C

sp3 sp2

sp3

s s

(a) C (b) C (c) C

Problem 1.15

Describe the bonding in these molecules in terms of hybridization of C and N, and the types of bonds between carbon and nitrogen, and if there are any lone pairs, describe what type of orbital contains these electrons.

(a) CH3CH"CH2 (b) CH3NH2

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42 Chapter 1 Covalent Bonding and Shapes of Molecules

1.8 Resonance

As chemists developed a deeper understanding of covalent bonding in organic compounds, it became obvious that, for a great many molecules and ions, no single Lewis structure provides a truly accurate representation. For example, Figure 1.23 shows three Lewis structures for the carbonate ion, CO322

, each of which shows carbon bonded to three oxygen atoms by a combination of one double bond and two single bonds. Each Lewis structure implies that one carbon-oxygen bond is dif- ferent from the other two. However, this is not the case. Experiments showed that all three carbon-oxygen bonds are identical.

Contributing structures Representations of a molecule or ion that differ only in the distribution of valence electrons.

Resonance hybrid

A molecule, ion, or radical described as a composite of a number of contributing structures.

Double-headed arrow

A symbol used to show that structures on either side are resonance contributing structures.

Figure 1.24

(a–c) The carbonate ion represented as a resonance hybrid of three equivalent

contributing structures. Curved arrows show the redistribution of valence electrons between one contributing structure and the next. (d) An electrostatic potential map of a carbonate ion shows that the negative charge is distributed equally among the three oxygens.

(a) ..

C O..

.. ..O..

O.. O.. ..

.. O.. ..

– ..

–

O..

.. – C

–

(b)

O..

.. C

– –..

(c) (d)

(a) ..

C O..

O..

–

..– ..

O O..

.. C

–..

..O..

– (c)

O O.. ..

.. C

O..

–..

O..

..–

Figure 1.23 (b)

(a– c) Three Lewis structures for the carbonate ion.

The problem for chemists, then, was how to describe the structure of molecules and ions for which no single Lewis structure is adequate and yet still retain Lewis structures. As an answer to this problem, Linus Pauling proposed the theory of resonance.

Combining Valence Bond (VB) and Molecular Orbital (MO)

Electron Confi guration of Atoms

Bond Angles and Shapes of Molecules