A basic principle of valence bond theory (VB theory) is that bonds are created by the overlap of atomic orbitals on adjacent atoms. Therefore, with VB theory the bonds are localized between adjacent atoms rather than delocalized over several atoms as in MO theory. This model correlates with Lewis pictures where two electrons are vi- sualized between atoms as a bond. To represent the bonds, lines are drawn between the atoms. However, the localization of bonds between atoms presents a problem for second-period elements. In forming covalent bonds, atoms of carbon, nitrogen, and oxygen (all second-period elements) use 2s and 2p atomic orbitals. The three 2p atomic orbitals are at angles of 90° to each other (Figure 1.9), and, if atoms of second-period elements used these orbitals to form covalent bonds, we would expect bond angles around each would be approximately 90°. However, we rarely observe bond angles of 90° in organic molecules. What we fi nd instead are bond angles of approximately 109.5° in molecules with only single bonds, 120° in molecules with double bonds, and 180° in molecules with triple bonds, as shown in Table 1.9.
To account for the observed bond angles in a way that is intuitive for chemists, Linus Pauling proposed that atomic orbitals for each atom should be thought of as fi rst combining to form new atomic orbitals, called hybrid orbitals, which then interact to form bonds by overlapping with orbitals from other atoms. The hybrid orbitals have the bond angles we observe around each atom, so molecular structure and bonding based on the overlap of hybrid orbitals provides an intuitive under- standing. Being able to construct organic molecules from the overlap of hybrid orbitals is an essential organic chemistry survival skill.
Hybrid orbitals are formed by combinations of atomic orbitals, a process called hybridization. Mathematically, this is accomplished by combining the wave func- tions of the 2s (c2s) and three 2p (c2px, c2py, c2pz) orbital wave functions. The num- ber of hybrid orbitals formed is equal to the number of atomic orbitals combined.
Elements of the second period form three types of hybrid orbitals, designated sp3, sp 2, and sp, each of which can contain up to two electrons.
sp3 Hybrid Orbitals—Bond Angles of Approximately 109.5°
The mathematical combination of the 2s atomic orbital and three 2p atomic orbit- als forms four equivalent sp3 hybrid orbitals described by four new wave functions.
Plotting c for the four new wave functions gives a three-dimensional visualization of the four sp3 hybrid orbitals. Each sp3 hybrid orbital consists of a larger lobe point- ing in one direction and a smaller lobe of opposite sign pointing in the opposite direction. The axes of the four sp3 hybrid orbitals are directed toward the corners of a regular tetrahedron, and sp3 hybridization results in bond angles of approxi- mately 109.5° (Figure 1.12). Note that each sp3 orbital has 25% s-character and 75% p-character because those are the percentages of the orbitals combined when constructing them (one 2s orbital, three 2p orbitals). We will refer back to these percentages several times in the text.
Valence bond theory A model of bonding that places electron pairs between adjacent atoms to create bonds
Hybrid orbital
An atomic orbital formed by the combination of two or more atomic orbitals.
Hybridization
The combination of atomic orbitals of different types.
sp3 Hybrid orbital
A hybrid atomic orbital formed by the combination of one s atomic orbital and three p atomic orbitals.
Ground state
1s 1s
•H H•
s∗1s
s1s
s∗1s
s1s
Excited state
1s 1s
•H
Energy H•
Energy
(a) (b)
Figure 1.11
A molecular orbital energy diagram for the hydrogen molecule, H2. (a) Ground state and (b) lowest excited state.
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1.7 A Combined Valence Bond and Molecular Orbital Theory Approach to Covalent Bonding 33 Atoms with four sp3 hybrid atomic orbitals are referred to as sp3 hybridized, or
as having a hybridization state of sp3. A diagram depicting this hybridization shows the creation of four orbitals of equal energy.
Energy 2s
sp3 2p
sp3 hybridization, with electron population for carbon
Population of these orbitals with electrons follows the standard rules for populating atomic orbitals. For example, for C with four valence electrons, each sp3 orbital contains a single electron. Carbon can therefore make four bonds, one with each sp3 hybrid. Nitrogen, with fi ve valence electrons, would have a lone pair and three singly occupied sp3 orbitals. The orbital populations of O and F follow in an analogous fashion.
You must remember that superscripts in the designation of hybrid orbitals tell you how many atomic orbitals have been combined to form the hybrid orbitals. You know that the designation sp3 represents a hybrid orbital because it shows a combination of s and p orbitals. The superscripts in this case tell you that one s atomic orbital and three p atomic orbitals are combined in forming the hybrid orbital. Do not confuse this use of superscripts with that used in writing a ground-state electron confi guration, as for example 1s 22s 22p5 for fl uorine. In the case of a ground-state electron confi gura- tion, superscripts tell you the number of electrons in each orbital or set of orbitals.
In Section 1.2, we described the covalent bonding in CH4, NH3, and H2O in terms of the Lewis model, and in Section 1.4 we used VSEPR to predict bond an- gles of approximately 109.5° in each molecule. Now let us consider the bonding in these molecules in terms of the overlap of hybrid atomic orbitals. To bond with four other atoms with bond angles of 109.5°, carbon uses sp3 hybrid orbitals. Carbon has four valence electrons, and one electron is placed in each sp3 hybrid orbital.
Each partially fi lled sp3 hybrid orbital then overlaps with a partially fi lled 1s atomic orbital of hydrogen to form the four sigma (s) bonds of methane, and hydrogen atoms occupy the corners of a regular tetrahedron (Figure 1.13). We address how to create and model these s bonds in Section 1.7C.
In bonding with three other atoms, the fi ve valence electrons of nitrogen are distributed so that one sp3 hybrid orbital is fi lled with a pair of electrons (the lone pair) and the other three sp3 hybrid orbitals have one electron each. Overlapping
(a) An sp3 orbital (b) Four sp3 orbitals in a tetrahedral arrangement
109.5°
(c) Computed
Cartoon
Figure 1.12 sp3 Hybrid orbitals.
(a) A single sp3 hybrid orbital in computed and cartoon form. (b) Three-dimensional cartoon representation of four sp3 hybrid orbitals centered on the same atom and directed toward the corners of a regular tetrahedron. (c) If four balloons of similar size and shape are tied together, they will naturally assume a tetrahedral geometry.
© Cengage Learning/Charles D. Winters
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34 Chapter 1 Covalent Bonding and Shapes of Molecules
O H H
Water Ammonia
Methane C
H H
H
H N
H H H H
H H
H
C H
H
H N
bonds formed by overlap of sp3 and 1s orbitals
H
H O
Unshared electron pair
Unshared electron pairs
Figure 1.13
Orbital overlap pictures of methane, ammonia, and water.
Computed
Cartoon 120⬚
90⬚
2p orbital sp2
sp2
sp2 sp2
sp2
sp2
(a) An sp2 orbital (b) Three sp2 orbitals (c) A 2p orbital perpendicular to three sp2 orbitals.
Figure 1.14
sp 2 Hybrid orbitals and a single p orbital on an sp 2 hybridized atom. (a) A single sp 2 hybrid orbital in computed and cartoon form. (b) Three sp 2 hybrized orbitals in a trigonal planar arrangement. (c) The lone p orbital.
of these partially fi lled sp3 hybrid orbitals with 1s atomic orbitals of three hydrogen atoms produces an NH3 molecule (Figure 1.13).
In bonding with two other atoms, the six valence electrons of oxygen are distributed so that two sp3 hybrid orbitals are fi lled, and the remaining two have one electron each. Each partially fi lled sp3 hybrid orbital overlaps with a 1s atomic orbital of hydrogen, and hydrogen atoms occupy two corners of a regular tetrahe- dron. The remaining two sp3 hybrid orbitals, each occupied by an unshared pair of electrons, are directed toward the other two corners of the regular tetrahedron (Figure 1.13).
sp2 Hybrid Orbitals—Bond Angles of Approximately 120°
The mathematical combination of one 2s atomic orbital wave function and two 2p atomic orbital wave functions forms three equivalent sp 2 hybrid orbital wave functions. Because they are derived from three atomic orbitals, sp 2 hybrid orbitals always occur in sets of three. As with sp 3 orbitals, each sp 2 hybrid orbital (three- dimensional plot of c) consists of two lobes, one larger than the other. The axes of the three sp 2 hybrid orbitals lie in a plane and are directed toward the corners of an equilateral triangle; the angle between sp 2 hybrid orbitals is 120°. The third 2p atomic orbital (remember 2px, 2py, 2pz) is not involved in hybridization (its wave function is not mathematically combined with the other three) and remains as two lobes lying perpendicular to the plane of the sp 2 hybrid orbitals. Figure 1.14 shows three equivalent sp 2 orbitals along with the remaining unhybridized 2p atomic or- bital. Each sp 2 orbital has 33% s-character and 67% p-character (one 2s orbital, two 2p orbitals).
An atom possessing three sp 2 hybrid orbitals and a single p atomic orbital is referred to as sp2 hybridized, or as having a hybridization state of sp 2. The
sp2 Hybrid orbital
A hybrid atomic orbital formed by the combination of one s atomic orbital and two p atomic orbitals.
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1.7 A Combined Valence Bond and Molecular Orbital Theory Approach to Covalent Bonding 35 energy-level diagram shows the creation of the three hybrid orbitals and a remain-
ing 2p orbital. With C, all four orbitals contain a single electron. Therefore, a car- bon atom makes three bonds with the sp 2 hybrids and one bond with a p orbital.
With N, a lone pair is residing in an sp 2 hybrid orbital, and with O, two lone pairs are residing in sp 2 orbitals. Verify the orbital population of O for yourself by plac- ing six valence electrons into the hybridized orbital diagram shown.
Energy 2s sp2
2p 2p
sp2 hybridization, with electron population for carbon
In Section 1.2, we covered a few apparent exceptions to the octet rule, where boron compounds such as BF3 are common examples. Analogously, VSEPR tells us that BH3 is trigonal planar, with 120o H!B!H bond angles. Therefore, sp 2 hybridization is the appropriate descriptor for B in such structures. Boron has three valence electrons, and one electron is placed in each sp2 hybrid orbital. Each par- tially fi lled sp 2 hybrid overlaps with a 1s hydrogen orbital, containing one electron, to form three B!H s bonds (Figure 1.15). The unhybridized 2p atomic orbital is empty. Note that BH3 is a highly reactive molecule, and generally dimerizes in solu- tion (see Section 6.4).
sp Hybrid Orbitals—Bond Angles of Approximately 180°
The mathematical combination of one 2s atomic orbital and one 2p atomic or- bital produces two equivalent sp hybrid orbital wave functions. Because they are derived from two atomic orbitals, sp hybrid orbitals always occur in sets of two.
The three-dimensional plot of c shows that the two sp hybrid orbitals lie at an angle of 180°. The axes of the unhybridized 2p atomic orbitals are perpendicular to each other and to the axis of the two sp hybrid orbitals. In Figure 1.16, sp hybrid orbitals are shown on the x-axis, and unhybridized 2p orbitals are on the y- and z-axes. Each sp orbital has 50% s-character and 50% p-character because those are the percentages of the orbitals combined when constructing them (one 2s orbital, one 2p orbital).
sp Hybrid orbital
A hybrid atomic orbital formed by the combination of one s atomic orbital and one p atomic orbital.
H
H
H B
Borane s bonds formed by the overlap of sp2 and 1s orbitals
Empty 2p obital H
B H H (a)
(b)
Figure 1.15
Covalent bond formation in borane, BH3. (a) Lewis structure for borane.
(b) Orbital overlap picture of borane.
z
(a) An sp orbital Computed
Cartoon
(b) Two sp orbitals (c) Two 2p orbitals
perpendicular to the sp hybrid orbitals sp
sp
y x
sp
sp
y x
2py 2pz
180⬚
Figure 1.16
sp Hybrid orbitals and two 2p orbitals on an sp hybridized atom. (a) A single sp hybrid orbital in computed and cartoon forms. (b) Two sp hybrid orbitals in a linear arrangement. (c) The two 2p orbitals in perpendicular orientations to the sp hybrid orbitals.
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36 Chapter 1 Covalent Bonding and Shapes of Molecules
You may have noticed by now that the cartoon representations of sp3, sp 2, and sp orbitals all look the same. Although the computed sp orbital is the most spherical and the sp 3 orbital is the most p-like with sp 2 between, chemists often do not attempt to render these differences in drawings.
An atom possessing two sp hybrid orbitals and two 2p orbitals is called sp hybridized, and the energy-level diagram for a carbon atom is shown below.
Energy 2s sp
2p 2p
sp hybridization, with electron population for carbon