Problems 1-15 + all bold numbered problems CHAPTER 10 ORBITAL HYBRIDIZATION and MOLECULAR ORBITALS Problems 1-15 + all bold numbered problems

ORBITALS AND BONDING THEORIES There are two major theories of bonding The Valence Bond (VB) Theory Simple Explains geometry An extension of the Atomic Theory Fails to account for some paramagnetic properties Fails to explain delocalized bonds The Molecular Orbital (MO) Theory More complex Explains magnetic properties Explains delocalized bonds

Two Theories of Bonding VALENCE BOND THEORY — Linus Pauling valence electrons are localized between atoms (or are lone pairs). half-filled atomic orbitals overlap to form bonds

Maximum Attraction Minimum Attraction Free atom Repulsion

Sigma Bond Formation by Atomic Orbital Overlap Two s orbitals overlap • ­ sigma bond ( s ) ¯ + H

Sigma Bond Formation by Atomic Orbital Overlap Two s orbitals overlap Two p atomic orbitals overlap s & p atomic orbitals overlap H + F H F

VALENCE BOND THEORY Bonds form when: atomic orbitals overlap, and two electrons with opposite spin are present. The resulting lower energy state is called a covalent bond. If the overlapping orbitals are 1s type orbitals, the resulting bond is called a s1s + 1s (previous H2) If the overlapping orbitals are 1s and 2p type orbitals, the resulting bond is called a s1s + 2p. If the overlapping orbitals are 2p type orbitals, the resulting bond is called a s2p + 2p

VALENCE BOND THEORY VBT works well for explaining atomic orbital overlap between 1s-1s, 2p-2p and 1s-2p to make new bonds What does VBT say about more complex molecules with more then 2 atom systems

? VALENCE BOND THEORY VBT can not account for a 109.5º angle in CH4 due to 2p orbitals constrained 90º bond angle AO of 90º do not correspond to 109.5º ?

Linus Pauling proposes Hybrid Orbital Theory A new theory is needed Linus Pauling proposes Hybrid Orbital Theory

Advanced Theories of Chemical Bonding Atomic Orbitals Molecules

Hybrid Orbitals Atomic orbitals in the free atoms are “Mixed” to make a new Hybrid Orbital for molecules with more then 2 atoms An example of mixing an s and p atomic orbital to make a NEW Hybrid sp orbital # AO = # of HO

New HO from AO sp2 sp3 sp3d s s p2 s p2 p p s p2 s p p3 p s p3 s p3 s + s s p2 s p2 p p s p2 + s p p3 p s p3 s p3 s p 3d d + s s p 3d p p s p 3d s p 3d

sp3d2 s p 3d 3d2 d s s p 3d2 p p s p 3d2 s p 3d2 s p 3d2 d + sp3d2 s s p 3d2 p p s p 3d2 s p 3d2 s p 3d2 d These new HO do two things Allow the orbitals to physically rearrange in such a fashion to adopt the 109.5º bond angle in the sp3 for example Account for 6 coordinate molecules as in the case of sp3d2

Hybrid Orbitals: a “Mixing” of AO’s Other possibilities one s with one p (just described) one s with two p’s one s with three p’s one s with three p’s and one d one s with three p’s and two d’s New Name sp sp2 sp3 sp3d sp3d2 These are the newly mixed Hybrid Orbitals

Hybridization of Atomic Orbitals Sp3 To form polyatomic molecules having three or more atoms, it is frequently necessary (always in the second period) to hybridize the atomic orbitals of the central atom to permit maximum orbital overlap and to maximize the number of bonds formed. Carbon, for example, always forms four (4) bonds.

Orbitals needed to hybridize

Bonding in CH4 Need to use 4 atomic orbitals — s, px, py, and pz — to form 4 new hybrid orbitals pointing in the correct direction.

Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals 4 C atom orbitals hybridize to form four equivalent sp3 hybrid atomic orbitals.

sp3 These hybrid atomic orbitals are linear combinations of the atomic orbitals. The number of hybrid orbitals produced is always equal to the number of atomic orbitals hybridized.

New Linear Combination

Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals 4 C atom orbitals hybridize to form four equivalent sp3 hybrid atomic orbitals.

Hybridization for water and ammonia is explained on page 445. sp3 Hybridization for water and ammonia is explained on page 445. Figures 10.8 & 10.9. (Examples 10.1 and 10.2 page 446.) Predict the hybridization and geometry for CHCl3 and OF2. Describe the sigma bonds in each molecule.

Figure 10.8

Figure 10.9

sp2 If one s orbital and two p orbitals are combined, the resulting hybrid orbitals are called sp2 orbitals. The trigonal planar shape of this set of three orbitals is consistent with the VSEPR theory. Figure 10.10, page 448, and Figure 10.8 (3rd ed.) illustrates this concept. The orbital box diagrams can be used to confirm the bonding. BH3 is and example (show model).

Figure 10.10

Using VB Theory Bonding in BF3 planar triangle angle = 120o F Boron configuration ­ ­¯ 2p 2s 1s •• • B planar triangle angle = 120o

Bonding in BF3 How to account for 3 bonds 120o apart using a spherical s orbital and p orbitals that are 90o apart? Pauling said to modify VP approach with ORBITAL HYBRIDIZATION — mix available orbitals to form a new set of orbitals — HYBRID ORBITALS — that will give the maximum overlap in the correct geometry.

Bonding in BF3 rearrange electrons hydridize orbs. unused p orbital three sp 2 hybrid orbitals ­ ­¯ 2p 2s

Bonding in BF3 rearrange electrons hydridize orbs. unused p orbital three sp 2 hybrid orbitals ­ ­¯ 2 p 2 s 120o three sp hybrid orbitals • • The three hybrid orbitals are made from 1 s orbital and 2 p orbitals  3 sp2 hybrids. • Now we have 3, half-filled HYBRID orbitals that can be used to form B- F sigma bonds.

Bonding in BF3 rearrange electrons hydridize orbs. unused p orbital three sp 2 hybrid orbitals ­ ­¯ 2 p 2 s 120o three sp hybrid orbitals • An orbital from each F overlaps one of the sp2 hybrids to form a B-F  bond.

sp Figure 10.11, page 448, & Figure 10.9 (3rd ed.) illustrates the outcome of hybridizing an s and a p orbital to produce two sp hybrid atomic orbitals with a linear geometry. BeF2 is an example of this type hybridization. Predict the hybridization and geometry for PF3 and BeH2. Describe the sigma bonds in each molecule. We would expect the first to be sp3 hybridized, but it actually uses the 3p atomic orbital (3rd period) instead and has approximately 90o bond angles.

Figure 10.11 36

Orbital Hybridization BONDS SHAPE HYBRID REMAIN 2 linear sp 2 p’s 3 trigonal sp2 1 p planar 4 tetrahedral sp3 none

dsp3 and d2sp3 These hybridizations require five (5) and six (6) atomic orbitals respectively and produce an equal number of hybrid atomic orbitals. The electronic geometries are trigonal-bipyramidal, and octahedral. Figure 10.12 provides an overview of these cases and a review of the others. (page 450) Examples 10.3 & 4 cover PF5 and others. Describe the hybridization, bonding, and geometry for SF4 and SF6.

Figure 10.12

Multiple Bonding The second type of covalent bond is the p bond. The pi bond (p) results from the sideways overlap of two atomic p orbitals. The electron density is above and below the plane. The second bond between two atoms is always a p bond as is the third bond in the case of a triple bond. Figures 11.8 (2nd ed.) & 10.13, 10.14, 10.16 and models.

Figure 10.13

Figure 10.14

Figure 10.16 2 p bonds

Bonding in Glycine

Multiple Bonds Consider ethylene, C2H4 H C sp 2 120o

Sigma Bonds in C2H4 H C sp 2 120o

p Bonding in C2H4 The unused p orbital on each C atom contains an electron and this p orbital overlaps the p orbital on the neighboring atom to form the p bond. (See Fig. 10.13) p orb. for p bond 3 sp 2 hybrid orbitals ­ ­¯ 2p 2s

Multiple Bonding in C2H4

Consequences of Multiple Bonding Restricted rotation around C=C bond.

Multiple Bonding Describe the hybridization, bonding, and geometry for H2CO and HCN. Also do a valence bond bonding diagram for each. Figure 10.15 for H2CO bonding. O3, ozone, is an excellent example of pi resonance and a need for a better theory, the delocalized molecular theory.

Figure 10.15

Isomers Resulting from p Bonding Since the pi bond is not free to rotate, two isomer are created, the cis and the trans. See page 457 and Figure 10.18. The cis structure has the same atoms on the same side of the double bond. The trans isomer has the atoms across the double bond diagonally. There is a third possible isomer which has both terminal atoms on the same central atom, but this is a structural isomer. Illustrate with C2H2Br2.

Figure 10.18

Isomers of C2H2Br2 Trans Cis

Two Theories of Bonding MOLECULAR ORBITAL THEORY — Robert Mullikan (1896-1986) valence electrons are delocalized valence electrons are in orbitals (called molecular orbitals) spread over entire molecule.

Benzene The bonding p in benzene, C6H6, can be explained using resonance, but that explanation leaves as many questions as answers. A theory involving delocalization of bonding p electrons is needed: The M.O. Theory. Figure 10.19 and 3rd ed.

Figure 10.19 57

10.3 MOLECULAR ORBITAL THEORY Instead of considering atomic orbitals or hybrid atomic orbitals localized on a single atom, we consider a set of orbitals common to the whole molecule, delocalized M.O. theory. In the case of localized M.O. theory, the orbitals are common to the two atoms being bonded. This new theory is needed to explain the paramagnetic property of oxygen and certain other diatomic molecules. Paramagnetic species have one or more unpaired electrons. Diamagnetic species have no unpaired electrons.

Paramagnetic/diamagnetic

MOLECULAR ORBITAL THEORY Molecular orbitals, like atomic orbitals, are assigned electrons according to the Pauli principle and Hund's rule. The electrons fill the lowest energy orbitals first with out pairing, then pair. Once these orbitals are filled, electrons are assigned to the next highest energy orbitals.

There are four principles in the M. O. T. 1) The number of molecular orbitals is always equal to the number of atomic orbitals for the atoms forming the molecule (or ion). For every bonding molecular orbital there is a corresponding antibonding orbital. Figure 10.21, page 461. In this case we see a sb and a s*. The bonding orbitals result from an in phase combination of the atomic orbitals, and the antibonding orbitals result from an out of phase combination to the atomic orbitals.

Figure 10.21

There are four principles in the M. O. T. 2) The bonding molecular orbital is always lower in energy than the parent atomic orbitals and stabilizes the molecule. The antibonding orbital is always higher in energy that the parent atomic orbitals and destabilizes the molecule. Figure 10.22, page 461. This figure illustrates the bonding for H2.

Figure 10.22 64

There are four principles in the M. O. T. 3) Electrons in the molecule are assigned to orbitals of successively higher energy according to the Pauli principle and Hund's rule. Bonding orbitals stabilize and antibonding orbitals destabilize the molecule. 4) Atomic orbitals combine most effectively to form molecular orbitals when the atomic orbitals have similar energies.

Bond order Bond order is defined as the number of net bonding electrons divided by two. B.O. = (# bonding e- - # antibonding e-)/2. The bond order can be fractional, but is never negative. A bond order of zero indicates that the molecule (ion) is not stable. Example 10.7 and Exercise 10.7.

Figure 10.24, page 463, illustrates the bonding for Li2. Continued Do a molecular orbital diagram and molecular orbital configuration for: H2- and He2+. Figure 10.24, page 463, illustrates the bonding for Li2. Do a molecular orbital diagram and molecular orbital configuration for: He2- and Be2+. Example 10.8 and Exercise 10.8.

Figure 10.24

Molecular Orbitals for Homonuclear Diatomic Molecules P orbitals can be used for both s molecular orbitals and p molecular orbitals. Figure 10.25 and 10.26, pages 464. This gives rise to a new form of molecular orbital diagram. Figure 10.27, page 465. Notice the differences with the p bonding orbitals lower in energy than the s2p bonding orbitals, but the reverse order for the antibonding orbitals.

Figure 10.25

Figure 10.26

Figure 10.27

Molecular Orbitals for Homonuclear Diatomic Molecules O.H. Table 10.1 page 466 for the second period molecules. Examples and Exercises 10.9. For heteronuclear diatomic ions and molecules, the element with the higher electronegativity always has the lower energy atomic orbitals, and receives the additional electrons if the ion is an anion. Do a molecular orbital diagram and molecular orbital configuration for: NO, OF-, and CN+. Give the bond order and magnetic properties for each.

Delocalized Molecular Theory O3 is an excellent example. Figure 10.28 page 469. The molecule has one p bond and two bonding sites. The bond order is 1.5, with 1 sigma bond between each oxygen atom and one p bond spread between the three atoms. The other pair of electrons is in a p nonbonding orbital. The molecule is diamagnetic.

Figure 10.28 0 e- 2 e- See the M.O. diagram page 468. 2 e-

Benzene Delocalized electrons Figure 10.19 Benzene Delocalized electrons

Figure 10.29 Benzene M.O. diagram

10.4 METALS AND SEMICONDUCTORS The atomic orbitals of metals form delocalized, conducting bands. Figure 10.30, page 470. In the case of metals with s and p orbitals, these bands overlap. This is called the Band theory. Use the Band theory to show how Mg and Al are conductors.

Figure 10.30 Sodium as a conductor

Lithium, a metal conductor

METALS AND SEMICONDUCTORS Nonmetals hybridize first and then form two bands, the valence band and the conduction band, with a gap between them. See Figure 10.32, page 471. If the gap is small as in Si and Ge which are semiconductors, the electrons are easily promoted from one band the other allowing for conduction.

Doping Si with Al

METALS AND SEMICONDUCTORS Use the Band theory to show how C and Ge behave. If Si and Ge are doped with atoms having 3 or 5 valence electrons, p and n type semiconductors are created. Figure 10.34, page 472.

Figure 10.34 85