Chapter 11
Theories of Covalent Bonding
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VALENCE BOND THEORY:
DEVELOPED BY LINUS PAULING, who received the Nobel Prize in 1954 for his work
A view of chemical bonding in which bonds arise from the overlap of atomic orbitals on two atoms to give a bonding orbital of electrons localized between the bonded atoms
RULE: Realize that Valence Bond Theory and all the others don't explain everything
The Central Themes of VB Theory
Basic Principle
A covalent bond forms when the orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of electrons.
(The two wave functions are in phase so the amplitude increasesbetween the nuclei.)
The Central Themes of VB Theory
Themes
A set of overlapping orbitals has a maximum of two electrons that must have opposite spins.
The greater the orbital overlap, the stronger (more stable) the bond.
The valence atomic orbitals in a molecule are different from those in isolated atoms.
There is a hybridization of atomic orbitals to form molecularorbitals.
Figure 11.1 Orbital overlap and spin pairing in three diatomic molecules.
Hydrogen, H2
Hydrogen fluoride, HF
Fluorine, F2
Regular atomic orbital overlap can explain these bonds.
VALENCE BOND THEORY:
Ha to Hb: 1sa to 1sb overlap radius = 74 pm
As overlap increases, strength of bond increases - both electrons are mutually attracted to both atomic nuclei.
At optimum distance between nuclei with maximum overlap, a sigma bond (strong primary bond) forms. Max electron density is along the axis of the bond
Ha to Fb: 1sa to 2pb direct overlap or bond
VALENCE BOND THEORY:
F to F: the picture looks like a 2p orbital on one F is overlapping with a 2p orbital on the other F atom, but actually each F is sp3 hybridized & electrons are localized between two atomic nuclei
VALENCE BOND THEORY:
We cannot use this direct overlap picture for CH4’s bonding. The 2s and the three 2p orbitals on each C do not fit into the CH4 molecule's 109o bond angles, since the 2p orbitals are at 90° to each other
Valence Bond Theory states that HYBRID orbitals of the outermost orbitals on an atom are formed from the atoms’ atomic orbitals
Hybrid Orbitals
The number of hybrid orbitals obtained equals the number of atomic orbitals mixed.
The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed.
Key Points
sp sp2 sp3 sp3d sp3d2
Types of Hybrid Orbitals
Figure 11.2 The sp hybrid orbitals in gaseous BeCl2.
atomic orbitals on Be
hybrid orbitals
orbital box diagrams
You have to know how to draw this energy hybrid formation.
Figure 11.2 The sp hybrid orbitals in gaseous BeCl2(continued).
orbital box diagrams with orbital contours
Figure 11.3 The sp2 hybrid orbitals in BF3.
You have to know how to draw this energy hybrid formation.
Note the three sigma bonds formed between B and each F.
Figure 11.4 The sp3 hybrid orbitals in CH4.
You have to know how to draw this energy hybrid formation.
Figure 11.5 The sp3 hybrid orbitals in NH3.
You have to know how to draw this energy hybrid formation.
Figure 11.5 continued The sp3 hybrid orbitals in H2O.
You have to know how to draw this energy hybrid formation.
VALENCE BOND THEORY
Expanded Valence Shells have hybrid orbitals using s, p & d atomic orbitals. Example: PCl5 P: [Ne]3s23p3
dsp3 hybridization results in 5 bonds and trigonal bipyramidal geometry
(You can write these as dsp3 or sp3d)
Figure 11.6 The sp3d hybrid orbitals in PCl5.
You have to know how to draw this energy hybrid formation.
Figure 11.7 The sp3d2 hybrid orbitals in SF6.
You have to know how to draw this energy hybrid formation.
Figure 11.8
The conceptual steps from molecular formula to the hybrid orbitals used in bonding.
Molecular formula
Lewis structure
Molecular shape and e-
group arrangement
Hybrid orbitals
Figure 10.1
Step 1
Figure 10.12
Step 2 Step 3
Table 11.1
SAMPLE PROBLEM 11.1 Postulating Hybrid Orbitals in a Molecule
SOLUTION:
PROBLEM: Use partial orbital diagrams to describe mixing of the atomic orbitals of the central atom leads to hybrid orbitals in each of the following:
(a) Methanol, CH3OH (b) Sulfur tetrafluoride, SF4
(a) (a) CH3OH
H
CH H
OH
The groups around C are arranged as a tetrahedron.
O also has a tetrahedral arrangement with 2 nonbonding e- pairs.
SFF
F
F
SAMPLE PROBLEM 11.1 Postulating Hybrid Orbitals in a Molecule
continued
2p
2s single C atomsingle C atom
sp3
hybridized hybridized C atomC atom
2p
2s single O atomsingle O atom
sp3
hybridized hybridized O atomO atom
(b) SF4 has a seesaw shape with 4 bonding and 1 nonbonding e- pairs.
3p
3s
3d
S atomS atomsp3d
3d
hybridized hybridized S atomS atom
VALENCE BOND THEORY
There can be more than one central atom, and each has its own hybridization and geometry
C2H6 and H2O2 and CH3COOH
C2H6: both C's are sp3 hybridized and can rotate around axis of bond.
H2O2: both O's are sp3 , etc.
Figure 11.9 The bonds in ethane(C2H6).
both C are sp3 hybridized s-sp3 overlaps to bonds
sp3-sp3 overlap to form a bondrelatively even
distribution of electron density over all bonds
VALENCE BOND THEORY: Multiple Bonds
H2CO: the Lewis structures shows a double bond between C and O, but we know it does not have twice the bond dissociation energy of a single C-O bond
Pauling proposed that there was only one sigma bond between any two atoms, and the other multiples were weaker pi bonds
If there are only 3 bonds around this carbon, it can't be sp3 hybridized - instead we have sp2 hybrid orbitals
sp2 hybridization results in only 3 bonds, and trig planar geometry, with 120° angles
bond is a sideways or parallel overlap of the p atomic orbitals rather than the direct overlap of bonds
Figure 11.10 The and bonds in ethylene (C2H4).
overlap in one position -
p overlap -
electron densityProper name is ethene.
VALENCE BOND THEORY
Look at acetylene: its geometry is linear. C is forming a triple bond to another C and a single bond to H, so that's only two bonds
Therefore sp hybridization results in only 2 bonds, and linear geometry
There are 2 bonds from the parallel overlap of the 2p orbitals remaining on both C's
Figure 11.11 The and bonds in acetylene (C2H2).
overlap in one position -
p overlap -
SAMPLE PROBLEM 11.2 Describing the Bond in Molecules
SOLUTION:
PROBLEM: Describe the types of bonds and orbitals in acetone, (CH3)2CO.
PLAN: Use the Lewis structures to ascertain the arrangement of groups and shape at each central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their orbital overlaps.
H3C
C
CH3
O
spsp33 hybridized hybridized
spsp33 hybridized hybridized
CC
C
O
H
H
HHH
H
spsp22 hybridized hybridized
bondsbond
CC
C
O
sp3
sp3
sp3
sp3
sp3
sp3
sp3
sp3
sp2 sp2
sp2
sp2
sp2sp2
H
HH
HH
H
H2CO hybrid orbitals and sigma and pi bond formation
Remember the C=C double bond has sigman and pi bonds.
The C has sigma bonds from its hybrid orbitals to the two H’s and the O. The leftover p orbitals will form the pi bond.
Figure 11.13 from 4th ed.
Restricted rotation of -bonded molecules in C2H2Cl2.
CIS TRANS
This cis/trans arrangement will be important in chem 2, organic chem and biology!
VALENCE BOND THEORY: RESONANCE
Resonance Structures and Bonding:
resonance structures involve an electron pair used alternately as a bond or a LP
Ozone: O3 O==O--O or O--O==O
All are sp2, trig planar, each has 3 sp2 orbitals and a p orbital remaining.
VALENCE BOND THEORY
Benzene: C6H6 has carbons with sp2 hybrids and 120o angles, each C has 2 bonds to other C's, 1 bond to H, and 1 bond electron available
Get "ring" of delocalized e-s
SUMMARY: draw the Lewis structure; determine arrangement of electron pairs using VSEPR, specify the hybrid orbitals to accommodate the e- pairs
Benzene sigma bond formation between C’s and C-Hs
The leftover p orbitals will form alternating pi bonds as shown in sketch.
MOLECULAR ORBITAL THEORY:
- explains why H2 forms easily and He2 does not - is an alternate way of viewing e- orbitals in molecules
where pure s and pure p orbitals combine to produce orbitals that are delocalized over the molecule
- they can have different energies and are assigned electrons just like we do in an atom - Pauli exclusion principle and Hund's rule included
Pauling's Valence Bond Theory does not explain everything
MO Theory doesn't either, but it does correctly predict the electronic structure of certain molecules that do not follow Lewis's approach, including the paramagnetism of certain molecules, like O2
The Central Themes of MO Theory
A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals.
Atomic wave functions are summed to obtain molecular wave functions. The number of molecular orbitals produced is always = # of atomic orbitals brought by the combining atoms (only orbitals on different atoms are combined). If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei).
If wave functions cancel each other, an antibonding MO is formed (a node of zero electron density occurs between the nuclei).
Atomic orbitals combine most effectively with orbitals of the same type and similar energy (s w/s, n=2 w/ n=2)
The electrons of the molecule are placed in bonding or antibonding orbitals of successively higher energy (just like Hund's rule).
Amplitudes of wave functions added
Figure 11.13
An analogy between light waves and atomic wave functions.
Amplitudes of wave functions
subtracted.
Figure 11.14 Contours and energies of the bonding and antibonding molecular orbitals (MOs) in H2.
The bonding MO is lower in energy and the antibonding MO is higher in energy than the AOs that combined to form them.
MOLECULAR ORBITAL THEORY
BOND ORDER: the number of bonding e- pairs shared by 2 atoms in a molecule
Fractional bond orders are possible in MO Theory!
Silberberg method:B.O. = ½(# of e- in bonding orbitals - # of e- in antibonding orbitals)
Figure 11.15 The MO diagram for H2.
En
erg
y
MO of H2
*1s
1s
AO of H
1s
AO of H
1s
H2 bond order = 1/2(2-0) = 1
Filling molecular orbitals with electrons follows the same concept as filling atomic orbitals.
Figure 11.16 MO diagram for He2+ and He2.
En
erg
y
MO of He+
*1s
1s
AO of He+
1s
MO of He2
AO of He
1s
AO of He
1s
*1s
1s
En
erg
y
He2+ bond order = 1/2 He2 bond order = 0
AO of He
1s
SAMPLE PROBLEM 11.3 Predicting Stability of Species Using MO Diagrams
SOLUTION:
PROBLEM: Use MO diagrams to predict whether H2+ and H2
- exist. Determine their bond orders and electron configurations.
1s1s
AO of HAO of H
1s1s
AO of HAO of H
MO of HMO of H22++
bond order = 1/2(1-0) = 1/2
HH22++ does exist does exist
MO of HMO of H22--
bond order = 1/2(2-1) = 1/2
H2- does exist
1s1s 1s1s
AO of HAO of H AO of HAO of H--
*2s
2s
2s2s
Figure 11.17
2s 2s
*2s
2s
Li2 bond order = 1 Be2 bond order = 0
Bonding in s-block homonuclear diatomic molecules.E
ner
gy
Li2Be2
Figure 11.18Contours and energies of s and p MOs through
combinations of 2p atomic orbitals.
Or the pz orbitals
Figure 11.19 Relative MO energy levels for Period 2 homonuclear diatomic molecules.
MO energy levels for O2, F2, and Ne2
MO energy levels for B2, C2, and N2
without 2s-2p mixing
with 2s-2p mixing
Memorize this!
Figure 11.20
MO occupancy and molecular properties for B2 through Ne2
Figure 11.21
The paramagnetic properties of O2
SAMPLE PROBLEM 11.4 Using MO Theory to Explain Bond Properties
SOLUTION:
PROBLEM: As the following data show, removing an electron from N2 forms an ion with a weaker, longer bond than in the parent molecules, whereas the ion formed from O2 has a stronger, shorter bond:
Explain these facts with diagrams that show the sequence and occupancy of MOs.Explain these facts with diagrams that show the sequence and occupancy of MOs.
Bond energy (kJ/mol)Bond energy (kJ/mol)
Bond length (pm)Bond length (pm)
NN22 NN22++ OO22 OO22
++
945945
110110
498498841841 623623
112112121121112112
N2 has 10 valence electrons, so N2+ has 9.
O2 has 12 valence electrons, so O2+ has 11.
SAMPLE PROBLEM 11.4 Using MO Theory to Explain Bond Properties
continued
2s
2s
2p
2p
2p
2p
N2 N2+ O2 O2
+
bond orders
1/2(8-2)=3 1/2(7-2)=2.5 1/2(8-4)=2 1/2(8-3)=2.5
2s
2s
2p
2p
2p
2p
bonding e- lost
antibonding e- lost
MO Theory Practice
1. Draw the bonding and antibonding molecular orbitals for H2.
2. Do Valence Bond Theory (hybridization) and MO Theory for both O2 and O2
2-. Which theory works better to explain the molecule and ion?
3. For N2, N2+ and N2
- comparea. Magnetic characterb. Net number of bondsc. Bond Orderd. Bond lengthe. Bond strength
Answers
1. See picture in text.
2. VB Theory shows O2 as sp2 hybridized with one bond and one bond. There are two lone pairs on each O. O2
2- has one bond, and each O has three lone pairs. MO Theory shows a bond order of 2 for O2 and that it is paramagnetic. MO Theory shows a bond order of 1 for O2
2- and diamagnetic. But MO Theory fits the real data that O2 is paramagnetic.
Answers con’t
N2 N2+ N2
-
a. Diamag Paramag Paramag
b. 2 1.5 1.5
c. 3 2.5 2.5
d. Short Longer Longer
e. Strong Weaker Weaker