Chapter #14 - Covalent Bonding: Orbitals 14.1 Hybridization and the Localized Electron Model 14.2 The Molecular Orbital Model 14.3 Bonding in Homonuclear Diatomic Molecules

14.4 Bonding in Heteronuclear Diatomic Molecules 14.5 Combining the Localized Electron and Molecular

Orbital Models 14.6 Orbitals: Human Inventions 14.7-14.11: Spectroscopy (will not be covered this quarter)

Hybridization and the Localized Electron Model Chapter 12:

Atomic orbitals, Properties of electrons, Wave functions, Electronic configurations, Aufbau principle, etc.

Chapter 13: General Concepts of Bonding in Molecules

- Types of bonds: ionic, covalent, etc. - Bond energies, lengths, polarities, etc. Localized Electron Model - Lewis dot structures - Resonance structures - The octet rule - VSEPR model

Chapter 14: What types of orbitals are used to form bonds?

Valence Bond Theory Basic Principle of Localized Electron Model: A covalent bond forms when the orbitals from two atoms overlap and a pair of electrons occupies the region between the two nuclei. Rule 1: Maximum overlap. The bond strength depends on the attraction of nuclei to the shared electrons, so: The greater the orbital overlap, the stronger the bond.

Valence Bond Theory Basic Principle of Localized Electron Model: A covalent bond forms when the orbitals from two atoms overlap and a pair of electrons occupies the region between the two nuclei. Rule 2: Spins pair. The two electrons in the overlap region occupy the same space and therefore must have opposite spins.

There may be no more than 2 electrons in a molecular orbital.

Valence Bond Theory Basic Principle of Localized Electron Model: A covalent bond forms when the orbitals from two atoms overlap and a pair of electrons occupies the region between the two nuclei. Rule 3: Hybridization. To explain experimental observations, Pauling proposed that the valence atomic orbitals in a molecule are different from those in the isolated atoms. We call this concept Hybridization

What is hybridization? • Atoms adjust to meet the “needs” of the molecule. • In a molecule, electrons rearrange in an attempt to give each atom a noble gas configuration and to minimize electron repulsion.

• Atoms in a molecule adjust their orbitals through hybridization in order for the molecule to have a structure with minimum energy. • The source of the valence electrons is not as important as where they are needed in the molecule to achieve a maximum stability.

Example: Methane

• 4 equivalent C-H covalent bonds • VSEPR predicts a tetrahedral geometry

The Valence Orbitals of a Carbon Atom

Carbon: 2s22p2

How do we explain formation of 4 equivalent C-H bonds?

Hybridization: Mixing of Atomic Orbitals to form New Orbitals for Bonding –

+

–

+

+ –

+ –

+

–

+

–

+

Other Representations of Hybridization:

y1 = 1/2[(2s) + (2px) + (2py) + (2pz)] y2 = 1/2[(2s) + (2px) - (2py) - (2pz)] y3 = 1/2[(2s) - (2px) + (2py) - (2pz)] y4 = 1/2[(2s) - (2px) - (2py) + (2pz)]

Hybridization is related to the number of valence electron pairs determined from VSEPR: Methane (CH4) VSEPR: AB4  tetrahedral  sp3 hybridized

Electron pair geometry determines hybridization, not vice versa!!

109.47 º

Hybridization is related to the number of valence electron pairs determined from VSEPR: Ammonia (NH3) VSEPR: AB3E  tetrahedral  sp3 hybridized

H

N 108.1 º

H

H

Hybridization is related to the number of valence electron pairs determined from VSEPR: Water (H2O) VSEPR: AB2E2  tetrahedral  sp3 hybridized

105.6 º

s bonding and p bonding • Two modes of bonding are important for 1st and 2nd row elements: s bonding and p bonding • These two differ in their relationship to the internuclear axis:

s bonds have electron density ALONG the axis

p bonds have electron density ABOVE AND BELOW the axis

Problem: Describe the hybridization and bonding of the carbon orbitals in ethylene (C2H4) VSEPR: AB3  trigonal planar  sp2 hybridized orbitals for s bonding

sp2 hybridized orbitals used for s bonding remaining p orbital used for p bonding

Bonding in ethylene (C2H4)

Problem: Describe the hybridization and bonding of the carbon orbitals in Carbon Dioxide (CO2) VSEPR: AB2  linear  sp hybridized orbitals for s bonding

Bonding in Carbon Dioxide (CO2)

Atoms of the same kind can have different hybridizations CH3

C

N:

Acetonitrile (important solvent and industrial chemical) H

H

C2

C1

N Bonds

H

s C2: AB4

C1: AB2 2s2 2px2py

sp sp

p p

s p p N:

sp3

ABE

2s2 2px2py2pz

sp

p p

sp lone pair

sp

What have we learned so far? • Molecular orbitals are combinations of atomic orbitals • Atomic orbitals are “hybridized” to satisfy bonding in molecules • Hybridization follows simple rules that can be deduced from the number of chemical bonds in the molecule and the VSEPR model for electron pair geometry

Hybridization • sp3 Hybridization (CH4) – This is the sum of one s and three p orbitals on the carbon atom – We use just the valence orbitals to make bonds – sp3 hybridization gives rise to the tetrahedral nature of the carbon atom

Hybridization • sp2 Hybridization (H2C=CH2) – This is the sum of one s and two p orbitals on the carbon atom – Leaves one p orbital uninvolved – this is free to form a p bond (the second bond in a double bond)

Hybridization • sp Hybridization (O=C=O) – This is the sum of one s and one p orbital on the carbon atom – Leaves two p orbitals free to bond with other atoms (such a O in CO2), or with each other as in HC≡CH

General Notes • This is a model and only goes so far, but it is especially helpful in understanding geometry and expanding Lewis dot structures. • Orbitals are waves. Hybridized orbitals are just the sums of waves – constructive and destructive interference.

The Localized Electron Model is very powerful for explaining geometries and basic features of bonding in molecules, but it is just a model. Major limitations of the LE model: 1) Assumes electrons are highly localized between the nuclei (sometimes requires resonance structures) 2) Doesn’t easily deal with unpaired electrons (incorrectly predicts physical properties in some cases) 3) Doesn’t provide direct information about bond energies

Example: O2 .. .. - Lewis dot structure .. O=O .. - All electrons are paired

Contradicts experiment!

The Molecular Orbital Model Basic premise: When atomic orbitals interact to form a bond, the result is the formation of new molecular orbitals H Y = EY Important features of molecular orbitals: 1. Atomic Orbitals are solutions of the Schrödinger equation for atoms. Molecular orbitals are the solutions of the same Schrödinger equation applied to the molecule.

Molecular Orbital Theory 2. Atomic Orbitals can hold 2 electrons with opposite spins. Molecular Orbitals can hold 2 electrons with opposite spins.

3. The electron probability for the Atomic Orbital is given by Y2. The electron probability for the Molecular Orbital is given by Y2. 4. Orbitals are conserved - in bringing together 2 atomic orbitals, we have to end up with 2 molecular orbitals! How does this work?

Molecular Orbitals are simply Linear Combinations of Atomic Orbitals Example: H2

s anti-bonding (s*)

-

+

Molecular Orbitals have phases (+ or -)

+ s bonding

Next Question: Why does this work?

Constructive and Destructive Interference

Constructive interference between two overlapping orbitals leads to a bonding orbital.

Destructive interference between two orbitals of opposite sign leads to an anti-bonding orbital.

Bonding is driven by stabilization of electrons • Electrons are negatively charged • Nuclei are positively charged

= + = nucleus The bonding combination puts electron density between the two nuclei - stabilization

The anti-bonding combination moves electron density away from region between the nuclei - destabilization

MO Diagrams • We can depict the relative energies of molecular orbitals with a molecular orbital diagram:

The new molecular orbital is lower in energy than the atomic orbitals

s* M.O. is raised in energy

s M.O. is lowered in energy H atom: (1s)1 electron configuration H2 molecule: (s1s)2 electron configuration

Same as previous description of bonding (Ch. 13)

s*

s

Filling Molecular Orbitals with Electrons 1) Orbitals are filled in order of increasing energy (Aufbau principle)

H2

Filling Molecular Orbitals with Electrons 2) An orbital has a maximum capacity of two electrons with opposite spins (Pauli exclusion principle)

He2

Filling Molecular Orbitals with Electrons 3) Orbitals of equal energy (degenerate orbitals) are half filled, with spins parallel, before any is filled completely (Hund’s rule)

Bond Order

Bond Order =

# bonding electrons

#anti-bonding electrons

2

The bond order is an indication of bond strength:

Greater bond order

Greater bond strength (Shorter bond length)

Bond Order: Examples Bond order = (2-0)/2 = 1

Single bond

H2

Stable molecule (436 kJ/mol bond)

Bond order = (2-2)/2 = 0

He2

No bond!

Unstable molecule (0 kJ/mol bond)

He2+ Bond order = (2-1)/2 = 1/2 Half of a single bond Can be made, but its not very stable (250 kJ/mol bond) Fractional bond orders are okay!

H2+

Bond order = (1-0)/2 = 1/2 Half of a single bond Can be made, but its not very stable (255 kJ/mol bond)

Forming Bonds • A s bond can be formed a number of ways:

– s, s overlap – s, p overlap – p, p overlap

Only orbitals of the same phase (+, +) can form bonds

Anti-bonding Orbitals • For every bonding orbital we form, we also form an antibonding orbital:

MO Theory in Bonding • Homonuclear atoms (H2, O2, F2, N2)

H2 (Only 1s orbitals available for bonding)

Covalent Bonding in Homonuclear Diatomics • AOs must overlap in space in order to participate in MOs • Covalent bonding is dominated by the valence orbitals (only valence orbitals are shown in the MOs)

Covalent Bonding in Homonuclear Diatomics Region of shared edensity

–

+

+

Valence configurations of the 2nd row atoms: Li 2s1

Be 2s2

B C 2s22p1 2s22p2

N 2s22p3

O 2s22p4

F 2s22p5

So far we have focused on bonding involving the s orbitals. What happens when we have to consider the p orbitals?

For diatomic molecules containing atoms with valence electrons in the p orbitals, we must consider three possible bonding interactions:

= nucleus

p-type

p-type

s-type Fig 14.35

Fig 14.36

(–) destructive mixing (+)

constructive mixing

Major limitations of the LE model: 2) Doesn’t easily deal with unpaired electrons (incorrectly predicts physical properties in some cases)

Example: O2 .. .. - Lewis dot structure .. O=O .. - All electrons are paired

Contradicts experiment!

Experiments show O2 is paramagnetic

A quick note on magnetism… Paramagnetic The molecule contains unpaired electrons and is attracted to (has a positive susceptibility to) an applied magnetic field Diamagnetic The molecule contains only paired electrons and is not attracted to (has a negative susceptibility to) an applied magnetic field

N2 Video

O2 Video

Example: the O2 Diatomic Oxygen atom has a 2s22p4 valence configuration

O atom

O atom

____ s2p* ___ ___ p2p*

Bond Order = (8-4)/2 = 2 O2 is stable

M.O. O2

___ ___ ___2p

___ ___ ___ 2p ___ ___ p2p ____ s2p

Energy

(498 kJ/mol bond strength)

____ s2s* ___ 2s

___ 2s ____ s2s

(s2s)2(s2s*)2(s2p)2(p2p)4(p2p*)2 Both have degenerate orbitals

A prediction from the M.O. diagram of O2

.. .. O=O .. .. The Lewis dot structure predicts O2 should be diamagnetic-all electrons are paired. The unpaired electrons predicted by the M.O. diagram should behave as small magnetsO2 should be magnetic!

What have we learned so far? 1. Molecular orbitals (MO) are linear combinations of atomic orbitals 2. Both s and p atomic orbitals can be mixed to form MOs 3. Molecular orbitals are bonding and anti-bonding 4. Bonding and anti-bonding MOs lead to the definition of the bond order 5. Bond order is related to the bond strength (bond dissociation energy)

A Complication… M.O. Diagram for B2 (similar for C2 and N2)

M.O. Diagram for O2 (similar for F2 and Ne2)

No s-p mixing s-p mixing

Why does s-p mixing occur? Electron repulsion!!

s2s and s2p both have significant e- probability between the nuclei, so e- in s2s will repel e- in s2p Effect will decrease as you move across the Periodic Table  increased nuclear charge pulls the s2s e- closer, making the s2s orbital smaller and decreasing the s2s and s2p interaction

MOs OF X2 MOLECULES sp orbital mixing (a little hybridization) • lowers the energy of the s2s orbitals and • raises the energy of the s2p orbitals. As a result, E(s2p) > E(p 2p) for B2, C2, and N2. As one moves right in Row 2, 2s and 2p get further apart in energy, decreasing s–p mixing  E(s2p) < E(p2p) for O2, F2, and Ne2. See text pages 680-681. Note that s–p mixing does not affect bond order or magnetism in the common diatomics (N2, O2, and F2). Hence it is not of much practical importance.

M.O. Diagram for N2 s*(2p)

p*

Electron energy (kJ mol-1)

p* -1,155

s(2p)

-1,240

-1,240

p

p -1,479

s*(2s) Valence

Valence -2,965

Core

s(2s)

Core

-37,875

-37,871

1s(N) + 1s(N)

1s(N) –1s(N)

When does s-p mixing occur? B, C, and N all have  1/2 filled 2p orbitals O, F, and Xe all have > 1/2 filled 2p orbitals • If 2 electrons are forced to be in the same orbital, their energies go up. • Electrons repel each other because they are negatively charged. • Having > 1/2 filled 2p orbitals raises the energies of these orbitals due to e- - e- repulsion s-p mixing only occurs when the s and p atomic orbitals are close in energy ( 1/2 filled 2p orbitals)

s-p mixing

No s-p mixing

Relating the M.O. Diagrams to Physical Properties (Fig 14.41)

Sample Problem: Using MO Theory to Explain Bond Properties Problem: Consider the following data for these homonuclear diatomic species: N N+ O O 2

2

2

2

+

Bond energy (kJ/mol) 945 841 498 623 Bond length (pm) 110 112 121 112 No. of valence electrons 10 9 12 11 Removing an electron from N2 decreases the bond energy of the resulting ion, whereas removing an electron from O2 increases the bond energy of the resulting ion. Explain these facts using MO diagrams. Plan: We first draw the MO energy levels for the four species, recalling that they differ for N2 and O2. Then we determine the bond orders and compare them with the data: bond order is related directly to bond energy and inversely to bond length.

Sample Problem - Continued Solution: The MO energy levels are: N2 N2+

Bond Orders: (8-2)/2 = 3

O2

O2 +

sp*

sp*

p2p*

p2p*

s2p

p2p

p2p

s2p

s2s*

s2s*

s2s

s2s

(7-2)/2 = 2.5

(8-4)/2 = 2

(8-3)/2 = 2.5

What have we learned so far? 1. Molecular orbitals (MO) explain the properties of valence electrons in molecules (Example: O2) 2. s and p atomic orbitals can be mixed to form s, s*, p, and p* molecular orbitals 3. Electrons in p or p* molecular orbitals can have the same energies: Degenerate orbitals 4. The ordering of s2p and p2p molecular orbitals depends

on the electron occupancy: s-p mixing

Bonding in Diatomic Molecules Review from Chapter 13: Covalent

Ionic Ionic

Covalent

Homonuclear: H2

Heteronuclear: HF

Electronegativity

Nonpolar covalent bond (450 kJ/mol bond)

Polar covalent bond (565 kJ/mol bond)

Figure 14.26

Figure 14.45

Electrons are not equally shared in heteronuclear bonds HF Electronegativity

Figure 14.45

Because F (EN = 4.0) is more electronegative than H (EN = 2.2), the electrons move closer to F. (Table 13.2 - electronegativities) This gives rise to a polar bond:

H

F

M.O.s of a Polar Covalent Bond: HF s Antibonding (s*) Mostly H(1s)

Zumdahl simplifies model and only considers electrons involved in bond.

H

F

H

F

s Bonding Mostly F(2p)

MOs OF XY MOLECULES Equal or unequal e sharing between 2 atoms is reflected in the composition of the MOs: When 2 atoms X and Y have the same electronegativity (purely covalent bond), their overlapping AOs have the same energy, and the bonding and anti-bonding MOs are each half X and half Y AO. All electrons spend equal time near X and Y. Examples: N2, O2, F2. If EN(Y) > EN(X) (polar covalent X+Y), the Y AO has lower energy than the X AO. The bonding MO is more like the Y AO and the anti-bonding MO more like the X AO. Bonding e spend more time near Y than X; vice versa for anti-bonding e. Example: CO.

MOs OF XY____ MOLECULES s* ___ ___ p* ↑ Energy

___ ___ ___ 2p ____ s ___ ___ p

___ ___ ___ 2p

____ s* ___ 2s

___ 2s ____ s

C Atom (4e–)

Electronegativity

___ ___ ___2p

___ 2s

Cδ+Oδ– (10e–) O Atom (6e–)

 CO Bond Order = 3.0 (same as N2).  CO Bond Energy = 1,076 kJ/mol (N2 = 945 kJ/mol).  Isoelectronic to CO and N2: CN–, NO+.  NO has 1e– in p*  bond order = 2.5; this e– is more on N than O; NO  NO+ easy…

Bonding in NO • Two possible Lewis dot structures for NO • The simplest structure minimizes formal charges and places the lone (unpaired) electron on the nitrogen. • The Lewis structure predicts a bond order of 2, but experimental evidence suggests a bond order between 2 and 3. • How does MO theory help us understand bonding in NO?

. .. N=O .. ..

.. . N=O .. .. -1

+1

When the electronegativities of the 2 atoms are more similar, the bonding becomes less polar.

2p

2p

2s

NO

Electronegativity

2s

N

. .. N=O .. .. EN(N) = 3.0 EN(O) = 3.4

O

Bond order = 2.5, unpaired electron is in a N-like orbital

NO is easily oxidized to form NO+. Why? What changes can we predict in the bonding and magnetism of the molecule?

NO

NO+

oxidation

Bond Order = (8-3)/2 = 2.5 Paramagnetic

Bond Order = (8-2)/2 = 3 Diamagnetic

M.O. diagram for NO -597

p2p *

p2p * (empty)

s2p -1307 -1444

p2p

p2p s2s* -1835

s2s

-3320

-1374

Key Points of MO Theory – Heteronuclear Molecules • The more electronegative atom has orbitals lower in energy than the more positive atom. • Electrons in bonding orbitals are closer to the more electronegative atom, anti-bonding electrons are closer to the more positive atom. • For most diatomic molecules, s-p mixing changes the orbital energy levels, but since these orbitals are almost always fully occupied, their order is often less important to us.

MO Theory Expectations • You should be able to: – predict which atomic orbitals are higher or lower in energy (based on electronegativity differences). – correctly label and fill a molecular orbital diagram. – correctly calculate bond order. – predict molecular magnetic properties based on orbital occupation. – understand how molecular properties change upon ionization (oxidation or reduction) of molecules.

Combining the Localized Electron and Molecular Orbital Models (into a convenient working model) (Zumdahl Section 14.5) Figure 14.47

Only the p bonding changes between these resonance structures - The M.O. model describes this p bonding more effectively.

Atomic Orbitals

Molecular Orbitals

Figure 14.51

Another example: Benzene

s bonding:

p bonding:

p atomic orbitals

p molecular orbital