© Prof. Zvi C. Koren1 19.07.10

Bonding OrbitalsBonding Orbitals

Models of Chemical Bonding

Valence Bond (VB) Theory Molecular Orbital (MO) Theory

Simplest Complex

© Prof. Zvi C. Koren2 19.07.10

Constructive Interference

Overlap Sum

התאבכות בונה

Consider two simple waves:

A

“in-phase”

Introduction to Valence Bond (VB) Theory

A

2A

© Prof. Zvi C. Koren3 19.07.10

Valence Bond (VB) Theory

• As two atoms approach each other, an orbital (wave) that describes

the motions of the valence e in an atom constructively interacts with an

orbital (wave) of an e on another atom.

• This constructive interference between two orbitals is called an

“overlap” of orbitals.

• The overlap region is between the two nuclei and leads to an increase

in “amplitude” of the orbital (wave) in that internuclear regon.

• This results in the “growth” of the orbital in the overlap region.

• This means that there is now an increase in the probability of finding

the e between the two nuclei

• This effectively means that there is an increase of electron density

(negative charge) between the two nuclei.

• Hence, this reduces the internuclear repulsion and stabilizes the

system.

• This stabilization is considered a chemical bond between two atoms.

• Conclusion: Overlap of valence orbitals Valence Bond (VB)

© Prof. Zvi C. Koren4 19.07.10

s-s bond

Notes about the Sigma Bond (overlapping region is what constitutes The Bond):• Constructive Interference increases e-density in the region between the 2 nuclei,

leading to stabilization. • The orbital overlap region is localized between the 2 nuclei.• bond (orbital overlap) is on the internuclear axis.

Sigma () Bonds

+

s s

H2H H

+

px px

F F

px-px bond(head-on approach)

:F:F:::

H:H

::

+

s

H

px

FH:F::

:

F2

x

HF

s-px bond

© Prof. Zvi C. Koren5 19.07.10

+

py

O

Pi () Bonds

py-py bond

x

y

z

O::O:::

:

O2

Note about the Pi Bond:

• bond (orbital overlap) is above and below the internuclear axis, but it’s still

localized between the 2 nuclei.

• One bond has two overlapping regions.

• A second bond is sometimes possible, pz-pz. This would then yield a total of 3

bonds (triple bond): 1 + 2.

py

O

(side-by-sideapproach)

© Prof. Zvi C. Koren6 19.07.10

Consider the Case of C + 4H CH4

Some of the bond angles would be 90o. Why?

Introduction to Hybridization Theory

Hybridization explains the molecular shapes of polyatomic molecules

Hybridization Theory:

• Pure Atomic Orbitals (AO’s), such as s, p, d, ..., belonging to a central

atom, “mix” to produce new Hybrid Orbitals (HO’s) on that atom.

• Each HO is composed of a Big Head(s), and a small tail(s), where the

“head” is oriented to produce the correct molecular geometry.

• Each single e-pair needs to be accomodated, at least partly, by an HO.

• The # of HO’s about a central atom = # of single e-pairs about it.

Hence, :NH3 and CH4 will each have 4 HO’s about the central atom.

• The # of HO’s = # of AO’s used in the “mixing” or hybridization.

• The orbitals used for hybridization are the s and p orbitals, and then the

d orbitals, etc.

the hybridization types, in order of increasing complexity, are:

sp (2 HO’s), sp2 (3), sp3 (4), sp3d or dsp3 (5), sp3d2 or d2sp3 (6).

(see the Table – next slide)

© Prof. Zvi C. Koren7 19.07.10

TOTAL # of Single E-Pairs

(bonding + lone)about the

Central Atom

ELECTRONIC

GEOMETRY

of the Single E-Pairs

about the Central Atom

# ofAtoms

Bondedto the

Central Atom

MOLECULAR

GEOMETRY

of the Atoms about

the Central Atom

2 Linear (180o) Linear2

3

TrigonalPlanar(120o)

3 Trigonal Planar

2 Bent (Angular)

4

Tetrahedral

(109.5o)

cos(tet)=–⅓

Tetrahedral4

3

2

Trigonal Pyramidal

Bent (Angular)

5

Trigonal

Bipyramidal

(120o, 90o)4

5 Trigonal Bipyramidal(lone e-pairs on equator)Bent Seesaw

3

2

Bent “T”

Linear

6Octahedral

(90o)

6 Octahedral

5

4

Bent-Square Pyramidal

Square Planar

Hybridization Types and Electronic & Molecular Geometries

axial

sp2

sp3

sp3d

or*

dsp3

sp3d2

or*

d2sp3

sp

Hybrid-ization

about theCentralAtom

equa-torial

* sp3d, sp3d2: all from same shell; dsp3, d2sp3: d from shell below.

© Prof. Zvi C. Koren8 19.07.10

Examples of Hybridization Types

NH3

Draw Lewis Electron-Dot Diagram (ן"שמ. ם.ח. ש.א): N

H

:HH

Total # of Single e-Pairs (bonding + lone) about the Central Atom = 4

Total # of Hybrid Orbitals (HO’s) formed about the Central Atom = 4

Total # of Pure Atomic Orbitals (AO’s) needed for Hybridization = 4

Pure Atomic Orbitals (AO’s) mixed in the Hybridization process: s + px, py, pz

Name of each HO produced =

Name of the type of hybridization = sp3

Show the Hybridization process:

Free N (Group 5A):

2s22p3

s2

p3

sp3 sp3 sp3 sp3

Bonding N:

(sp3)2 (sp3)1 (sp3)1 (sp3)1

(continued)

Hund’s Rule: 5 e’s in 4 degenerate orbitals

sp3 hybridization

© Prof. Zvi C. Koren9 19.07.10

(continued)

Draw the Electronic Geometry

about the Central Atom:

N

NH3

(tetrahedral)

N

Draw the HO’s

about the Central Atom

And place the e’s in the HO’s:

sp3

Show each Bond resulting from the

Orbital Overlap of the relevant orbitals:

N

sp3

sp3sp3

sp3

Question: What would CH4 look like?

sp3-ssp3-s

© Prof. Zvi C. Koren10 19.07.10

4. Draw the HO’s about central atom and the AO’s about the

terminal atoms (draw in class)

Examples with Hybrid Atomic Orbitals

Consider CH4

1. Draw Lewis Structure: H–C–H

H

HThis structure does not

indicate the actual

geometry, at this point.

2. Determine Hybridization Type AND Electronic Geometry

about Central Atom:

# of e-pairs about central C = 4:

4 HO’s 4 (sp3) HO’s sp3-hybridization

Electronic Geometry = Tetrahedral

(“Step-by-Step”)

3. Determine the Molecular Geometry about Central Atom:

# of e-pairs about central C = 4; # of atoms about central C = 4

Molecular Geometry = Tetrahedral (Bond Angles = ____)

© Prof. Zvi C. Koren11 19.07.10

4. Draw the HO’s about each central atom and the AO’s about the

terminal atoms (draw in class)

Examples with Hybrid Atomic Orbitals

Consider C2H4 (ethylene, ethene)

1. Draw Lewis Structure: H–C=C–H

HThis structure does not

indicate the actual

geometry, at this point.

2. Determine Hybridization Type AND Electronic Geometry about

Central Atom:

# of SINGLE e-pairs about EACH central C = 3:

3 HO’s 3 (sp2) HO’s sp2-hybridization (one p unused)

Electronic Geometry = Trigonal Planar

(“Step-by-Step”)

3. Determine the Molecular Geometry about EACH Central Atom:

# of e-pairs about each C = 3; # of atoms about each C = 3

Molecular Geometry = Trigonal Planar (Bond Angles = ____)

H

© Prof. Zvi C. Koren12 19.07.10

Do the following molecules:

HCCH acetylene, ethyne

PF5 phosphorus pentachloride

SF6 sulfur hexafluoride

© Prof. Zvi C. Koren13 19.07.10

So, what’s in the Hybrid Orbitals?

• Lone (non-bonding) e’s – one or two.

• Future Sharing (Bonding) e’s,

which will be used in the formation of bonds –

one e (for a regular covalent bond)

or two e’s (for a coordinate covalent bond).

How can we automatically determine the number of HO’s about a

central nonmetallic atom in a covalent compound?

# of HO’s = # of single e-pairs about the central atom in the

Lewis structure, i.e., “ + lone” pairs.

So What’s in the Hybrid Orbitals?(Summary)

© Prof. Zvi C. Koren14 19.07.10

Recall:

Pure Atomic Orbitals can overlap to produce σ bonds:

s overlapping s σs-s Example: H–H

s overlapping p σs-p Example: H–F

p overlapping p (head-on) σp-p Example: F–F

Now,

Hybrid AO’s can also form σ-bonds through overlapping::

• a pure AO and a hybrid AO

• a hybrid AO with another hybrid AO

Examples follow …

© Prof. Zvi C. Koren15 19.07.10

bond sp2-s

Sigma Bonds in Ethylene, C2H4

sp2-sp2 bond

C C+ C–C

px px πpx-px

π-Bonding

Note:

One π bond with 2

overlapping regions

© Prof. Zvi C. Koren16 19.07.10

© Prof. Zvi C. Koren17 19.07.10

H–CC–H acetylene, ethyne

© Prof. Zvi C. Koren18 19.07.10

Explain why the 2 methylene groups (-CH2) are in perpendicular planes

© Prof. Zvi C. Koren19 19.07.10

© Prof. Zvi C. Koren20 19.07.10

Summary of Valence Bond (VB) Theory

A Chemical Bond ( or or ) consists of:

• an overlap of two (pure or hybrid) atomic orbitals, as in

the constructive interference (התאבכות בונה) of two waves

• this overlap increases the electron density between the two

atoms (nuclei), which

• decreases the internuclear repulsion, and increases the

attraction between each nuclei and the resulting new

electron “cloud”

• Note: the overlap is localized between the atoms

What is a Chemical Bond?

What is the nature of the “Chemical Glue” that binds two atoms

together?

© Prof. Zvi C. Koren21 19.07.10

Bonding OrbitalsBonding Orbitals

Models of Chemical Bonding

Valence Bond (VB) Theory Molecular Orbital (MO) Theory

Simplest Complex

Part 2

© Prof. Zvi C. Koren22 19.07.10

Destructive InterferenceConstructive Interference

בונההתאבכות הורסתהתאבכות

Consider two EXTREME simple-wave profiles

Introduction to Molecular Orbital Theory

“in-phase”“out-of-phase”

2A

© Prof. Zvi C. Koren23 19.07.10

bonding

antibonding

nodal plane

Atomic electronic configuration for H: 1s1

Molecular electronic configuration for H2:2s1

(Do: H2–, H2

+, He2, He2+)

Bond Order:

Net # of bonding pairs

Recall:

Diamagnetism

vs.

Paramagnetisms1σ

*1

σs

© Prof. Zvi C. Koren24 19.07.10

*

pσ

pσ

pxπ

pxpx

pz

σ and π Bonding and Antibonding MO’s from AO’s

pz

py π:Also

*py π:Also*

pxπ

© Prof. Zvi C. Koren25 19.07.10

MO electronic configuration of B2:

Why is π2plower in energy

than σ2p?

Molecular Orbital Energy Level Diagram

1s – – 1s*s1

σ

s1σ

2s – – 2s*

s2σ

s2σ

2p – – – – – – 2p

p2π

*p2

π

p2σ

*p2

σ–

–

–

–

–

– –

–

– –

AO’s AO’sMO’s

En

ergy

Do also:

C2, N2, O2,

F2, Ne2;

NO, OF;

O2–, O2

+

2

2p

2*s2

2

2sπσ σ

© Prof. Zvi C. Koren26 19.07.10

According to VB Theory

(Lewis Electron-Dot Diagram):

According to MO Theory:

O=O

The Truth!

Is O2 Diamagnetic or Paramagnetic?

O=O. .

© Prof. Zvi C. Koren27 19.07.10

Molecular Orbitals and Vision

© Prof. Zvi C. Koren28 19.07.10

Summary of Molecular Orbital (MO) Theory

What is a Chemical Bond?

What is the nature of the Chemical Glue that binds two atoms

together?

A Chemical Bond (, * or , *) consists of:

• an overlap of two OR MORE (pure or hybrid) atomic orbitals;

• TWO types of overlaps (wave interactions) are considered:

constructive interference bonding <-- (התאבכות בונה) MO,

destructive interference antibonding <-- (התאבכות הורסת) MO

• the constructive overlap increases the electron density between the two

atoms (nuclei), which

• decreases the internuclear repulsion, and increases the attraction

between each nuclei and the resulting new electron “cloud”

• Note: Each overlap (MO) is delocalized, and is spread over two OR

MORE atoms

Summary of Molecular Orbital (MO) Theory

© Prof. Zvi C. Koren29 19.07.10

A Comparison of Chemical Bonding Theories

Lewis E-Dot

Structures

Valence-Bond

(VB) Theory

Molecular-Orbital

(MO) Theory

Is the bond localized

between the 2 nuclei?

Yes: e-particles are positioned in-between the 2 nuclei.

Yes: overlap is

fixed to a region

between nuclei.

NO!!!. It’s delocalized.2 AO’s fuse together to form the MO that is spread over the entiremolecule.

Type and Name

of Bonds

single, double,

and triple bonds

σ and π bonds σ and π bonding

molecular orbitals

(MO’s), and σ* and

π* antibonding MO’s

Type of

interactions

between e’s

pairing-up of lone

(unpaired) e’s:

Koren’s Principle

of Lonely e-Hearts

Club

Constructive

Interference

between atomic

orbitals (AO’s)

Constructive

AND

Destructive

Interferences

between AO’s

Nature of the

Chemical Bond(-) e-particles

between (+) nuclei

overlap between e-waves (orbitals)

increases (-) e-density between (+) nuclei