The Chemical Bond I Bonds as Orbital Overlap Molecular Orbital Diagrams Hybridization Additional...

The Chemical Bond I

Bonds as Orbital OverlapMolecular Orbital DiagramsHybridizationAdditional Bonding Schemes

CHEM 3722 Chapter 12 2

Atomic Orbitals and Orientation We’ve solved hydrogen-like atoms and found the orbital

shapes Let’s get the orientation of each down

Our orbitals had no specific orientation, except with respect to each other

We’ll use some alternate pictures that have a specific orientation For example:

2 210

2 2,1,1 2,1, 1

2 2,1,1 2,1, 1

2

12

21

22

z

x

y

p z

p x

p y

p

p

pi

y

zz

yx

Rotate by 45°

X Y Z( )

X Y Z( )

2,1,1xp


Orbitals Pictures We’ll picture the orbitals in this way

In terms of energy, we write these as an energy level diagram

ypzp

2zd

2 2x yd

yzd

s

Two different phases

s

E

2zd 2 2x y

d yzdxyd

xzd

s

yp zpxp


The Energetics of Bonding I Can imagine the bonding process in terms of bringing two

hydrogen atoms together from far away As they approach, the E lowers as the atomic orbitals begin to

interact The interaction is composed of (1) nuclear-nuclear repulsion,

(2) electron-electron repulsion, and (3) electron-nuclear attraction

The most stable distance (minimum energy on this potential energy curve) is where the attractions outweigh the repulsions

Increased Increased electron density electron density

between the between the nuclei stabilizes nuclei stabilizes the molecule!the molecule!


The Energetics of Bonding II But, need to know why an atom would bond?

All bonds result in the lowering of energy of the electrons in the system

Not all electrons are lowered in energy, but the net result is a more stable arrangement of the electrons

Consider the H2 molecule Each has one occupied orbital: 1s Let’s ‘watch’ the energy change

But what about He2?

Atomic orbitalRegion of energy

where two electrons can reside

Result of bonding

Called molecular orbitals. Formed from the two atomic

orbitals interacting. Note that the net effect is two lower

energy e-’s.

There is no net E-loss There is no net E-loss in this alteration of in this alteration of electron energies. electron energies. That is, the energy That is, the energy

released in lowering 2 released in lowering 2 ee-- is used to promote is used to promote

the other 2. Thus, this the other 2. Thus, this bond doesn’t happen: bond doesn’t happen:

nonbonding! nonbonding!


Molecular Orbitals I To picture the MO’s, consider them as the “overlap” of the

AO’s. Phase of overlap matters

Since made from s-orbitals, we’ll denote this MO in similar terms But, we’ll use Greek letters for bonds

Call the overlap a molecular orbital If overlap is out of phase, then we’ll denote it as an antibonding

orbital (*) Other orbital can overlap similarly

Look at p and s

Overlap of s-Overlap of s-orbitalsorbitals

Internuclear axisInternuclear axis

If overlap is along this If overlap is along this axis, then the MO formed axis, then the MO formed isis ..


Molecular Orbitals IIIn terms of

probability, we can see that

bondingbonding regions show an

enhanced electron density between the two

nuclei. The probability is high that the electron-

nucleus attraction will keep nuclei together.

AntibondingAntibonding regions show a

reduced electron density between the nuclei, and

thus the electron-nucleus

attraction is away from the stable

bond length.


Molecular Orbitals III Any set of orbitals that overlap along the internuclear axis

are considered to be bonds. And the antibonding MO is a * bond

Here are a few other examples

Can also make a -bond with d-orbitals

x

y2 2 2 2x y x y

d d

=

py py


Molecular Orbitals IV Any set of orbitals that

overlap perpendicular to the internuclear axis are said to -bond The antibonding orbital is

* Any set of orbitals that

overlap at any other angle to the internuclear axis are said to -bond The antibonding orbital is

* Best example is two dyz

orbitals


Putting It All Together Carbon Monoxide

First draw Lewis Dot Structure This shows 3 bonding pairs (between nuclei) and 2 nonbonding pairs Expect a , a and another bond

Now consider orientation and orbitals involved (we’ll draw 2 of 3 dimensions) This should match Lewis Structure

We see py-py overlap forming bond

We see p bonds in px-px and pz-pz overlap

C O

C O

-bondpz

px

-bond

In the other *

In the other


More Diatomic MO-Diagrams Homonuclear diatomics show a slight change as Z increases

mo’s appear before mo’s until Z = 7 (Nitrogen)


Polyatomic Molecules MO’s are easy to create for diatomics

Things get tougher if we add atoms Take AlCl3 as an example

Doesn’t obey octet rule Lewis dot structure shows three single bonds

Thus, three bonds Structure looks like this:

How do p-orbitals arrange themselves this way and stay orthogonal? Don’t appear to be perpendicular

Make a basis set of the H-like atomic orbitals & make new orbitals Requires us to make linear combinations of atomic orbitals to

make NEW atomic orbitals Call this hybridization

But why? Can we justify this?

AlClCl

Cl


Hybridization Cl has it’s p-orbitals ready to bond to the Al, but Al has two

types of valence orbitals available: s and p (px, py, pz) This means that the lowest energy orbital available for overlap

is the s. But, only one Cl can bond with this orbital To make three equal energy orbitals available to the Cl’s, Al

“hybridizes”

So we use the H-like orbitals to generate three different but energetically equivalent atomic orbitals In math terms, the linear combinations

are…

2 1 233

1 1 14 23

1 1 14 23

z

y z

y z

sp s p

s p p

s p p

Energ

y

s

p pp

sp2 sp2 sp2

p


sp2 hybrids and AlCl3 We can picture the hybrid orbitals as spreading out

perpendicular to the remaining p-orbital They are in the xy-plane Three lobes must get as far apart as possible This is a trigonal planar arrangement of hybrid orbitals

Can see how the orbitals ‘do’ this pictorially, too

sp2 hybrid orbitalof Aluminum

p-orbital of Chlorine


sp hybrids If need two identical bonding orbitals, use an s and a p

orbital in an sp hybrid For example, LiH2

1( )

2

1( )

2

z

z

sp s p

s p

Pictorially, the linear combination goes like


Multiple Bonds In sp and sp2 hybridization, there remains a p-orbital (or

two) Can this orbital involve itself in some sort of bonding? Sure, but not along the internuclear axis, so must be -bonding!

This is the basis for double and triple bonds For example, consider ethane


sp3 hybrids If need four identical bonding orbitals, use an s and all three p

orbitals in an sp3 hybrid For example, H2O

OHH

3 1 ( )2

1 ( )2

1 ( )2

1 ( )2

x y z

x y z

x y z

x y z

sp s p p p

s p p p

s p p p

s p p p

H

H

O


Other Bonding Types So far, only showed covalent bonding Other bonds

Metallic Ionic Coordinate Covalent Three center, two electron bonds

Ionic Bonds Purely Coulombic interactions Electrons are not “shared” they are transferred (in a sense) NaCl is perfect example

NaCl = Na+--Cl- or Na---Cl+

We know first ionic species is best, but both are probably present in any sample NaCl has character of both, but has mainly the character of Na+ -- Cl-


Coordinate Covalent Often the e’s shared in a covalent type bond don’t come

from both atoms, but instead from one atom, molecule, or ion For Example: W(CO)6

Usually occurs with a transition metal as central atom (d-orbitals are the key)

Species that donates both electrons is called a ligand CO and O2 are both ligands for Hemoglobin, and this is why CO

can suffocate you when inhaled in great amounts Not only is it a substitute ligand, it also bonds better because the O

can pull electron density from the C. This makes the Carbon antibonding MO a better electron donar AND it makes the ‘backbonding’ more stabilizing Backbonding is the donation of electron density of the metal back to the

ligand In regular O2, the nonpolar nature of the molecule limits these

effects


3 Center, 2 Electron Bonds Most bonds are between two atoms

They are 2 center, 2 electron bonds (2c-2e bonds) A center is a nucleus

3c-2e bonds occur when two electrons hold together 3 nuclei

Most common examples: Al2H6 and B2H6

The second is called diborane BH3 is hard to make because diborane is so stable in

comparison Orbital overlap looks like BB

H

H

HHH H

sp3 hybrid orbital of boron 2

sp3 hybrid orbital of boron 1

s-orbital of H

21

The Chemical Bond I Bonds as Orbital Overlap Molecular Orbital Diagrams Hybridization Additional...

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