Chemistry and the material world123.102

Lecture 6Matthias Lein

Valence Bond Theory

A brief introduction into Valence Bond theory.

How hybridization arises out of the need to describe geometry

Different modes of hybridization.

How multiple bonds can be described through sp2 and sp hybrids.

Walter Heitler1904 – 1981, Germany

Fritz London,1900 – 1954, Germany

Linus Pauling1901 – 1994, United States

1927: First quantum mechanical description of bonding H

2

“The nature of the chemical bond”1939

Methane, CH4

Is experimentally known to be tetrahedral.

That means that all HCH angles are 109.5˚

There is no intuitive way to construct a tetrahedral

molecule in MO theory

The s orbital of carbon is spherically symmetric

The three p orbitals are at 90˚ to each other.

The valence configuration of C (2s22p2) suggests that there are

only two electrons available for bonding.

The solution is to create suitable hybrid orbitals that show the

desired behaviour.

The tetrahedral case

In order to obtain a different set of orbitals we mix ¼ s and ¾ p for each of the four sp3 hybrid orbitals.

All four sp3 hybrid orbitals have the same energy level.

The energy of the sp3

hybrid orbitals has to be between the original s and p orbitals.

More precisely: The energy will be

¼ Es + ¾ E

p

The four resulting sp3 hybrid orbitals will arrange themselves into a tetrahedron out of symmetry reasons.

Electron repulsion is often mentioned in this context, but has nothing to with the arrangement of the hybrid orbitals in VB theory.

Note that the similarity between VB and VSEPR is useful but coincidental.

Note: The phases of the orbitals are not shown. Also not shown are the smaller lobes of the sp3 hybrid orbitals.

The Formation of CH4

Note: The colors have been used to indicate orbitals from different atoms. The phases of the orbitals are not shown. Also not shown are the smaller lobes of the sp3 hybrid orbitals.

Remember:

We could, in principle describe CH4 in terms of MO theory.

But because we new that CH4 is tetrahedral we chose a different way

to construct our molecular orbitals.

It is important to bear in mind that:

We chose to describe CH4 in terms of sp3 hybridization.

Therefore sp3 hybridization is a consequence of CH4 being

tetrahedral and not the reason for CH4 being tetrahedral.

Step 1: The Lewis structure...

...tells us that oxygen is surrounded by four sets of electron pairs. VSEPR theory then tells us that H

3O+ must be

tetrahedral (trigonal pyramidal).

Step 2: The hybridization...

...shows that oxygen can form two bonds and has two lone pairs.

Step 3: The molecule...

...shows three identical hydrogen atoms. Formally two H atoms and one H+ cation which forms an electron pair bond with two electrons coming from oxygen.

Example: The hydronium ion, H3O+

The trigonal planar case

In order to obtain a different set of orbitals we mix s and ⅓ ⅔ p for each of the three sp2 hybrid orbitals.

All three sp2 hybrid orbitals have the same energy and the remaining p orbital retains its original energy level.

Note: The phases of the sp2 hybrid orbitals are not shown. Also not shown are the smaller lobes of the sp2 hybrid orbitals. In red: A possible bonding s orbital.

The three resulting sp2 hybrid orbitals are arranged in a trigonal planar fashion. The un-hybridized p orbital is perpendicular to the plane of the sp2

hybrid orbitals.

One example for a molecule with an sp2 hybridized atom is BF3.

The unoccupied p orbital has consequences for the reactivity of BF3. The

boron atom in BF3 is two electrons short of an octet and therefore reacts

readily with molecules that have an additional electron such as NH3.

Once the electronic octet on B is complete the atom has four pairs of electron pairs and hence re-hybridizes to reflect the new tetrahedral coordination.

The linear case

In order to obtain a different set of orbitals we mix ½ s and ½ p for each of the two sp hybrid orbitals.

Both sp hybrid orbitals have the same energy and the remaining two p orbital retains their original (degenerate) energy level.

Note: The phases of the sp hybrid orbitals are not shown. Also not shown are the smaller lobes of the sp hybrid orbitals. In red: A possible bonding s orbital.

One example for a molecule with an sp hybridized atom is BeH

2.

In order to stabilize itself beryllium hydride forms long chains with 3 center 2 electron bonds.

Once the electronic octet on Be is complete, the atom has four pairs of electron pairs and hence re-hybridizes to reflect the new tetrahedral coordination.

...H2-BeH

2-BeH

2-BeH

2-BeH

2-...

Multiple bonds

Lewis structures and VSEPR predict that compounds with multiple bonds have distinctly different geometries.

For example:carbon atoms with one double bond are planar.carbon atoms with one triple bond are linear.

This can be rationalized in termsof VB as well.

The key is the separation of the σand the bonds.π

Note that the bond is essentially the same as in MO theory. It is πconstructed from the overlap of two p orbitals.

Today we coveredA brief introduction into Valence Bond theory

Qualitative MO theory is not intuitive.Qualitative VB theory is not hard.Quantitative MO theory is complicated, but manageable.Quantitative VB theory is very complicated numerically.

How hybridization arises out of the need to describe geometry(and NOT how geometry is determined by hybridization)

How to get four sp3 hybrid out of one s and three p orbitals.How to get three sp2 hybrid out of one s and two p orbitals.How to get two sp hybrid out of one s and one p orbital.That orbitals not participating in the hybridization retain their original shape and energy

How multiple bonds can be described through sp2 and sp hybrids.

How the bond is made of un-hybridized p orbitals.π