Chem 1045 - General Chemistry 1

Fall 1996

Dr. Michael Blaber

Text: Chemistry the Central Science, Brown, LeMay and Bursten, 6^th Edition Lecture 28 November 6/8 1996

Molecular Geometry and Bonding Theories

Hybrid Orbitals

Multiple Bonds

9.4 Hybrid Orbitals

For polyatomic molecules we would like to be able to explain:

• The number of bonds formed
• Their geometries

sp Hybrid Orbitals

Consider the Lewis structure of gaseous molecules of BeF₂:

• The VSEPR model predicts this structure will be linear
• What would valence bond theory predict about the structure?

The fluorine atom electron configuration:

• 1s²2s²2p⁵

• There is an unpaired electron in a 2p orbital
• This unpaired 2p electron can be paired with an unpaired electron in the Be atom to form a covalent bond

The Be atom electron configuration:

• 1s²2s²

• In the ground state, there are no unpaired electrons (the Be atom is incapable of forming a covalent bond with a fluorine atom
• However, the Be atom could obtain an unpaired electron by promoting an electron from the 2s orbital to the 2p orbital:

This would actually result in two unpaired electrons, one in a 2s orbital and another in a 2p orbital

• The Be atom can now form two covalent bonds with fluorine atoms
• We would not expect these bonds to be identical (one is with a 2s electron orbital, the other is with a 2p electron orbital)

However, the structure of BeF₂ is linear and the bond lengths are identical

• We can combine wavefunctions for the 2s and 2p electrons to produce a "hybrid" orbital for both electrons
• This hybrid orbital is an "sp" hybrid orbital

• The orbital diagram for this hybridization would be represented as:

Note:

• The Be 2sp orbitals are identical and oriented 180° from one another (i.e. bond lengths will be identical and the molecule linear)
• The promotion of a Be 2s electron to a 2p orbital to allow sp hybrid orbital formation requires energy.
• • The elongated sp hybrid orbitals have one large lobe which can overlap (bond) with another atom more effectively
  • This produces a stronger bond (higher bond energy) which offsets the energy required to promote the 2s electron

sp² and sp³ Hybrid Orbitals

Whenever orbitals are mixed (hybridized):

• The number of hybrid orbitals produced is equal to the sum of the orbitals being hybridized
• Each hybrid orbital is identical except that they are oriented in different directions

BF₃

Boron electron configuration:

• The three sp² hybrid orbitals have a trigonal planar arrangement to minimize electron repulsion

• An s orbital can also mix with all 3 p orbitals in the same subshell

CH₄

• Thus, using valence bond theory, we would describe the bonds in methane as follows: each of the carbon sp³ hybrid orbitals can overlap with the 1s orbitals of a hydrogen atom to form a bonding pair of electrons

H₂O

Oxygen

Hybridization Involving d Orbitals

Atoms in the third period and higher can utilize d orbitals to form hybrid orbitals

PF₅

Similarly hybridizing one s, three p and two d orbitals yields six identical hybrid sp³d² orbitals. These would be oriented in an octahedral geometry.

• Hybrid orbitals allows us to use valence bond theory to describe covalent bonds (sharing of electrons in overlapping orbitals of two atoms)
• When we know the molecular geometry, we can use the concept of hybridization to describe the electronic orbitals used by the central atom in bonding

Steps in predicting the hybrid orbitals used by an atom in bonding:

1. Draw the Lewis structure

2. Determine the electron pair geometry using the VSEPR model

3. Specify the hybrid orbitals needed to accommodate the electron pairs in the geometric arrangement

NH₃

1. Lewis structure

2. VSEPR indicates tetrahedral geometry with one non-bonding pair of electrons (structure itself will be trigonal pyramidal)

3. Tetrahedral arrangement indicates four equivalent electron orbitals 9.5 Multiple Bonds

The "internuclear axis" is the imaginary axis which passes through the two nuclei in a bond:

The covalent bonds we have been considering so far exhibit bonding orbitals which are symmetrical about the internuclear axis Bonds in which the electron density is symmetrical about the internuclear axis are termed "sigma" or "s" bonds

In multiple bonds, the bonding orbitals arise from a different type arrangement:

• Multiple bonds involve the overlap between two p orbitals
• These p orbitals are oriented perpendicular to the internuclear (bond) axis

This type of overlap of two p orbitals is called a "pi" or "" bond

In p bonds:

• The overlapping regions of the bonding orbitals lie above and below the internuclear axis (there is no probability of finding the electron in that region)
• The size of the overlap is smaller than a s bond, and thus the bond strength is typically less than that of a s bond

Generally speaking:

• A single bond is composed of a s bond
• A double bond is composed of one s bond and one p bond
• A triple bond is composed of one s bond and two p bonds

C₂H₄ (ethylene; see structure above)

• The arrangement of bonds suggests that the geometry of the bonds around each carbon is trigonal planar
• Trigonal planar suggests sp² hybrid orbitals are being used (these would be s bonds)

What about the electron configuration?

Carbon: 1s² 2s² 2p²

• Thus, we have an extra unpaired electron in a p orbital available for bonding
• This extra p electron orbital is oriented perpendicular to the plane of the three sp² orbitals (to minimize repulsion):

• The unpaired electrons in the p orbitals can overlap one another above and below the internuclear axis to form a covalent bond

• This interaction above and below the internuclear axis represents the single p bond between the two p orbitals

Experimentally, we know that the 6 atoms of ethylene lie in the same plane. If there was a single s bond between the two carbons, there would be nothing stopping the atoms from rotating around the C-C bond. But, the atoms are held rigid in a planar orientation. This orientation allows the overlap of the two p orbitals, with formation of a p bond. In addition to this rigidity, the C-C bond length is shorter than that expected for a single bond. Thus, extra electrons (from the p bond) must be situated between the two C-C nuclei.

C₂H₂ (acetylene)

• The linear bond arrangement suggests that the carbon atoms are utilizing sp hybrid orbitals for bonding

• This leaves two unpaired electrons in p orbitals
• To minimize electron replusion, these p orbitals are at right angles to each other, and to the internuclear axis:

• These p orbitals can overlap two form two p bonds in addition to the single s bond (forming a triple bond)

Delocalized Bonding

localized electrons are electrons which are associated completely with the atoms forming the bond in question

In some molecules, particularly with resonance structures, we cannot associate bonding electrons with specific atoms

C₆H₆ (Benzene)

Benzene has two resonance forms

• The six carbon - carbon bonds are of equal length, intermediate between a single bond and double bond
• The molecule is planar
• The bond angle around each carbon is approximately 120°

The apparent hybridization orbital consistent with the geometry would be sp² (trigonal planar arrangement)

• This would leave a single p orbital associated with each carbon (perpendicular to the plane of the ring)

With six p electrons we could form three discrete p bonds

• However, this would result in three double bonds in the ring, and three single bonds
• This would cause the bond lengths to be different around the ring (which they are not)
• This would also result in one resonance structure being the only possible structure

The best model is one in which the p electrons are "smeared" around the ring, and not localized to a particular atom

• Because we cannot say that the electrons in the p bonds are localized to a particular atom they are described as being delocalized among the six carbon atoms

Benzene is typically drawn in two different ways:

• The circle indicates the delocalization of the p bonds

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