Atomic and Molecular OrbitalsAtomic and Molecular Orbitals

The horizontal rows of the periodic table are called The horizontal rows of the periodic table are called Periods.Periods.

Each period represents a different quantum energy Each period represents a different quantum energy level.level.

All of the atoms in a given row have a set of electrons All of the atoms in a given row have a set of electrons at various energy levels (i.e. the principle quantum at various energy levels (i.e. the principle quantum level; 1, 2, 3 etc.)level; 1, 2, 3 etc.)

The highest energy level is called the valence shell.The highest energy level is called the valence shell. Within each period there may be 1, 2, 3 or 4 sublevels, Within each period there may be 1, 2, 3 or 4 sublevels,

designated as s, p, d, and f. These are atomic orbitals.designated as s, p, d, and f. These are atomic orbitals.

Recall the following principles from General ChemistryRecall the following principles from General Chemistry

One way to show the relative energies of the One way to show the relative energies of the quantum levels and the atomic orbitals is the quantum levels and the atomic orbitals is the diagram below:diagram below:

3 d

3 p

2 p

1 s

2 s

3 s

Quantum energylevel 3

Quantum energylevel 2

Quantum energylevel 1

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

We are most interested in level 2, where carbon is. Note thatWe are most interested in level 2, where carbon is. Note thatwhen atomic orbitals are of the same energy, they are calledwhen atomic orbitals are of the same energy, they are calleddegenerate. degenerate. For simplicity, we refer to atomic orbitals and For simplicity, we refer to atomic orbitals and their quantum levels as 1s, 2s, 2p, 3s etc.their quantum levels as 1s, 2s, 2p, 3s etc.

The three dimensional picture of an atomic orbital is The three dimensional picture of an atomic orbital is actually a combination of all the individual equations actually a combination of all the individual equations which describe, in terms of energy, repulsive forces, which describe, in terms of energy, repulsive forces, etc., just where an electron is most likely to be etc., just where an electron is most likely to be found in relation to the nucleus at any given point in found in relation to the nucleus at any given point in time. The calculations provide what is known as a time. The calculations provide what is known as a probability distributionprobability distribution. This model is used for . This model is used for isolated atoms. So, pictures that you see that isolated atoms. So, pictures that you see that describe the “shape” of an orbital, are really describe the “shape” of an orbital, are really probability distributions. For example, when we say probability distributions. For example, when we say that an that an ss orbital is spherical, what we are really orbital is spherical, what we are really mean is that there is a 90% probability that you can mean is that there is a 90% probability that you can find an electron in that spherical space at any given find an electron in that spherical space at any given time.time.

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

nucleus

"up wave" "down wave"

2-D

2 = 3-D

postive amplitude

negative amplitude

"up wave" "down wave"

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

1. The location of an electron can be considered as a wave1. The location of an electron can be considered as a wave property. Different amplitudes are shown as different colorsproperty. Different amplitudes are shown as different colors or by using + (positive) and - (negative) signs. Note that these or by using + (positive) and - (negative) signs. Note that these do not signify charge. Nodes are areas where the probability do not signify charge. Nodes are areas where the probability of finding an electron is zero.of finding an electron is zero.2. An atomic orbital is an area of high probable electron density.2. An atomic orbital is an area of high probable electron density.

p orbitals; there are 3 of thesep orbitals; there are 3 of these

nodenode

positive amplitude

negative amplitude

node

nodeor

When two atomic orbitals overlap, and one electron from each is shared between the two nuclei, the new probability distribution is called a molecular orbital (MO). When two atomic orbitals overlap, we get two molecular orbitals, not one. This is called the linear combination of atomic orbitals (LCAO).

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

1s 1s

H atom AO

H atom AO

sigma () bonding MO

sigma* () antibonding MO

s + s

=

=

s + s

=

=

Two H atoms (each with one AO) connectingto form a bond between them gives two MOs

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

2p 2p

pi () bonding MO

pi* () antibonding MO

p + p

=

=

p + p

=

=

The p MO’s that we will The p MO’s that we will consider result from consider result from side by side overlap of side by side overlap of two p AO’s. Lobes of thetwo p AO’s. Lobes of thesame wave amplitude cansame wave amplitude canline up (constructiveline up (constructiveoverlap), which give bondingoverlap), which give bondingMO’s. The lining up of lobesMO’s. The lining up of lobeswith opposite amplitudeswith opposite amplitudes(destructive overlap) (destructive overlap) gives anti-bonding MO’s.gives anti-bonding MO’s.The bond formed by theThe bond formed by theconstructive parallel constructive parallel overlap of two p AO’s isoverlap of two p AO’s isa a bond. bond.

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

2s

1s

2p

Electron configuration for C

Using the AO and MO theory Using the AO and MO theory that we have just reviewed, wethat we have just reviewed, wecan draw an MO diagram for a can draw an MO diagram for a typical C-H bond. To do so, wetypical C-H bond. To do so, wemust consider the electronicmust consider the electronicconfiguration of carbon. Since configuration of carbon. Since we are interested in the valence we are interested in the valence electrons, we look at quantumelectrons, we look at quantumnumber 2 electrons only, the 2number 2 electrons only, the 2ss2222pp22. Based upon this, we. Based upon this, wewould expect C to form only two bonds, since only twowould expect C to form only two bonds, since only twoelectrons, those in the p AO, are unpaired.electrons, those in the p AO, are unpaired.

2p

1s

bonding MO

antibonding MO

Possible MO diagram for a C-H bond

The MO diagram for one C-H bondThe MO diagram for one C-H bondusing the classic AO model wouldusing the classic AO model wouldlook something like the diagram tolook something like the diagram tothe right. One of the p electrons fromthe right. One of the p electrons fromC is bonding to the s electron fromC is bonding to the s electron fromH to form a C-H bond.H to form a C-H bond.

This looks good on paper,This looks good on paper,but we know from experimentalbut we know from experimentalevidence that C doesn’t just formevidence that C doesn’t just formtwo bonds, it forms four bonds!two bonds, it forms four bonds!Thus, our model needs to beThus, our model needs to bechanged. Experimental evidencechanged. Experimental evidenceindicates that C forms 4 indicates that C forms 4 identical bonds to H.identical bonds to H.

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

We know that:We know that:1. Carbon always forms 4 bonds.1. Carbon always forms 4 bonds.2. But carbon can be bonded to 2,3 or 4 ‘things’.2. But carbon can be bonded to 2,3 or 4 ‘things’.3. If all the ‘things’ are the same, like 4 H’s, all the 3. If all the ‘things’ are the same, like 4 H’s, all the bonds are identical in length and strength.bonds are identical in length and strength.4. When bonded to three ‘things’, one bond is 4. When bonded to three ‘things’, one bond is shorter and stronger than the other two shorter and stronger than the other two degenerate bonds.degenerate bonds.5. When bonded to two ‘things’, one bond is 5. When bonded to two ‘things’, one bond is even shorter and stronger.even shorter and stronger.

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

sp

Hybridization produces 4 AO, energy between s and p

hybridizes to

sp3

To accommodate the experimental observations we need:To accommodate the experimental observations we need:Four degenerate AO’s which will ‘mix’ or combine to formFour degenerate AO’s which will ‘mix’ or combine to formfour degenerate MO’s. This mixing is also known as four degenerate MO’s. This mixing is also known as ““hybridizing”. For carbon, we have an s and three p orbitalshybridizing”. For carbon, we have an s and three p orbitalsin the second energy level. This means that we have a in the second energy level. This means that we have a total of four orbitals; one of them is total of four orbitals; one of them is ss, and the other three, and the other threeare are p’sp’s. When these four orbitals mix or hybridize, we get. When these four orbitals mix or hybridize, we getfour degenerate four degenerate spsp33 orbitals. orbitals.

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

s

Hybridization gives 4 AO, 3 with energy between s and p and one unhybridized p

hybridizes to

sp2p p

p

When C has only three ‘things’ bonded to it, we need threeWhen C has only three ‘things’ bonded to it, we need threeAO’s to form those three bonds. This means that we haveAO’s to form those three bonds. This means that we haveto combine one s and two p atomic orbitals, to give a totalto combine one s and two p atomic orbitals, to give a totalof three degenerate of three degenerate spsp22 orbitals. Remember that there is a orbitals. Remember that there is ap AO that has not been pulled into this overlap. Thisp AO that has not been pulled into this overlap. Thisunhybridized p AO has an unshared electron and it forms aunhybridized p AO has an unshared electron and it forms abond, a second bond, to ‘something else’. The situation whenbond, a second bond, to ‘something else’. The situation whenC is only bonded to two things is analogous.C is only bonded to two things is analogous.

SpSp3 3 Hybridized Orbitals: TetrahedralHybridized Orbitals: Tetrahedral Geometry Geometry

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

SpSp22 Hybridized Orbitals: Trigonal Planar Geometry Hybridized Orbitals: Trigonal Planar Geometry

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

Sp Hybridized Orbitals: Linear GeometrySp Hybridized Orbitals: Linear Geometry

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

Single Bond: Single Bond: bond bond

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

Double Bond: 1 Double Bond: 1 and 1 and 1

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

Triple Bond: 1 Triple Bond: 1 bond and 2 bond and 2 bonds bonds

5. Atomic and Molecular Orbitals5. Atomic and Molecular Orbitals

Tetrahedral geometry: bond angle = 109.5 Tetrahedral geometry: bond angle = 109.5 00

Trigonal planar geometry: bond angle = 120Trigonal planar geometry: bond angle = 120 0 0

Linear geometry: bond angle = 180 Linear geometry: bond angle = 180 00

H

CH

H

H

CH

H

H

107.3 0

109.5. 0

O

C

H H

120 0

C C HH

180 0

IsomersIsomersIsomers are different compounds with the sameIsomers are different compounds with the samemolecular formula. For example, if you are givenmolecular formula. For example, if you are giventhe molecular formula Cthe molecular formula C33HH88, there are two possible, there are two possible

structures that you could draw:structures that you could draw:

CH3 CH2 CH2 CH3

CH3 CH CH3

CH3

andand

n-butanen-butane

isobutaneisobutane

IsomersIsomers

Also, whereas you can have rotation about single bonds,Also, whereas you can have rotation about single bonds,you cannot have rotation about double bonds. In otheryou cannot have rotation about double bonds. In otherwords, double bonds are rigid. One of the consequenceswords, double bonds are rigid. One of the consequencesof this is that there may be more than one way to draw aof this is that there may be more than one way to draw aformula that contains double bonds. For example, thereformula that contains double bonds. For example, thereare two ways to draw the molecule CHare two ways to draw the molecule CH33-CH=CH=CH-CH=CH=CH33::

C C

H

CH3H3C

H

C C

H

HH3C

CH3

cis-2-butene trans-2-butene

These two structures actually represent two completelyThese two structures actually represent two completelydifferent molecules. When the two identical groups are on different molecules. When the two identical groups are on the same side, it is called the same side, it is called cis.cis. When they are on opposite When they are on oppositesides, it is called sides, it is called trans.trans.

IsomersIsomers

Cis and Trans isomers are called Cis and Trans isomers are called Stereoisomers. Stereoisomers. Stereoisomers are isomers that differ from one another Stereoisomers are isomers that differ from one another only in terms of the spatial orientation of the atoms, notonly in terms of the spatial orientation of the atoms, notin the bonding order of the atoms. in the bonding order of the atoms. Cis and trans isomers Cis and trans isomers are also known as are also known as geometric isomers.geometric isomers.

n-Butane and isobutane are n-Butane and isobutane are constitutional isomers. constitutional isomers. Constitutional (structural)Constitutional (structural) isomers differ in their bonding isomers differ in their bonding sequence. In other words, their atoms are connectedsequence. In other words, their atoms are connecteddifferently.differently.

Molecular Dipole MomentsMolecular Dipole MomentsThe polarity of an individual bond is measured as its dipoleThe polarity of an individual bond is measured as its dipolemoment. The symbol for dipole moment is moment. The symbol for dipole moment is , and it is , and it is measured in units of measured in units of debye (D).debye (D). You already know how to You already know how to identify a polar bond, and how to determine the directionidentify a polar bond, and how to determine the directionof the bond polarity. But it is possible to consider the of the bond polarity. But it is possible to consider the dipole moment of the molecule as a whole. The dipole moment of the molecule as a whole. The molecularmoleculardipole moment is the vector sum of all the individual bonddipole moment is the vector sum of all the individual bonddipole moments.dipole moments. This vector sum reflects both the This vector sum reflects both the magnitude and direction of magnitude and direction of each individual bond dipole each individual bond dipole moment. Example: both moment. Example: both formaldehyde and COformaldehyde and CO22 have have

the have polar C=O bonds, the have polar C=O bonds, but only formaldehyde has a but only formaldehyde has a molecular dipole moment.molecular dipole moment.

O C OO

H

H

formaldehyde = 2.3 D

carbon dioxide = 0

Dipole-Dipole ForcesDipole-Dipole Forces

Dipole-dipole forces are attractive intermolecularDipole-dipole forces are attractive intermolecularforces resulting from the attraction of the positiveforces resulting from the attraction of the positiveand negative ends of the molecular dipole and negative ends of the molecular dipole moments in polar molecules. Two types of moments in polar molecules. Two types of dipole-dipole forces are dipole-dipole forces are London DispersionLondon DispersionForces and Hydrogen Bonding.Forces and Hydrogen Bonding.

Hydrogen BondingHydrogen BondingHydrogen bonding refers to a particularly strong inter-Hydrogen bonding refers to a particularly strong inter-molecular attraction between a nonbonding pair of molecular attraction between a nonbonding pair of electrons and an electrophilic O-H or N-H hydrogen.electrons and an electrophilic O-H or N-H hydrogen.Note, however, that it is much weaker than a single bond.Note, however, that it is much weaker than a single bond.To see examples of hydrogen bonding, refer to pageTo see examples of hydrogen bonding, refer to page65 in your text book.65 in your text book. Molecules capable of hydrogen Molecules capable of hydrogen bonding have higher boiling points than molecules of bonding have higher boiling points than molecules of comparable size and molecular weights.comparable size and molecular weights.

CH3 CH2 OH

ethanol, bp 78 0CH3 O CH3

dimethyl ether, bp - 25 0

London Dispersion ForcesLondon Dispersion ForcesLondon dispersion forces are intermolecular forces London dispersion forces are intermolecular forces resulting from the attraction of coordinated temporary resulting from the attraction of coordinated temporary dipole moments induced adjacent molecules. It is the dipole moments induced adjacent molecules. It is the principle attractive force in nonpolar molecules. principle attractive force in nonpolar molecules. See pageSee page64 of your text book for examples of this phenomenon.64 of your text book for examples of this phenomenon.The effects of London forces can be observed whenThe effects of London forces can be observed whenexamining the boiling points of simple hydrocarbons. Theexamining the boiling points of simple hydrocarbons. Themore highly branched isomeric alkanes are, the lower themore highly branched isomeric alkanes are, the lower theboiling point because of decreased surface area.boiling point because of decreased surface area.

CH3 CH2 CH2

n-pentane, bp 36 0C

CH2 CH3 CH3 CH CH2

isopentane, bp 28 0C

CH3

CH3

CH3 C CH3

isopentane, bp 10 0C

CH3

CH3