AP Chemistry - Molecular Orbital Theory

Molecular Orbital Molecular Orbital TheoryTheory

Atomic OrbitalsAtomic Orbitals Heisenberg Uncertainty Principle states that it is Heisenberg Uncertainty Principle states that it is

impossible to define what time and where an impossible to define what time and where an electron is and where is it going next. This makes it electron is and where is it going next. This makes it impossible to know exactly where an electron is impossible to know exactly where an electron is traveling in an atom.traveling in an atom.

Since it is impossible to know where an electron is Since it is impossible to know where an electron is at a certain time, a series of calculations are used to at a certain time, a series of calculations are used to approximate the volume and time in which the approximate the volume and time in which the electron can be located. These regions are called electron can be located. These regions are called Atomic Orbitals. These are also known as the Atomic Orbitals. These are also known as the quantum states of the electrons.quantum states of the electrons.

Only two electrons can occupy one orbital and they Only two electrons can occupy one orbital and they must have different spin states, ½ spin and – ½ spin must have different spin states, ½ spin and – ½ spin (easily visualized as opposite spin states).(easily visualized as opposite spin states).

Orbitals are grouped into subshells.Orbitals are grouped into subshells. This field of study is called quantum mechanics.This field of study is called quantum mechanics.

Atomic SubshellsAtomic Subshells These are some examples of atomic orbitals:These are some examples of atomic orbitals:

S subshell: (Spherical shape) There is one S orbital in S subshell: (Spherical shape) There is one S orbital in an s subshell. The electrons can be located anywhere an s subshell. The electrons can be located anywhere within the sphere centered at the atom’s nucleus.within the sphere centered at the atom’s nucleus.

P Orbitals: (Shaped like two balloons tied together) P Orbitals: (Shaped like two balloons tied together) There are 3 orbitals in a p subshell that are denoted as There are 3 orbitals in a p subshell that are denoted as ppxx, p, pyy, and p, and pzz orbitals. These are higher in energy than orbitals. These are higher in energy than the corresponding s orbitals. the corresponding s orbitals.

http://www.chm.davidson.edu/ronutt/che115/AO.htm

http://www.chm.davidson.edu/ronutt/che115/AO.htm

Atomic Subshells Atomic Subshells (cont’d)(cont’d)

D Orbitals: The d subshell is divided into 5 orbitals (D Orbitals: The d subshell is divided into 5 orbitals (dxy, dxz, dyz, dz

2 and dx2

-y2). These orbitals have a very complex . These orbitals have a very complex

shape and are higher in energy than the s and p orbitals.shape and are higher in energy than the s and p orbitals.

Molecular Orbital TheoryMolecular Orbital Theory

The goal of molecular orbital theory is The goal of molecular orbital theory is to describe molecules in a similar way to describe molecules in a similar way to how we describe atoms, that is, in to how we describe atoms, that is, in terms of orbitals, orbital diagrams, terms of orbitals, orbital diagrams, and electron configurations. and electron configurations.

Forming a Covalent Bond Forming a Covalent Bond

Molecules can form bonds by sharing Molecules can form bonds by sharing electronelectron Two shared electrons form a single bond Two shared electrons form a single bond

Atoms can share one, two or three pairs of Atoms can share one, two or three pairs of electronselectrons forming single, double and triple bondsforming single, double and triple bonds

Other types of bonds are formed by Other types of bonds are formed by charged atoms (ionic) and metal atoms charged atoms (ionic) and metal atoms (metallic).(metallic).

Atomic and Molecular Atomic and Molecular Orbitals Orbitals (cont’d)(cont’d)

Orbital MixingOrbital Mixing When atoms share electrons to form a bond, When atoms share electrons to form a bond,

their atomic orbitals mix to form molecular their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they bonds. In order for these orbitals to mix they must:must:

Have similar energy levels.Have similar energy levels. Overlap well.Overlap well. Be close togetherBe close together..

This is and example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons.

http://library.thinkquest.org/27819/ch2_2.shtml

Energy Diagram of Sigma Energy Diagram of Sigma Bond Formation by Orbital Bond Formation by Orbital

OverlapOverlap

spsp33 Hybrid atomic Hybrid atomic orbitalsorbitals

spsp22 Hybrid atomic Hybrid atomic orbitalsorbitals

sp Hybrid atomic orbitalssp Hybrid atomic orbitals

Multiple bonds with VBMultiple bonds with VB


Each line in the diagram represents Each line in the diagram represents an orbital.an orbital.

The molecular orbital volume The molecular orbital volume encompasses the whole molecule.encompasses the whole molecule.

The electrons fill the molecular The electrons fill the molecular orbitals of molecules like electrons orbitals of molecules like electrons fill atomic orbitals in atomsfill atomic orbitals in atoms


Electrons go into the lowest energy Electrons go into the lowest energy orbital available to form lowest orbital available to form lowest potential energy for the molecule.potential energy for the molecule.

The maximum number of electrons The maximum number of electrons in each molecular orbital is two. in each molecular orbital is two. (Pauli exclusion principle) (Pauli exclusion principle)

One electron goes into orbitals of One electron goes into orbitals of equal energy, with parallel spin, equal energy, with parallel spin, before they begin to pair up. (Hund's before they begin to pair up. (Hund's Rule.) Rule.)

Diatomic Molecular Diatomic Molecular Orbital TheoryOrbital Theory In the case of diatomic molecules, the interactions are easy to In the case of diatomic molecules, the interactions are easy to

see and may be thought of as arising from the constructive see and may be thought of as arising from the constructive interference of the electron waves (orbitals) on two different interference of the electron waves (orbitals) on two different atoms, producing a bonding molecular orbital, and the atoms, producing a bonding molecular orbital, and the destructive interference of the electron waves, producing an destructive interference of the electron waves, producing an antibonding molecular orbitalantibonding molecular orbital

A Little Math is need to understand

Only a Little I promise!

•This Approach is called LCAO-MO (Linear Combination of Atomic Orbitals to Produce Molecular Orbitals)

Atomic and Molecular Atomic and Molecular OrbitalsOrbitals

In atoms, electrons occupy In atoms, electrons occupy atomic orbitalsatomic orbitals, but in , but in molecules they occupy similar molecules they occupy similar molecular orbitalsmolecular orbitals which surround the molecule.which surround the molecule.

The two 1s atomic orbitals combine to form two The two 1s atomic orbitals combine to form two molecular orbitals, one bonding (molecular orbitals, one bonding () and one antibonding ) and one antibonding ((*). *).

http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html

• This is an illustration of molecular orbital diagram of H2.• Notice that one electron from each atom is being “shared” to form a covalent bond. This is an example of orbital mixing.

The He “dimer”The He “dimer”

Examples of Sigma Bond Examples of Sigma Bond FormationFormation

Molecular Orbital Molecular Orbital Diagram (HDiagram (H22))


Molecular Orbitals from Molecular Orbitals from p A.O.sp A.O.s

NOTE: Symmetry is important in forming M.O. from A.O.s (LCAO)

Molecular Orbitals from Molecular Orbitals from p A.O.sp A.O.s

MO Diagram for OMO Diagram for O22

http://www.chem.uncc.edu/faculty/murphy/1251/slides/C19b/sld027.htm

M.O.s from OM.O.s from O22

1s

1s 2s

2s

2p 2p

2p

Molecular Orbital Molecular Orbital Diagram (HF)Diagram (HF)


Valence MOs

1s

FH HF

2s

2p

Energy Levels in HFThis diagram shows the allowed energy levels of

Isolated H (1s1) and F (1s22s22p5) atoms and, between them, the HF molecule.

Note:1. F 1s is at much lower energy than H 1s (because of the higher nuclear charge)

2. F 1s2 electrons are core electrons. Their energy does not change when HF is formed.

3. H 1s and F 2p valence electrons go into molecular orbitals with new energies.

1s

FH HF

2s

2p

Molecular Orbitals in HF

This core orbital is almost unchanged from the F 1s orbital. The electrons are bound tightly to the F nucleus.

This non-bonding molecular orbital (n) has an almost spherical lobe showing only slight delocalisation between the two nuclei.Non-bonding orbitals look only slightly different to atomic orbitals, and have almost the same energy.

H F

n

n

Molecular Orbitals in HF

These two degenerate (filled) HOMO’s are centred on the F atom, like 2px and 2py orbitals.

This MO, which is is like a 2pz orbital, is lower in energy in

the molecule (a bonding orbital), and one lobe is

delocalised around the H atom.

This (empty) LUMO is an antibonding orbital with a node on the interatomic axis between H and F.

Electrons in these two orbitals are not shared (much) by the fluorine nucleus. They behave like the 2p orbitals and are also non-bonding (n).

1s

FH HF

2p

n

n

n n

Molecular Orbital Molecular Orbital Diagram (CHDiagram (CH44))

So far, we have only look at molecules with two atoms. So far, we have only look at molecules with two atoms. MO diagrams can also be used for larger molecules. MO diagrams can also be used for larger molecules.


Molecular Orbital Diagram Molecular Orbital Diagram (H(H22O)O)

The second set of combinations with symmetry (orthogonal to the first set):

This produces an MO over the molecule with a node on the bond between the F atoms. This is thus a bonding MO of u symmetry.

Molecular Orbital Theory

Diatomic molecules: The bonding in F2

2pxA

+

This produces an MO around both F atoms that has two nodes: one on the bond axis and one perpendicular to the bond. This is thus an antibonding MO of g symmetry.

u = 0.5 (2pxA + 2pxB)

2pxB

-

g* = 0.5 (2pxA - 2pxB)

2pxA 2pxB

F

Ene

rgy

FF2

2s 2s

2g

2u*

2p

2p

3g

3u*

1u

1g*

Molecular Orbital TheoryMO diagram for F2

(px,py)pz

You will typically see the diagrams drawn in this way. The diagram is only showing the MO’s derived from the valence electrons because the pair of MO’s from the 1s orbitals are much lower in energy and can be ignored.

Although the atomic 2p orbitals are drawn like this: they are actually all the same energy and could be drawn like this:

at least for two non-interacting F atoms.

Notice that there is no mixing of AO’s of the same symmetry from a single F atom because there is a sufficient difference in energy between the 2s and 2p orbitals in F.

Also notice that the more nodes an orbital of a given symmetry has, the higher the energy.

Note: The the sake of simplicity, electrons are not shown in the atomic orbitals.

F

Ene

rgy

FF2

2s 2s

2g

2u*

2p

2p

3g

3u*

1u

1g*

Molecular Orbital TheoryMO diagram for F2

(px,py)pz

Another key feature of such diagrams is that the -type MO’s formed by the combinations of the px and py orbitals make degenerate sets (i.e. they are identical in energy).

The highest occupied molecular orbitals (HOMOs) are the 1g* pair - these correspond to some of the “lone pair” orbitals in the molecule and this is where F2 will react as an electron donor.

The lowest unoccupied molecular orbital (LUMO) is the 3u* orbital - this is where F2 will react as an electron acceptor.

HOMO

LUMO

B

Ene

rgy

BB2

2s 2s

2g

2u*

2p

2p

3g

3u*

1u

1g*

Molecular Orbital TheoryMO diagram for B2

(px,py)pz

In the MO diagram for B2, there several differences from that of F2. Most importantly, the ordering of the orbitals is changed because of mixing between the 2s and 2pz orbitals. From Quantum mechanics: the closer in energy a given set of orbitals of the same symmetry, the larger the amount of mixing that will happen between them. This mixing changes the energies of the MO’s that are produced.

The highest occupied molecular orbitals (HOMOs) are the 1u pair. Because the pair of orbitals is degenerate and there are only two electrons to fill, them, each MO is filled by only one electron - remember Hund’s rule. Sometimes orbitals that are only half-filled are called “singly-occupied molecular orbtials” (SOMOs). Since there are two unpaired electrons, B2 is a paramagnetic (triplet) molecule.

HOMO

LUMO

Remember that the separation between the ns and np orbitals increases with increasing atomic number. This means that as we go across the 2nd row of the periodic table, the amount of mixing decreases until there is no longer enough mixing to affect the ordering; this happens at O2. At O2 the ordering of the 3g and the 1u MO’s changes. As we go to increasing atomic number, the effective nuclear charge (and electronegativity) of the atoms increases. This is why the energies of the analogous orbitals decrease from Li2 to F2. The trends in bond lengths and energies can be understood from the size of each atom, the bond order and by examining the orbitals that are filled.

Diatomic molecules: MO diagrams for Li2 to F2

Molecular Orbital Theory

2s-2pz mixing

Molecule Li2 Be2 B2 C2 N2 O2 F2 Ne2

Bond Order 1 0 1 2 3 2 1 0

Bond Length (Å) 2.67 n/a 1.59 1.24 1.01 1.21 1.42 n/a

Bond Energy (kJ/mol) 105 n/a 289 609 941 494 155 n/a

Diamagnetic (d)/ Paramagnetic (p)

d n/a p d d p d n/a

In this diagram, the labels are for the valence shell only - they ignore the 1s shell. They should really start at 2g and 2u*.

Modern MO Modern MO calculationscalculations

W. Kohn(1923-)

J. A. Pople(1925-2004)

Nobel prize in Chemistry1998

ConclusionsConclusions

Bonding electrons are localized Bonding electrons are localized between atoms (or are lone pairs).between atoms (or are lone pairs).

Atomic orbitals overlap to form bonds.Atomic orbitals overlap to form bonds. Two electrons of opposite spin can Two electrons of opposite spin can

occupy the overlapping orbitals.occupy the overlapping orbitals. Bonding increases the probability of Bonding increases the probability of

finding electrons in between atoms.finding electrons in between atoms. It is also possible for atoms to form It is also possible for atoms to form

ionic and metallic bonds.ionic and metallic bonds.

ReferencesReferences http://www.chemguide.co.uk/atoms/properties/at

omorbs.html http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.ht

ml http://en.wikipedia.org/wiki/Molecular_orbital_th

eory http://library.thinkquest.org/27819/ch2_2.shtml

AP Chemistry - Molecular Orbital Theory

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