Molecular Orbitals Molecular Orbitals An approach to bonding in - - PowerPoint PPT Presentation

Molecular Orbitals Molecular Orbitals

An approach to bonding in which orbitals An approach to bonding in which orbitals encompass the entire molecule, rather than encompass the entire molecule, rather than being localized between atoms. being localized between atoms.

Molecular Orbitals Molecular Orbitals

Molecular orbitals result from the Molecular orbitals result from the combination of atomic orbitals. combination of atomic orbitals. Since orbitals are wave functions, they can Since orbitals are wave functions, they can combine either constructively (forming a combine either constructively (forming a bonding molecular orbital), or destructively bonding molecular orbital), or destructively (forming an antibonding molecular orbital). (forming an antibonding molecular orbital).

Molecular Orbitals Molecular Orbitals

Molecular orbitals form when atomic orbitals Molecular orbitals form when atomic orbitals with similar energies and proper symmetry can with similar energies and proper symmetry can

• verlap.
• verlap.

Atomic orbitals with differing energies or the Atomic orbitals with differing energies or the wrong spatial orientation (orthogonal) do not wrong spatial orientation (orthogonal) do not combine, and are called combine, and are called non-bonding non-bonding orbitals.

• rbitals.

Molecular Orbital Theory Molecular Orbital Theory

In order to simplify things, we’ll consider the In order to simplify things, we’ll consider the interaction of the orbitals containing valence interaction of the orbitals containing valence electrons to create molecular orbitals. electrons to create molecular orbitals. The wave functions of hydrogen atom A and The wave functions of hydrogen atom A and hydrogen atom B can interact either hydrogen atom B can interact either constructively or destructively. constructively or destructively.

Rules for linear combination Rules for linear combination

• 1. Atomic orbitals must be roughly of the same energy.
• 2. The orbital must overlap one another as much as

possible- atoms must be close enough for effective

• verlap.
• 3. In order to produce bonding and antibonding MOs,

either the symmetry of two atomic orbital must remain unchanged when rotated about the internuclear line or both atomic orbitals must change symmetry in identical manner.

Linear combination of atomic orbitals Linear combination of atomic orbitals

Typical molecular energy levels diagram of an octahedral complex showing the frontier orbitals in the tinted box Singly degenerate s a1g Triply degenerate p t1u Doubly degenerate d eg Triply degenerate d t2g

A B g- identical under inversion u- not identical

Rules for the use of MOs Rules for the use of MOs

* When two AOs mix, two MOs will be produced

* Each orbital can have a total of two electrons (Pauli principle) * Lowest energy orbitals are filled first (Aufbau principle) * Unpaired electrons have parallel spin (Hund’s rule) Bond order = ½ (bonding electrons – antibonding electrons)

Molecular Orbital Theory Molecular Orbital Theory

Constructively: Constructively: Ψ Ψ(

(σ σ) ) or

• r Ψ

Ψ+

+ = (

= (1/√2 )

1/√2 ) [

[φ φ(1s

(1sa

a)

) +

+ φ φ(1s

(1sb

b)

) ]

] Destructively: Destructively: Ψ Ψ(

(σ σ*) *) or

• r Ψ

Ψ-

• = (

= (1/√2 )

1/√2 ) [

[φ φ(1s

(1sa

a)

) -

• φ

φ(1s

(1sb

b)

) ]

]

cA = cB = 1

+. +.

. . +

bonding ψg

Amplitudes of wave functions added

ψg = N [ψA + ψB] Constructive interference Constructive interference

The accumulation of electron density between the nuclei put the electron in a position where it interacts strongly with both nuclei. The energy of the molecule is lower Nuclei are shielded from each other

Amplitudes of wave functions subtracted.

Destructive interference Destructive interference

Nodal plane perpendicular to the H-H bond Nodal plane perpendicular to the H-H bond axis (en density = 0) axis (en density = 0) Energy of the en in this orbital is higher. Energy of the en in this orbital is higher.

+.

• .

. .

node antibonding ψu = N [ψA - ψB] cA = +1, cB = -1 ψu

+

• ΨA-ΨB

The electron is excluded from internuclear region The electron is excluded from internuclear region   destabilizing destabilizing Antibonding Antibonding

When 2 atomic When 2 atomic orbitals

• rbitals combine there are 2

combine there are 2 resultant resultant orbitals

• rbitals.

low energy bonding orbital low energy bonding orbital high energy high energy antibonding antibonding orbital

• rbital

1s

b

1s

a

σ1s σ* E

1s

Molecular Molecular

• rbitals
• rbitals

Eg

• Eg. s

. s orbitals

• rbitals

Molecular Orbital Theory Molecular Orbital Theory

The bonding orbital is The bonding orbital is sometimes given the sometimes given the notation notation σ σg

g, where the

, where the g g stands for stands for gerade gerade, or , or symmetric with respect symmetric with respect to a center of inversion. to a center of inversion.

+ +

• The signs on the molecular orbitals indicate the sign of

the wave function, not ionic charge.

Molecular Orbital Theory Molecular Orbital Theory

The anti-bonding orbital The anti-bonding orbital is sometimes given the is sometimes given the notation notation σ σu

u, where the

, where the u u stands for stands for ungerade ungerade, or , or asymmetric with respect asymmetric with respect to a center of inversion. to a center of inversion.

+ +

• The signs on the molecular orbitals indicate the sign of

the wave function, not ionic charge.

11.4 eV 109 nm

H H2

2 Location of Bonding orbital 4.5 eV

LCAO of n A.O ⇒ n M.O.

Period 2 Diatomic Molecules Period 2 Diatomic Molecules

For the second period, assume that, due to a For the second period, assume that, due to a better energy match, better energy match, s s orbitals combine with

• rbitals combine with s

s

• rbitals, and
• rbitals, and p

p orbitals combine with

• rbitals combine with p

p orbitals.

• rbitals.

The symmetry of The symmetry of p p orbitals permits end-on-

• rbitals permits end-on-

end overlap along the bond axis, or side-by-side end overlap along the bond axis, or side-by-side

• verlap around, but not along, the internuclear
• verlap around, but not along, the internuclear

axis. axis.

dx2-dy2 and dxy

Cl4Re ReCl4 2-

A B g- identical under inversion u- not identical

MOs using MOs using p p orbitals

• rbitals

Some texts will use the symmetry designations of Some texts will use the symmetry designations of g g (gerade) or (gerade) or u u (ungerade) instead of indicating bonding or anti-bonding. (ungerade) instead of indicating bonding or anti-bonding. For these orbitals, the anti-bonding orbital is asymmetric about the For these orbitals, the anti-bonding orbital is asymmetric about the bond axis, and is designated as bond axis, and is designated as σ σu

• u. Note that the designations of

. Note that the designations of u u or

• r g

g do not do not correlate with bonding or anti-bonding. correlate with bonding or anti-bonding.

+

+ +

• σg

σu

π π Molecular Orbitals Molecular Orbitals

The orbital overlap side-by-side is less than The orbital overlap side-by-side is less than that of overlap along the bond axis (end-on- that of overlap along the bond axis (end-on- end). As a result, the bonding orbital will be end). As a result, the bonding orbital will be higher in energy than the previous example. higher in energy than the previous example.

side-by-side

• verlap

+ + +

Molecular Orbital Diagram Molecular Orbital Diagram

This is a molecular This is a molecular

• rbital energy level
• rbital energy level

diagram for the diagram for the p p

• rbitals. Note that the
• rbitals. Note that the

σ σ bonding orbital is bonding orbital is lowest in energy due to lowest in energy due to the greater overlap the greater overlap end-on-end. end-on-end.

2p 2p σg πu πg σu

Place labels Place labels g g or

• r u

u in this diagram in this diagram σg π∗g σ∗u πu

Molecular Orbital Diagrams Molecular Orbital Diagrams

1. 1.

Electrons preferentially occupy molecular Electrons preferentially occupy molecular

• rbitals that are lower in energy.
• rbitals that are lower in energy.

2. 2.

Molecular orbitals may be empty, or contain Molecular orbitals may be empty, or contain

• ne or two electrons.
• ne or two electrons.

3. 3.

If two electrons occupy the same molecular If two electrons occupy the same molecular

• rbital, they must be spin paired.
• rbital, they must be spin paired.

4. 4.

When occupying degenerate molecular When occupying degenerate molecular

• rbitals, electrons occupy separate orbitals
• rbitals, electrons occupy separate orbitals

with parallel spins before pairing. with parallel spins before pairing.

Molecular Orbital Diagrams Molecular Orbital Diagrams

Although molecular orbitals form from inner Although molecular orbitals form from inner (core) electrons as well as valence electrons, (core) electrons as well as valence electrons, many molecular orbital diagrams include only many molecular orbital diagrams include only the valence level. the valence level.

First period diatomic molecules First period diatomic molecules

σ1s2

H Energy H H2 1s 1s σg σu*

Bond order = ½ (bonding electrons – antibonding electrons) Bond order: 1

σ1s2, σ*1s2

He Energy He He2 1s 1s σg σu*

Molecular Orbital theory is powerful because it allows us to predict whether molecules should exist or not and it gives us a clear picture of the of the electronic structure of any hypothetical molecule that we can imagine. Diatomic molecules: The bonding in He2

Bond order: 0

Second period diatomic molecules Second period diatomic molecules

σ1s2, σ*1s2, σ2s2

Bond order: 1

Li Energy Li Li2 1s 1s 1σg 1σu* 2s 2s 2σg 2σu*

σ1s2, σ*1s2, σ2s2, σ*2s2

Bond order: 0

Be Energy Be Be2 1s 1s 1σg 1σu* 2s 2s 2σg 2σu*

Diatomic molecules: Homonuclear Molecules of the Second Period

Simplified Simplified

Simplified Simplified

Diamagnetic??

2σ g 2σ u

*

3σ g 1πu 1πg* 3σ u*

MO diagram for B MO diagram for B2

2

Li : 200 kJ/mol F: 2500 kJ/mol

Same symmetry, energy mix- the one with higher energy moves higher and the one with lower energy moves lower

2σ g 2σ u

*

3σ g 1πu 1πg* 3σ u*

B B B2

2s 2s 2σg 2σu* 2p 2p 3σg 3σu* 1πu 1πg*

(px,py)

HOMO LUMO

MO diagram for B MO diagram for B2

2

Paramagnetic

1σg 1π u 1π

g

1σ g 1πu 1π g C2

Diamagnetic

Paramagnetic ?

X

1σg 1π u 1π

g

1σg 1πu 1π

g

Li2 to N2 O2 and F2

General MO diagrams

Distance between b-MO and AO

Heteronuclear Diatomics….

• The energy level diagram is not symmetrical.
• The bonding MOs are

closer to the atomic

• rbitals which are

lower in energy.

• The antibonding MOs

are closer to those higher in energy.

c – extent to which each atomic

• rbitals contribute to MO

If cA>cB the MO is composed principally of φA

Rules for Combining Atomic Rules for Combining Atomic Orbitals Orbitals

For heteronuclear molecules: For heteronuclear molecules:

• 1. The bonding orbital(s) will reside
• 1. The bonding orbital(s) will reside

predominantly on the atom of lower orbital predominantly on the atom of lower orbital energy (the more electronegative atom). energy (the more electronegative atom).

• 2. The anti-bonding orbital(s) will reside
• 2. The anti-bonding orbital(s) will reside

predominantly on the atom with greater orbital predominantly on the atom with greater orbital energy (the less electronegative atom). energy (the less electronegative atom).

HF HF

The 2s and 2p The 2s and 2px

x orbitals

• rbitals
• n fluorine interact with
• n fluorine interact with

the 1s orbital on hydrogen. the 1s orbital on hydrogen. The p The py

y and p

and pz

z orbitals

• rbitals
• n fluorine lack proper
• n fluorine lack proper

symmetry to interact with symmetry to interact with hydrogen, and remain as hydrogen, and remain as non-bonding orbitals. non-bonding orbitals.

HF HF

The anti-bonding The anti-bonding

• rbital resides primarily on
• rbital resides primarily on

the less electronegative the less electronegative atom (H). atom (H). Note that the Note that the subscripts subscripts g g and and u u are not are not used, as the molecule no used, as the molecule no longer has a center of longer has a center of symmetry. symmetry.

Carbon monoxide Carbon monoxide

In carbon In carbon monoxide, the bonding monoxide, the bonding

• rbitals reside more on
• rbitals reside more on

the oxygen atom, and the oxygen atom, and the anti-bonding the anti-bonding

• rbitals reside more on
• rbitals reside more on

the carbon atom. the carbon atom.

Carbon monoxide Carbon monoxide

CO is a highly CO is a highly reactive molecule with reactive molecule with transition metals. transition metals. Reactivity typically Reactivity typically arises from the arises from the h highest ighest

• ccupied

ccupied m molecular

• lecular
• rbital (HOMO), when

rbital (HOMO), when donating electrons. donating electrons.

Carbon monoxide Carbon monoxide

When acting as an When acting as an electron pair acceptor, electron pair acceptor, the the l lowest

• west

u unoccupied noccupied m molecular

• lecular
• rbital (LUMO), is

rbital (LUMO), is significant. significant.

Carbon monoxide Carbon monoxide

When acting as an When acting as an electron pair donor, electron pair donor, the the h highest ighest o

• ccupied

ccupied m molecular

• lecular o
• rbital

rbital (HOMO), is (HOMO), is significant. significant.

The highest

• ccupied molecular
• rbital of CO is a

molecular orbital which puts significant electron density on the carbon atom.

The lowest unoccupied molecular orbital of CO is the π* orbitals. The lobes of the LUMO are larger on the carbon atom than

• n the oxygen atom.

CO as a Ligand CO as a Ligand

Carbon monoxide is known as a Carbon monoxide is known as a σ σ donor and donor and a a π π acceptor ligand. It donates electrons from its acceptor ligand. It donates electrons from its HOMO to form a sigma bond with the metal. HOMO to form a sigma bond with the metal.

CO as a Ligand CO as a Ligand

Carbon monoxide accepts electrons from Carbon monoxide accepts electrons from filled filled d d orbitals on the metal into its antibonding

• rbitals on the metal into its antibonding

(LUMO) orbital. (LUMO) orbital.

CO as a Ligand CO as a Ligand

This phenomenon is called This phenomenon is called back bonding back bonding. The . The increased electron density in the antibonding orbitals of increased electron density in the antibonding orbitals of CO causes an increase in the C-O bond length and a CO causes an increase in the C-O bond length and a decrease in its stretching frequency. decrease in its stretching frequency.

MOs for Larger Molecules MOs for Larger Molecules

Group theory is usually used to develop Group theory is usually used to develop molecular orbital diagrams and drawings of molecular orbital diagrams and drawings of more complicated molecules. When a central more complicated molecules. When a central atom is bonded to several atoms of the same atom is bonded to several atoms of the same element (H element (H2

2O, BF

O, BF3

3, or PtCl

, or PtCl4

4 2- 2-], group theory can

], group theory can be used to analyze the symmetry of the orbitals be used to analyze the symmetry of the orbitals

• f the non-central atoms, and then combine
• f the non-central atoms, and then combine

them with the appropriate orbitals of the central them with the appropriate orbitals of the central atom. atom.

MOs for Larger Molecules MOs for Larger Molecules

The orbitals of the non-central atoms are The orbitals of the non-central atoms are called called group orbitals group orbitals. In considering a simple . In considering a simple example, H example, H2

2O, we obtain group orbitals using

O, we obtain group orbitals using the two the two 1s 1s orbitals on the hydrogen atoms.

• rbitals on the hydrogen atoms.

Group Orbitals of Water Group Orbitals of Water

The A The A1

1 representation has both

representation has both 1s 1s orbitals with

• rbitals with

positive wave functions: H positive wave functions: Ha

a+H

+Hb

b.

. The B The B1

1 representations is H

representations is Ha

a+H

+Hb

b.

.

Molecular Orbitals of Water Molecular Orbitals of Water

Since the Since the 2p 2py

y orbital on oxygen doesn’t match

• rbital on oxygen doesn’t match

the symmetry of the group orbitals of hydrogen, the symmetry of the group orbitals of hydrogen, it will remain non-bonding. The other orbitals it will remain non-bonding. The other orbitals

• n oxygen will combine with the appropriate
• n oxygen will combine with the appropriate

group orbitals to form bonding and antibonding group orbitals to form bonding and antibonding molecular orbitals. molecular orbitals.

4p 4s 3d x2-y2 z2 xy xz yz NB MOs Bonding MOs Six donor orbitals 6NH3 each donating 2 e-s Antibonding MOs Atomic orbitals in metal ion Atomic orbitals in ligand ion Molecular orbitals Molecular Orbital diagram for [CoIII(NH3)6]3+

∆ο

Oh σ bonding

4p 4s 3d x2-y2 z2 xy xz yz NB MOs Bonding MOs Six donor orbitals 6 F- each donating 2 e-s Antibonding MOs Atomic orbitals in metal ion Atomic orbitals in ligand ion Molecular orbitals Molecular Orbital diagram for CoF6

3-

∆ο

Oh σ bonding

Clearly good σ donor ligand Result in good M-L overlap  Strongly antibonding eg set

t2g eg t2g ML6 σ-only ML6 σ + π Stabilization (empty π-orbitals on ligands) ∆o ∆’o ∆o has increased Case 1 (CN-, CO, C2H4) empty π-orbitals on the ligands M→L π-bonding (π-back bonding) t2g (π) t2g (π*) eg

t2g eg t2g

ML6 σ-only ML6 σ + π

Case 2 (Cl-, F-) filled π-orbitals on the ligands L→ M π-bonding (filled π-orbitals) Stabilization Destabilization t2g (π) t2g (π*) eg

∆’o ∆o

∆ o has decreased

Strong field Weak field Putting it all on one diagram.

Summary: strong σ- or π-donor  weak field ligands. π-acceptors  strong field ligands. π donor ligands lower in E than t2g. π acceptor ligands higher in E than t2g.

Or