general chemistry lecture 19

8/13/2019 General Chemistry Lecture 19

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Overlap of p OrbitalsFor a given distance, end-to-end overlap is greater than side-to-side

overlap.

Thus, !2p will be more stable, i.e. lower in energy, than "2p.

end-to-end

side-to-side

p

p

Molecular Orbital Diagram for O2 F 2 Ne 2Note that:(1) 8 atomic orbitals

give 8 molecular

orbitals.

(2) !2p is more

stable than "2p


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Molecular Orbital Diagram for FFluorine has 7 valence

electrons, i.e. there are 14electrons in MOs.

The electron configuration is:

(!2s)2(!*2s)

2(!2p)2("2p)

4("*2p)4.

Bond order =8 6

2= 1

i.e. the bond order correspondsto the single bond predicted bysimple valence considerationswith fluorine having a valenceof one.

Molecular Orbital Diagram for OOxygen has 6 valenceelectrons, i.e. there are 12

electrons in MOs.

Two electrons in !* orbitals

are unpaired,i.e.O2is

paramagnetic.

The electron configuration is:

("2s)2("*

2s)2("

2p)2(!

2p)4(!*

2p)2.

Bond order =8 4

2= 2


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Paramagnetism of O A success for MO Theory The Lewis structure of O2predicts it to be diamagnetic, whereas it

is paramagnetic .

O O

O O

The Lewis structure of O2has an O=O double bondwith no unpaired electrons, i.e.diamagnetic.

O O

O O

Lewis structures with unpaired electrons are unusual:

OO singlebond; each oxygen has 7 electronsO O

O O

OO triple bond; each oxygen has 9 electrons MO theory predicts that O2is paramagneticwith a double bond!

Molecular Orbital Diagram for C?

Carbon has 4 valenceelectrons, i.e. there are 8

electrons in MOs.

Adopting the MO diagram for

O2, the !orbitals of C2would

possess two unpaired

electrons and C2would be

paramagnetic.

But C2is diamagnetic!Is this a failure of MO theory?


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Molecular Orbital Diagram for B?Boron has 3 valence electrons,

i.e. there are 6 electrons inMOs.

Adopting the same MOdiagram for O2, there wouldbe no unpaired electrons in B2,i.e. it should be diamagnetic.But B2is paramagnetic!Another failure for MOtheory?

Molecular Orbital Diagram for C2A new MO diagram is required to explain why C2is diamagnetic.

Paramagnetic C2 Diamagnetic C2experimental)

Switch in orbital

energies. Why?

Especially unusual

because !overalp

is supposed to be

better than "

overlap?


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Molecular Orbital Diagram for B2... and why B2is paramagnetic.

Diamagnetic B2 Paramagnetic B2experimental)

Switch in orbital

energies. Why?

Especially unusual

because !overalp

is supposed to be

better than "

overlap?

Origin of the Switch in the pand pEnergy Levels

The energy of the "orbital remains essentially constant, whereasthe energy of the orbitalincreases in energy moving from F2to B2,rising above that of the "orbital at N2.


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Origin of the Switch in the pand pEnergy Levels

The reason for the switching is concerned with the fact that it is agross oversimplificationto consider that an atomic orbital on oneatom will interact with only oneatomic orbital on another atom.Thus, orbital interactions are not restricted to pairs of orbitals, evenfor diatomic molecules.

For example, a 2pzorbital on atom A does not only have the ability

to interact with the 2pzorbital on atom B, but can also interactwith the s orbitalon atom B.

orbitals

orbitalsA B

A B

Origin of the Switch in the pand pEnergy LevelsThus, a 2pzorbital on atom A could interact with boththe 2pzand 2s orbitals ofatom B to give threemolecular orbitals which possess varying degrees of pzand scharacter.

This is known as orbital mixing(or hybridization).However, the hybrids are not required to have integer spnvalues and any ratios

are possible.

The important result is that the !2porbital no longer has pure p character and

its energy may rise above that of "2p.

A Bno sp mixing

2pz 2pz

2s

with sp mixingA B

2pz 2pz

2s

100 % p

100 % s

100 % p


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Origin of the Switch in the 2pand 2pEnergy LevelsAs a consequence of this interaction, the orbital energies are

perturbed. In essence, the lower energy orbital is stabilized, andthe higher energy orbital is destabilizedas they mix-in each other'scharacter.The extent of the interaction depends upon the 2s 2p energy gap.

A Bno sp mixing

2pz 2pz

2s

with sp mixingA B

2pz 2pz

2s

100 % p

100 % s

100 % p


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General Molecular Orbital Diagrams for Homonuclear Diatomics

sp mixing

Li2 Be2 B2 C2 N2("abnormal" pattern due

to small energy gap)

O2 F2("normal" pattern dueto large energy gap)

not pure p2p

!2p*

"2p*

2s"2s*

"2s

2p

2s

!2p

"2p

2p!2p*

"2p*

2s"2s*

""2s"

2p

2s

!2p

""2p"

not pure s

largegap:littlesp

orbitalmixing

Electron configurations for the diatomic molecules:B2, C2, N2, O2, F2, Ne2

VE: 6 8 10 12 14 16


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Bond Order Bond Energy and Bond Length For similar systems,

(i) bond energy increaseswith increase in bond order, and(ii) bond length decreaseswith increase in bond order.For example N2, with a triple bondhas the shortestand strongestbond.

Bonding in Heteronuclear DiatomicsMolecular orbital diagrams for heteronucleardiatomics (AB) are constructed in a similarmanner for homonuclear diatomics, but there isan important difference resulting from the factthat the energies of the atomic orbitals of Aand B are different.Specifically, the MO diagram is skewed, with theatomic orbitals of the more electronegativeelement A) being lower in energy.The relative contributions of each atomic orbitalto a given MO are not equal and the MOcorresponds more closely to the atomic orbitalthat it is closest to in energy.Thus, the electron pair in the bonding orbital isnot shared equally between the atoms and thebond is polar.

A is moreelectronegative than B


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Molecular Orbital Diagram for HFWhich orbitals on F are capable of

interacting with the H 1s orbital?

The 1s and 2s orbitals of F are

much too low in energyto interactwith the H 1s orbital.

The 2pxand 2pyorbitals of F arenot of appropriate symmetrytointeract with the H 1s orbital.

Only the 2pzorbital is of

appropriate symmetry and energy

to interact.

Bond order = 1

2 lone pairs

1 lone pairF

H

the threelone pairs arenot equal

2s

2p

2s

2p

CO

CO

!

"2

!*

"1

"1*

"2*

MO Diagram of COTo a first approximation, the bondingmay be described in terms of theformation of(i) "-orbitals derived from overlap ofthe 2s and 2pzorbitals on C and O, and(ii) !-orbitals derived from the overlapof the 2pxand 2py.

However, the s and p orbitals aresufficiently close in energy thatadditional orbital mixing occurs which

lowers the energy of "1and raises theenergy of "2.

CO bond order is 3

C O

8e 8e

+

Molecular Orbital Diagram s for AB Involving -Bonding

You are not required to be able toreproduce this MO diagram from memory;however you should know how tointerpret it.


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Molecular Orbitals in Polyatomic MoleculesMolecular orbital theory for polyatomic molecules follows the same

principles as those for diatomic molecules, but the molecular orbitals are

spread over all atoms of the molecule , not just pairs of atoms.An electron pair in any stabilized bonding*) molecular orbitalhelps bind thewhole molecule, not just an individual pair of atoms - this is an importantdistinction with valence-bond theory where the focus is on pairs of atoms.

The description of the bonding clearly becomes more complex as the numberof atoms increases, but some simple examples will illustrate the principles.

One important notion is that not all combinations of atom ic orbitals arepossible, because the molecular orbital must possess a symmetry that iscompatible with the symmetry of the molecule. A detailed understanding ofthis concept is beyond the scope of this course, but a qualitative

appreciation can be obtained by inspection.

* As molecules become more complex and the molecular orbitals spread overmany atoms, the terms "bonding" and "antibonding" become vague unlessone specifies a pair of atoms and orbitals. The important factor is therelative energiesof the occupied orbitals, not their names.

Molecular Orbital Diagram for H2O To construct the MO diagram for molecules of the type AHnit isfirst useful to consider the possible combinations of the H atomorbitals(even though they do not directly overlap).For H2O, two combinations are possible: in-phase and out-of-phase.These are so-called symmetry adapted orbitals.

We then consider how these symmetry-adapted orbitals could interactwith the 2s and 2p orbitals of oxygen.

H

O

H

H

O

H

in phase out of phase


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Molecular Orbital Diagram for H2OWhich orbitals on oxygen can interact with the in-phase combination?

H

O

H

in phasez

y

x

Molecular Orbital Diagram for H2O Both 2s and 2pzhave appropriate symmetry to interact with the in-phase combination of hydrogen 1s orbitals.

H

O

H

in phasez

y

x

H

O

H

H

O

H

2pzs


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Molecular Orbital Diagram for H2OWhich orbitals on oxygen can interact with the out-of-phasecombination of hydrogen orbitals?

H

O

H

out of phasez

y

x

Molecular Orbital Diagram for HOOnly 2pyhas appropriate symmetry to interact with the out-of-phasecombination of hydrogen 1s orbitals.

H

O

H

py

H

O

H

out of phasez

y

x


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Molecular Orbital Diagram for H2OWhich orbital does the oxygen 2pxinteract with?

H

O

H

H

O

H

in phase out of phase

z

y

x

2px

Molecular Orbital Diagram for H2O The oxygen 2pxis unable to interact with either combination it

remains nonbonding.

H

O

H

H

O

H

in-phase and out-of-phase overlap cancelsresulting in no overall interaction

z

y

x


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Molecular Orbital Diagram for H2OThe MO diagram for H2O is obtained by connecting permittedsymmetry combinations.Three MOsresult from the in-phase combination of hydrogen atomorbitals.

O

2H

2pz

2s

H

H

note: this is not "twoorbitals", but is a

symmetry adapted orbitalthat has coefficients of

0.5 from each AO.

bonding

antibonding

nonbonding

Molecular Orbital Diagram for HOTwo MOsresult from the out-of-phase combination of hydrogenatom orbitals.

O

2H

2py

H

H

note: this is not "twoorbitals", but is a

symmetry adapted orbitalthat has coefficients of

0.5 from each AO.

bonding

antibonding


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Molecular Orbital Diagram for HOThe complete MO diagram....

O

2H

2p

2s

H

H

H

H

in-phase out-of-phase

2px

Molecular Orbitals for HONote that the molecular orbitals spread over all three atoms.


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O

2H

2p

2s

H

H

H

H


2px

2pxis a pure nonbonding orbital on

oxygen, and the other also

approximates to a lone pair note

that there are not two lone pairsof equal energy.

Molecular Orbitals for HOThe "lone pairs" are a pure p orbital and an sp

nhybrid.

H

O

H

H

O

H

spn hybridp orbital


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O

2H

2p

2s

H

H

H

H


2px

two bonding orbitals holding twohydrogens to oxygen note thatthey do not have the same energy,i.e. there are not "two equivalentelectron pair bonds".

For additional information see:

MOs for polyatomic molecules.pdf(excerpted fromJ. Chem. Ed. 2004, 81, 997), in the Supplementary Material

section of CourseWorks.


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Molecular Orbital Theory and Molecular StructureHow do we use MO theory to predict the structures of molecules?

In essence, we calculate the MO diagrams for all possiblestructures and then determine which structure has the lowestenergy because the electrons are in MOs with lowest overall energy.

Energy

Structure 1 Structure 2 Structure 3Most stable

Molecular Orbital Diagram for Linear HO

O

2H

2p

2s

H

H

H

H

in-phase out-of-

phase

2px,2pz

H

O

H

H

O

H

pure lonepairs


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Molecular Orbital Diagram for Linear and Bent HO

O

2H

2p

2s

2px,2pz

pure lonepairsO

2H

2p

2s

2px

So why is water bent?

Bending allows the pzorbital to interact with the in-phase

combination of hydrogen orbitals, thereby stabilizing it.

stabilized

Linear Bent

Molecular Orbital Diagram for Linear and Bent HO

O

2H

2p

2s

2px,2pz

pure lonepairsO

2H

2p

2s

2px

So why is water bent?

Bending allows the pzorbital to interact with the in-phasecombination of hydrogen orbitals, thereby stabilizing it.

stabilized

Linear Bent


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Molecular Orbital Interactions for Linear and Bent HOBending allows the pzorbital to interact with the in-phase

combination of hydrogen orbitals, thereby stabilizing it.

H

O

H

pzH

O

H

pzmay

interact with

H orbitals

when HOH

angle is less

than 180

pz

No overallinteractionpossible

when linear

destructive constructive

Comparison of Chemical Bonding ModelsLewis Model: A covalent bond involves a shared pair of electronsand the composition of molecules is rationalized by appealing to theoctet rule.

VSEPR Theory: Provides a simple means of "predicting" the shapesof simple molecules.

Valence Bond VB) Theory:Involves localizedbonding between pairsof atoms (cf. Lewis) resulting from the overlap of orbitals on eachatom; the orbitals may be either pure atomic orbitals or hybridorbitals. This method requires one to know the structure of themolecule in order to utilize the appropriate hybrids.

Molecular Orbital MO ) Theory: Molecular orbitals are obtained bythe overlap of appropriate atomic orbitals on all atoms; the bondingis, therefore, delocalizedover the entire molecule. MO theoryprovides the most insight into the nature of the bonding inmolecules, but becomes increasingly complex to apply as themolecules become larger.

general chemistry lecture 19

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