lecture on vbt and mo

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A recapitulation of orbital overlapand VBT

followed by MOT

Theories of Chemical BondingTheories of bonding: explanations for chemical bond, Lewis dot structures and the following.

Valance-bond (VB) theory

Hybridization of atomic orbitals

Multiple covalent bonds

Molecular orbital (MO) theory

Delocalized electrons

Bonding in metals

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Theories of chemical bonding 3

Energy of Interaction Between Two H Atoms

Potentialenergy

distance

346 kJ mol 1

H H bond

+346 kJ mol 1

antibonding

Energies of attraction and repulsionas functions of distance between twoH atoms are shown here.

The minimum of the attraction forceoccur atHH bond length of 74 pm, at which,the antibonding orbital is +346 kJmole1 above 0, energy when Hatoms are far apart.

How does energy affect the two-atom system?


The Valence-bond Method

Valence bond method considers the covalent bond as a result of overlap of atomic orbitals.Electrons stay in regions between the two atoms. Some bond examples

s-s s-p s-d p-p p-d d-dH-H H-C H-Pd C-C Se-F Fe-Fe (?)Li-H H-N in Pd P-P

H-F hydride

But overlapping of simple atomic orbitals does not explain all the features. Thus, we have totake another look, or do something about atomic orbitals hybridization.

How does valence-bond approach explain the formation ofchemical bonds?

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Hybridization of Atomic OrbitalsThe solutions of Schrodinger equation led to these atomic orbitals.

1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.

However, overlap of these orbitals does not give a satisfactory explanation. In order to explainbonding, these orbitals are combined to form new set of orbitals this method is calledhybridization.

During the lecture, these hybridized orbitals will be explained:sp 2 sp hybrid orbitals from mixing of a s and a p orbital

sp 2 3 sp2 hybrid orbitals from mixing of a s and 2 p orbitalsp3 fill in you explanation please

sp3d 5 sp3d hybrid orbitals from mixing of a s and 3 p and a d orbitalsp3d 2 ____________

Provide a description for hybrid orbitals sp, sp2, sp3, sp3d, and sp3d2


The sp Hybrid Orbitals

The sp hybrid orbitals: formation oftwo sp hybrid orbitals

+ + + - = + -

+ + - = - +

hybridization of s and p orbitals = 2 sp hybrid orbitals

_ _ __ __

__ __ __ Two sp hybrid orbitlas =>

Two states of Be

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Bonds with sp Hybrid Orbitals

Formations of bonds in these molecules are discussed during the lecture. Be prepared to do thesame by yourself.

ClBeCl HCCH HCN : O=C=O

Double and triple bonds involve pi p bonding, and the the application of valence bondmethod to p bonds will be discussed.

You are expected to be able to draw pictures to show the p bonding.


A p Bond

Overlap of 2 2p orbitals for theformation of p bond

Sigma (s) bond is symmetric about axis.

Pi (p) electron distribution above and below axis witha nodal plane, on which probability of finding electronis zero; p bond is not as strong as sigma - lessoverlap.

Nodal plane

Bonding of C2H4

C2s 2p 2p 2p

sp2 sp2 sp2 2p

How are pi bonds formed?

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Triple Bonds in H-CC-HH-C-C-H: three s bonds due to overlapping of 1sH spC; spC spC; and spC 1sH.

Two p bonds in HCCH and HCN triple bonds are due to overlapping of p orbitals results.

Draw and describe how atomic orbitals overlap to form allbonds in acetylene, HCCH

py over lap

px over lapH H

sp hybrid orbitals

Two nodal planes of p bonds areperpendicular to each other.in p bond

in p bond

C2s 2p 2p 2psp sp 2p 2p


Two p Bonds in HCCH

A triple bond consists of a sigma and two pi bonds. Overlaps of two sets of porbitals form of two p bonds.

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Bonding of CO2For CO2, the C atom forms a s bond and a p bond with each of two O atoms. The two nodalplanes of the two p bonds are also perpendicular.

During the lecture, I draw diagrams and explain the two s two p bonds in CO2. You areexpected to be able to do the same, in a test.

py over lap in p bond

Overlap pp in s bonds

px over lap in p bond

O=C=O or H2C=C=CH2Discuss the bonding of allene H2C=C=CH2

See extra problems B17 in the handout

Resonance structures

: O C O :

: O C O :

. .


09_174

O C O

sigma bond(1 pair of electrons) pi bond

(1 pair ofelectrons)

pi bond(1 pair ofelectrons)

(a)

O C O

Bonding in CO2 another view

Compare with H2C=C=CH2

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The sp2 Hybrid Orbitals

Ground state and excited state electronicconfiguration of B

_ _ _ __

_ __ __

The hybridization of a s and two p orbitalsled to 3 sp2 hybrid orbitals for bonding.

Compounds involving sp2 hybrid orbitals:BF3, CO3

2, H2CO, H2C=CH2, NO3, etc

Nov. 25


An example of using sp2 hybrid orbitals

__ orbitals for bonding?

Dipole moment = ____?

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Bonding of H2C=CH2 molecules

Utilizing the sp2 hybrid orbitals, each C atom form two HC s bondsfor a total of 4 s HC bonds. The CC s bond is common to both Catoms.

A CC p bond is formed due to overlap of p orbitals from each ofthe C atoms.

Hybrid orbitals (sp2) for HCand CC s bond

Overlap of p orbital for CC p bond

C2s 2p 2p 2p

sp2 sp2 sp2 2p


The sp3 Hybridized OrbitalsGround state and excited state electronicconfiguration of C

_ _ _ _

_ _ __

The hybridization of a s and three p orbitalsled to 4 sp3 hybrid orbitals for bonding.

Compounds involving sp3 hybrid orbitals:CF4, CH4, : NH3, H2O::, SiO4

4, SO42, ClO4

,etc

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Failures of Valence Bond Theory

(1) Assumed the electrons were localized; did notaccount for resonance.

(2) Assumed radicals do not exist; all electronswere paired.

(3) Gave no information on bond energies; did notexplain the following general trends:

(i) An increase in bond energy correspondedto an increase in bond order

(ii) A decrease in bond length correspondsto an increase in bond order.

The Delocalized Approach to Bonding: Molecular Orbital Theory

The localized models for bonding we have examined (Lewis and VBT) assume thatall electrons are restricted to specific bonds between atoms or in lone pairs. Incontrast, the delocalized approach to bonding places the electrons in MolecularOrbitals (MOs) - orbitals that encompass the entire molecule and are not associatedwith any particular bond between two atoms. In most cases, MO theory provides uswith a more accurate picture of the electronic structure of molecules and it gives usmore information about their chemistry (reactivity).

Two (sp-1s) Be-H bonds.

Be HH

sp 1s

Localized Bonding

1

2

Delocalized Bonding

MO diagram for BeH2

The two bondingMOs in BeH2

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Molecular Orbital Theory

Molecular orbitals are constructed from the available atomic orbitals in a molecule. This isdone in a manner similar to the way we made hybrid orbitals from atomic orbitals in VBT.That is, we will make the MOs for a molecule from Linear Combinations of Atomic Orbitals(LCAO). In contrast to VBT, in MO theory the atomic orbitals will come from several or allof the atoms in the molecule. Once we have constructed the MOs, we can build an MOdiagram (an energy level diagram) for the molecule and fill the MOs with electrons using theAufbau principle.

Some basic rules for making MOs using the LCAO method:

1) n atomic orbitals must produce n molecular orbitals (e.g. 8 AOs must produce 8MOs).

2) To combine, the atomic orbitals must be of the appropriate symmetry.

3) To combine, the atomic orbitals must be of similar energy.

4) Each MO must be normal and must be orthogonal to every other MO.

+ +

1H 1s Be 2s H 1s

This produces an MO over themolecule with a node between theatoms (it is also symmetrical aboutthe H-H axis). This is known as anantibonding MO and is given thelabel * because of its symmetry.The star indicates antibonding.


Diatomic molecules: The bonding in H2HA HB

Each H atom has only a 1s orbital, so to obtain MOs for the H2 molecule, we mustmake linear combinations of these two 1s orbitals.

Consider the addition of the two 1s functions (with the same phase):

1sA 1sB

+

This produces an MO around both Hatoms and has the same phaseeverywhere and is symmetricalabout the H-H axis. This is knownas a bonding MO and is given thelabel because of its symmetry.

Consider the subtraction of the two 1s functions (with the same phase):

1sA 1sB

-

Remember that: - +is equivalent to:

= 0.5 (1sA + 1sB)

* = 0.5 (1sA - 1sB)

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Molecular Orbital TheoryDiatomic molecules: The bonding in H2

HA HBYou may ask Why is called bonding and * antibonding? What does this mean?How do you know the relative energy ordering of these MOs?Remember that each 1s orbital is an atomic wavefunction (1s) and each MO is also a wave

function, , so we can also write LCAOs like this:

Remember that the square of a wavefunction gives us a probability density function, so thedensity functions for each MO are:

= 1 = 0.5 (1sA + 1sB) * = 2 = 0.5 (1sA - 1sB)

(1)2 = 0.5 [(1sA1sA) + 2(1sA1sB) +(1sB 1sB)]

(2)2 = 0.5 [(1sA1sA) - 2(1sA1sB) +(1sB 1sB)]and

The only difference between the two probablility functions is in the cross term (in bold), whichis attributable to the kind and amount of overlap between the two 1s atomic wavefunctions (theintegral (1sA 1sB) is known as the overlap integral, S). In-phase overlap makes bondingorbitals and out-of-phase overlap makes antibonding orbitalswhy?

(1)2 = 0.5 [(1sA1sA) + 2(1sA1sB) +(1sB 1sB)]

(2)2 = 0.5 [(1sA1sA) - 2(1sA 1sB) +(1sB 1sB)]

Let us discuss the answer to the last questions

Diatomic molecules: The bonding in H2HA HB

Consider the electron density between the two nuclei: the red curve is the probability densityfor HA by itself, the blue curve is for HB by itself and the brown curve is the density youwould get for 1sA + 1sB without any overlap: it is just (1sA)

2 + (1sB)2 {the factor of is to

put it on the same scale as the normalized functions}.

The increase of electron density between the nuclei from the in-phase overlap reduces theamount of repulsion between the positive charges. This means that a bonding MO will belower in energy (more stable) than the corresponding antibonding MO or two non-bonded Hatoms.

The function (1)2 is shown in green

and has an extra + 2 (1sA 1sB) ofelectron density than the situation whereoverlap is neglected.

The function (1)2 is shown in pink and

has less electron density between thenuclei {- 2(1sA1sB)} than the situationwhere overlap is neglected.

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Molecular Orbital TheoryDiatomic molecules: The bonding in H2

HA HBSo now that we know that the bonding MO is more stable than the atoms by themselvesand the * antibonding MO, we can construct the MO diagram.

H

En

ergy

HH2

1s 1s

g

*u

To clearly identify the symmetry of thedifferent MOs, we add the appropriatesubscripts g (symmetric with respect to theinversion center) and u (anti-symmetric withrespect to the inversion center) to the labelsof each MO.

The electrons are then added to the MOdiagram using the Aufbau principle.

Note:The amount of stabilization of the MO (indicated by the red arrow) is slightly less than theamount of destabilization of the * MO (indicated by the blue arrow) because of the pairing ofthe electrons. For H2, the stabilization energy is 432 kJ/mol and the bond order is 1.

Bond Order =(# of e 's in bonding MO's) - (# of e 's in antibonding MO's)

2

- -

Molecular Orbital TheoryDiatomic molecules: The bonding in He2

He also has only 1s AO, so the MO diagram for the molecule He2 can be formed in anidentical way, except that there are two electrons in the 1s AO on He.

He

En

ergy

HeHe2

1s 1s

g

*u

Molecular Orbital theory is powerful because it allows us to predict whethermolecules should exist or not and it gives us a clear picture of the of the electronicstructure of any hypothetical molecule that we can imagine.

The bond order in He2 is (2-2)/2 = 0, so themolecule will not exist.

However the cation [He2]+, in which one of

the electrons in the * MO is removed,would have a bond order of (2-1)/2 = , sosuch a cation might be predicted to exist.The electron configuration for this cationcan be written in the same way as we writethose for atoms except with the MO labelsreplacing the AO labels:

[He2]+ = 2*1

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This produces an MO over themolecule with a node between the Fatoms. This is thus an antibondingMO of *u symmetry.

Molecular Orbital TheoryDiatomic molecules: The bonding in F2

Each F atom has 2s and 2p valence orbitals, so to obtain MOs for the F2 molecule, we mustmake linear combinations of each appropriate set of orbitals. In addition to the combinationsof ns AOs that weve already seen, there are now combinations of np AOs that must be

considered. The allowed combinations can result in the formation of either or typebonds.

2pzA

+

This produces an MO around both Fatoms and has the same phaseeverywhere and is symmetricalabout the F-F axis. This is thus abonding MO of g symmetry.

* = 0.5 (2pzA + 2pzB)2pzB

2pzA

-

= 0.5 (2pzA - 2pzB)2pzB

The combinations of symmetry:

This produces an MO over themolecule with a node on the bondbetween the F atoms. This is thus abonding MO of u symmetry.


Diatomic molecules: The bonding in F2

2pyA

+

This produces an MO around both Fatoms that has two nodes: one on thebond axis and one perpendicular tothe bond. This is thus anantibonding MO of *g symmetry.

= 0.5 (2pyA + 2pyB)2pyB

-

* = 0.5 (2pyA - 2pyB)

The first set of combinations of symmetry:

2pyA 2pyB

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

This produces an MO over themolecule with a node on the bondbetween the F atoms. This is thus abonding MO of u symmetry.


Diatomic molecules: The bonding in F2

2pxA

+

This produces an MO around both Fatoms that has two nodes: one on thebond axis and one perpendicular tothe bond. This is thus anantibonding MO of *g symmetry.

= 0.5 (2pxA + 2pxB)

2pxB

-

* = 0.5 (2pxA - 2pxB)

2pxA 2pxB

F

En

ergy

FF2

2s 2s

2g

2*u

2p

2p

3g

3*u

1u

1*g

Molecular Orbital TheoryMO diagram for F2

(px,py)pz

Atypical diagram:

Only shows the MOs derived fromthe valence electrons because thepair of MOs from the 1s orbitalsare much lower in energy and canbe ignored.

the atomic 2p orbitals are actuallyall the same energy for two non-interacting F atoms.

Notice that there is no mixing ofAOs of the same symmetry from asingle F atom because there is asufficient difference in energybetween the 2s and 2p orbitals in F.

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

Note: for the sake of simplicity,electrons are not shown in theatomic orbitals.

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F

En

ergy

FF2

2s 2s

2g

2*u

2p

2p

3g

3*u

1u

1*g

Molecular Orbital TheoryMO diagram for F2

(px,py)pz

Another key feature of suchdiagrams is that the -type MOsformed by the combinations of thepx and py orbitals make degeneratesets (i.e. they are identical inenergy).

The highest occupied molecularorbitals (HOMOs) are the 1*g pair- these correspond to some of thelone pair orbitals in the moleculeand this is where F2 will react as anelectron donor.

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

HOMO

LUMO

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lecture on vbt and mo

Documents

p bondoverlap

p orbitalsp3

pi p bonding

hybrid orbitals sp

s bonds

h h bond

sp2 hybrid orbitals

sp3d hybrid orbitals