[PPT] - Carbon sp sp hybrids hybrids: Acetylene and the : Acetylene and PowerPoint Presentation

SLIDE 1

C C C C

H H H H

Carbon Carbon sp sp hybrids hybrids: Acetylene and the : Acetylene and the Triple bond Triple bond C C2

2H

H2

2 is H

is H-

CC

CC-

H

H

Form Form sp sp on each C leaving 2p

n each C leaving 2px

x, 2p

, 2py

y “unused”

“unused” Predicts linear structure. Above are all Predicts linear structure. Above are all σ σ σ σ σ σ σ σ bonds bonds

sp sp sp sp sp sp sp sp

+ +

+

+

SLIDE 2

C C C C

2p 2px

x

2p 2px

x

2p 2py

y

2p 2py

y

sp sp H H-

C

C-

C

C-

H

H Uses up 2 valence Uses up 2 valence e e-

for each C in

for each C in sp sp (and 2 from 1s H). (and 2 from 1s H). Leaves 2 valence Leaves 2 valence e e -

for each C unused.

for each C unused. Put last valence Put last valence e e-

into

into π

π π π π π π π orbitals

rbitals

formed from formed from 2p 2px

x, 2p

, 2py

y

H H H H

SLIDE 3

2 2 e e-

in π

in πx

x

2 2 e e-

in π

in πy

y

Gives two π bonds connecting carbon atoms. π bonds are at right Gives two π bonds connecting carbon atoms. π bonds are at right angles to each other. Total C angles to each other. Total C-

C bonds are now 3, one

C bonds are now 3, one σ σ σ σ σ σ σ σ, 2 , 2 π π Short Comparison of Bond Order, Bond Length, Bond Energy Short Comparison of Bond Order, Bond Length, Bond Energy C C-

C

C C C-

C

C C C-

C

C Molecule Molecule Bond Order Bond Order Bond Length Bond Length Bond E, Bond E, kcal/mole kcal/mole Ethane, C Ethane, C2

2H

H6

6

1 (1 1 (1 σ σ σ σ σ σ σ σ) ) 1.54Å 1.54Å 83 83 Ethylene, C Ethylene, C2

2H

H4

4

2 (1 2 (1σ σ σ σ σ σ σ σ, 1 , 1π π) ) 1.35 1.35Å Å 125 125 Acetylene, C Acetylene, C2

2H

H2

2

3 (1 3 (1σ σ σ σ σ σ σ σ, 2 , 2π π) ) 1.21 1.21Å Å 230 230

SLIDE 4

Although energy of π* in ethylene < σ σ σ σ, conjugated polylenes have even lower energy π levels. These absorb light at longer wavelength- sometimes even in visible (human eye’s light perception). Conjugated polyenes: C=C-C=C-C=C polyene C=C-C-C=C-C 2 essentially independent double bonds.

Conjugation and Conjugation and Delocalization Delocalization of

f

Electrons and Bonds Electrons and Bonds

Double bonds ALTERNATE! Double bonds ALTERNATE!

SLIDE 5

Could draw Could draw π

π π π π π π π bonds between any 2 C’s

bonds between any 2 C’s This gives This gives delocalized delocalized structure structure C C C C C C C C C C C C

π π π π π π π π*

* bonds

bonds drawn are drawn are not unique! not unique! Delocalizing Delocalizing electrons generally lowers their energy. electrons generally lowers their energy. C C C C C C C C C C C C ψ ψ ψ ψ ψ ψ ψ ψMO

MO = (

= (Const Const)[2p )[2py

y(1) + 2p

(1) + 2py

y(2)

(2) + 2p + 2py

y(3) + 2p

(3) + 2py

y(4) +2p

(4) +2py

y(5)

(5) + 2p + 2py

y(6) +………]. Add 2p

(6) +………]. Add 2py

y

Atomic Atomic Orbitals Orbitals on each C

n each C

Delocalized Delocalized Molecular Molecular Orbital spans many atoms Orbital spans many atoms

SLIDE 6

π π π π π π π π States in the 4 Carbon

States in the 4 Carbon Polyene Polyene Butadiene Butadiene

2p orbitals

(one each on 4 carbons)

π π π π bonding

levels

π π π π* antibonding

levels E=hν

ν ν ν (photon)

E=h E=hν

ν ν ν ν ν ν ν for butadiene << E=h

for butadiene << E=hν

ν ν ν ν ν ν ν for ethylene

for ethylene C C C C Molecular Molecular Orbital Energies Orbital Energies

Energy Energy

4 4 Delocalized Delocalized π π π π π π π π Bonding Bonding States Constructed States Constructed From 4 2py From 4 2py C atomic orbs C atomic orbs H H2

2C=CH

C=CH-

HC=CH

HC=CH2

2

SLIDE 7

C C C C C C H H H H H H H H H H H H sp sp2

2

120˚ 120˚

Benzene Benzene C C6

6H

H6

6. This is a

. This is a planar planar closed ring compound of closed ring compound of carbon which has carbon which has sp sp2

2 carbon hybrids:

carbon hybrids: Each C uses 3 of 4 valence Each C uses 3 of 4 valence e e-

in sp

in sp2

2 hybrid bond structure

hybrid bond structure to make 1 C to make 1 C-

H bond 2 C

H bond 2 C-

C bonds.

C bonds. Electron Electron Delocalization Delocalization in Carbon in Carbon Ring Ring Compounds Compounds

SLIDE 8

π π π π π π π π

r
r

Are left with 1 valence e Are left with 1 valence e-

and a 2p orbital for each C

and a 2p orbital for each C

Can make 3 Can make 3 π

π π π π π π π bonds in two different ways. Called two

bonds in two different ways. Called two resonance resonance structures.

structures. System alternates between the two different forms.

System alternates between the two different forms. This is localized picture! This is This is localized

localized picture!

picture!

SLIDE 9

– – – – – – – – – – – –

H H H H H H H H H H H H

+ + + + + +

Benzene Benzene C C6

6H

H6

6 planar

planar closed ring compound closed ring compound with with sp sp2

2 carbon hybrids

carbon hybrids leaves 6 valence electrons leaves 6 valence electrons and 6 p and 6 p orbitals

rbitals unused

unused

Can form Can form π π π π π π π π bonds with bonds with these p these p orbitals

rbitals.

. However, However,these these π π π π π π π π bonds bonds have the ability to have the ability to delocalize

delocalize

around the entire around the entire ring of 6 carbons ring of 6 carbons

ψ ψ ψ ψ ψ ψ ψ ψMO

MO = (

= (Const Const)[2p )[2py

y(1) + 2p

(1) + 2py

y(2)

(2) + 2p + 2py

y(3) + 2p

(3) + 2py

y(4) +2p

(4) +2py

y(5)

(5) + 2p + 2py

y(6)]

(6)] Add Add 6 6 2p 2py

y Atomic

Atomic Orbitals Orbitals on each C

n each C

Delocalized Delocalized Picture Picture

There are 6 such combinations! There are 6 such combinations!

SLIDE 10

Can therefore think of Can therefore think of electrons as electrons as delocalized delocalized And often see And often see symbol for C symbol for C6

6H

H6

6 as

as

ψ ψ ψ ψ ψ ψ ψ ψMO

MO = (

= (Const Const)[2p )[2py

y(1) + 2p

(1) + 2py

y(2)

(2) + 2p + 2py

y(3) + 2p

(3) + 2py

y(4) +2p

(4) +2py

y(5)

(5) + 2p + 2py

y(6)]

(6)] Add Add 6 6 2p 2py

y Atomic

Atomic Orbitals Orbitals on each C

n each C

SLIDE 11

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ Beginnings Beginnings

f a “valence” band
f a “valence” band

Beginnings Beginnings

f a “conduction”
f a “conduction”

↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ band band

Energy Energy + + _ _ π π1

1 b b

π π3

3 b b

π π2

2 b b

0 (isolated C 2p) 0 (isolated C 2p) Antibonding orbitals Antibonding orbitals Bonding Bonding orbitals

rbitals

“Band “Band

← ← ← ← ← ← ← ←

Gap” Gap”

Circle indicates this delocalization. This delocalized orbital comes from adding all 2p orbitals in phase ( + on top) and ( - on bottom). Can actually form a total of 6 delocalized M.O.’s for benzene (6 2p Atomic Orbital’s → → → → 6 M.O.’s). → → → →

SLIDE 12

Energy of 3 π bonding orbitals lower than energy of 2p (isolated)

rbitals on C from which they come. π antibonding are higher

than isolated 2p. When put 6 e- into delocalized orbital get ~ (1/2) π bond per C-C pair (1e- in π). Each C-C pair has one σ σ σ σ and (1/2) π. Find experimentally all C-C bonds are of equal length (1.390Å) and between that of C-C bond and C=C σ σ σ σ, π bond lengths. If now consider bond energy of benzene, might guess it equals 6 C-C sigma bonds, 6 C-H sigma bonds, and 3 (C-C) π bonds.

SLIDE 13

Actually find benzene is Actually find benzene is more more stable than this! stable than this!

Delocalization Delocalization of

f e

e-

over 6
ver 6 orbitals
rbitals gives set

gives set

f 3 M.O.’s which have lower energy than
f 3 M.O.’s which have lower energy than

3 π C 3 π C-

C bonds on ethylene.

C bonds on ethylene. i.e. i.e.→ → → → → → → →

Energy of (π Energy of (π1

1b b)

)2

2 + (π

+ (π2

2b b)

)2

2 + (π

+ (π3

3b b)

)2

2 < Energy of 3 π

< Energy of 3 π2

2 ethylene ethylene

Difference is ~ 160 Difference is ~ 160 kjoules kjoules/mole. This turns out to be about the /mole. This turns out to be about the energy of one whole ethylene π bond. energy of one whole ethylene π bond. i.e. Energy of (π i.e. Energy of (π1

1b b)

)2

2 + (π

+ (π2

2b b)

)2

2 + (π

+ (π3

3b b)

)2

2 ≅

≅ ≅ ≅ ≅ ≅ ≅ ≅ Energy of Energy of 4

4 π

π2

2 eth. eth.

SLIDE 14

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ Beginnings Beginnings

f a “valence” band
f a “valence” band

Beginnings Beginnings

f a “conduction”
f a “conduction”

↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ band band

Energy Energy + + _ _ π π1

1 b b

π π3

3b b

π π2

2b b

0 (isolated C 2p) 0 (isolated C 2p) Antibonding orbitals Antibonding orbitals Bonding Bonding orbitals

rbitals

“Band “Band

← ← ← ← ← ← ← ←

Gap” Gap”

2 2∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆E EEth

Eth

More accurately: Energy of (π2

b)2 = (π3 b)2 ≅

≅ ≅ ≅ π2

eth

And: Energy of (π1

b)2 ≅

≅ ≅ ≅ 2 π2

eth

SLIDE 15

Bonding in Solids

Think of a solid as a single giant molecule with roughly 1023 atoms. Electrons can travel over the whole solid via delocalized orbitals that cover all 1023 atoms. Consider first the situation where each individual atom of the solid has just one orbital contributing to bonding. In this case must get 1023 molecular orbitals because atomic

rbitals map into molecular orbitals, one for one.

SLIDE 16

Because there are so many “molecular” energy levels (one for each molecular orbital), levels form a band in energy space →

→ → →

1023 equivalent Atomic

rbitals

Band of 1023 delocalized molecular orbitals of slightly diffent energies Energy Energy E E

SLIDE 17

Delocalized Delocalized Bonding in Metals Bonding in Metals Consider Lithium metal. The Lithium atom has the atomic Consider Lithium metal. The Lithium atom has the atomic configuration 1s configuration 1s2

22s

2s1

1 with the 2p level unfilled.

with the 2p level unfilled. As in any molecule with a filled core shell like 1s As in any molecule with a filled core shell like 1s2

2,

, these electrons do not participate in bonding. Still, they these electrons do not participate in bonding. Still, they form a form a delocalized delocalized band with 10 band with 1023

23 molecular

molecular orbitals

rbitals that

that are completely filled. are completely filled. The The valence

valence electrons 2s

electrons 2s1

1 and the unfilled 2p

and the unfilled 2p orbitals

rbitals are more

are more

interesting. The 10
interesting. The 1023

23 2s atomic

2s atomic orbitals

rbitals form a band of

form a band of 10 1023

23 “molecular”

“molecular” orbitals

rbitals. This band is only

. This band is only half half filled filled because each 2s because each 2s1

1 orbital has only

rbital has only one
ne e

e-

.

. There are three 2p There are three 2p orbitals

rbitals on each atom leading to
n each atom leading to

a band of 3 a band of 3× × × × × × × ×10 1023

23 molecular

molecular orbitals

rbitals. This band is “empty”

. This band is “empty” but overlaps in energy the 2s band but overlaps in energy the 2s band →

→ → → → → → →

SLIDE 18

Energy, E Energy, E

10 1023

23

equivalent equivalent 2s Atomic 2s Atomic

rbitals
rbitals

3x10 3x1023

23

equivalent equivalent 2p Atomic 2p Atomic

rbitals
rbitals

10 1023

23

equivalent equivalent 1s Atomic 1s Atomic

rbitals
rbitals

10 1023

23 half filled 2s

half filled 2s delocalized delocalized molecular molecular orbitals

rbitals in band

in band Overlapping of 2 Overlapping of 2s s and 2 and 2p p

rbital bands
rbital bands

3 x 10 3 x 1023

23 2

2p p delocalized delocalized molecular molecular

rbitals
rbitals in band

in band 10 1023

23 filled 1

filled 1s s delocalized delocalized Molecular Molecular orbitals

rbitals in band

in band