CarbonCarbon spsp hybridshybrids:: AcetyleneAcetylene andand thethe TripleTriple bondbond

CC2HH2 isis HH--CCCC--HH

FormForm spsp onon eacheach CC leavingleaving 2p2px,, 2p2py “unused”“unused”

H - sp C sp + +-+ sp C sp H

PredictsPredicts linearlinear structure.structure. AboveAbove areare allall σσ bondsbonds H-C-C-H Uses up 2 valence e- for each C in sp (and 2 from 1s H). Leaves 2 valence e - for each C unused.

2py 2py

Put last valence 2px e- into ππ orbitals sp formed from H C C H 2px, 2py 2px - - 2 e in πx 2 e in πy

Gives two π bonds connecting carbon atoms. π bonds are at right angles to each other. Total C-C bonds are now 3, one σσ, 2 π

Short Comparison of Bond Order, Bond Length, Bond Energy

C-C C-C C-C Molecule Bond Order Bond Length Bond E, kcal/mole σσ Ethane, C2H6 1 (1 ) 1.54Å 83 σσ Ethylene, C2H4 2 (1 , 1π) 1.35Å 125 σσ Acetylene, C2H2 3 (1 , 2π) 1.21Å 230 ConjugationConjugation andand DelocalizationDelocalization ofof ElectronsElectrons andand BondsBonds

Although energy of π* in ethylene < 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 2 essentially independent double bonds.

C=C-C=C-C=C polyene

DoubleDouble bondsbonds ALTERNATE!ALTERNATE! Could draw ππ bonds between any 2 C’s

ππ* bonds C C C C C C drawn are not unique!

ψψ This gives delocalized structure MO = (Const)[2py(1) + 2py(2) + 2py(3) + 2py(4) +2py(5) + 2py(6) +………]. Add 2py Atomic Orbitals on each C C C C C C C

Delocalized Molecular Orbital spans many atoms Delocalizing electrons generally lowers their energy. ππ StatesStates inin thethe 44 CarbonCarbon PolyenePolyene ButadieneButadiene EnergyEnergy H2C=CH-HC=CH2 π* antibonding levels

E=hν (photon) 2p orbitals (one each on 4 carbons)

π bonding νν νν levels E=h for butadiene << E=h for ethylene Molecular Orbital Energies

4 Delocalized ππ Bonding C C C C States Constructed From 4 2py C atomic orbs Benzene C6H6. This is a planar closed ring compound of carbon which has sp2 carbon hybrids:

H H

C C Electron 120˚ Delocalization

H C sp2 C H in Carbon Ring Compounds C C

H H

Each C uses 3 of 4 valence e- in sp2 hybrid bond structure to make 1 C-H bond 2 C-C bonds. AreAre leftleft withwith 11 valencevalence ee- andand aa 2p2p orbitalorbital forfor eacheach CC

ππ oror

Can make 3 ππ bonds in two different ways. Called two resonance structures. System alternates betweenbetween thethe twotwo differentdifferent forms.forms.

ThisThis is islocalizedlocalizedlocalizedpicture!picture! BenzeneBenzene CC6HH6 planarplanar DelocalizedDelocalized PicturePicture closedclosed ringring compoundcompound 2 withwith spsp carboncarbon hybridshybrids H H leavesleaves 66 valencevalence electronselectrons + + and 6 p orbitals unused – – and 6 p orbitals unused + + H H – – + + CanCan formform ππ bondsbonds withwith thesethese pp orbitalsorbitals.. – – H H ψψ MO = (Const)[2py(1) + 2py(2) + 2p (3) + 2p (4) +2p (5) y y y However,However,thesethese ππ bondsbonds + 2py(6)] Add 6 2py Atomic havehave thethe abilityability toto delocalizedelocalize Orbitals on each C aroundaround thethe entireentire There are 6 such combinations! ringring ofof 66 carbonscarbons CanCan thereforetherefore thinkthink ofof electronselectrons asas delocalizeddelocalized

ψψ MO = (Const)[2py(1) + 2py(2) + 2py(3) + 2py(4) +2py(5) + 2py(6)] Add 6 2py Atomic Orbitals on each C

AndAnd oftenoften seesee

symbolsymbol forfor CC6HH6 asas 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). → BeginningsBeginnings Energy ofof aa “conduction”“conduction” ↓↓ bandband + Antibonding orbitals “Band“Band 0 (isolated C 2p) ←← π b π b 2 3 Gap”Gap” _ Bonding orbitals π b 1 ↑↑ BeginningsBeginnings ofof aa “valence”“valence” bandband Energy of 3 π bonding orbitals lower than energy of 2p (isolated) orbitals 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 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, 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. Actually find benzene is more stable than this! DelocalizationDelocalization ofof ee- overover 66 orbitalsorbitals givesgives setset ofof 33 M.O.’sM.O.’s whichwhich havehave lowerlower energyenergy thanthan 33 ππ CC--CC bondsbonds onon ethylene.ethylene. i.e.i.e.→→

b 2 b 2 b 2 2 Energy of (π1 ) + (π2 ) + (π3 ) < Energy of 3 π ethylene

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

b 2 b 2 b 2 ≅≅ 2 i.e. Energy of (π1 ) + (π2 ) + (π3 ) Energy of 44 π eth. b 2 b 2 ≅ 2 More accurately: Energy of (π2 ) = (π3 ) π eth b 2 ≅ 2 And: Energy of (π1 ) 2 π eth

BeginningsBeginnings Energy ofof aa “conduction”“conduction” ↓↓ bandband + Antibonding orbitals “Band“Band 0 (isolated C 2p) ←←

b 2∆E b π2 Eth π3 Gap”Gap” _ Bonding orbitals π b 1 ↑↑ BeginningsBeginnings ofof aa “valence”“valence” bandband 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 orbitals map into molecular orbitals, one for one. Because there are so many “molecular” energy levels (one for each molecular orbital), levels form a band in energy space →

E

Energy 1023 equivalent Band of 1023 delocalized Atomic molecular orbitals of orbitals slightly diffent energies Delocalized Bonding in Metals

Consider Lithium metal. The Lithium atom has the atomic configuration 1s22s1 with the 2p level unfilled.

As in any molecule with a filled core shell like 1s2, these electrons do not participate in bonding. Still, they form a delocalized band with 1023 molecular orbitals that are completely filled.

The valencevalence electrons 2s1 and the unfilled 2p orbitals are more interesting. The 1023 2s atomic orbitals form a band of 1023 “molecular” orbitals. This band is only half filled because each 2s1 orbital has only one e- .

There are three 2p orbitals on each atom leading to a band of 3××1023 molecular orbitals. This band is “empty” but overlaps in energy the 2s band →→ p p 1 and 2 and 2 2s s s 2 molecular molecular molecular molecular Lithium 1s in band in band in band in band delocalized delocalized delocalized delocalized s s orbitals orbitals delocalized delocalized delocalized delocalized orbitals orbitals orbitals orbitals p p Overlapping2 of orbital bands Overlapping2 of orbital bands in band in band 2 2 23 23 filled 1 filled filled 1 filled half filled 2s 2s half filled 23 half filled 2s 2s half filled 23 23 23 Molecular Molecular 10 Molecular Molecular 10 orbitals 3 x 10 orbitals 3 x 10 10 molecular 10 molecular 23 23 23 23 23 23 10 10 10 10 orbitals orbitals 3x10 3x10

orbitals orbitals 1s Atomic 1s Atomic 1s Atomic 1s Atomic equivalent equivalent orbitals

orbitals 2s Atomic 2s Atomic 2s Atomic 2s Atomic equivalent equivalent equivalent equivalent 2p Atomic 2p Atomic 2p Atomic 2p Atomic

Energy, E Energy, Energy, E Energy,