- H. Predicts linear structure. Above are all σ bonds

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1 arbon sp hybrids: : Acetylene and the Triple bond 2 2 is - - Form sp on each leaving 2p x, 2p y unused - sp sp + + sp sp - Predicts linear structure. Above are all σ bonds

2 --- Uses up 2 valence e - for each in sp (and 2 from 1s ). Leaves 2 valence e - for each unused. Put last valence 2p y 2p y 2p x e - into π orbitals formed from 2p x, 2p y 2p x sp

3 2 e - in π x 2 e - in π y Gives two π bonds connecting carbon atoms. π bonds are at right angles to each other. Total - bonds are now 3, one σ,, 2 π Short omparison of Bond Order, Bond Length, Bond Energy Molecule Bond Order Bond Length Bond E, kcal/mole Ethane, (1 σ) 1.54Å 83 Ethylene, (1σ,, 1π) Å 125 Acetylene, (1σ,, 2π) Å 230

4 onjugation and Delocalization of Electrons and Bonds 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). onjugated polyenes: =--=- 2 essentially independent double bonds. =-=-= polyene Double bonds ALTERNATE!

5 ould draw π bonds between any 2 s π * bonds drawn are not unique! This gives delocalized structure ψ MO = (onst( onst)[2p y (1) + 2p y (2) + 2p y (3) + 2p y (4) +2p y (5) + 2p y (6) + ]. Add 2p y Atomic Orbitals on each Delocalized Molecular Orbital spans many atoms Delocalizing electrons generally lowers their energy.

6 Energy π States in the 4 arbon Polyene Butadiene 2 =-= = 2 π* antibonding levels 2p orbitals (one each on 4 carbons) E=hν (photon) E=hν for butadiene << E=hν for ethylene Molecular Orbital Energies π bonding levels 4 Delocalized π Bonding States onstructed From 4 2py atomic orbs

7 Benzene 6 6. This is a planar closed ring compound of carbon which has sp 2 carbon hybrids: 120 sp 2 Electron Delocalization in arbon Ring ompounds Each uses 3 of 4 valence e - in sp 2 hybrid bond structure to make 1 - bond 2 - bonds.

8 Are left with 1 valence e - and a 2p orbital for each π or an make 3 π bonds in two different ways. alled two resonance structures. System alternates between the two different forms. This is localized picture! This is islocalized picture!

9 Benzene 6 6 planar closed ring compound with sp 2 carbon hybrids leaves 6 valence electrons and 6 p orbitals unused ψ MO an form π bonds with these p orbitals. MO = (onst( onst)[2p y (1) + 2p y (2) + 2p y (3) + 2p y (4) +2p y (5) + 2p y (6)] Add 6 2p y Atomic Orbitals on each There are 6 such combinations! Delocalized Picture owever,these π bonds have the ability to delocalize around the entire ring of 6 carbons +

10 an therefore think of electrons as delocalized ψ MO MO = (onst( onst)[2p y (1) + 2p y (2) + 2p y (3) + 2p y (4) +2p y (5) + 2p y (6)] Add 6 2p y Atomic Orbitals on each And often see symbol for 6 6 as

11 ircle indicates this delocalization. This delocalized orbital comes from adding all 2p orbitals in phase ( + on top) and ( - on bottom). an actually form a total of 6 delocalized M.O. s for benzene (6 2p Atomic Orbital s 6 M.O. s). Energy + _ π 2 b π 1 b 0 (isolated 2p) π 3 b Beginnings of a conduction band Antibonding orbitals Bonding orbitals Band Gap Beginnings of a valence band

12 Energy of 3 π bonding orbitals lower than energy of 2p (isolated) orbitals on from which they come. π antibonding are higher than isolated 2p. When put 6 e - into delocalized orbital get ~ (1/2) π bond per - pair (1e - in π). Each - pair has one σ and (1/2) π. Find experimentally all - bonds are of equal length (1.390Å) and between that of - bond and = σ, π bond lengths. If now consider bond energy of benzene, might guess it equals 6 - sigma bonds, 6 - sigma bonds, and 3 (-) π bonds.

13 Actually find benzene is more stable than this! Delocalization of e - over 6 orbitals gives set of 3 M.O. s which have lower energy than 3 π - bonds on ethylene. i.e. Energy of (π 1b ) 2 + (π 2b ) 2 + (π 3b ) 2 < Energy of 3 π 2 ethylene Difference is ~ 160 kjoules/mole. This turns out to be about the energy of one whole ethylene π bond. i.e. Energy of (π 1b ) 2 + (π 2b ) 2 + (π 3b ) 2 Energy of 4 π 2 eth.

14 More accurately: Energy of (π 2b ) 2 = (π 3b ) 2 π 2 eth And: Energy of (π 1b ) 2 2 π 2 eth Energy + _ π 2 b π 1 b 2 E Eth 0 (isolated 2p) π 3 b Beginnings of a conduction band Antibonding orbitals Bonding orbitals Band Gap Beginnings of a valence band

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

16 Because there are so many molecular energy levels (one for each molecular orbital), levels form a band in energy space E Energy equivalent Atomic orbitals Band of delocalized molecular orbitals of slightly diffent energies

17 Delocalized Bonding in Metals onsider Lithium metal. The Lithium atom has the atomic configuration 1s 2 2s 1 with the 2p level unfilled. As in any molecule with a filled core shell like 1s 2, these electrons do not participate in bonding. Still, they form a delocalized band with molecular orbitals that are completely filled. The valence electrons 2s 1 and the unfilled 2p orbitals are more interesting. The s atomic orbitals form a band of molecular orbitals.. This band is only half filled because each 2s 1 orbital has only one e -. There are three 2p orbitals on each atom leading to a band of molecular orbitals.. This band is empty but overlaps in energy the 2s band

18 Energy, E Energy, E 3x10 23 equivalent 2p Atomic orbitals equivalent 2s Atomic orbitals 3 x p delocalized molecular orbitals in band Overlapping of 2s 2 and 2p2 orbital bands half filled 2s delocalized molecular orbitals in band Lithium 1s 2 2s equivalent 1s Atomic orbitals filled 1s1 delocalized Molecular orbitals in band