1 + s 12 1 e 1 = 1 = c 1 1 + c 1 2 1 - s 12 1 e 2 = - 2 = c 1 1 - c 1 2 bonding antibonding
DESCRIPTION
Ethylene system of ethyleneTRANSCRIPT
![Page 1: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/1.jpg)
1 + S12
1E1 =
1 = c11 + c12
1 - S12
1E2 = -
2 = c11 - c12
bonding
antibonding
![Page 2: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/2.jpg)
Let overlap term go to zeroOverlap term is non zero
![Page 3: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/3.jpg)
C CH
H H
HEthylene
system of ethylene
![Page 4: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/4.jpg)
H2 C2H4
![Page 5: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/5.jpg)
antibondingempty orbital
bondingfille with 2 e-
![Page 6: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/6.jpg)
Now let us look at a more complicated system.
Three Orbitals!
H
H
H H
H
H
H
HH
H
Allyl anion
![Page 7: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/7.jpg)
1 23 How do we calculate
the energies and coefficientsof the MO’s?
We are going to use the LCAOapproximation to make threeMO’s.
Use Symmetry!
The ends are the same so they must contibuteequally to any MO. So we can make linear combinationswhere atoms one and three contribute equally.1 = pz1 + pz3 2 = pz1 - pz3
3 = pz2 The second carbon is unique.
![Page 8: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/8.jpg)
pza Ĥ pza = E = = 0Coulomb integral
pza Ĥ pzb = Eint = Interaction integral
Only if the two p orbitals are adjacentotherwise Interaction is 0.
pza pza = 1normalized
pza pzb = 0assume overlap = 0
Huckel Approximation
![Page 9: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/9.jpg)
1 23 How do we calculate
the energies and coefficientsof the MO’s?
We are going to use the LCAOapproximation to make threeMO’s.
Use Symmetry!
The ends are the same so they must contibuteequally to any MO. So we can make linear combinationswhere atoms one and three contribute equally.1 = pz1 + pz3 2 = pz1 - pz3
3 = pz2 The second carbon is unique.
![Page 10: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/10.jpg)
1 23
1 = pz1 + pz3
We need to normalizeour LCAOs 1
2 = 1
N2(pz1 + pz3 ) (pz1 + pz3 ) = 1
N2 (pz12
+ 2pz3 pz1 + pz32
) = 1 1 + 2 x 0 + 1
N2 x 2 = 1 So N = 12
![Page 11: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/11.jpg)
1 23 How do we calculate
the energies and coefficientsof the MO’s?
We are going to use the LCAOapproximation to make threeMO’s.
Use Symmetry!
The ends are the same so they must contibuteequally to any MO. So we can make linear combinationswhere atoms one and three contribute equally.
1 = (pz1 + pz3 ) 2 = ( pz1 - pz3 )
3 = pz2 The second carbon is unique.
12
12
![Page 12: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/12.jpg)
1 = (pz1 + pz3 )
2 = ( pz1 - pz3 )
3 = pz2
12
12
1 23
Same Symmetry
1 23
1 23
1 32
1 2 3
![Page 13: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/13.jpg)
1 = (pz1 + pz3 ) 3 = pz2
12
1 3
1 23
1 23-
1 3
1 23
1 23+ Bonding MO
Antibonding MO
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1 = (pz1 + pz3 )
3 = pz2
12
(pz1 + pz3 ) Ĥ pz2 = 12 21
2 = 2
1 23
3
+
Energy =
2
1 23
1
12
![Page 15: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/15.jpg)
1 = (pz1 + pz3 )
-3 = -pz2
12
(pz1 + pz3 ) Ĥ (- pz2) = 12 - 21
2 = - 2
Energy =
2 -
1 23
3
-1 2
3
1
12
![Page 16: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/16.jpg)
1 23
3
+
Energy =
1 23
1
12
1 23
2
Bonding
![Page 17: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/17.jpg)
1 23
3
-
Energy =
1 23
1
12
2
2 -1 3
Antibonding
![Page 18: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/18.jpg)
1 23
What about 2 ?
Thereis no overlapbetween ends so
E = 0
![Page 19: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/19.jpg)
1 3
1 23
1 23
2 -
2
0
H
H
HH
H
H
H
H H
H
![Page 20: 1 + S 12 1 E 1 = 1 = c 1 1 + c 1 2 1 - S 12 1 E 2 = - 2 = c 1 1 - c 1 2 bonding antibonding](https://reader034.vdocuments.us/reader034/viewer/2022051009/5a4d1b6e7f8b9ab0599b4778/html5/thumbnails/20.jpg)
This is painful!
It makes the brain hurt.
So use a computer instead.
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