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Lecture 31: Polyatomic Molecules
A course evaluation is scheduled for the last 20
minutes of the lecture on Monday March 27
The material in this lecture covers the following in Atkins.
14 Molecular orbitals for polyatomic systems
14.8 Walsh diagrams
(a) The Walsh diagram for H2X
Lecture on-line
Polyatomic Molecules (PowerPoint)Polyatomic Molecules (PDF)
Handouts for this lecture
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C H WS
i = 1,n k = 1,n
k ik ikk=1
k=n = 0
i
ik k
k=1
k=nC p
k = 1,n ; i = 1,n
=
Polyatomic MoleculesWe shall in the following
develop a simplified modelfor AH and AH moleculesbased on molecular orbitaltheory
2 3
A
H H
H
A
H
H
A key point will be to understandhow the optimal bond anglechanges with the number of
valence electronsBeH H
=180
Se
H H
=90
We shall be using linearvariation theory to calculateenergies
..express molecularorbitals as a linearcombination of atomicorbitals (LCAO)
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Polyatomic MoleculesAH2
H1H2
1sA
H1H2
2sA
H1H2
2pb2
1H2
2pb1
A
1sH1
The atomic orbitals are :
A
1sH2
The 1s and 2s are toolow in energy to participate
in the bonding with 1s(core orbitals). They will go
unchanged from A over intoAH each holding 2 electrons
A A
H
2
H1 H2
2pa1
This is a simplification(approximation)
in the case of 2sA
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Polyatomic MoleculesAH2
H1H2
2pb2
1H2
2pb1
A
1sH1
The atomic orbitals are :
A
1sH2
The molecular orbitalswill be linear combinationsof atomic orbitals.
Only atomic orbitalson different centersthat overlap will mix
To make use of this
we make two newcombinations of thehydrogen 1s orbitals
A
1sa1
A
1sb2
H1 H2
2pa1
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Polyatomic MoleculesAH2
H1 H2
2pb2
1H2
2pb1
The atomic orbitals are :
A
1sa1
A
1sb2
H1
H2
2pa1
Inspection indicates that2p will overlap (interact)
with 1s
a
a
1
1
1sH(a1)
2pa1
A
1sb2
2pb2
2p with 1sb2 b2
2p will not interactb1
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Heteronuclear diatomic molecules Linear variation theory
A
B
E
+
E
+ = ++ +
C CA A B B
- = + C CA A B B
This is an in - phasebonding orbital withthe largest contributionfrom of lowest energyA
This is an out - of-phase anti - bondingorbital withthe largestcontribution from
of highest energy
B
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Polyatomic MoleculesAH2
The interaction between 2p
and 1s will give rise toa
a
1
1
A
1sa1H1H2
2pa1
2a1
..anti - bondingorbital 2a1
..bondingorbital 1a 1
1a1
1a a a1 1 1p s= +1
2
21
2
1
2a a a1 1 1p s= +1
22
1
21
The orbital energies are :
1a1 = + o cos( / )2
2a1= o cos( / )2
The interaction large forsmall . It is zero for = 180
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A
1sb2
H1H2
2pb2
Polyatomic MoleculesAH2
The interaction between 2pand 1s will give rise to
b
b2
2
A
1b2
..anti - bondingorbital 2b2..bondingorbital 1b 2
A
2b2
1b b b2 2p s= +1
2
21
2
12
2b b b2 2p s= +1
22
1
21 2
The orbital energies are :
1b2 = + o sin( / )2
2b22= o sin( / )
The interaction small forsmall . It is max. for = 180
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1b2= + o sin( / )2
1a1= + o cos( / )2
Polyatomic MoleculesAH2
Correlation diagram AH2BeH2 and BH2+
Configuration (1b2)2
= 180 H A H
BH , AlH (1b a2 2 2 1) ( )2 11
BH 131 127
AlH 120 127
exp theor
2
2
A
1b2
A
2b2
2a1
1a1
180 90
H1
H2
1b1
A
1b2
H1 H2
1b1
1a1
2a1
A
2 b 2
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1b2= + o sin( / )2
1a1= + o cos( / )2
Polyatomic MoleculesAH2
Correlation diagram AH2
SiH BH (1b a2 2- 2 1, ) ( )2 21
SiH 92 90
BH 102 90
exp
2
2-
Theor
Configuration (1b a b2 12
1) ( )2 1 1
NH PH AsH92 91
H O CH H
99 93
2 2 2
2+
2-
2+
exp
exp
103
111
SS
tthheeoorr = 90
A
1b2
A
2b2
2a1
1a1
180 90
H1 H2
1b1
A
1b2
H1 H2
1b1
1a1
2a1
A2 b 2
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1b2= + o sin( / )2
1a1 = + o cos( / )2
Polyatomic Molecules AH2Correlation diagram AH 2
Configuration (1b a b2 12
1) ( )2 1 1
tthheeoorr
= 90
OH SH SeH92 91
H F NH104
2 2 2
2 + 2-
exp
exp
105
118
Excited statesAH Config
NH (1b a b 144 127
PH (1b a b 123 127
CH (1b a b 136 127
SiH (1b a b 123 127
2 exp theo
2 2 11
1
2 2 1 1 1
2 2 11
1
2 2 1
1
1
) ( )
) ( )
) ( )
) ( )
2 2
2 2
2 1
2 1
1 1
1 1
1 1
1 1
A
1b2
A
2b2
2a1
1a1
180 90
H1 H2
1b1
A
1b2
H1 H2
1b1
1a1
2a1
A2 b 2
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Polyatomic MoleculesAH2
A
1b2
A
2b2
2a1
1a1
180 90
H1 H2
1b1
A
1b2
H1 H2
1b1
1a1
2a1
A
2 b2
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Polyatomic Molecules
=120
trigonal planar
AH3
=10990trigonal pyramidal
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2pa2pex 2pey
1sa 1sex 1sey
Polyatomic Molecules AH3
The atomic orbitals are :
Interactions are possible
between (2p 1s(2p 1s ; (2p 1s
a aex ex ey ey
, );, ) , )
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120 90
1a
2a
1ex
2ex
1ey
2ey
2a
1a
2ex
1ex
1ey
2ey
Polyatomic Molecules AH3
BH AlH : (1e)
;3 3
4
theo exp
;
= =120 120
(1e)AH
CH 120 109SiH 110 109
PH 113 109
4
3 exp theo
3
33+
1 1aa
(1e)
AHNH 108 90PH 93 90AsH 92 90
SbH 91 90
4
3 exp theo3
3
3
3
1 2aa
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Polyatomic Molecules The fragment approach
Organic molecules are made up of sp,sp and sp carbon centers2 3
H
C C
C
C
H
sp3 hybrides
sp2 hybrides
sp hybrides
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Polyatomic Molecules The fragment approach
Alternatively, organic molecules are made upof CR (sp),CR ( sp ) and CR (sp ) fragments2
23
3
H
C C
C
C
H
H C
1
1x 1y 2
bonds
bond
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Polyatomic Molecules The fragment approach
Alternatively, organic molecules are made upof CR (sp),CR ( sp ) and CR (sp ) fragments2
23
3
H
C C
C
C
H
bonds
bond
b2
1a1
1b1
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Polyatomic Molecules The fragment approach
Alternatively, organic molecules are made upof CR (sp),CR ( sp ) and CR (sp ) fragments2
23
3
H
C C
C
C
H
bond
1a1
1ex 1ey
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What you must learn from this lecture
1. For EH (n = 2,3) you must be able to constructthe molecular orbitals as linear combinations ofthe p - orbitals on the main - group element Eand linear combinations of the 1s orbitals on
hydrogen
n
2. Be able to account for the variation in
the orbital energies of EH a functionof the HEH bond angle, and its influenceon the structure of EH as a function of thenumber of valence electrons.
n
n
as
3. Be able to account for the bonding inorganic hydrocarbons in terms of thefrontier orbitals of CR, CR , and CR2 3