• Linear and non-linear triatomic systems
• Walsh diagram for triatomic systems • Hybrid MOs and bond angles
VII. Polyatomic molecules and VII. Polyatomic molecules and chemical bondschemical bonds
VIIVII--2. Walsh diagram for 2. Walsh diagram for triatomictriatomic systems systems
Walsh Walsh diagramdiagram
Use Walsh diagram predict bond angle
90 1802 g3 u
1 ,1u u
4 g5 u
12a13a21b11b
14a
22b
Liner BeHLiner BeH22
+ ++
1sHa 2sBe 1sHb
+ ─ -+
1sHa 2PzBe 1sHb
2PyBe 2PxBe
+ --
1sHa 2sBe 1sHb
g2
u3
uu 1 ,1
g4
+++
1sHb 2sO,2PzO 1sHa
2a1-
+
+─
- +
1sHb 2PyO 1sHa
1b2
+--
1sHb 2sO,2PzO 1sHa
+
-
3a1
1b1=2PxONonNon--Liner OHLiner OH22
BeH2 222 321 ugg
90 1802 g3 u
1 ,1u u
4 g5 u
12a13a21b11b
14a
22b
Lowest in energy
Lowest in energy
Use Walsh diagram predict bond angle BH2
Bond angle = 131° 12
22
12
1 3121 abaa
90 1802 g3 u
1 ,1u u
4 g5 u
12a13a21b11b
14a
22b
Use Walsh diagram predict bond angle OH2
Lowest in energy Bond angle = 104.5° 212
12
22
12
1 13121 babaa
90 1802 g3 u
1 ,1u u
4 g5 u
12a13a21b11b
14a
22b
Use the following Walsh diagram predict bond angles of molecules:
2OF )1(
2NO )2(
2CN )3(
and then write down electronic configurations
PCIIweek14-3作業 A26
Bond angle90 1801 g
3 u
5 u6 g
21a
12a
24b
13a
14a
22b
2 g
4 g
7 u
1 u
2 g
3 u8 g9 u
23b11b15 a16a
12b
17 a25b
11a
21b
sp hybrid orbital
zpssp 222
1
zpssp 222
1 - +
+
+ -+
z
Angle between sp+ and sp-_is 180 degree
)(12
1 HsBesp )(12
1 HsBesp Bond MOs
VIIVII--3. Hybrid MOs and bond angles 3. Hybrid MOs and bond angles
HH
HH
+-
sp2 hybrid orbital (Trigonal planar molecular geometry)
z
y
yz pcpcscisp 2222 3212
zpcscsp 221 12
- +++ = z
y
--
+
+++ =z
y6/
yz pcpcscsp 26/cos26/sin22 222
--
++++ =
z
y
yz pcpcscsp 26/cos26/sin23 222
01 c0c+
+
+
02 c
Corresponding diagram before
06/sin212 ccc
0233121 222222 rdspsprdspsprdspsp
1c 21
2 c
31c
32 21 cc
0,0,0 21 ccc
06/sin6/cos 2222
2 ccc
21 cc
21c
c
111 22 rdspsp
zpssp 2322
3112
yz ppssp 2212
612
3122
yz ppssp 2212
612
3132
Note：sign and p orbital --- depend on axis directions
++
+
Hssp 112
1 2 Bond MOs
Hssp 122
1 2
Hssp 122
1 2
This is case in text book Large balloon is minus sign
yx
yx
x
ppssp
ppssp
pssp
2212
612
313
2212
612
312
2322
311
2
2
2
xp2 yp2
Sign here
PCIIweek14-4作業 A27
Given sp2 orbitals in the following axis-system and signs
Write down expression of sp2(i) orbitals (i=1,2,3) directly
OH2 : two lone-pair and two bonding orbitals
O
●●
●●
34
O
H H 2 1
z
y
xz
yz
yz
pcpcsc
pcpcsc
2sin2cos2
2sin2cos2
112
111
xz
xz
papasa
papasa
2sin2cos2
2sin2cos2
114
113
104.45
2
2
11
02cos021
22211
21
221
ccdd
ccd
042324131 dddd
θccc
sin21 2cos 11
Same β aaa
sin21 2cos 11
0coscos2cos2cos0coscos11 caac
2cos2cos
2cos2cos 312cos 109.5 2 sp3
yz
yz
pps
pps
22sincos2
sincos1
21
22sincos2
sincos1
21
2
2
2
2
2
1
Bonding orbitals
Lone-pair orbitals
xz
xz
pps
pps
22sincos2
sincos1
21
22sincos2
sincos1
21
2
2
4
2
2
3
11cossin1
cossin
2
2
2
2
Relation between bonding and lone-pair orbitals
45.1042 If bond angle is
coscoscos
Angle between bond and lone-pair orbitals
010.109
042.1152
cossin0:
cos0sin:
1
3
aabb
109.10
2 104.45
PCIIweek14-5作業 A28
If we select Cartesian axis in the following way, writedown two lone-pair and twobonding orbitals directly.
2
2
34
12
Thinking about if the two planes are not orthogonal
)2()2(22 4321 yxz pcpcpcsc We need use
