VII. Polyatomic molecules and chemical bondsocw.nctu.edu.tw/upload/classbfs121011493657351.pdf · VII-2. Walsh diagram for triatomic systems Walsh diagram Use Walsh diagram predict

• 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