BA

+- -

(Bonding)(Bonding)2pz

Atomic Orbitals Atomic Orbitals of Atoms A,Bof Atoms A,B

z z

A B

2p 2p

- - ++

Molecular OrbitalsMolecular Orbitals

A- -+ +

B

* (Antibonding)(Antibonding)2pz

Nodal Plane

2p z -2pz

- -++A B

2p2pzz(A) + 2p(A) + 2pzz(B)(B)

2p2pzz(A) - 2p(A) - 2pzz(B)(B)

z Axis is taken to be line through A, Bz Axis is taken to be line through A, B

zaxis

zaxis

Bonding with 2p OrbitalsBonding with 2p Orbitals

Atomic Orbitals Atomic Orbitals of Atoms A,Bof Atoms A,B

Molecular OrbitalsMolecular Orbitals

A B

+

+

-

-2px -2px

A B

+ +

- -2p x2p x

2p (bonding)

A B

+

-

A B

+

+-

-

(antibonding)*2p

Nodal Plane

2p2pxx(A) - 2p(A) - 2pxx(B)(B)

2p2pxx(A) + 2p(A) + 2pxx(B)(B)

z

x

x

z

Note: orbital is Note: orbital is to bond (z) axis to bond (z) axis

A,B NodalPlane

Bonding with 2p Orbitals (cont)Bonding with 2p Orbitals (cont)

Notational DetailNotational Detail

Oxtoby uses two different notations for orbitals Oxtoby uses two different notations for orbitals in the 4th and 5th editions of the class text:in the 4th and 5th editions of the class text:

2px2px* i* in the 4th edition becomes g2pxg2px* in the 5th edition

2px2px i in the 4th edition becomes u2pxu2px in the 5th edition

2pz2pz i in the 4th edition becomes g2pzg2pz in the 5th edition

2pz2pz* i* in the 4th edition becomes u2pzu2pz* in the 5th edition

CORRELATION DIAGRAMCORRELATION DIAGRAM for second period diatomic molecules

E

*2pz

* 2p y* 2p x

2px2py

2pz

*2pz

* 2p x* 2p y

2pz

2px2py

2p 2p

2s 2s

*2s

2s

2p 2p

2s 2s

*2s

2s

(6 Valence(6 Valenceelectronselectronsfor eachfor eachatom)atom)

(3 Valence(3 Valenceelectrons electrons for each for each atom)atom)

BB22

Z ≤ 7Z ≤ 7OO22

Z ≥ 8Z ≥ 8Molecular OrbitalsMolecular OrbitalsMolecular OrbitalsMolecular Orbitals Note unpairedNote unpairedelectronselectrons

Note order offilling 2pz

DegenerateDegenerate orbitalsorbitals

Molecular Orbitals of Homonuclear Diatomic Molecules

(Å)

HeHe22

LiLi22

BeBe22

BB22

CC22

NN22

OO22

FF22

NeNe22

2

4

2

4

6

8

10

12

14

16

1

0

1

0

1

2

33

2

1

0

0.740.74

5252

2.672.67

2.452.45

1.591.59

1.241.24

1.101.10

1.211.21

1.411.41

--

431

.000008

105

9

289

599

942942

494

154

-

Valence Electron Configuration# Valence# ValenceElectronsElectrons

Bond Length

Bond Order

Bond Bond EnergyEnergy(kJ/mole)(kJ/mole)

Mole-Mole-culecule

HH22

((2s2s))22((2s2s*)*)22((2p2pzz))22((2p2p))44((2p2p*)*)44

((2s2s))22((2s2s*)*)22((2p2pzz))22((2p2p))44((2p2p*)*)22

((2s2s))22((2s2s*)*)22((2p2p))4 4 ((2p2pzz))22

((2s2s))22((2s2s*)*)22((2p2p))44

((2s2s))22((2s2s*)*)22((2p2p))22

((2s2s))22((2s2s*)*)22

((2s2s))22

((1s1s))22((1s1s*)*)22

((1s1s))22

((2s2s))22((2s2s*)*)22((2p2pzz))22((2p2p))44((2p2p*)*)44((2p2pzz*)*)22

Bonding in Polyatomic MoleculesBonding in Polyatomic Molecules

Basically two ways to approach polyatomics.Basically two ways to approach polyatomics.

First is to use First is to use delocalized M.O.’sdelocalized M.O.’s where where ee -- are not confined to a are not confined to a single bond (region between 2 atoms) but can wander over 3 or single bond (region between 2 atoms) but can wander over 3 or more atoms. We will use this approach later for C bonding.more atoms. We will use this approach later for C bonding.

Second is to use Second is to use hybridization of atomic orbitalshybridization of atomic orbitals and then use these and then use theseto form localized (usually) bonds.to form localized (usually) bonds.

Localized BeHLocalized BeH22 orbitals: orbitals:

++

BeBe

++

++

++

spsp+ +

spsp- -

Add spAdd sp++ + 1s + 1sto get to get localizedlocalizedBe-H bondBe-H bond

}Add spAdd sp-- + 1s + 1sto get localizedto get localizedBe-H bondBe-H bond

}HH HH

..

.. ..

..

––

––

++

++

H 1s + (spH 1s + (sp-- )) H 1s + (spH 1s + (sp++

))

BeBe HHHH BeBe

andand

++ .... ++.. ..––––

BHBH33 Fragment: Fragment:

spsp22

hybridhybrid

--

++

120˚120˚

Boron NucleusBoron Nucleus

Second spSecond sp22 points points along this directionalong this direction

Third spThird sp22

points alongpoints alongthis directionthis direction

•

33 sp sp22

hybridshybrids120˚120˚

Overlap with H 1s to give 3 B-H bonds Overlap with H 1s to give 3 B-H bonds in a planein a plane pointing pointing at at 120º120º with respect to each other: BH with respect to each other: BH33

BB

Note B has 3 Note B has 3 valence electronsvalence electrons

1s1s222s2s222p2p

++

++++

++HH

++HH

++HH

120˚

2s + 2p2s + 2pxx + 2p + 2pyy + 2p + 2pzz sp sp33 gives gives 4 hybrid orbitals4 hybrid orbitals which point to which point to

the corners of a tetrahedron. Angle between is the corners of a tetrahedron. Angle between is 109º28’109º28’ spsp33 [1/4 s, 3/4 p]. Tetrahedral hybrids. [1/4 s, 3/4 p]. Tetrahedral hybrids.

4 H atoms have 4 x 1s 4 H atoms have 4 x 1s 4 valence 4 valence e e --

EE

2s2s22

2p2p

1s1s22

spsp33 spsp33 spsp33spsp33

1s1s22

Geometry of carbon spGeometry of carbon sp33/H 1s Bonds in methane (CH/H 1s Bonds in methane (CH44):):

spsp33 hybridization on C leads to 4 bonds. CH hybridization on C leads to 4 bonds. CH44 is a is a

good example.good example.

CC

HH

HH

HH HH

Summary of Hybridization ResultsSummary of Hybridization Results

BeHBeH22 22 sp sp linear H-Be-Hlinear H-Be-H

BHBH33 33 sp sp22 trig. plane trig. plane

(120º H-B-H (120º H-B-H angle)angle)

CHCH44 44 sp sp33 tetrahedral tetrahedral

(109º28’ (109º28’ H-C-H angles)H-C-H angles)

ExampleExample Groups Attached Groups Attached Hybrid Hybrid GeometryGeometryto Center Atomto Center Atom

2pz

2py

2px

1s

1s

1s

Localized Bonds and Lone Pair ElectronsLocalized Bonds and Lone Pair Electrons

NH3

This predicts 90º geometry

3H, 1s (no choice) N: 1s22s22p3

NitrogenNitrogennucleusnucleus

H atom 1sorbital

N

107˚H

HH

Geometry of NHGeometry of NH33 found to be Trigonal Pyramidal found to be Trigonal Pyramidal

4 N sp4 N sp33 orbitals combine with 3 1s H orbitals to give 3 sp orbitals combine with 3 1s H orbitals to give 3 sp33, 1s M.O.’s, 1s M.O.’sleaving one spleaving one sp33 hybrid left hybrid left

Of 5 valence Of 5 valence e e -- in N, 2 go into one sp in N, 2 go into one sp33 orbital, 3 go into other 3 sp orbital, 3 go into other 3 sp33,s.,s.(combined with H (1s))(combined with H (1s))

One of the driving forces for the tetrahedral configuration is that One of the driving forces for the tetrahedral configuration is that it puts bonding and lone pair electron groups as far away from it puts bonding and lone pair electron groups as far away from each other as possible.each other as possible.

N

H

HH

•• •• Lone PairLone Pair

NN

Electron pair repulsion effect is largest for small central atoms Electron pair repulsion effect is largest for small central atoms like B, N, O.like B, N, O.

As go to larger central atoms (e.g. S or metals) frequently As go to larger central atoms (e.g. S or metals) frequently find this effect not so large and start to get things closer find this effect not so large and start to get things closer to pure p orbital bonds (90º structures)to pure p orbital bonds (90º structures)

For example, HFor example, H22S has H-S-H angle of 92º.S has H-S-H angle of 92º.

OO

HH

HH

Lone pairs stick into and out of paper

HH22O:O:

4 sp4 sp33 hybrids. Use hybrids. Use 22 to make MO bonds with H 1s. to make MO bonds with H 1s.

Predicts H-O-H bondPredicts H-O-H bondof 109º28” - of 109º28” - Find 105ºFind 105º

O 1s22s22p4 (6 valence e-)2H 1s (2e-)

• •• •