z axis a b z z s*(antibonding) - columbia university€¦ · z x x z note: orbital is ^ to bond (z)...
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BA+- -
s (Bonding)(Bonding)2pz
Atomic Atomic OrbitalsOrbitalsof Atoms A,Bof Atoms A,B
z z
A B
2p 2p
- - ++
Molecular Molecular OrbitalsOrbitals
A- -+ +
B
s* ((AntibondingAntibonding))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 Bonding with 2p OrbitalsOrbitals
Atomic Atomic OrbitalsOrbitalsof Atoms A,Bof Atoms A,B
Molecular Molecular OrbitalsOrbitals
A B
+
+
-
-2px -2px
A B
+ +
- -2p x2p x
2pp (bonding)
A B
+
-
A B
+
+-
-
(antibonding)p*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 Bonding with 2p Orbitals Orbitals (cont)(cont)
Notational DetailNotational Detail
Oxtoby Oxtoby uses two different notations for uses two different notations for orbitals orbitals in the 4th and 5th editions of the class text:in the 4th and 5th editions of the class text:
p2px2px* i* in the 4th edition becomes pg2pxg2px* in the 5th edition
p2px2px i in the 4th edition becomes pu2pxu2px in the 5th edition
ss2pz2pz i in the 4th edition becomes ssg2pzg2pz in the 5th edition
ss2pz2pz* i* in the 4th edition becomes ssu2pzu2pz* in the 5th edition
CORRELATION DIAGRAMCORRELATION DIAGRAM for second period diatomic molecules
E
s*2pz
p* 2p yp* 2p x
p2pxp2py
s 2pz
s*2pz
p* 2p xp* 2p y
s 2pz
p2pxp2py
2p 2p
2s 2s
s*2s
s 2s
2p 2p
2s 2s
s*2s
s 2s
(6 Valence(6 Valenceelectronselectronsfor eachfor eachatom)atom)
(3 Valence(3 Valenceelectrons electrons for each for each atom)atom)
BB22Z Z ≤≤ 7 7
OO22Z Z ≥≥ 8 8Molecular Molecular OrbitalsOrbitalsMolecular Molecular OrbitalsOrbitals Note unpairedNote unpaired
electronselectrons
Note order offilling s2pz
DegenerateDegeneratepp 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
52522.672.67
2.452.45
1.591.59
1.241.24
1.101.10
1.211.21
1.411.41
--
431
.000008105
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
((ss2s2s))22((ss2s2s*)*)22((ss2p2pzz))22((pp2p2p))44((pp2p2p*)*)44
((ss2s2s))22((ss2s2s*)*)22((ss2p2pzz))22((pp2p2p))44((pp2p2p*)*)22
((ss2s2s))22((ss2s2s*)*)22((pp2p2p))4 4 ((ss2p2pzz))22
((ss2s2s))22((ss2s2s*)*)22((pp2p2p))44
((ss2s2s))22((ss2s2s*)*)22((pp2p2p))22
((ss2s2s))22((ss2s2s*)*)22
((ss2s2s))22
((ss1s1s))22((ss1s1s*)*)22
((ss1s1s))22
((ss2s2s))22((ss2s2s*)*)22((ss2p2pzz))22((pp2p2p))44((pp2p2p*)*)44((ss2p2pzz*)*)22
↑↑ ↑↑
↑↑ ↑↑
Bonding in Bonding in PolyatomicPolyatomic Molecules MoleculesBasically two ways to approach Basically two ways to approach polyatomicspolyatomics..
First is to use First is to use delocalized delocalized M.O.M.O.’’ss 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 hybridization of atomic orbitalsorbitals and then use these and then use theseto form localized (usually) bonds.to form localized (usually) bonds.
Localized BeHLocalized BeH22 orbitalsorbitals::
++
BeBe
++
++
++spsp++
spsp--
Add spAdd sp++ + 1s + 1sto getto getlocalizedlocalizedBe-H bondBe-H bond
}Add spAdd sp-- + 1s + 1sto get localizedto get localizedBe-H bondBe-H bond
}HH HH
..
.. ..
..
––
––
++
++
BHBH33 Fragment: Fragment:
spsp22
hybridhybrid
--
++
120120˚̊
Boron NucleusBoron Nucleus
Second spSecond sp22 points points along this directionalong this direction
Third spThird sp22
points alongpoints alongthis directionthis direction
•
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 120120ºº with respect to each other: BH with respect to each other: BH33
BBNote 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 4 hybrid orbitalsorbitals which point to which point to the corners of a tetrahedron. Angle between is the corners of a tetrahedron. Angle between is 109109ºº2828’’ 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 ÆÆ 4 valence 4 valence e e --
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
HHHH 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 (120(120ºº H-B-H H-B-H
angle)angle)
CHCH44 44 sp sp33 tetrahedral tetrahedral (109(109ºº2828’’ 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 found to be TrigonalTrigonal Pyramidal Pyramidal
4 N sp4 N sp33 orbitals orbitals combine with 3 1s H combine with 3 1s H orbitalsorbitals to give 3 sp to give 3 sp33, 1s M.O., 1s M.O.’’ssleaving 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.
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 (90to pure p orbital bonds (90ºº structures) structures)
For example, HFor example, H22S has H-S-H angle of 92S has H-S-H angle of 92ºº..