Symmetry and Molecular Orbitals (II)ocw.nctu.edu.tw/.../ichemistry_lecturenotes/ich-5-2.pdf ·...
Transcript of Symmetry and Molecular Orbitals (II)ocw.nctu.edu.tw/.../ichemistry_lecturenotes/ich-5-2.pdf ·...
Symmetry and MolecularOrbitals (II)
Rules of Molecular Orbitals
Rules for forming bonding and antibonding MOsnumber of total molecular orbitals = number of total atomic orbitalsatomic orbitals have the right symmetryatomic orbitals overlap wellatomic orbitals have similar energy
Rules for filling electrons are the same for MOs and AOs.start filling from the lowest energy orbitalfollows Pauli exclusion principle and Hund's rule
Provides molecular energy informationExplains magnetic behaviorCan provide molecular structural explanation, but moredifficult to comprehend than VB theory
LCAO-MO
•LCAO –linear combination of atomic orbitals
= cii
MO spreads over ALL molecule (delocalized)More nodes, less stablesame sign, bondingdifferent sign, antibondingAO lower in E, MO lower in E
LCAO-MOHeteronuclear Diatomic Molecules
•A more electronegative•B less electronegative
+
+
+ +
+ -
SALCSALC –symmetry adapted linear
combinations, the linearcombinations of atomic orbitalsof specified symmetry
Linear combination among orbitalswith wrong symmetry notconsidered
Linear combination among ALLorbitals (AO, MO) with rightsymmetry are allowed (calledorbital mixing)
MO Symmetrybond: no nodal plane passing through internuclear axisbond: 1 nodal plane passing through internuclear axisbond: 2 nodal planes passing through internuclear axis
+ +
+ +
+ +
+ +
-
++
+-
-
--
-- -
MO Symmetry
MO Symmetry
B.MO
A.MO
g: geradeu: ungerade
+ +
+ +
+
+ +-
- -
-
-
Symmetry of C3v Group Orbitals
Linear H3
3= 1SA - 21/2 1SB + 1SC
2= 1SA - 1SC
1= 1SA + 21/2 1SB + 1SC+ + +
+ +
+-
-
Node
2
1
0
The Particle in a Box
+ + +
+ +
+-
-
++
+ +
--
Node
2
1
0
Triangular H3
a1 = 1SA + 1SB + 1SC
e = 1SA - 1SC
1SA - 21/2 1SB + 1SC
+
+
+ + ++-
-
a, b : nondegeneratee: doubly degeneratet: triply degenerate
Node 0 1 1
Walsh Diagram –Correlation Diagram
+ + +
+ +
+-
-
+
+
+ + ++-
-
H3+ stable
Simplest3 center2 e bond
Character Tables
I: Mulliken symbol.A, B: 1D E: 2D T: 3DA: 1D symmetric about the principal axis (1)B: 1D unsymmetric about the principal axis (1)
II: Irreducible representations for the groupIII: Transformation properties of vectors and
rotations along the x, y and z axisIV: Transformation properties of squares and binary
products of the coordinates
(yz)
Total Representation for C2vIndividually block diagonalized matrices
Reduced to 1D matricesx [ 1] [-1] [ 1] [-1]y [ 1] [-1] [-1] [ 1]
z [ 1] [ 1] [ 1] [ 1]
irreducible representationΓx = 1 -1 1 -1Γy = 1 -1 -1 1Γz = 1 1 1 1ΓRz = 1 1 -1 -1z
Symmetry of OOrbitals in H2O
•2px - B1
•2py - B2
•2pz - A1
•2s - A1
(spherical, highest symmetry)
(yz)
(yz)
Symmetry of H Group Orbitals in H2O
= HA1s - HB1s B2
= HA1s + HB1s A1
MO of H2O
O orbitals 2s 2py 2px
2pz
H group orbitals + -
A1 B2 B1
H2O has 3A1 2B2 1B1 MOs
3A1 bonding, nonbonding, antibonding
2B2 bonding, antibonding
1B1 nonbonding
MO of H2O 1a1
•BondingO2s + O2pz + +
MO of H2O 2a1
•NonbondingO2s - O2pz + +
MO of H2O 3a1
•AntibondingO2s + O2pz - +
MO of H2O 1b2
•BondingO2py + -
MO of H2O 2b2
•AntibondingO2py - -
MO of H2O 1b1
•NonbondingO2px
Localization of Bonds –MO View
MO =>delocalized view
Sum and differenceof MOs =>localized view
Localized View ~Hybridizeddescription in VB
Molecular Shape and MO
8 e7 e6 e5 e4 e
105o103o136o131o180o
OH2NH2CH2BH2BeH2
Molecular Shape and MO
Molecular Shape and MOBeH2 NH2
OH2
BH2CH2
Localized vs DelocalizedDescription of MO
Localized Appropriate•Bond strengths•Bond lengths•VSEPR description
of moleculargeometry
•Bronsted acidity
Delocalized Appropriate•Electronic spectra•Photoionization•Electron attachment•Magnetism•Walsh description of
molecular geometry•Standard potentials
Symmetry of N Orbitals in NH3
•2px 2py - E
•2pz - A1
•2s - A1
(spherical,highestsymmetry)
Symmetry of H Group Orbitals in NH3
a1 = 1SA + 1SB + 1SC
e = 1SA - 1SC
1SA - 21/2 1SB + 1SC
+
+
+ + ++-
-
a, b : nondegeneratee: doubly degeneratet: triply degenerate
Node 0 1 1
MO of NH3
N orbitals 2s 2py 2px
2pz
H group orbitals a1 e
A1 E
NH3 has 3A1 2E MOs
3A1 bonding, nonbonding, antibonding
2E bonding, antibonding (doubly degenerate)
MO of NH3 1a1
•BondingN2s + N2pz + a1
MO of NH3 2a1
•NonbondingN2s - N2pz + a1
MO of NH3 3a1
•AntibondingN2s + N2pz - a1
MO of NH3 1e
•Bonding(N2px,N2py) + e
MO of NH3 2e
•Antibonding(N2px,N2py) - e
NH3 MO
NH3 MO
Steps to Construct MO of ABn
•Determine the molecular symmetry•Determine the symmetry of the orbitals of
central atom (A) and the group orbitals (Bn)•MOs can be constructed from A orbitals and
B orbitals of same symmetry•Consider the relative energy and the overlap
among the orbitals to decide if the interactionis bonding, nonbonding, or antibonding
MO of SF6
S orbitals
•2px 2py 2pz -T1u
•2s -A1g
F orbitals
•T1u
•Eg
•A1g
4 pairs of electrons in A1g & T1u are shared by 7 Atoms
Electron DeficiencyAntibonding
Nonbonding
Bonding+
+
++
+ +-
-
B BH
MO Theory of Solids
N AO gives N MOBand
MO Bands
N AO gives N MO withvery small energy gap
S and P Bands in 1D Solid
Discrete & Overlapping Bands
Weak AOinteractions
Narrow bands
Strong AOinteractions
Wide bands
Fermi Level - HOMO
Band with empty levels conduct electric current
Conductor Insulator Semiconductor
ConductionBand
ValenceBand
Fermi Distribution and Semiconductor
Intrinsic semiconductor
Fermi Distribution
n-type p-type
Extrinsic Semiconductor
ConductionBand
ValenceBand
p-n Junction Diode
Density of States (DOS)
Metal Semimetal
X-ray Emission
Empty state generated bye bombardment