Download Topics • Introduction • Molecular Structure and Bonding • Molecular

Topics
•
•
•
•
•
•
•
•
Introduction
Molecular Structure and Bonding
Molecular Symmetry
Molecular Orbital Theory
Coordination Complexes
Electronic Spectra of Complexes
Reactions of Metal Complexes
Organometallic Chemistry
Molecular Structure and Bonding
• Lewis Structures
• Valence Bond Theory
• MO Theory
1
Lewis Structures
• “first step” bonding model
• Simple rules, no calculations but easy to use
– 1. Two electrons pair to form each bond
– 2. Eight electrons are present to form a filled
valence shell (the octet rule).
• Process
– 1. Add up all of the available valence electrons
– 2. Use two to form each bond between atoms
– 3. Distribute the electrons in pairs so that each
atom has an octet of valence electrons from a
combination of lone pairs and bonds.
Lewis Structures: Addendum
• Resonance
– it might require the construction of resonance
structures to adequately describe the electron
distribution
• Formal charge
– required to determine which possible structures
are the lowest energy
– The lowest formal charge resonance structure is
the most energetically favorable.
• Hypervalence
2
Valence Bond Theory
• expresses Lewis concepts in quantum
mechanical ways
• VB for H2:
• for two hydrogen atoms:
ψ = ψ A(1)ψ B ( 2)
• bringing them together improves the
energetics and we have a first approximation:
ψ = ψ A(1)ψ B ( 2) + ψ A( 2)ψ B (1)
VB: Improving H2
• including other possible arrangements paints
an increasingly realistic picture
• it is possible that the two electrons could be
found at or near one nucleus:
ψ = ψ A(1)ψ B ( 2 ) + ψ A( 2)ψ B (1) + λ (ψ A(1)ψ A( 2 ) + ψ B (1)ψ B ( 2) )
covalent
ionic
3
VB Theory Describing H2
• Improving our VB model of H2 using various
assumptions brings us closer to the
experimental results
Bond Length
(pm)
Experimental
Bond Energy
(kJ mol-1)
458
Initial
24
90
Mixing
303
86.9
Shielding
365
74.3
Ionic Contrib.
388
74.9
VB Theory
Model
74.1
VB: Hybridization
• integral to forming bonds in VB theory
• formally based on the concept of promotion, mixing of
similar wavefunctions to form degenerate
wavefunctions
• process involves mixing pure atomic orbitals to form
new “hybrid” orbitals
• Stated another way, we use linear combinations of
atomic orbital wavefunctions to meet the demands of
geometry and valence.
• requires that you get out as many orbitals as you put
in
4
VB: sp3 Hybridization
• most well known example constructed from
one s and three p orbitals:
1
1
1
1

ψ sp 3a = ψ s + ψ px + ψ py + ψ pz 
2
2
2
2

1
1
1
1
ψ sp 3b = ψ s − ψ px − ψ py + ψ pz 

2
2
2
2

1
1
1
1
ψ sp 3c = ψ s + ψ px − ψ py − ψ pz 
2
2
2
2

1
1
1
1
ψ sp 3d = ψ s − ψ px + ψ py − ψ pz 
2
2
2
2

Other Popular Hybridizations
Hybrid
Geometry
Bond Angles
sp
Linear
180
sp2
Trigonal
120
sp3
Tetrahedral
109.5
dsp3
TBP or
Square
pyramidal
90, 120
d2sp3
Octahedral
90
5
Molecular Orbital Theory
• similar tools, fundamentally different
approach
– two nuclei are positioned at an equilibrium
distance and electrons are added to the system
– rather than assuming that two atoms come
together
• we are still unable to solve the Schrodinger
equation, so we use an approximation to
provide the correct MOs:
– Linear Combination of Atomic Orbitals (LCAO)
LCAO
• Same idea as hybridization: get the same
number of MO’s out as atomic orbitals you
put in.
ψ b = ψ A +ψ B
ψ a = ψ A −ψ B
bonding
antibonding
• Bonding: interference increasing the electron
density between nuclei
• Antibonding: interference decreasing the
electron density between nuclei
6
MO Theory for H2+
• Given the H2+ system (I.e. two hydrogen
nuclei, one electron)
• Formation of the MO’s of the system gives us
two orbitals:
ψ b = ψ A +ψ B
ψ a = ψ A −ψ B
• Add in one electron: you get an electron
configuration of : ψb(1)
• This is the same as saying: ψA(1)+ ψB(1)
MO Theory for H2
• Now take two hydrogen nuclei but add two
electrons instead of just one
ψ b = ψ A +ψ B
ψ a = ψ A −ψ B
• So when we put the electrons into the
system, the wavefunction for the entire
system becomes:
ψ = ψ b (1)ψ b (2) = [ψ A (1) + ψ B (1)][ψ A (2) + ψ B (2)]
ψ = ψ A (1)ψ A (2) + ψ B (1)ψ B (2) + ψ A (1)ψ B (2) + ψ A (2)ψ B (1)
7
Electron Distribution: the Overlap Integral
• the electron distribution is given by ψ2
• So for ψb and ψa :
ψ b2 = ψ A2 + 2ψ Aψ B + ψ B2
ψ a2 = ψ A2 − 2ψ Aψ B + ψ B2
• When integrated over space the cross
term becomes the overlap integral (S) and
is very important for bonding theory
• Effectively measures the extent to which
the wavefunctions alter the electron
density between the nuclei
Symmetry and Overlap
• So in general:
– S>0 gives bonding
– S<0 gives antibonding
– S=0 gives nonbonding orbitals
• Consistent with previous VB and
“handwaving” arguments that strength of
bonding derives from degree of overlap
8
Energetics and Overlap
• molecular orbital energy level diagram
(MOELD)
_
ψ a = ψ A −ψ B
Energy
1sA
+
1sB
ψ b = ψ A +ψ B
+
ψA
ψB
Populating the MOELD: H2
• MO Energy Level Diagrams are not very
interesting ..... without electrons in them
• let’s use our MOELD for H2:
ψa
Energy
1sA
1sB
↑↓
ψb
ψA
ψB
• Each H brings
one electron
• Each orbital
can hold two
electrons
• Electrons will
populate the
lowest
available
energy level
9
Bond Order
Bond _ Order =
1
( n − n* )
2
• where
– n is the number of electrons in bonding orbitals
– n* is the number of electrons in antibonding
orbitals
• So for H2
Bond order = ½ ( 2 – 0 ) = 1
Populating the MOELD: He2
• Let’s try He2 with our MOELD
↑↓
ψa
Energy
1sA
1sB
↑↓
• Bond Order is 0
ψb
ψA
• Each He brings
two electrons
• Each orbital can
hold two
electrons
ψB
10
Symmetry Labels: Names of MO’s
• σ, π, δ are symmetry labels, used to identify
the MO’s that we construct
• similar to s, p, d etc.
• σ - sigma symmetry indicates that the MO is
symmetrical with respect to rotation around
the internuclear axis, i.e. has no nodal
planes.
• π - pi symmetry indicates that the MO has a
nodal plane at the internuclear axis.
• δ - delta indicates that there are two
internuclear nodal planes.
Symmetry Labels: Additional Information
• *, g, u are used to provide as super and sub
scripts to provide further information
• * indicates the presence of a nodal plane
perpendicular to the internuclear axis
– designates the orbital as antibonding
• g (gerade, german for even) indicates the
parity of a MO, i.e. does it change sign when
it is inverted through its center? g = no
• u (ungerade, german for odd) indicates that
the MO does change sign upon inversion
11
σ Molecular Orbital Construction
• s+s
and
s-s
• pz+pz
and
pz-pz
π Molecular Orbital Construction
12
MO’s for Homonuclear Diatomics
• preceding pictures of MO’s formed from
atomic orbitals can be summarized as:
Sigma Orbitals
Pi Orbitals
σ1s = 1sA + 1sB
π2py = 2pyA + 2pyB
σ*1s = 1sA - 1sB
π2px = 2pxA + 2pxB
σ2s = 2sA + 2sB
π*2py = 2pyA - 2pyB
σ*2s = 2sA - 2sB
π*2px = 2pxA - 2pxB
}
}
σ2p = 2pA + 2pB
σ*2p = 2pzA - 2pzB
MO Energy Level Diagrams II
• π orbitals are formed
– degenerate set
• Hund’s rule:
“electrons occupy
orbitals to maximize the
spin multiplicity where
possible”
• σ 1s combination
typically isolated from
other orbitals
– inner shell/core electrons
similar to atomic orbitals
13
Electronic Configuration in MO’s
H2
1σg2
Li2
1σg2 1σu*2 2σg2
F2
1σg2 1σu*2 2σg2 2σu*2 3σg2 1πu4 1πg*4
or
KK 2σg2 2σu*2 3σg2 1πu4 1πg*4
Mixing: A Complication
• assumption: only atomic orbitals of identical
energy contribute to molecular orbitals
• actually: any orbital with the same symmetry
may contribute to the composition of an MO,
energy differences only reduce the degree of
contribution.
• case in point:
– 2s, 2p orbitals are very similar in energy
– σ orbitals formed from combinations of 2s and 2p
orbitals undergo mixing
14
Mixed MOELD
No Mixing
Mixing 1σg 2σg
Properties of C2
↑
↑
↑↓
↑↓
↑ ↓↑ ↓
↑↓
↑↓
↑↓
Paramagnetic
Diamagnetic
15
Heteronuclear Species
• energy level comparisons are relatively
simple for homonuclear species
• MO’s built for heteronuclear species depend
on the relative energy levels of the
contributing atomic orbitals
CO: A Heteronuclear Species
• the molecular orbitals of CO
16
Nonbonding Orbitals
• Effectively, orbitals present in a molecule
from one of the substituents that do no
overlap with orbitals of other substituents
• As they do not combine with other
components they are not raised or lowered in
energy
• They are not used in the bonding but still are
present in the molecule
– Present in the electron energy levels
– Can be very important source or sink of electron
density, particularly in transition metal complexes
Polyatomics
• Typically a ligand field is constructed
corresponding to group orbitals around a
central atom
• These are derived from symmetry operations
which arise from the overall shape and
symmetry of the molecule or complex
17
Generalizations on Polyatomics
ψ = ∑ ciφi
i
• Linear combination of all the atomic orbitals
of the same symmetry
– Some ci will be very small depending on energy
levels
• Forming MO’s
– Antibonding character and Orbital energy increase
with number of orbital nodes.
– Minimal interactions exist between non-nearest
neighbour atoms
– Atomic Orbitals with lower energy produce lower
energy Molecular Orbitals, i.e E(s+s ) < E(p+p)
More Symmetry Labels
• With mixing and non-linear molecules, labels
become very difficult to assign
• Symmetry is used to assign the labels to
particular orbitals
–
–
–
–
A non-degenerate
B non-degenerate
E double degenerate
T triply degenerate
• These typically replace the σ and π labels
used for linear systems
18
Comparison of VB and MO Theory
• VB
– rapid, graphical way of determining possible
bonding
– predicts structure and overall geometry well
• MO
– lots of energy information
– great for spectroscopy and predicting electronic
behaviour
– requires symmetry resources to determine
structure and bonding
19