Download MO Diagrams for O2 and N2

MO Diagrams for O2 and N2
Drawing MO diagrams - always same number of MOs as AOs.
- more electronegative element on the right - lower in energy.
-----------------------------------------------------------------------------------------------------------------Paramagnetic
σ*2p
O2
Bond order of 2 (O=O)
π*2p
2p
2p
π2p
σ2p
larger ΔE
σ*2s
2s
2s
σ2s
O
O2
O
-----------------------------------------------------------------------------------------------------------------σ*2p
N2
Diamagnetic
Bond order of 3 (N≡N)
π*2p
2p
2p
σ2p
Very strong NN bond
Unlike O2, the σ2p and π2p orbitals are
switched in energy (see next page)
smaller ΔE
π2p
HOMO = σ2p, LUMO = π*2p
σ*2s
2s
2s
σ2s
N
N2
N
MO Diagram for CO
σ*2p
LUMO
π*2p
2p
σ2p
2p
HOMO (slightly antibonding)
π2p
2s
σ*2s
2s
σ2s
C
CO
O
- CO is isoelectronic with N2 (C has one less electron than N, O has one more) – MO diagram is
very similar to that of N2.
- Diamagnetic, Bond order of 3 (C≡O)
- Important: HOMO = σ2p (weakly antibonding), LUMO = π*2p (strongly antibonding)
- Since O is far more electronegative than C, would expect a large dipole moment with δ- on O.
However, CO actually has only a small dipole moment (0.1 Debye) with the δ- on Carbon!
Usually electronegativities are a good indication of the direction and magnitude of the dipole on
a molecule, but especially in molecules where orbitals with antibonding character are occupied,
things are not so straightforward.
-----------------------------------------------------------------------------------------------------------------Ordering of MOs in O2 is σ2p, π2p, π*2p, σ*2p but in N2 and CO, the order is π2p, σ2p, π*2p, σ*2p
Reason - O2 - larger ΔE between s and p orbitals Æ less orbital mixing
- larger ΔE because across the period (B,C,N,O,F) more protons added to the
nucleus, which pulls the electrons in closer to the nucleus (lower energy). This
effect is felt more strongly by the s-orbitals than the p-orbitals, so the energy of
the s-orbitals drops more rapidly than that of the p-orbitals.
- N2 and CO - mixing between the σ2p and the σ*2s orbitals raises the energy of the σ2p
above the π2p.
Crystal Field Theory
•
•
Very wrong theory (for transition metal organometallic chemistry), but quite useful.
Easy way to roughly predict the ordering of the energy levels for a TM compound.
-
Ligand lone pair thought of as a point charge (e.g. for Cl-, H- or CN-) or the partial negative
charge of a dipole (e.g. for :OH2, :NH3 or :PF3).
Ligands attracted to the TM cation since they are point charges Æ purely electrostatic
bonding assumed.
Any interactions between the electrons of the ligand and those of the metal are repulsive Æ
no covalent bonding (σ, π or δ) exists according to this theory!!!
-
dz2, dx2-y2
axial, eg
Δo
TM
d-orbitals
inter-axial, t2g
dxz, dyz, dxy
-
The axial orbitals (eg symmetry in an octahedral environment) point directly towards the
ligands so according to crystal field theory, are raised in energy (unfavourable interaction
between the electrons of the ligands and those of the metal)
-
The inter-axial orbitals (t2g symmetry in an octahedral environment) do not point directly
towards the ligands, so are lower in energy than the axial orbitals.
Crystal Field Theory
Square pyramidal and Square Planar Geometry from Octahedral
dx2-y2
dz2, dx2-y2
dx2-y2
large ΔE
dz2
dxy
Δo
dz2
dxy
TM
d-orbitals
dxz, dyz
dxz, dyz, dxy
dxz, dyz
M
M
M
octahedral
square pyramidal
square planar
-
From the octahedral crystal field splitting diagram, pull off one of the ligands along the
z-axis.
-
Since this partly removes an unfavourable (according to CF theory) interaction in the
z-direction, all orbitals with a z-component (dz2, dxz and dyz) fall in energy. The others go up
in energy.
-
Removing the other ligand on the z-axis has the same effect, leading to the energy level
diagram for a square planar complex. Note the large energy gap between the dxy and dx2-y2
orbitals. As a result, square planar complexes are almost exclusively those of d8 metals (all
metal orbitals are filled except the dx2-y2) and so have 16 electrons rather than 18. See later.
-
Crystal field theory is therefore quite useful for quickly predicting the order of the energy
levels in transition metal complexes. However, the assumption that all bonding is ionic and
no covalent interactions occur is unrealistic. According to this assumption, CO (an excellent
ligand for reasonably electron rich metals) would be predicted to be a terrible ligand (no
negative charge and v. small dipole), ligands would not be expected to bond to metals that do
not have a formal positive charge (i.e. Pd(PPh3)4 and Fe(CO)42- would definitely not exist),
ligands cannot be σ-donors, π-donors or π-acceptors, and it is therefore impossible to assess
why Δo varies with the ligands as it does.
Crystal Field Splitting Diagram for Tetrahedral Geometry
OCTAHEDRAL
TETRAHEDRAL
Inter-axial orbitals point more
directly at the 4 ligands Æ more of an
unfavourable interaction between the
ligand electrons and those of the metal
Æ higher in energy
Axial orbitals point less
directly at the 4 ligands Æ less of an
unfavourable interaction between the
ligand electrons and those of the metal
Æ lower in energy
t2
d orbitals
Δt ~ 4/9 Δo
Δt is much smaller than Δo partly
because none of the metal orbitals
point directly at the ligands, so overlap
is less efficient.
e
M
[ML4]
The same type of approach can be extended in order to figure out the splitting pattern of the
d-orbitals for a variety of other common geometries. Starting from octahedral, one can derive
Jahn-Teller distorted octahedral geometry, square pyramidal and square planar geometry.
By placing the ligands either in the 8 corners or on the 12 edges of a cube, one can derive the
crystal field splitting diagram for 8-coordinate cubic or 12-coordinate cube-octahedral geometry
(similar approach to that used for tetrahedral geometry). The splitting pattern for trigonal planar
geometry can be derived by considering which orbitals or groups of orbitals point most directly
towards the ligands. A similar approach can be used for trigonal bipyramidal geometry, although
the actual ordering of the orbitals is more difficult to rationalise using such simple arguments.
MO theory ~ Ligand Field Theory
Constructing an MO diagram for an octahedral complex
Symmetry Adapted combinations of Ligand σ-orbitals in an Octahedral Complex
-
In an octahedral environment, the metal orbitals (3d, 4s, 4p for a 1st row TM) divide by
symmetry into 4 sets: s = a1g, p = t1u, axial d = eg, inter-axial d = t2g.
-
The orbitals of the six ligands can be combined to give six symmetry-adapted linear
combinations which are of the correct symmetry to interact with the s, 3 x p and 2 x axial-d
orbitals, but not the inter-axial d orbitals.
-
The result is that 3 orbitals (the inter-axial d-orbitals) are non-bonding, while the rest (6 metal
orbitals and 6 ligand orbitals) combine to form six bonding and six anti-bonding MOs. See
next page.
-
This is a much more correct approach than crystal field theory, but is not as easy to use.
MO energy levels for an octahedral complex
(only σ-bonding considered)
t1u*
4p (t1u)
a1g*
4s (a1g)
eg*
ΔO
3d (eg + t2g)
t2g
(a1g + t1u + eg)
eg
TM
6L
t1u
a1g
•
•
The six bonding orbitals are filled with 12 electrons from the six ligands
Orbitals shown in red (t2g and eg*) are the frontier orbitals where d-electrons reside.
π-bonding ligands
(the above MO diagram does not take into account π-bonding)
filled orbital
M
•
L
M
empty orbital
M
L
L
σ-donor
π-donor
π-acceptor
NH3, CH3-, H-
Cl-, OH-, NR2-, OH2
CO, NO+, CN-
For π-acceptor ligands, the bonding is SYNERGIC: σ-donation to the metal strengthens
π-backbonding to the ligand, and π-donation from the metal to the ligand strengthens the
σ-donor component of bonding.
•
This is because σ-donation leads to increased electron density on the metal, which allows
increased π-backdonation. Conversely, π-backdonation reduces the amount of electron
density on the metal, which allows more σ-donation from the ligand to the metal.
Cr(CO)6: Octahedral complex with good π-acceptor ligands
σ-interaction
M
lobe of
acceptor orbital
(whole orbital
not shown)
C
π-interaction
O
M
C
O
M
C
O
slightly antibonding
HOMO of CO
axial d-orbitals
strongly antibonding
π* orbitals of CO
Note: The 12 empty π*-orbitals of the six CO ligands in a molecule like [Cr(CO)6] can be
combined to form 12 linear combinations of orbitals (3 x T1u, 3 x T2g, 3 x T1g, 3 x T2u). Only the
three linear combinations with T2g symmetry are of the correct symmetry to interact with the t2g
orbitals (dxy, dxz and dyz) on the metal.
MO energy levels for an octahedral complex
with π-acceptor ligands (e.g. [Cr(CO)6])
t1u*
4p (t1u)
a1g*
4s (a1g)
t2g*
π* orbitals of CO (t2g)
eg*
large
ΔO
3d (eg + t2g)
t2g
(a1g + t1u + eg)
eg
Cr
6 CO
t1u
a1g
•
π-backdonation to CO from the t2g orbitals (which are non-bonding in the absence of
π-interactions between the metal and the ligands).
•
The 3 t2g orbitals and 3 high lying π* orbitals of the CO ligands form 3 bonding MOs and
3 antibonding MOs.
•
Since the CO π* orbitals are empty, the d-electrons occupy the bonding MO from this
interaction.
•
The result is (1) a very large Δo, so the eg orbital is likely to remain empty.
(2) the t2g orbital is strongly bonding (wants to be filled with 6 electrons)
Æ complexes of strong π-acceptor ligands are the most likely to obey the 18 electron rule
Simplified picture of how π-acceptor and π-donor interactions affect
the MO diagram - Only the frontier orbitals are shown
t2g*
π* (t2g)
eg*
eg*
L
large
ΔO
π-acceptor ligands
increase ΔO
t2g
TM complex with
σ-bonding only
t2g
[Cr(CO)6]
with π-backdonation
from Cr to CO
eg*
π-donor ligands
decrease ΔO
eg*
small
ΔO
t2g*
t2g
TM complex with
σ-bonding only
t2g
L
TM complex with πdonation from
Ligand to Metal
π-donor ligands
•
π-donation from the ligands to the t2g orbitals Æ the 3 t2g metal orbitals and 3 low lying, filled
ligand orbitals of π-symmetry form 3 bonding MOs and 3 antibonding MOs.
•
Since the interacting ligand orbitals are full, these electrons occupy the bonding MO from this
interaction, and the d-electrons occupy the antibonding MO.
•
The result is (1) a small Δo
(2) the t2g orbital is weakly antibonding
The Spectrochemical Series of Ligands
Using MO theory (Ligand Field Theory) instead of Crystal Field Theory, we have seen that
ligands can be σ-donors, π-donors or π-acceptors, and that the nature of the ligands strongly
affects Δo in octahedral complexes.
This effect can often be seen visually: e.g. for [CoIIIX(NH3)5]n+ (a d6, 18-electron complex).
X
n
IClNH3
2
2
3
Colour of
the
complex
Purple
Pink
Yellow
eg
Colour
absorbed
Yellow
Green
Blue
Δo
d
t2g
•
The colour of the complexes above results from promotion of an electron from the t2g orbital
to the eg orbital. The energy of light absorbed therefore corresponds to the size of Δo.
[Note: this type of simple treatment can only be applied in certain cases (e.g. d1 or d9
complexes and octahedral 3d complexes with a d4 or d6 configuration). For other
configurations, it is necessary to consult a Tanabe-Sugano diagram and apply a more rigorous
treatment].
•
For complexes with a single absorption in the visible region of the spectrum, the colour of
light absorbed can be determined from the colour wheel (the colour of the light absorbed is
found opposite the colour of the complex)
•
Since the order of energy is blue > green > yellow, then the NH3 complex can be seen to have
a larger Δo than the Cl- complex, which has a larger Δo than the I- complex.
Since the effect of the ligands on the size of Δo is a visible change, the resulting series of ligands
is called the spectrochemical series. The order of ligands in the spectrochemical series follows
their behaviour as π-donors, σ-donors or π-acceptors very nicely. For Δo:
I- < Br- < S2- < SCN- < Cl- < F- < OH- < OH2 < MeCN < NH3 < PR3 < CN- < CO < NO+
good π-donors
│ OK π-donors │
σ-donors
│
good π-acceptors
However, these π-affects are not the whole story, because organometallic ligands such as CH3or H- are located high in the spectrochemical series (H- is similar to CO). Both H- and CH3(in the absence of α-agostic interactions) are purely σ-donor ligands, so their ability to act as high
field ligands is a result of their extremely high σ-donor ability.
The Spectrochemical Series of Metals
Δo depends not only on the nature of the ligands, but also on the metal and its oxidation state.
The spectrochemical series for metal ions (approximate) is shown below:
Mn2+ < Ni2+ < Co2+ < Fe2+ < V2+ < Co3+ < Mn4+ < Mo3+ < Rh3+ < Ru3+ < Pd4+ < Ir3+ < Pt4+
This series is not quite as regular as the spectrochemical series of ligands, but there are obvious
trends:
(1) Δo increases with increasing oxidation number (Co2+ < Co3+ etc.)
Reason - Metal ions in a higher oxidation state have greater polarising power Æ bonding
becomes more covalent and less ionic
(the nephelauxetic effect = Latin for cloud expanding).
(2) Δo increases down a group (Co3+ << Rh3+ < Ir3+)
Reasons - Improved M-L bonding for larger 4d and 5d orbitals relative to the 3d orbitals.
- Higher effective nuclear charge (i.e. the actual charge on the metal in a Rh(III)
complex will be higher than in an analogous Co(III) complex because heavier
congeners are easier to oxidise).