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Electronic Spectroscopy of Polyatomics
We shall discuss the electronic spectroscopy of the following
types of polyatomic molecules:
1. general AH2 molecules, A = first-row element
2. formaldehyde
3. benzene & aromatic complexes (Hückel theory)
4. transition metal complexes
In considering the electronic spectra of polyatomic molecules,
symmetry arguments are very important, and each MO will
belong to a symmetry species associated with the point group
of the molecule.
It is possible for polyatomic molecules that have linear ground
states to change to bent conformations in the excited states,
thereby changing the symmetry species associated with each
of the MOs (e.g., H-C/C-H is linear in the 1Eg+ ground state
but trans bent in the first excited state)
The total electron density and resulting surface of the total
molecule is relatively easy to visualize, but identifying and
rationalizing contributions from individual electrons to certain
localized properties within a molecule is the real challenge:
notably, promotion of electrons from one orbital to another
(transitions) or removal of electrons (ionization) must both
obey symmetry selection rules.
AH2 Molecules: pHAH = 180o
The AH2 molecules have two possible extreme geometries:
linear (D4h) and bent at 90o (C2v)
pHAH = 180o: Symmetry labels from the D4h point group are
assigned to all of the AOs (internuclear axis along z):
2s AO on the A atom is spherically symmetric, Fg+
2pz AO on the A atom is along z, Fu+
2px, 2py AOs on the A atom are degenerate, Bu
1s AO on H cannot by itself be assigned a symmetry species,
but rather is treated as a set with its partner by considering inphase and out-of-phase contributions:
+
Fg+
+
In-phase 1s+1s H AOs
+
Fu+
-
Out-of-phase 1s-1s H AOs
Rules for MO formation are the same as for diatomics:
(1) AOs must be of the same symmetry to form an MO
(2) The MOs that make significant contributions to bonding
and anti-bonding, have significantly different character
than the AOs from which they are made, and are
composed of AOs of comparable energies.
The 1s+1s H AOs combine with the 2s on A only, since they
both have Fg+ symmetry (no Fg-, MOs so omit +). The MO is
labelled 2Fg, (convention is to number MOs of the same
symmetry in order of increasing energy). If 2s AO on A is
out-of-phase with the 1s+1s AO, the anti-bonding 3Fg MO is
formed (nodal plane between A and H).
AH2 Molecules: pHAH = 90o
The 2s, 2px, 2py, 2pz on the A atom are assigned to the a1, b1,
b2 and a1 symmetry species, respectively (C2v point group, zaxis along the C2 rotation axis).
The 1s H AOs are again broken down into in-phase and outof-phase contributions:
+
a1
+
In-phase 1s+1s H AOs
+
b2
-
Out-of-phase 1s-1s H AOs
The 1s+1s a1 AO combines with 2s or 2pz AOs on A to give
the 2a1, 3a1 and 4a1 MOs (see Walsh diagram).
The 2py AOs on A can combine only with the 1s-1s AOs to
make the 1b2 and 2b2 MO, but 2px cannot combine with AOs
on the H atoms, and becomes the 1b1 lone pair MO.
Constructing the MOs:
Using the aufbau principle, e- can be fed pairwise into the
MOs to construct the ground or excited state configurations
for the molecule (2 e-for F, 4 e-for B, 6 e- for *, etc.).
The label X is for the ground state; A, B, C, ... are used for the
excited states with the same multiplicity as X; and a, b, c, ...
are used for excited state with different multiplicity.
Sometimes the tilde (~) is used above the label to differentiate
it from symmetry species labels.
Walsh Diagram
The Walsh diagram shows the correlation of the MOs as the
HAH angle changes from 90o to 180o (z axis in the linear
molecule becomes the y axis in the bent molecule)
pHAH 180o:
Note that the non-bonding
1Fg MO is not shown, very
much like the 1s AO of the
A atom
pHAH 90o:
Note that the non-bonding
1a1 MO is not shown, very
much like the 1s AO of the
A atom
The 1s-1s AOs combines with the 2pz AO on A (both Fu+
symmetry) to form the 1Fu and 2Fu MOs, which are bonding
and anti-bonding, respectively.
The 2px and 2py AOs on A cannot combine with either set of
H 1s AOs for symmetry reasons - thus they remain as doubly
degenerate AOs on A, labelled as the 1Bu MOs.
MOs are arranged in order of increasing energy, based on the
principle that those with decreased s character or increased
number of nodes will be higher in energy. (e.g., 2Fg and 1Fu
MOs are bonding btw. A and H, but the nodal plane through A
makes 1Fu higher in energy).
Configurations and Geometries
Some ground and excited state configurations are below:
Molecule
Configuration
State
pHAH
LiH2
(1σg)2 (2σg)2 (1σu)1
X̃ 2Σ%u
180o (?)
(1a1)2 (2a1)2 (3a1)1
à 2A1
< 180o (?)
(1σg)2 (2σg)2 (1σu)2
X̃ 1Σ%g
180o (?)
(1a1)2 (2a1)2 (1b2)1 (3a1)1
ã 3B2, Ã B2
< 180o(?), < 180o(?)
(1a1)2 (2a1)2 (1b2)2 (3a1)1
X̃ 2A1
131o
(1σg)2 (2σg)2 (1σu)2 (1πu)1
à Πu
2
180o
(1a1)2 (2a1)2 (1b2)2 (3a1)2
ã 1A1
102.4o
(1a1)2 (2a1)2 (1b2)2 (3a1)2 (1b1)1
3
1
X̃ B1, b˜ B1
134o, 140o
(1a1)2 (2a1)2 (1b2)2 (3a1)2 (1b1)1
X̃ B1
(1a1)2 (2a1)2 (1b2)2 (3a1)1 (1b1)2
à A1
(1a1)2 (2a1)2 (1b2)2 (3a1)2 (1b1)2
X̃ A1
BeH2
BH2
CH2
NH2(H2O+)
H2O
1
2
103.4o (110.5o)
2
144o (180.0o)
1
104.5o
(all bond angles are determined from electronic spectra, except LiH2 and BeH2, which are unknown species)
1a1 or 1Fg AO is non-bonding, favouring neither the bent nor
linear shapes. Occupation of 2Fg or 1Fu favours linearity,
since energies are lowest for 180o angle (Walsh).
Thus, LiH2 and BeH2 should have linear ground states.
Promotion of an electron to the next highest MO (i.e., the 3a11Bu) has a drastic effect, since this MO favours the bent
geometry energetically.
Thus, from molecules like BH2 and CH2, which have been
experimentally proven to have bent geometries, one e- in the
3a1-1Bu MO counterbalances the four e-in the 2a1-2Fg and 1b21Bu MOs, predicting that BeH2 and LiH2 should be bent in the
excited state.
Configurations and Geometries, 2
BH2 has a X2A1 ground state, where the angle is known to be
131o (due to the single e- in the 3a1 MO). However, if this eis promoted to the 1b1-1Bu MO produces a linear molecule (no
particular geometry favoured).
CH2 has two electrons in the 3a1 MO, favoured by a very
small angle of 102.4o. Promotion of an e- from 3a1 to 1b1
results in both singlet and triplet states, where the molecule is
still bent but with a larger angle. The triplet state of CH2,
X3B1, lies lower in energy (by 37.75 kJ mol-1) than the singlet
state, a1A1. So the former is the ground state, and the latter a
low-lying excited state.
NH2 has similar geometry changes to CH2, the only difference
in configuration being an extra electron in the 1b1 MO, which
does not seem to favour any particular geometry. The H2O+
ion (isoelectronic with NH2), is also equite similar.
H2O has a ground configuration with 2 e- in the 3a1 orbital,
strongly favouring a bent molecule. Excited states of H2O
have an e- promoted from the 1b1 MO to a large (size of the
molecule), high-energy MO called a Rydberg orbital - this
orbital has little influence on the geometry of the molecule, so
H2O in the “Rydberg states” has essentially the same
geometry as the ground state.
Summary: Thus, the Walsh MO diagram predicts (and agrees
with theory & experiment) that AH2 molecules with 4 or less
valence e- are have linear ground states, while those with 5 or
more will have bent ground states.
BAB Molecules
The symmetric non-hydride molecules BAB are common
molecular species which can also be rationalized with a Walsh
diagram, and a Walsh diagram can be constructed using the
same principles asfor AH2.
Valence s and p electrons complicate matters. Molecules
should be linear with 16 or less valence electrons, and bent
with 17 or more electrons.
Linear examples: C3 (12 VE); CO2 (16 VE)
Bent examples: NO2 (17 or 18 VE); O3 (18 VE)
Exceptions: SiC2 (isovalent with C3; T-shaped) - the reason
for this is that Walsh’s rules are for covalently bound
molecules, not ionic molecules (i.e., Si+C2-).
Formaldehyde
Formaldehyde has 16 e-. 12 e- are involved in the following
MO’s: 3 F bonding, 3 F* anti-bonding, 1 B bonding, 1 B* antibonding and 2 lone pair (oxygen).
The MO diagram for formaldehyde can be constructed by
assigning symmetry species to all of the AOs used to construct
the MOs:
C2v
E
C2
σ(xz)
σ(yz)
2H (1s)
2
0
2
0
a1 + b1
C (2s)
1
1
1
1
a1
C (2px)
1
-1
1
-1
b1
C (2py)
1
-1
-1
1
b2
C (2pz)
1
1
1
1
a1
O (2s)
1
1
1
1
a1
O (2px)
1
-1
1
-1
b1
O (2py)
1
-1
-1
1
b2
O (2pz)
1
1
1
1
a1
The O(2s) AO is mixed with the C-O and C-H F bonding
orbitals, which all have a1 symmetry, so these three MOs are a
mixture of F-bonding and lone pair character (see diagram next
page).
The O(2p) lone pair (2b2) falls between the 1b1 and 2b1 (B and
B*) MOs, and the electrons in these orbitals are the main
concern of electronic spectroscopy. The 2b2 n MO is the
highest occupied molecular orbital (HOMO), and the 2b1 B*
MO is the lowest unoccupied molecular orbital (LUMO).
Spacings absorb in the UV/visible region!
Formaldehyde, 2
The complete MO diagram is shown below:
The 4 valence electrons can occupy the higher energy MOs:
H
H
H
+
C
_
C
O
1b1(B)
bonding
+
H
O
_
2b2(n)
non-bonding
y
H
H
+
C
_
O
+
z
2b1(B*)
anti-bonding
Energy increases as B < n < B*.
ground configuration: ...(1b1)2(2b2)2, state: X1A1
Promotion of a electron from the non-bonding (n) 2b2 MO to
the anti-bonding (B*) 2b1 MO gives an excited configuration:
...(1b1)2(2b2)1(2b1)1 which has the states: a3A2 and A1A2.
Formaldehyde, 3
6 outer valence e- are involved in major electronic transitions:
Ground: (5a1)2(1b1)2(2b2)2 (X1A1 state)
First excited state: (5a1)2(1b1)2(2b2)1(2b1)1
(gives rise to a3A2 and A1A2 states)
HOMO-LUMO transition involves transfer of in-plane, nonbonding O2py (2b2) e- to the anti-bonding C-O B* (2b1) MO.
This B*7n transition occurs for =C=O, =C=S, -N=O, -NO2 and
-O-N=O chromophores.
The A1A2-X1A1 transition is electric-dipole forbidden, but is
one of the most famous electronic spectra (3530 - 2300 Å). It
shows up because of vibronic coupling with the L4 out-ofplane bend (b1) (since A2qB1 = B2, the A1A2-X1A1 borrows
some intensity from the B1B2-X1A1 transition near 1750 Å.
Formaldehyde, 4
Not only is formaldehyde a prototype for electronic spectroscopy
for heteronuclear chromophores, it was also the first electronic
transition studied with fine rotational detail describing an
asymmetric top.1
The A1A2-X1A1 transition can be observed by laser excitation,
where a tunable laser excites the A state, and then total
fluorescence is monitored.
Much of the fine structure is unexplained by the simple electronic
picture. Long progressions are attributed to the L2 CO stretching
mode, but also, non-planarity of the excited state.
1. Clouthier & Ramsay, Ann. Rev. Phys. Chem. 34, 31, (1983)
2. Miller & Lee, Chem. Phys. Lett. 33, 104, (1975)
Formaldehyde, 5
The a and A states of formaldehyde and other similar
molecules are known as nB* states, and the a - X and A - X
transitions such as that described above are known more
commonly as B*-n or n-to-B* transitions.
The B*-n transitions are easily distinguished from the more
common B*-B transitions (which occur in many aromatic
systems), since the former are blue shifted in a hydrogen
bonding solvent. This is due to interaction of 1s AO of OH
groups (e.g., ethanol) with the n orbital, which increases the
energy of the B*-n transition.
The e- in the 2b1 B* MO energetically favour a pyramidal
shape for the CH2O molecule, because the B* MO can overlap
with 1s + 1s AO’s on the H atoms and the 2s AO on the C
atom, resulting in an increase in s character in this MO and a
lowering of energy relative to the planar molecule (two
equivalent schema shown below):
_
+
H
H
C
O
The bend of the C-H bond away from a the usual plane of the
CH2O molecule is 38o in the A1A2 state and 43o in the a3A2
state. Note the MO’s must be reclassified in terms of the Cs
point group for these excited states.
Formaldehyde, 6
A Walsh-type diagram can be constructed for formaldehyde,
which correlates the MOs of the planar C2v ground state and
the Cs first excited state:
Electronic Spectra of Aromatics
In molecules with electrons in B-orbitals (notably conjugated
organic aromatic systems), the ground and excited states of the
molecule, can be described by an approximate LCAO method
known as the Hückel method.
The secular determinant used for diatomics (Lecture 9a) can
be expanded for general use with polyatomics:
/0
00 H & ES
H22 & E ... H2n & ES2n
00 12
12
00
00
!
!
!
00
00
00 H1n & ES1n H2n & ES2n ... Hnn & E
H11 & E
H12 & ES12 ... H1n & ES1n
/0
00
00
00 ' 0
00
00
00
00
where Hnn are the Coulomb integrals, Hmn (m … n) are the
resonance integrals, Smn (m … n) are the overlap integrals, and
E is the orbital energy. This may be abbreviated as:
|Hmn & ESmn | ' 0
Use of the Hückel method requires that a number of
approximations be made, and that only the B electrons are
considered.
Hückel Method
1. Only B electrons are considered, e- in F MOs are neglected.
The B and F MOs in highly symmetric molecules do not
have the proper symmetry for overlap, so in this case this is
not even an approximation. In less symmetric molecules,
the energies of the F MOs are much less than the B MOs
(and F* MOs greater than the B* MOs), so that F MOs can
still be neglected.
2. For m … n:
Smn
' 0
3. When m = n, Hnn is the same for all atoms (set to "):
Hnn ' "
4. When m … n, Hmn is the same for any pair of directly bonded
atoms (set to $):
Hmn ' $
5. When m and n are not directly bonded
Hmn ' 0
The B-electron wavefunctions are given by
R ' j ciPi
i
where Pi correspond to only the 2p AOs on C, N and O atoms
which are involved in the B MOs.
Benzene
The Hückel treatment of benzenes 6 2pz AOs give a secular
determinant:
/0
00
00
00
00
00
00
00
00
00
00
0
x 1 0 0 0 1
1 x 1 0 0 0
0 1 x 1 0 0
0 0 1 x 1 0
0 0 0 1 x 1
1 0 0 0 1 x
/0
00
00
00
00
00 ' 0
00
00
00
00
00
0
where:
"& E
$
' x
Solving the determinant (or by methods of solving
simultaneous equations), the solutions are obtained:
x ' ±1, ±1 or ±2
E ' " ± $, " ± $, or " ± 2$
The E = " ± $ solution appears twice, meaning it is a doubly
degenerate MO energy level, and the resonance integral $ is
negative, as usual. The 6 MOs are:
" - 2$
"-$
"
E
"+$
" + 2$
The aufbau principle can
be used to fill up the MOs
in the usual way, the
doubly degenerate MOs
are the HOMO and
LUMO in this case.
Benzene, 2
The symmetry species of the D6h
point group can be assigned to the
MOs (only parts above the rings
are shown, parts below are
identical, but of opposite parity)
The energy of the MOs increases
with the increasing number of
nodal planes perpendicular to the
ring. MOs are antisymmetric w.r.t.
reflection through the ring plane,
just like the p AOs from which
they are constructed.
The ground configuration is:
...(1a2u)2 (1e1g)4, and is a totally
symmetric singlet state: X1A1g
If an e- is promoted from e1g MO to a e2u MO, then the first
excited configuration is ...(1a2u)2 (1e1g)3 (1e2u)1, Since a single
vacancy in 1e1g can be treated like an electron, this
configuration has the same states as the configuration arising
from ...(1a2u)2 (1e1g)1 (1e2u)1.
Thus, the symmetry species of the orbital part of the electronic
wavefunction is obtained from
o
'(Re ) ' e1g × e2u ' B1u % B2u % E1u
In the partially occupied MOs, e- may be parallel (S = 1) or
antiparallel (S = 0), meaning there are six possible states:
1,3
B1u, 1,3B2u, 1,3E1u.
Transition Metal Complexes
Transition metal complexes have partially filled 3d, 4d and 5d
AOs (here we consider the first transition series, 3d)
Transition metals readily form complexes of all sorts, e.g.,
[Fe(CN)6]4-, Ni(CO)4 and [CuCl4]2-.
Atoms or collections of atoms that bond to the transition metal
centre are referred to as ligands. Ligands are normally
arranged in a highly symmetrical manner:
4-
CN
CO
CN
NC
Fe
Ni
CN
NC
CN
octahedral
OC
Cl
Cl
CO
CO
tetrahedral
2-
Cu
Cl
Cl
square planar
we will focus on the octahedral case.
Two specialized forms of MO theory:
Crystal Field Theory:
In a transition metal complex, the higher energy occupied
MOs can be regarded as the perturbed d AOs. If this
perturbation is weak, the ligands can be treated as point
charges located octahedrally on the axes of the Cartesian
coordinate system (i.e., like Na+ surrounded by its 6 nearest
neighbour Cl- ions).
Ligand Field Theory:
When ligands interact more strongly with the d AOs, the MOs
of the ligands must be taken into account.
Crystal Field Theory
In the presence of six octahedrally arranged point charges on
the Cartesian axes of the 5 d AOs, the d AOs are perturbed an
assigned according to the Oh point group.
Symmetry species for a variety of point groups are below:
d-orbitals
Point Group
dz 2
dx 2 & y 2
dxy
dyz
Oh
eg
t 2g
Td
e
t2
)
dxz
D3h
a1
D4h
a1g
D4h
σg+
C2v
a1
a1
a2
C3v
a1
a1
a2
e
C4v
a1
b1
b2
e
D2d
a1
b1
b2
e
D4h
a1
eN
b1g
eO
b2g
eg
δg
e2
πg
b2
b1
e3
Crystal Field Theory, 2
The set of 5 degenerate d AOs break into doubly degenerate eg
and triply degeneate t2g orbitals in a regular octahedral
crystal field.
The d(z2) and d(x2-y2) AOs have much of their electron density
along the metal-ligand (M-L) bonds, and e- therein experience
much more repulsion by the ligand e- than do the d(xz), d(yz)
and d(xy) orbitals.
Thus, the eg orbitals are pushed up in energy by (3/5))0 and
the t2g orbitals are pushed down in energy by (2/5))0, where )0
is the eg - t2g splitting or crystal field splitting.
eg
(3/5))0
d
E
(2/5))0
t2g
The value of )0 normally corresponds to absorption in the
visible (and sometimes UV) portion of the spectrum,
accounting for the beautiful colourations of transition metal
complexes ()0 is also known as 10Dq, or )T for tetrahedral
complexes, ) for misc. symmetry, etc.).
Crystal Field Theory, 3
For d1, d2, d3, d8, d9 and d10 configurations, e- prefer to have
parallel spins for minimum energy, and pair as the levels fill
according to the Pauli-exclusion principle.
e.g., [Cr(H2O)6]3+, Cr3+ has a d3 configuration (lost one d and
two s electrons from a 4s23d4 configuration). Each electron
goes into a separate t2g orbitals with parallel spin to minimize
energy, giving a quartet ground state (X4A2g).
For d4, d5, d6 and d7 configurations, the way the electrons are
fed into the orbitals depends upon the size of the splitting )0:
(a) If small, e- prefer to go to the eg orbitals with parallel
spins. (b) If large, e- prefer to go to the t2g orbitals with
antiparallel spins.
(a)
(b)
Ligand Field Theory
When ligands interact more strongly with the d AOs, the MOs
of the ligands must be taken into account.
Ligand MOs are roughly classified as two types:
F MOs, cylindrically symmetrical about the M-L bond
B MOs, not cylindrically symmetrical about the M-L bond
The former is normally stronger, and may be provided by a
lone pair (one of the most studied cases is the lone pair orbital
on the CO ligand in metal carbonyl complexes).
The F MOs can be classified in different point groups with
different ligand arrangements. For example, in octahedral
ML6, it can be shown that the 6 ligand F MOs are split into a1g,
eg and t1u orbitals. The effect of these ligand MOs is to
interact with d orbitals of the same symmetry. The crystal
field orbital increases in energy, and the ligand orbital energy
decreases. The net effect is an increase in )0, which leads to
low spin complexes rather than high spin complexes.
Electronic Transitions
A d6 T.M. complex might have an MO diagram like this:
The F bonding orbitals are filled by the 12 valence e-, and
remaining 6 valence e- fill t2g and eg orbitals accordingly.
All of this gives rise to very complex manifolds of states
which will not be derived here - however there is a
simpliflication that can be used in interpreting electronic
spectra of octahedral t.m. complexes:
All higher energy orbitals which may be occupied are t2g or eg:
since g means “symmetric w.r.t. inversion through the centre
of the molecule”, all states must also be g (so all excited and
ground states from t2g and eg occupancy are g states: however all g-g transitions are forbidden, as in homonuclear diatomic
molecules.
How do such complexes absorb radiation???
Electronic & Vibronic Selection Rules
The answer is that interaction may occur between the motion
of electrons and vibrational motions, so that some of the
vibronic transitions are allowed.
Recall that for diatomics a large number of good quantum
numbers exist such that selection rules can be expressed solely
through these numbers. However, in non-linear polyatomic
molecules, the “goodness” of quantum numbers deteriorates
because of the complicated number of motions that are
present, such that there is only one number remaining: the
total electron spin quantum number, S
Thus, the selection rule )S = 0 still applies, unless there is an
atom with high nuclear charge in the molecule (i.e., tripletsinglet transitions are weak in benzene, but much more intense
in iodobenzene).
For the orbital part of the electronic wavefunction, the
selection rules for transitions between two electronic states
depend completely on the symmetry of the states.
Electronic transitions involve the interaction between the
molecule and the electric component of the electromagnetic
radiation - so selection rules are the same as for IR vibrational
transitions in polyatomic molecules.
So the electronic transition intensity is proportional to *Re*2,
where:
Re '
m
)(
))
Re µRe dJe
Selection Rules, 2
For an allowed transition, *Re* … 0, and the symmetry
requirement for this is:
)
))
'(Re) × '(µ) × '(Re ) ' A
or for transitions between non-degenerate states:
)
))
'(Re) × '(µ) × '(Re ) e A
The components of Re along the Cartesian axes are:
m
Re,x '
)(
))
Re µ x Re dJe
Re,y '
m
)(
))
Re µ y Re dJe
Re,z '
m
)(
))
Re µ z Re dJe
and since
|R e| ' (Re,x)2 % (Re,y)2 % (Re,z)2
electronic transitions are allowed if any of the above terms are
non-zero. So, for a transition to be allowed:
)
))
)
))
)
))
'(Re) × '(T x) × '(Re ) ' A
'(Re) × '(T y) × '(Re ) ' A
'(Re) × '(T z) × '(Re ) ' A
If the product of two symmetry species is totally symmetric,
those symmetry species must be the same, thus:
)
))
'(Re) × '(Re ) ' '(T x) and/or '(T y) and/or '(T z)
is the general selection rule for a transition between two
electronic states (remember, replace = with e if degenerate
states are involved).
Selection Rules, 3
If the lower state of the transition is the ground state of a
molecule with all of its MO’s filled (no unpaired e-: a closedshell molecule), then the ground electronic state is totally
symmetric and the selection rule simplifies to:
)
'(Re) ' '(T x) and/or '(T y) and/or '(T z)
If vibrations are excited in either the upper or lower electronic
state (or both), the vibronic transition moment is:
m
Which has the same selection rules as for electronic trans.:
R ev '
)
(
))
R)ev µ Rev dJev
))
'(Rev ) × '(Rev ) ' '(T x) and/or '(T y) and/or '(T z)
and since:
'(Rev ) ' '(Re) × '(Rv)
then:
)
))
)
))
'(Rv) × '(Rv ) × '(Re) × '(Re ) ' '(T x) and/or '(T y) and/or '(T z)
It so happens that very often that the same vibration is excited
in both states, '(RvN) = '(RvO), and the selection rule is the
same as the electronic selection rule. If no vibrations are
excited in the upper or lower state, then '(RvN) or '(RvO) will
be totally symmetric.
Vibrational & Rotational Structure
Vibrational coarse structure is seen in the electronic bands of
some molecules. For example, the A1B2u - X1A1g absorption
spectrum of benzene has this coarse structure below:
Rotational fine structure can be observed, and in principle is
similar to that observed in IR vibrational spectra - though
greater changes in rotational constants are seen between
electronic states. Below are spectra of type B (left: top
experimental, bottom calculated) and type A and C (right, both
calculated) showing rotational fine structure in the A1B2u -X1Ag
system of 1,4-difluorobenzene.
Summary of Chromophores
The absorption of a photon which causes an electronic
transition can often be traced to specific electrons in the
molecule. For example, if there is a C=O group in the
molecule, an absorption around 290 nm will be observed
(though the precise location will depend on the nature of the
molecule). Functional groups that have characteristic optical
absroptions are called chromophores, their presence often
accounts for the colouration of substances.
All of the examples in this summary are different types of
chromophores.
Group
ῡ /cm&1
λmax/nm
εmax/(L mol-1 cm-1)
C=O (π*-π)
61,000
163
15,000
57,300
174
5,500
C=O (π*-n)
37,000-35,000
270-290
10-20
H2O (π*-n)
60,000
167
7,000
(1) d-d transitions
These transitions involve the promotion
of electrons between non-degenerate d
orbitals on transition metal atoms (e.g.,
[Ti(OH2)6]3+, eg - t2g transition near
20,000 cm-1 (500 nm), and the
wavenumber of the absorption
maximum suggests )0 • 20,000 cm-1)
Summary of Chromophores, 2
(2) vibronic transitions
Major problem with interpretation of visible spectra of
octahedral complexes is that d-d transitions are forbidden.
The Laporte selection rule says that the only allowed
transitions are those accompanied by a change in parity (u : g
and g : u only allowed).
The d-d transition is parity forbidden b/c it
corresponds to a g-g transition -but
vibration of the molecule can destroy the
inversion symmetry of the molecule, and
then the g, u classification no longer
applies. Removal of the centre of
symmetry gives rise to a vibronically
allowed transition (though it is weakly
allowed).
(3) charge-transfer transitions
Absorption of radiation may occur as the result of transfer of
an electron from a ligand MO into the d orbitals of the metal
atom, or vice versa. Such transitions are associated with the emoving over large distances, meaning the transition moment
dipoles are very large and absorptions very intense. For
example, in MnO4- ions, the intense violet colour results from
an electron transfer from an MO largely confined on O to an
MO confined on Mn - this is a ligand-metal charge transfer
(LMCT) transition. The reverse, a metal-ligand charge
transfer (MLCT) transition, is also possible (e.g., e- from d
orbitals into B* MOs of aromatic ligands is a very common
example).
Summary of Chromophores, 3
(4) B*-B and B*-n transitions
B*-B transitions
Absorption by a C=C double bond excites the B
e- into an anti-bonding B* orbital, and the
chromophore activity is therefore due to a B*-B
transition. For unconjugated double bonds,
absorption occurs around 180 nm (UV), or 7 eV
for the transition to occur.
When the C=C bond is in a conjugated chain,
the energies of the MOs are closer together, and
the B*-B transition absorbs at longer
wavelengths (can even move to visible region
for really long conjugated chains).
B*-n transitions
The transition responsible for absorption in
carbonyl compounds involves the lone pairs
on the O atom in the C=O bond. The concept
of the “lone pair” means that there is an MO
in which the e- are largely confined to the O
atom.
One of these electrons in the n MO may be
excited into an empty B* MO, giving rise to a
B*-n transition, with typical absorption
energies around 4 eV (290 nm). These are
symmetry forbidden transitions, and as a
result, are very weak.
Key Concepts
1.
It is possible for polyatomic molecules (notably, AH2
type molecules) that have linear ground states to change
to bent conformations in the excited states, thereby
changing the symmetry species associated with each of
the MO’s.
2.
AH2 molecules are examined in details, with the Walsh
diagram applied to monitor the relationship between
MOs in linear and bent molecules in the ground and
excited states.
3.
Formaldehyde is examined in detail, as being on of the
basic C=O chromophores. The B*-n transition is
responsible for absorption of visible radiation.
4.
Hückel theory is developed to treat molecules containing
C=C chromophores, where the B*-B transition is
important for strong absorption.
5.
Transition metal complexes can be treated with crystal
field or ligand theory, depending on the interactions
between the ligands and transition metals. Most of these
complexes have d-d transitions, and the metal centre are
chromophores absorbing in the visible region of the EM
spectrum.
6.
Electronic symmetry selection rules are defined, with the
only quantum number selection rule being )S = 0. g - g
and u - u transitions, which are symmetry forbidden, may
weakly occur as the result of accompanying vibronic
transitions