Electronic Spectroscopy of PolyatomicsWe shall discuss the electronic spectroscopy of the followingtypes of polyatomic molecules:1. general AH2 molecules, A = first-row element2. formaldehyde3. 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 willbelong to a symmetry species associated with the point groupof the molecule.

It is possible for polyatomic molecules that have linear groundstates to change to bent conformations in the excited states,thereby changing the symmetry species associated with eachof the MOs (e.g., H-C/C-H is linear in the 1Eg

+ ground statebut trans bent in the first excited state)

The total electron density and resulting surface of the totalmolecule is relatively easy to visualize, but identifying andrationalizing contributions from individual electrons to certainlocalized properties within a molecule is the real challenge:notably, promotion of electrons from one orbital to another(transitions) or removal of electrons (ionization) must bothobey 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 areassigned 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, Bu1s AO on H cannot by itself be assigned a symmetry species,but rather is treated as a set with its partner by considering in-phase and out-of-phase contributions:

Fg+

+ +Fu

+

+ -

In-phase 1s+1s H AOs 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 characterthan the AOs from which they are made, and arecomposed of AOs of comparable energies.

The 1s+1s H AOs combine with the 2s on A only, since theyboth have Fg

+ symmetry (no Fg-, MOs so omit +). The MO is

labelled 2Fg, (convention is to number MOs of the samesymmetry in order of increasing energy). If 2s AO on A isout-of-phase with the 1s+1s AO, the anti-bonding 3Fg MO isformed (nodal plane between A and H).

The 2s, 2px, 2py, 2pz on the A atom are assigned to the a1, b1,b2 and a1 symmetry species, respectively (C2v point group, z-axis along the C2 rotation axis).

AH2 Molecules: pHAH = 90o

a1

+ +b2

+ -

In-phase 1s+1s H AOs Out-of-phase 1s-1s H AOs

The 1s H AOs are again broken down into in-phase and out-of-phase contributions:

The 1s+1s a1 AO combines with 2s or 2pz AOs on A to givethe 2a1, 3a1 and 4a1 MOs (see Walsh diagram).The 2py AOs on A can combine only with the 1s-1s AOs tomake the 1b2 and 2b2 MO, but 2px cannot combine with AOson the H atoms, and becomes the 1b1 lone pair MO.

Using the aufbau principle, e- can be fed pairwise into theMOs to construct the ground or excited state configurationsfor 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 theexcited 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 differentiateit from symmetry species labels.

Constructing the MOs:

Walsh DiagramThe Walsh diagram shows the correlation of the MOs as theHAH angle changes from 90o to 180o (z axis in the linearmolecule becomes the y axis in the bent molecule)

pHAH 180o:Note that the non-bonding1Fg MO is not shown, verymuch like the 1s AO of theA atom

pHAH 90o:Note that the non-bonding1a1 MO is not shown, verymuch like the 1s AO of theA atom

The 1s-1s AOs combines with the 2pz AO on A (both Fu+

symmetry) to form the 1Fu and 2Fu MOs, which are bondingand anti-bonding, respectively.The 2px and 2py AOs on A cannot combine with either set ofH 1s AOs for symmetry reasons - thus they remain as doublydegenerate AOs on A, labelled as the 1Bu MOs.

MOs are arranged in order of increasing energy, based on theprinciple that those with decreased s character or increasednumber of nodes will be higher in energy. (e.g., 2Fg and 1FuMOs are bonding btw. A and H, but the nodal plane through Amakes 1Fu higher in energy).

Molecule Configuration State pHAH

LiH2 (1σg)2 (2σg)2 (1σu)1 X 2Σ%u 180o (?)

(1a1)2 (2a1)2 (3a1)1 A 2A1 < 180o (?)

BeH2 (1σg)2 (2σg)2 (1σu)2 X 1Σ%g 180o (?)

(1a1)2 (2a1)2 (1b2)1 (3a1)1 a 3B2, A 1B2 < 180o(?), < 180o(?)

BH2 (1a1)2 (2a1)2 (1b2)2 (3a1)1 X 2A1 131o

(1σg)2 (2σg)2 (1σu)2 (1πu)1 A 2Πu 180o

CH2 (1a1)2 (2a1)2 (1b2)2 (3a1)2 a 1A1 102.4o

(1a1)2 (2a1)2 (1b2)2 (3a1)2 (1b1)1 X 3B1, b 1B1 134o, 140o

NH2(H2O+) (1a1)2 (2a1)2 (1b2)2 (3a1)2 (1b1)1 X 2B1 103.4o (110.5o)

(1a1)2 (2a1)2 (1b2)2 (3a1)1 (1b1)2 A 2A1 144o (180.0o)

H2O (1a1)2 (2a1)2 (1b2)2 (3a1)2 (1b1)2 X 1A1 104.5o

State

X 2Σ%uA 2A1

X 1Σ%ga 3B2, A 1B2

X 2A1

A 2Πu

a 1A1

X 3B1, b 1B1

X 2B1

A 2A1

X 1A1

Some ground and excited state configurations are below:Configurations and Geometries

(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 norlinear 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 3a1-1Bu) has a drastic effect, since this MO favours the bentgeometry energetically.

Thus, from molecules like BH2 and CH2, which have beenexperimentally proven to have bent geometries, one e- in the3a1-1Bu MO counterbalances the four e-in the 2a1-2Fg and 1b2-1Bu MOs, predicting that BeH2 and LiH2 should be bent in theexcited state.

BH2 has a X2A1 ground state, where the angle is known to be131o (due to the single e- in the 3a1 MO). However, if this e-is promoted to the 1b1-1Bu MO produces a linear molecule (noparticular geometry favoured).

Configurations and Geometries, 2

CH2 has two electrons in the 3a1 MO, favoured by a verysmall angle of 102.4o. Promotion of an e- from 3a1 to 1b1results in both singlet and triplet states, where the molecule isstill bent but with a larger angle. The triplet state of CH2,X3B1, lies lower in energy (by 37.75 kJ mol-1) than the singletstate, a1A1. So the former is the ground state, and the latter alow-lying excited state.

NH2 has similar geometry changes to CH2, the only differencein configuration being an extra electron in the 1b1 MO, whichdoes 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 H2Ohave an e- promoted from the 1b1 MO to a large (size of themolecule), high-energy MO called a Rydberg orbital - thisorbital has little influence on the geometry of the molecule, soH2O in the “Rydberg states” has essentially the samegeometry as the ground state.

Summary: Thus, the Walsh MO diagram predicts (and agreeswith theory & experiment) that AH2 molecules with 4 or lessvalence e- are have linear ground states, while those with 5 ormore will have bent ground states.

The symmetric non-hydride molecules BAB are commonmolecular species which can also be rationalized with a Walshdiagram, and a Walsh diagram can be constructed using thesame principles asfor AH2.

BAB Molecules

Valence s and p electrons complicate matters. Moleculesshould be linear with 16 or less valence electrons, and bentwith 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 reasonfor this is that Walsh’s rules are for covalently boundmolecules, not ionic molecules (i.e., Si+C2-).

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

Formaldehyde has 16 e-. 12 e- are involved in the followingMO’s: 3 F bonding, 3 F* anti-bonding, 1 B bonding, 1 B* anti-bonding and 2 lone pair (oxygen).

Formaldehyde

The MO diagram for formaldehyde can be constructed byassigning symmetry species to all of the AOs used to constructthe MOs:

The O(2s) AO is mixed with the C-O and C-H F bondingorbitals, which all have a1 symmetry, so these three MOs are amixture of F-bonding and lone pair character (see diagram nextpage).The O(2p) lone pair (2b2) falls between the 1b1 and 2b1 (B andB*) MOs, and the electrons in these orbitals are the mainconcern of electronic spectroscopy. The 2b2 n MO is thehighest occupied molecular orbital (HOMO), and the 2b1 B*MO is the lowest unoccupied molecular orbital (LUMO). Spacings absorb in the UV/visible region!

Formaldehyde, 2The complete MO diagram is shown below:

C OHH

C OHH

_

2b1(B*)anti-bonding

+

+

y

z

+

_

The 4 valence electrons can occupy the higher energy MOs:

1b1(B)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 tothe anti-bonding (B*) 2b1 MO gives an excited configuration:...(1b1)2(2b2)1(2b1)1 which has the states: a3A2 and A1A2.

C O

H

H +

_

2b2(n)non-bonding

Formaldehyde, 36 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, non-bonding 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 isone of the most famous electronic spectra (3530 - 2300 Å). Itshows up because of vibronic coupling with the L4 out-of-plane bend (b1) (since A2qB1 = B2, the A1A2-X1A1 borrowssome intensity from the B1B2-X1A1 transition near 1750 Å.

Formaldehyde, 4Not only is formaldehyde a prototype for electronic spectroscopyfor heteronuclear chromophores, it was also the first electronictransition studied with fine rotational detail describing anasymmetric top.1

1. Clouthier & Ramsay, Ann. Rev. Phys. Chem. 34, 31, (1983)2. Miller & Lee, Chem. Phys. Lett. 33, 104, (1975)

The A1A2-X1A1 transition can be observed by laser excitation,where a tunable laser excites the A state, and then totalfluorescence is monitored.

Much of the fine structure is unexplained by the simple electronicpicture. Long progressions are attributed to the L2 CO stretchingmode, but also, non-planarity of the excited state.

Formaldehyde, 5The a and A states of formaldehyde and other similarmolecules are known as nB* states, and the a - X and A - Xtransitions such as that described above are known morecommonly as B*-n or n-to-B* transitions.

The B*-n transitions are easily distinguished from the morecommon B*-B transitions (which occur in many aromaticsystems), since the former are blue shifted in a hydrogenbonding solvent. This is due to interaction of 1s AO of OHgroups (e.g., ethanol) with the n orbital, which increases theenergy of the B*-n transition.

The e- in the 2b1 B* MO energetically favour a pyramidalshape for the CH2O molecule, because the B* MO can overlapwith 1s + 1s AO’s on the H atoms and the 2s AO on the Catom, resulting in an increase in s character in this MO and alowering of energy relative to the planar molecule (twoequivalent schema shown below):

C O

HH

_ +

The bend of the C-H bond away from a the usual plane of theCH2O molecule is 38o in the A1A2 state and 43o in the a3A2state. Note the MO’s must be reclassified in terms of the Cspoint group for these excited states.

Formaldehyde, 6A Walsh-type diagram can be constructed for formaldehyde,which correlates the MOs of the planar C2v ground state andthe Cs first excited state:

Electronic Spectra of AromaticsIn molecules with electrons in B-orbitals (notably conjugatedorganic aromatic systems), the ground and excited states of themolecule, can be described by an approximate LCAO methodknown as the Hückel method.

The secular determinant used for diatomics (Lecture 9a) canbe expanded for general use with polyatomics:

/000000000000000

/000000000000000

H11 & E H12 & ES12 ... H1n & ES1n

H12 & ES12 H22 & E ... H2n & ES2n

! ! !

H1n & ES1n H2n & ES2n ... Hnn & E

' 0

where Hnn are the Coulomb integrals, Hmn (m … n) are theresonance integrals, Smn (m … n) are the overlap integrals, andE is the orbital energy. This may be abbreviated as:

|Hmn & ESmn | ' 0Use of the Hückel method requires that a number ofapproximations be made, and that only the B electrons areconsidered.

Hückel Method1. Only B electrons are considered, e- in F MOs are neglected.

The B and F MOs in highly symmetric molecules do nothave the proper symmetry for overlap, so in this case this isnot 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 canstill 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 bondedatoms (set to $):

Hmn ' $

5. When m and n are not directly bondedHmn ' 0

The B-electron wavefunctions are given byR ' j

iciPi

where Pi correspond to only the 2p AOs on C, N and O atomswhich are involved in the B MOs.

BenzeneThe Hückel treatment of benzenes 6 2pz AOs give a seculardeterminant:

/0000000000000000000000

/0000000000000000000000

x 1 0 0 0 11 x 1 0 0 00 1 x 1 0 00 0 1 x 1 00 0 0 1 x 11 0 0 0 1 x

' 0

where:" & E$

' x

Solving the determinant (or by methods of solvingsimultaneous equations), the solutions are obtained:

x ' ±1, ±1 or ±2

E ' " ± $, " ± $, or " ± 2$

The E = " ± $ solution appears twice, meaning it is a doublydegenerate MO energy level, and the resonance integral $ isnegative, as usual. The 6 MOs are:

" - 2$

" - $

" + $

" + 2$

"

E

The aufbau principle canbe used to fill up the MOsin the usual way, thedoubly degenerate MOsare the HOMO andLUMO in this case.

Benzene, 2The symmetry species of the D6hpoint group can be assigned to theMOs (only parts above the ringsare shown, parts below areidentical, but of opposite parity)

The energy of the MOs increaseswith the increasing number ofnodal planes perpendicular to thering. MOs are antisymmetric w.r.t.reflection through the ring plane,just like the p AOs from whichthey are constructed.

The ground configuration is:...(1a2u)2 (1e1g)4, and is a totallysymmetric singlet state: X1A1g

If an e- is promoted from e1g MO to a e2u MO, then the firstexcited configuration is ...(1a2u)2 (1e1g)3 (1e2u)1, Since a singlevacancy in 1e1g can be treated like an electron, thisconfiguration has the same states as the configuration arisingfrom ...(1a2u)2 (1e1g)1 (1e2u)1.

Thus, the symmetry species of the orbital part of the electronicwavefunction is obtained from

'(Roe) ' e1g × e2u ' B1u % B2u % E1u

In the partially occupied MOs, e- may be parallel (S = 1) orantiparallel (S = 0), meaning there are six possible states:1,3B1u, 1,3B2u, 1,3E1u.

Transition Metal ComplexesTransition metal complexes have partially filled 3d, 4d and 5dAOs (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 metalcentre are referred to as ligands. Ligands are normallyarranged in a highly symmetrical manner:

CN

Fe

CN

NC CN

CNNCNi

CO

OC COCO

CuCl Cl

ClCl

4- 2-

octahedral tetrahedral square planarwe will focus on the octahedral case.

Crystal Field Theory:In a transition metal complex, the higher energy occupiedMOs can be regarded as the perturbed d AOs. If thisperturbation is weak, the ligands can be treated as pointcharges located octahedrally on the axes of the Cartesiancoordinate system (i.e., like Na+ surrounded by its 6 nearestneighbour Cl- ions).

Ligand Field Theory:When ligands interact more strongly with the d AOs, the MOsof the ligands must be taken into account.

Two specialized forms of MO theory:

d-orbitals

Point Group dz 2 dx 2 & y 2 dxy dyz dxz

Oh eg t2g

Td e t2

D3h a )

1 eN eO

D4h a1g b1g b2g eg

D4h σg+ δg πg

C2v a1 a1 a2 b2 b1

C3v a1 a1 a2 e

C4v a1 b1 b2 e

D2d a1 b1 b2 e

D4h a1 e2 e3

dz 2 dx 2 & y 2 dxy dyz dxz

eg t2g

e

a )

1

a1g

Crystal Field TheoryIn the presence of six octahedrally arranged point charges onthe Cartesian axes of the 5 d AOs, the d AOs are perturbed anassigned according to the Oh point group.

Symmetry species for a variety of point groups are below:

Crystal Field Theory, 2The set of 5 degenerate d AOs break into doubly degenerate egand triply degeneate t2g orbitals in a regular octahedralcrystal field.

The d(z2) and d(x2-y2) AOs have much of their electron densityalong the metal-ligand (M-L) bonds, and e- therein experiencemuch 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 andthe t2g orbitals are pushed down in energy by (2/5))0, where )0is the eg - t2g splitting or crystal field splitting.

eg

t2g

d(3/5))0

(2/5))0E

The value of )0 normally corresponds to absorption in thevisible (and sometimes UV) portion of the spectrum,accounting for the beautiful colourations of transition metalcomplexes ()0 is also known as 10Dq, or )T for tetrahedralcomplexes, ) for misc. symmetry, etc.).

For d1, d2, d3, d8, d9 and d10 configurations, e- prefer to haveparallel spins for minimum energy, and pair as the levels fillaccording to the Pauli-exclusion principle.

Crystal Field Theory, 3

e.g., [Cr(H2O)6]3+, Cr3+ has a d3 configuration (lost one d andtwo s electrons from a 4s23d4 configuration). Each electrongoes into a separate t2g orbitals with parallel spin to minimizeenergy, giving a quartet ground state (X4A2g).

For d4, d5, d6 and d7 configurations, the way the electrons arefed into the orbitals depends upon the size of the splitting )0:(a) If small, e- prefer to go to the eg orbitals with parallelspins. (b) If large, e- prefer to go to the t2g orbitals withantiparallel spins.

(a) (b)

Ligand Field TheoryWhen ligands interact more strongly with the d AOs, the MOsof the ligands must be taken into account.Ligand MOs are roughly classified as two types:F MOs, cylindrically symmetrical about the M-L bondB MOs, not cylindrically symmetrical about the M-L bondThe former is normally stronger, and may be provided by alone pair (one of the most studied cases is the lone pair orbitalon the CO ligand in metal carbonyl complexes).

The F MOs can be classified in different point groups withdifferent ligand arrangements. For example, in octahedralML6, 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 tointeract with d orbitals of the same symmetry. The crystalfield orbital increases in energy, and the ligand orbital energydecreases. The net effect is an increase in )0, which leads tolow spin complexes rather than high spin complexes.

Electronic TransitionsA d6 T.M. complex might have an MO diagram like this:

The F bonding orbitals are filled by the 12 valence e-, andremaining 6 valence e- fill t2g and eg orbitals accordingly.

All of this gives rise to very complex manifolds of stateswhich will not be derived here - however there is asimpliflication that can be used in interpreting electronicspectra 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 centreof the molecule”, all states must also be g (so all excited andground states from t2g and eg occupancy are g states: however -all g-g transitions are forbidden, as in homonuclear diatomicmolecules.

How do such complexes absorb radiation???

Electronic & Vibronic Selection RulesThe answer is that interaction may occur between the motionof electrons and vibrational motions, so that some of thevibronic transitions are allowed.Recall that for diatomics a large number of good quantumnumbers exist such that selection rules can be expressed solelythrough these numbers. However, in non-linear polyatomicmolecules, the “goodness” of quantum numbers deterioratesbecause of the complicated number of motions that arepresent, such that there is only one number remaining: thetotal electron spin quantum number, S

Thus, the selection rule )S = 0 still applies, unless there is anatom with high nuclear charge in the molecule (i.e., triplet-singlet transitions are weak in benzene, but much more intensein iodobenzene).

For the orbital part of the electronic wavefunction, theselection rules for transitions between two electronic statesdepend completely on the symmetry of the states.

Electronic transitions involve the interaction between themolecule and the electric component of the electromagneticradiation - so selection rules are the same as for IR vibrationaltransitions in polyatomic molecules.

So the electronic transition intensity is proportional to *Re*2,

where:

R e ' mR)

e( µR))

e dJe

Selection Rules, 2For an allowed transition, *Re* … 0, and the symmetryrequirement for this is:

'(R)

e) × '(µ) × '(R))

e ) ' A

or for transitions between non-degenerate states:

'(R)

e) × '(µ) × '(R))

e ) e A

The components of Re along the Cartesian axes are:Re,x ' mR

)

e( µ x R

))

e dJe Re,y ' mR)

e( µ y R

))

e dJe Re,z ' mR)

e(µ z R

))

e dJe

and since|R e| ' (Re,x)

2% (Re,y)

2% (Re,z)

2

electronic transitions are allowed if any of the above terms arenon-zero. So, for a transition to be allowed:

'(R)

e) × '(Tx) × '(R))

e ) ' A

'(R)

e) × '(Ty) × '(R))

e ) ' A

'(R)

e) × '(Tz) × '(R))

e ) ' A

If the product of two symmetry species is totally symmetric,those symmetry species must be the same, thus:

'(R)

e) × '(R))

e ) ' '(Tx) and/or '(Ty) and/or '(Tz)is the general selection rule for a transition between twoelectronic states (remember, replace = with e if degeneratestates are involved).

Selection Rules, 3If the lower state of the transition is the ground state of amolecule with all of its MO’s filled (no unpaired e-: a closed-shell molecule), then the ground electronic state is totallysymmetric and the selection rule simplifies to:

'(R)

e) ' '(Tx) and/or '(Ty) and/or '(Tz)

If vibrations are excited in either the upper or lower electronicstate (or both), the vibronic transition moment is:

R ev ' mR)(

ev µ R))

ev dJev

Which has the same selection rules as for electronic trans.:

'(R)

v) × '(R))

v ) × '(R)

e) × '(R))

e ) ' '(Tx) and/or '(Ty) and/or '(Tz)

'(R)

ev) × '(R))

ev) ' '(Tx) and/or '(Ty) and/or '(Tz)

and since:'(Rev) ' '(Re) × '(Rv)

then:

It so happens that very often that the same vibration is excitedin both states, '(RvN) = '(RvO), and the selection rule is thesame as the electronic selection rule. If no vibrations areexcited in the upper or lower state, then '(RvN) or '(RvO) willbe totally symmetric.

Vibrational & Rotational StructureVibrational coarse structure is seen in the electronic bands ofsome molecules. For example, the A1B2u - X1A1g absorptionspectrum of benzene has this coarse structure below:

Rotational fine structure can be observed, and in principle issimilar to that observed in IR vibrational spectra - thoughgreater changes in rotational constants are seen betweenelectronic states. Below are spectra of type B (left: topexperimental, bottom calculated) and type A and C (right, bothcalculated) showing rotational fine structure in the A1B2u -X1Agsystem of 1,4-difluorobenzene.

Group υ/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

υ/cm&1

61,000

Summary of ChromophoresThe absorption of a photon which causes an electronictransition can often be traced to specific electrons in themolecule. For example, if there is a C=O group in themolecule, an absorption around 290 nm will be observed(though the precise location will depend on the nature of themolecule). Functional groups that have characteristic opticalabsroptions are called chromophores, their presence oftenaccounts for the colouration of substances.

(1) d-d transitionsThese transitions involve the promotionof electrons between non-degenerate dorbitals on transition metal atoms (e.g.,[Ti(OH2)6]3+, eg - t2g transition near20,000 cm-1 (500 nm), and thewavenumber of the absorptionmaximum suggests )0 • 20,000 cm-1)

All of the examples in this summary are different types ofchromophores.

(2) vibronic transitionsMajor problem with interpretation of visible spectra ofoctahedral complexes is that d-d transitions are forbidden. The Laporte selection rule says that the only allowedtransitions are those accompanied by a change in parity (u : gand g : u only allowed).

Summary of Chromophores, 2

The d-d transition is parity forbidden b/c itcorresponds to a g-g transition -butvibration of the molecule can destroy theinversion symmetry of the molecule, andthen the g, u classification no longerapplies. Removal of the centre ofsymmetry gives rise to a vibronicallyallowed transition (though it is weaklyallowed).

(3) charge-transfer transitionsAbsorption of radiation may occur as the result of transfer ofan electron from a ligand MO into the d orbitals of the metalatom, or vice versa. Such transitions are associated with the e-moving over large distances, meaning the transition momentdipoles are very large and absorptions very intense. Forexample, in MnO4

- ions, the intense violet colour results froman electron transfer from an MO largely confined on O to anMO confined on Mn - this is a ligand-metal charge transfer(LMCT) transition. The reverse, a metal-ligand chargetransfer (MLCT) transition, is also possible (e.g., e- from dorbitals into B* MOs of aromatic ligands is a very commonexample).

Summary of Chromophores, 3

B*-B transitionsAbsorption by a C=C double bond excites the Be- into an anti-bonding B* orbital, and thechromophore activity is therefore due to a B*-Btransition. For unconjugated double bonds,absorption occurs around 180 nm (UV), or 7 eVfor the transition to occur.

When the C=C bond is in a conjugated chain,the energies of the MOs are closer together, andthe B*-B transition absorbs at longerwavelengths (can even move to visible regionfor really long conjugated chains).

The transition responsible for absorption incarbonyl compounds involves the lone pairson the O atom in the C=O bond. The conceptof the “lone pair” means that there is an MOin which the e- are largely confined to the Oatom.

One of these electrons in the n MO may beexcited into an empty B* MO, giving rise to aB*-n transition, with typical absorptionenergies around 4 eV (290 nm). These aresymmetry forbidden transitions, and as aresult, are very weak.

(4) B*-B and B*-n transitions

B*-n transitions

Key Concepts1. It is possible for polyatomic molecules (notably, AH2

type molecules) that have linear ground states to changeto bent conformations in the excited states, therebychanging the symmetry species associated with each ofthe MO’s.

2. AH2 molecules are examined in details, with the Walshdiagram applied to monitor the relationship betweenMOs in linear and bent molecules in the ground andexcited states.

3. Formaldehyde is examined in detail, as being on of thebasic C=O chromophores. The B*-n transition isresponsible for absorption of visible radiation.

4. Hückel theory is developed to treat molecules containingC=C chromophores, where the B*-B transition isimportant for strong absorption.

5. Transition metal complexes can be treated with crystalfield or ligand theory, depending on the interactionsbetween the ligands and transition metals. Most of thesecomplexes have d-d transitions, and the metal centre arechromophores absorbing in the visible region of the EMspectrum.

6. Electronic symmetry selection rules are defined, with theonly quantum number selection rule being )S = 0. g - gand u - u transitions, which are symmetry forbidden, mayweakly occur as the result of accompanying vibronictransitions