Molecular spectroscopy II: Electronic transitions
Characteristic frequencies and wavelengths
Hierarchy of energy levels Eel >> Erot >> Evib
Energy
Energy
Energy
Rotational transitions
Vibrational transitions
Electronic transitions
different vibrational states
different electronic states
Eel
different rotation states
Erot
Evib
Internuclear distance
 = 100 – 500 nm
UV ‐ visible region Internuclear distance
 = 2 – 100 m
infrared region Internuclear distance
 = 1 mm – 10 cm microwave region The nuclei after an electronic transition are subjected to different forces and the molecule may respond by starting to vibrate. The resulting vibrational structure of electronic transitions can be resolved for gaseous samples, but in a liquid or solid the lines usually merge together and result in a broad, almost featureless band. Superimposed on the vibrational transitions that accompany the electronic transition of a molecule in the gas phase is an additional branch structure that arises from rotational transitions.
The absorption spectrum of chlorophyll in the visible region.
Ultraviolet spectrum of gaseous SO2
Vibrational structure in electronic spectra of molecules: Franck–Condon principle
Franck–Condon principle:
Because the nuclei are so much more massive than the electrons, an electronic
transition takes place very much faster than the nuclei can respond.
vertical transition: Nuclear coordinates do not change!
Note that the upper curve is usually displaced to greater equilibrium bond lengths because electronically excited states usually have more antibonding character than electronic ground states.
According to the Franck–Condon principle, the most intense vibronic transition is from the ground vibrational state to the vibrational state lying vertically above it. Transitions to other vibrational levels also occur, but with lower intensity.
As a result of the transition, electron density is rapidly built up in new regions of the molecule and removed from others. The initially stationary nuclei suddenly experience a new force field, to which they respond by beginning to vibrate
F = ‐ grad (V)
Franck‐Condon factors
Re
A typical absorption spectrum of a molecule
What determines intensities of different spectral transitions?
Several nearby states have an appreciable probability of the nuclei being at the initial separation Re. Therefore, transitions occur to all the vibrational states in this region, but most intensely to the state with a vibrational wavefunction that peaks most strongly near Re.
Franck‐Condon factors
Born‐Oppenheimer approximation:
Dipole moment operator is a sum over all nuclei at “Rj” and electrons at “rk” in the molecules
 i (r , R)   i (r )i ( R )
total wave function
  e rk  e Z j R j
k
electron part
vibrational part
j

 fi   *f   i d


 fi    f  f  e rk  e Z j R j   ii d


k

j


Electronic states
are orthogonal
 fi  e   f rk  i d   f i d  e Z j   f R ji d   f  i d
k


 fi    e    f rk  i d    f  i d   


f
, i

j
k

f
, i
S ( f , i )
= Transition dipole moment arising from the redistribution of electrons
S ( f ,i ) = Overlap integral between the vibrational state i in the initial electronic
state and the vibrational state f in the final electronic state
The intensity of the transition is proportional to the square modulus, |μfi|2,
Example: Calculating a Franck–Condon factor
Consider the transition from one electronic state to another, their bond lengths being Re and Re′ and their force constants equal. Calculate the Franck–Condon factor for the 0–0 transition and show that the transition is most intense when the bond lengths are equal.
Solution: we need to calculate S(0,0), the overlap integral of the two ground‐state vibrational wavefunctions, and then take its square.
Use the wavefunctions for a harmonic oscillator:
1/2
Origin of colours: Chromophore
A chromophore is the part of a molecule responsible for its color. (χρῶμα means ”colour,”
φέρω means ”to carry”)
The color arises when a molecule absorbs certain wavelengths of visible light and transmits or reflects others. The chromophore is a region in the molecule where the energy difference between two different molecular orbitals falls within the range of the visible spectrum. Visible light that hits the chromophore can thus be absorbed by exciting an electron from its ground state into an excited state. One of the most important chromophores are conjugated pi‐bond
systems.
Example: ‐carotene
The chlorophyll
Chlorophyll (also chlorophyl) is a green pigment plants. Its name is derived from the Greek words χλωρος, chloros ("green") and φύλλον, phyllon ("leaf"). Chlorophyll allows plants to absorb energy from light. Chlorophyll absorbs light most strongly in the blue and red regions of spectrum. However, it is a poor absorber of green and near‐green portions of the spectrum, hence its green color.
Structure of chlorophyll c1
Conjugated pi‐bond systems: * transition
A C=C double bond in a molecule acts as a chromophore. One of its important transitions is the
* transition, in which an electron is promoted from a  orbital to the corresponding
antibonding orbital.
LUMO= 2*
In Ethene, the energy needed to excite
electronically the molecule, from the
ground state 12 to the first excited state
11 2*1 is provided by 7 eV: Ethene
absorbs the UV light (=170 nm).
HOMO= 1
When the ‐conjugation pathway in the molecule is extended, the HOMO‐LUMO separation
energy, EL‐H decreases. If EL‐H is on the order of the energy of visible light E=h, then the
molecules, such as the long carotenoid molecules, absorb visible light at a certain frequency (in
the green). The photons with another energy, i.e. the radiations with other frequencies, are
reflected towards our eyes and that gives the “orange” color of carrots that contains a lot of ‐
carotenes.
‐carotene
The fates of electronically excited states
Before
Molecule in excited state
After
A radiative decay process is a process in which a molecule discards its excitation energy as a photon.
After
Molecule in ground state
Before
Molecule in excited state
After
A nonradiative decay, is a process in which the excess energy is transferred into the vibration, rotation, and translation of the surrounding molecules due to collisions
After
Molecule in ground state
Radiative decay: Fluorescence and phosphorescence
In fluorescence, spontaneous emission of radiation occurs within a few nanoseconds after the exciting radiation is extinguished. In phosphorescence, the spontaneous emission may persist for long periods (even hours, but characteristically seconds or fractions of seconds). The difference suggests that phosphorescence involves the storage of energy in a reservoir from which it slowly leaks.
Fluorescence
The sequence of steps leading to
fluorescence. After the initial absorption,
the upper vibrational states undergo
radiationless decay by giving up energy to
the surroundings. A radiative transition
then occurs from the vibrational ground
state of the upper electronic state.
Energy
Energy
Internuclear distance
Internuclear distance
An absorption spectrum shows a vibrational structure characteristic of the upper state. A fluorescence spectrum shows a structure characteristic of the lower state; it is also displaced to lower frequencies
Phosphorescence
The sequence of events leading to phosphorescence for a molecule with a singlet ground state. The first steps are the same as in fluorescence, but the presence of a triplet excited state plays a decisive role. Due to the spin‐orbit coupling the molecule may undergo intersystem crossing, a transition between states of different multiplicity, and become a triplet state. This happens at the point where the singlet and triplet excited states have the same energy. We can expect intersystem crossing to be important when a molecule contains a moderately heavy atom (such as S, sulfur), because then the spin–
orbit coupling is large.
When an excited molecule crosses into a triplet state, it is now stepping down the triplet’s vibrational ladder. Reaching the lowest vibrational state, the molecule cannot radiate its energy because return to the ground electronic state is spin‐forbidden. The radiative transition, however, is not totally forbidden because the spin–orbit coupling that was responsible for the intersystem crossing also breaks the selection rule. The molecules are therefore able to emit weakly, and the emission may continue long after the original excited state was formed.
Curiosity: The term "phosphorescence", meaning glow of phosphorus (P) after illumination, originally derives from this property of phosphorus, although this word has since been used for a different physical process that produces a glow. The glow of phosphorus itself originates from oxidation of the white (but not red) phosphorus— a process now termed chemiluminescence.
Dissociation
A dissociation is characterized by an absorption
spectrum composed of two parts:
• a vibrational progression
• a contiuum absorption
When absorption occurs to unbound states of the upper electronic state, the molecule dissociates and the absorption is a continuum. Below the dissociation limit the electronic spectrum shows a normal vibrational structure.