1. Topic III: Spectroscopy and Photochemistry Chapter 13 Electronic Spectra

2. The absorption spectrum of chlorophyll
Chlorophyll absorbs in the red and blue regions, and green light is not absorbed significantly.

3. Electronic transitions: Ultraviolet and visible spectra
As the changes of the electronic distribution of a molecule, the energies of the photons emitted or absorbed are of order of several eV (1 eV = cm-1 or 96.5 kJ mol-1). The absorption spectra of electronic transitions lie in the visible and ultraviolet regions of the EM wave spectrum.
An example in photobiology is the photosynthesis when chlorophyll absorbs red and blue light: The primary energy-harvesting step by which our planet captures energy from the Sun.
In some cases, the relocation of an electron may be so extensive that it results in the breaking of a bond and the dissociation of the molecule.
An electronic absorption of a species in a solution is typically very broad and consists of several broad bands.

4. The electronic absorption of a species in a solution
Whenever an electronic transition takes place, it is accompanied by the excitation of vibrations of the molecule. The electronic absorption band consists of many superimposed bands that merge together to give a single broad band with unresolved vibrational structure.

5. Diatomic molecules
The molecule has cylindrical symmetry about the internuclear axis of the molecule.
The total orbital angular momentum of the electrons around the internuclear axis is given as Lћ, where
|L| = 0, 1, 2, 3, .. are specified as S, P, D,.., respectively.
The value of L is simply an add of the components of angular momentum of individual electrons on the internuclear axis.
L = l1 +l2 + l3 + ..
L : Total orbital angular momentum
S : Total spin angular momentum
L : Projection of L on the internuclear axis
S : Projection of S on the internuclear axis
W : Sum of L and S

6. Orbital angular momentum
An electron in the s molecular orbital has no angular momentum on the internuclear axis (l = 0) , since the cylindrial symmetry. The ground state of H2+ with electronic configuration 1s2g is assigned as S (2Sg).
A p electron in a diatomic molecular orbital has one unit of orbital angular momentum about the internuclear axis (l = ± 1). If there are two p electrons, the total angular momentum may be one of two possible cases.
Case 1: L = 0 , if the two electrons travel in the opposite direction around the interuclear axis, the orbital is assigned as S.
Case 2: L = ± 2, if the two electrons travel in the same direction around the internuclear axis, the orbital is assigned as D.

7. Spin and parity of electronic orbitals
The right superscript is for the reflection symmetry in a plane containing the two nuclei.
The left superscript 2S+1 is for the total spin S of the electrons.
The ground state of O2 having one electron in 1pg,x and one in 1pg,y. The electronic state of O2 is
The right subscript is for the overall parity of the orbital with respect to the center of the molecule. The parity is defined as the symmetry under inversion through the center of the molecule.
Example:
The ground state of a closed-shell homonuclear diatomic molecules is
The ground state of a close-shell heteronuclear diatomic molecule is

8. Selection rules for electronic spectra
For linear molecules
Conservation of angular momentum
Angular momentum of photon has a spin of 1.

9. Vibrational structure in electronic spectra
The ultraviolate spectrum of SO2 in the gas phase
Because nuclei are so much more massive than electrons, an electronic transition takes place faster than the nuclei can respond. The most intense electronic transition is from the ground vibrational state to the vibrational state that lies vertically above it in the upper electronic state. Transitions to other vibrational levels also occur, but with lower intensity.

10. Frank-Condon principle
Classical mechanical interpretation
Quantum mechanical interpretation
The molecule undergoes a transition to the upper vibrational state that most closely resembles the vibrational wavefunction of the vibrational ground state of the lower electronic state. The two wavefunctions have the greatest overlap integral of all the vibrational states of the upper electronic state.

11. Frank-Condon factor
The transition intensity is proportional to the Franck-Condon factor, the overlap of the vibrational state wavefunction in the upper electronic state with the vibrational state wavefunction in the lower electronic state.

12. Decay of excited states
In a solution or in a condensed medium, a molecule in an electronic excited state by absorbing a photon can decay through two kinds of processes:
Radiative decay: processes in which the molecule discard its excitation energy as a photon
Non-radiative (radiationless) decay: processes in which the excitation energy is transferred into vibrational, rotational and translational energies of surrounding solvent molecules.
The excited molecules may also dissociate or take part in a chemical reaction.

13. Two processes of radiative decay
Fluorescence
Spontaneous emission of radiation from electronic singlet states
Phosphorescence
Spontaneous emission of radiation from electronic triplet states
The decays of the two processes have different time scales.
Decay time of fluorescence:
Nano- to milli-seconds (10-9 to 10-3 s)
Decay time of Phosphorescence:
Seconds to hours (10-1 to 103 s)

14. Steps for fluorescence
The absorption spectrum is located at lower wavelengths and the fluorescence spectrum is at higher wavelengths.
The (0,0) vibrational transition in the absorption spectrum may not be exactly coincident with the (0,0) transition in the fluorescence spectrum.

15. Steps for phosphorescence
The electronic ground state is a spin singlet state (S).
The electronic excited states have spin singlet (S*) and spin triplet (T) states and the potential energy curves of the two excited states intersect at some point. At the intersect, the two excited states share a common geometry.
The molecule may transfer from S* to T through intersystem crossing (ISC), which is a non-radiative process.
The molecule in the triplet state may decay back to the electronic ground state by a radiative emission, which is the phosphorescence. But. the decay time is very long, since the radiation is spin forbidden.
Naphthalene (C10H8)

16. Dissociation and predissociation
Internal conversion:
A non-radiative process to convert the molecule to another state of the same multiplicity at the intersection of the two potential energy curves.

18. Laser
LASER
Light Amplification by Stimulated Emission of Radiation

19. Population inversion Requirement I: A meta-stable excited state
To create a meta-stable excited state, which has a long enough lifetime for it to participate in stimulated emission
Requirement II: Population inversion
The excited state has a greater population than in the lower state where the transition is terminated.

20. Three-level and four-level lasers
Three-level laser
Four-level laser
Examples
Ruby laser:
A small proportion of Cr+3 in Al2O3
Nd:YAG laser
A small proportion of Nd+3 in YAG Y3Al5O12

21. Cavity and mode characteristics
The laser mediate is confined in a cavity, a region between two mirrors, which reflect the light back and forth.
The photons in the cavity have a particular frequency, direction of travel and state of polarization.
The wavelengths of the photons sustained by the cavity are called the resonant modes.
Laser radiation is the EM waves in space and time coherence.
L is the length of the cavity
n is an integer.

22. Pulsed lasers
Due to the problem of overheating, a laser can be operated only in pulses of ms or ms, so that the medium has a chance to cool.
One way of achieving pulses of laser is by Q-switching, a modification of the resonance characteristics of the laser cavity.
Principle of Q-switching

23. Mode locking for pulsed laser of ps
The frequencies of resonant modes in the cavity of length L are nc/2L, with n an integer. The interferences of N modes, with n = 0,1,...,N-1, can lock their phases.
Intensity of mode-locked laser
There are a series of peaks with maxima separated by t = 2L/c, the round-trip travel transit of the light in the cavity. The peaks have an intensity of (E0N)2 and become sharp as N is increased. The width of each peak is roughly 4L/Nc.
Example: If L = 15 cm, the separation of peaks is 1 ns. If there are N = 1000 modes contributed, the width of the pulses is 2 ps.

24. Features for efficient laser action

25. Examples of lasers A. Gas Laser: to generate high powers
He- Ne laser: wavelength of 632.8nm
The coincidental matching of the He and Ne energy separations. The He atoms can transfer their excess energy to Ne atoms during a collision.
The mole ratio of He and Ne in the mixture is about 5:1.
CO2 laser: wavelength of 10.8 mm
The vibrational levels of N2 coincide with the antisymmetric stretching energy levels of CO2.
The laser action comes from the transition of the lowest level of the antisymmetric stretch to the lowest level of the symmetric stretch.

26. Exciplex and excimer lasers
Exciplex (Excited complex): AB* (XeCl*)
Excimer (Excited dimer): AA* (ArAr*)
Exciplex laser:
XeCl* with wavelength of 308 nm
KrF* with wavelength of 249 nm
The potential energy of an exciplex has a minimum, so an exciplex survives for 10 ns.
As the exciplex decays to its ground state by radiating a photon, the two atoms separate because the potential energy of their ground state is repulsive. There is never any population in the ground state.

27. Exercises
13A.3(a) 13A.4(a)
13B.1(a) 13B.1(b)
13C.1(a) 13C.2(a)