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CHAPTER 13 Molecular Spectroscopy 2: Electronic Transitions

I. General Features of Electronic spectroscopy.

A. Visible and ultraviolet photons excite electronic state transitions.

εphoton = 120 to 1200 kJ/mol. Table 13A.1 Colour, frequency, and energy of light B. Electronic transitions are accompanied by vibrational and rotational

transitions of any Δν, ΔJ (complex and rich spectra in gas phase). In liquids and solids, this fine structure merges together due to collisional broadening and is washed out.

Chlorophyll in solution, vibrational fine structure in gaseous SO2 UV visible spectrum.

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C. Molecules need not have permanent dipole to undergo electronic transitions. All that is required is a redistribution of electronic and nuclear charge between the initial and final electronic state.

Transition intensity ~ |µ|2

where µ is the magnitude of the transition dipole moment given by:

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µ = ψfinal∫ ˆ µ ψinitialdτ

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where

ˆ µ = −e r i

electrons∑ + e Zi

r i

nuclei∑

r i = vector position of the particle

D. Franck-Condon principle: Because nuclei are so much more massive and

sluggish than electrons, electronic transitions can happen much faster than the nuclei can respond.

Electronic transitions occur vertically on energy

diagram at right. (Hence the name vertical transition)

Transition probability depends on vibrational

wave function overlap (Franck-Condon factor). In this example:

ν = 0 ν’ = 0 have small overlap ν = 0 ν’ = 2 have greatest overlap

Now because the total molecular wavefunction can be approximately factored into 2 terms, electronic wavefunction and the nuclear position wavefunction (using Born-Oppenheimer approx.) the transition dipole can also be factored into 2 terms also:

µ = µelectronic

Si,f

Si,f= ψ

f,vibr∫ ψi,vibr

dτ = Franck −Condon factor i,j

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See derivation “Justification 14.2”

II. Electronic Spectra of Diatomics. A. Term symbols - ways of identifying and classifying the electronic states of

diatomics. Here is molecular oxygen for example.

The large symbol denotes total orbital angular momentum about the internuclear axis

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= Λ

Σ for Λ = 0

Π for Λ =1

Δ for Λ = 2

The upper left superscript denotes multiplicity, just as in atom terms.

1= singlet, 2=doublet, 3=triplet

The overall parity is either g or u, given as a lower right subscript.

For Σ terms, a + or - is used to indicate behavior of the wavefunction under reflection in a plane containing the nuclei.

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Example, the ground state of any closed-shell homonuclear diatomic is

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1Σg

1=singlet, spin is zero, all electrons paired It’s sigma because for a closed shell the total orbital angular

momentum is ZERO. Parity to inversion is g

Molecular oxygen has unpaired electrons in its ground state.

B. Selection rules for diatomics.

1. Rules governing changes in angular momentum (it must be conserved, and a photon has spin =1):

orbital angular mom total spin spin about tot ang mom about internuc axis about internuc axis about internuc 2. Two selection rules concerned with changes in symmetry.

a. Σ terms, only Σ + ↔ Σ + and Σ - ↔ Σ - transitions are allowed. b. the Laporte selection rule for centrosymmetric molecules

(those with a centre of inversion) and atoms states that:

The only allowed transitions are transitions that are accompanied by a change of parity.

That is, u ! g and g ! u transitions are allowed, but g ! g and u ! u transitions are forbidden.

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III. Electronic Spectra of Polyatomics A. Chromophores = “color bringers” = groups of atoms with characteristic

optical (uv-visible region) absorptions. Table 13A.2 Absorption characteristics of some groups and molecules B. n ! pi* and pi ! pi* transitions. C=C C=O

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C. d-d transitions, important in transition metal complexes.

In an isolated atom, the d orbitals are degenerate. In a molecule, the environment around the atom is no longer spherically symmetric, and there is a splitting of these 5 energies.

Above is octahedral titanium hexahydrate ion, and its crystal field

splitting pattern.

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D. Ligand to metal charge-transfer transitions.

1. Transfer of an electron from a ligand-centered molecular orbital to the d-orbitals of the central atom.

2. Electron moves a considerable distance, resulting in a large transition

dipole and thus an intense absorption. Permanganate ion, for example, transition of electron localized on oxygen to an orbital localized on Mn.

IV. Fates of Electronically Excited States.

A. Two main kinds of decay.

1. Radiative decay process = molecule makes a transition to a lower energy state and the energy is emitted as a photon of light.

a. Fluorescence = rapid decay (lifetime ~ nanoseconds)

characteristic of selection-rule allowed downward transitions. b. Phosphorescence = slower decay (lifetime ~ ms to s)

characteristic of selection-rule forbidden downward transitions 2. Nonradiative decay process = molecule transfers its excitation energy

into the surrounding molecules through collisions, exciting their translational, vibrational, and rotational energies.

3. Example of absorption followed by fluorescence emission.

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4. Example of absorption followed by phosphorescence, showing

intersystem crossing from excited singlet to excited triplet electronic states.

B. Third type of decay of excited

electronic state = Dissociation and predissociation.

1. dissociation = breaking of

chemical bonds in the excited electronic state.

Excitation into continuum

energies above the level of the excited vibrational states.

Molecule dissociates in the next

nuclear vibration.

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2. Predissociation = electronically and

vibrationally excited molecule makes a nonradiative internal conversion to another electronic state of like multiplicity, but which is dissociative. Excited vibrational states near in energy to the crossover point between the two curves are blurred.

V. Lasers (Light Amplification by Stimulated Emission of Radiation). A. General Principles.

1. Must have a metastable excited state (one with lifetime long enough to participate in stimulated emission).

2. Must have some way of creating a population inversion to

significantly populate the excited state. (Ordinary equilibrium would always have lower states more populated than upper ones.)

3. Pumping process achieves this inversion - electrical discharge often

used, or a chemical reaction may produce lots of molecules in an excited state.

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4. Light amplification cavity must be constructed with partially transmitting mirrors at each end. Mirrors are spaced apart a half-wavelength multiple of the laser transition wavelength.

5. Not all wavelengths will produce

laser action, only resonant modes.

6. The light that is amplified by

continually reflecting back and forth in the cavity is coherent radiation, that is, all in the same phase spatially and temporally (all photons in the same quantum state).

7. A fraction of the light that makes

it through the mirror on one end and is extremely intense and in a coherent beam.

B. Applications of Lasers (Enormous). Read the textbook.