Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 25 Electronic Spectroscopy

Physical Chemistry 2Physical Chemistry 2ndnd Edition EditionThomas Engel, Philip Reid

Chapter 25 Chapter 25 Electronic Spectroscopy

© 2010 Pearson Education South Asia Pte Ltd

Physical Chemistry 2nd EditionChapter 25: Electronic Spectroscopy

ObjectivesObjectives

• Understanding of electronic transitions



OutlineOutline

1. The Energy of Electronic Transitions2. Molecular Term Symbols3. Transitions between Electronic States of

Diatomic Molecules

4. The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules

5. UV-Visible Light Absorption in Polyatomic Molecules

6. Transitions among the Ground and Excited States

7. Singlet–Singlet Transitions: Absorption and Fluorescence



OutlineOutline

8.Intersystem Crossing and Phosphorescence9.Fluorescence Spectroscopy and Analytical

Chemistry10.Ultraviolet Photoelectron Spectroscopy11.Single Molecule Spectroscopy12.Fluorescent Resonance Energy Trasfer

(Fret)13.Linear and Circular Dichroism



25.1 The Energy of Electronic Transitions25.1 The Energy of Electronic Transitions

• Electronic excitations are responsible for giving color to the objects we observe.

• UV-visible spectroscopy provides a very useful qualitative tool for identifying molecules and determine energy levels in molecules.



25.2 Molecular Term Symbols25.2 Molecular Term Symbols

• In electronic excitations, molecular term describe the electronic states of molecules.

• L and S (ML and MS) is chosen to be the z axis, and S are to specify individual states in diatomic molecules.

where mli, mls = z components of orbital and spin angular momentum for the i th electron in its molecular orbital.

n

isiS

n

iliL mMmM

11

and



Example 25.1Example 25.1

What is the molecular term symbol for the H2 molecule

in its ground state? In its first two excited states?




In the ground state, the H2 molecule is described by

the (1σg)2 configuration. For both electrons, ml=0. Therefore, Λ=0, and we are dealing with a Σ term. Because of the Pauli principle, one electron has ms=+1/2 and the other has ms=-1/2. Therefore, MS=0 and it follows that S=0. It remains to be determined whether the MO has g or u symmetry. Each term in the antisymmetrized MO is of the form σg x σg. Recall that the products of two even or odd functions is even, and the product of an odd and an even function is odd.




Therefore, the product of two g (or two u) functions is a g function, and the ground state of the H2 molecule is 1Σg

In the first excited state, the configuration is (1σg)(1σu), and because the electrons are in separate MOs, this configuration leads to both singlet states and triplet states. Again, because ml=0 for both electrons, we are dealing with a Σ term.




Because the two electrons are in different MOs, for each electron, giving ms values of -1, 0 (twice), and +1. This is consistent with S=1 and S=0. Because the product of a u and a g function is a u function,both singlet and triplet states are u functions. Therefore, the first two excited states are described by the terms 3Σu and 1Σu. Using Hund’s first rule, we conclude that the triplet state is lower in energy than the singlet state.



25.3 Transitions Between Electronic States of 25.3 Transitions Between Electronic States of Diatomic Diatomic Molecules Molecules

• Diatomic molecules have spacing between the various rotational-vibrational-electronic states which is large to allow individual states to be resolved.

• Each of the molecular bound states of O2 has well-defined vibrational and rotational energy levels.



25.4 The Vibrational Fine Structure of Electronic 25.4 The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules Transitions in Diatomic Molecules

• Vibrational and rotational quantum numbers can change during electronic excitation.

• Born-Oppenheimer approximation can be used to determine vibrational transition between electronic states.

where R1,…,Rm depends on position of the nuclei

r1,…rn depends on the position of electrons

mlvibrationafixedm

fixedn

electronicmn RRRRrrRRrr ,...,,...,,,...,,...,,,..., 11111



25.4 The Vibrational Fine Structure of 25.4 The Vibrational Fine Structure of Electronic Electronic Transitions in Diatomic Molecules Transitions in Diatomic Molecules

• Franck-Condon principle states that transitions between electronic states correspond to vertical lines on an energy versus inter-nuclear distance diagram.

• Electronic transitions occur on a timescale that is very short compared to the vibrational period of a molecule



25.5 UV-Visible Light Absorption in Polyatomic 25.5 UV-Visible Light Absorption in Polyatomic Molecules Molecules

• Rotational and vibrational transitions are possible if an electronic transition occurs in polyatomic molecules.

• The concept of chromophores is useful for electronic spectroscopy of polyatomic molecules.

• A chromophore is a chemical entity embedded within a molecule that absorbs radiation at the same wavelength in different molecules.



25.5 UV-Visible Light Absorption in 25.5 UV-Visible Light Absorption in Polyatomic Polyatomic Molecules Molecules

• The intensity of absorption for (a) an atom, (b) a diatomic molecule, and (c) a polyatomic molecule.



25.5 UV-Visible Light Absorption in 25.5 UV-Visible Light Absorption in Polyatomic Polyatomic Molecules Molecules

• The energy difference between the initial and final states determines the frequency of the spectral line.

• The energy increases in the sequence nπ*, π π*, and σσ*.



25.6 Transitions among the Ground and Excited 25.6 Transitions among the Ground and Excited StatesStates

• There are possible transitions among the ground and excited electronic states.



25.6 Transitions among the Ground and 25.6 Transitions among the Ground and Excited StatesExcited States

The 2 types of transitions are:• Radiative transitions

- photon is absorbed/emitted• Nonradiative transitions

- energy transferred between molecule to the surroundings



25.7 Singlet–Singlet Transitions:25.7 Singlet–Singlet Transitions: Absorption and Fluorescence Absorption and Fluorescence

• Beer’s law is used to quantify what is meant by strong and weak absorption.

where I0 = incident light intensity at frequency of interest It = intensity of transmitted light c = concentration l = path length ε = strength of the transition (molar extinction coefficient)

lcI

I t

0

log



25.7 Singlet–Singlet Transitions:25.7 Singlet–Singlet Transitions: Absorption and Fluorescence Absorption and Fluorescence

• Integral absorption coefficient is a measure of the probability that an incident photon will be absorbed in a specific electronic transition.

dvvA



25.8 Intersystem Crossing and Phosphorescence25.8 Intersystem Crossing and Phosphorescence

• Probability of intersystem crossing transitions is enhanced by two factors: similar molecular geometry in the excited singlet and triplet states.

• Fluorescence spectroscopy is good for detecting chemical species if wavelength of the emission lies in the visible-UV where there is little noise near room temperature.



25.9 Fluorescence Spectroscopy and Analytical 25.9 Fluorescence Spectroscopy and Analytical ChemistryChemistry

• The goal of the human genome is to determine the four bases, A, C, T, and G, in DNA that encode all the genetic information.

• Laser-induced fluorescence spectroscopy consist of 3 parts:

a) DNA cut into small pieces, replicate many copies, and put into A, C, T and G mixture to modified the bases.

b) Lengths of the partial replicas measured using capillary electrophoresis



25.9 Fluorescence Spectroscopy and 25.9 Fluorescence Spectroscopy and Analytical ChemistryAnalytical Chemistry

c) Measure the time for each of the partial replicas spent in capillary, to determines length and terminating base.



25.10 25.10 Ultraviolet Photoelectron Spectroscopy

• Spectroscopy gives information on the energy difference between initial and final states, but not transition energy level.

• UV photoelectron spectroscopy is to identify the orbital energy level from which an electronic transition originates.




• The kinetic energy of ejected electron is the total energy required to form the positive ion via photoionization, by

where Ef = energy of the cation

vibrationffkinetic hvnEhvE

2

1




• Koopmans’ theorem states the 3 assumptions for Ef equal to εorbital :

a) Nuclear positions are unchanged in the transition (Born-Oppenheimer approximation).

b) Orbitals for the atom and ion are the same (frozen orbital approximation).

c) Total electron correlation energy in the molecule and ion are the same.



25.11 25.11 Single Molecule Spectroscopy

• The “true” absorption band for an individual molecule is observed only if the number of molecules in the volume being sampled is very small

• Conformation of a biomolecule is the arrangement of its constituent atoms in space

• Primary structure is determined by the backbone of the molecule

• Tertiary structure refers to the overall shape of the molecule



25.11 25.11 Single Molecule Spectroscopy



25.12 25.12 Fluroscent Resonance Energy Transfer (FRET)

• FRET is a form of single molecule spectroscopy that has proved to be very useful in studying biochemical systems

• Resonance energy transfer is where the emission spectrum of the donor overlaps the absorption spectrum of the acceptor

• Theodor Förster states that

6

01

r

Rk

Dret



25.13 25.13 Linear and Circular Dichroism

• Transition dipole moment is defined by

• The arrows in successive images indicate the direction of the electric field vector as a function of time or distance

• In linear dichroism spectroscopy, the variation of the absorbance with the orientation of plane-polarized light is measured

diffi *

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Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 25 Electronic Spectroscopy