1 Part III Physical Chemistry III Points and credit: Approximately 20% for quiz & homework 80% final examination Note*Extra points for good students Instructor: Assoc. Prof. Dr. Pornthep Sompornpisut Office hour: Mon. & Tue. 1pm to 2pm + MHMK Bld.

-Textbooks : No particular textbook Thomas Engel “Quantum Chemistry & Spectroscopy” 2 nd edition (Chapter 7, 8, 14 & 16). 2 Study materials -PP lectures: Download from my facebook Send your name and student ID to my , I will send you an invited message for joining the group. You can later add Facebook ID of your friends into the group. Science Library

3 -Bring a Scientific Calculator to the class -Laptop, notebook, tablet are allowed for the purpose of the class study only. Study tools

4 1.An Introduction to Spectroscopy 2.Vibrational Spectroscopy: Harmonic oscillator model treated by classical vs quantum mechanics 3.Rotational Spectroscopy : Rigid rotor model treated by classical vs quantum 4.Electronic Spectroscopy: electronic transition Main topics

5 An Introduction to Spectroscopy Outlines Electromagnetic radiation: the dual nature of EM Properties of electromagnetic waves and particles Electromagnetic Spectrum Spectroscopic techniques and two major categories The relationship between electronic, vibrational, rotational state energies Spontaneous emission vs Stimulated emission

6 An Introduction to Spectroscopy -Spectroscopy are tools that chemists have to elucidate chemical structure, bonding, properties and reactivity of the molecules. -In most spectroscopies, atoms or molecules absorb electromagnetic radiation and undergo transitions between allowed quantum states. What if molecules had a continuous energy spectrum?

7 Electromagnetic Radiation : a form of energy whose behavior is described by the properties of both wave and particles. The dual nature of EM Wave nature Particle nature Behavior: absorption & emission Behavior: refraction & diffraction

8 The oscillations in the electric and magnetic fields are perpendicular to each other, and to the direction of the wave’s propagation Propagation EM electric fieldmagnetic field

9 - velocity, - amplitude, - frequency, wavelength, wavenumber - phase angle, etc. Ex. The amplitude of the oscillating electric field at any point along the propagating wave Max. amplitude Phase angleFrequency Properties of electromagnetic wave

Wavelength ( ) Wavenumber ( ṽ ) 10 c = the speed of light, 3 x 10 8 m/s Wavelength & wavenumber Units: m cm -1

11 Ex. The wavelength of the sodium D line is 589 nm. What are the frequency and the wavenumber for this line? The frequency and wavenumber of the sodium D line are

12 h = Planck’s constant, 6.6 x J s c = the speed of light, 3 x 10 8 m/sec Particle properties of electromagnetic radiation Ex. What is the energy of a photon from the sodium D line at 589 nm. The photon energy is The energy of a photon

13 The Electromagnetic Spectrum  Increasing energy Increasing wavelength 

14 Types of Atomic & Molecular Transitions  -rays: nuclear X-rays: core-level electrons Ultraviolet (UV): valence electrons Visible (Vis): valence electrons Infrared (IR): molecular vibrations Microwave: molecular rotations, X-band electron spin Radio waves: nuclear spin, electron spin

15 1)Energy transfer or absorption or emission of photons by an atom or molecule 2)Electromagnetic radiation undergoes a change in amplitude, phase angle, polarization, or direction of propagation Two major categories of spectroscopic techniques

16 1)Energy transfer or absorption or emission of photons by an atom or molecule Undergo transition between energy states

17 Type of energy transfer Spectral region Spectroscopic techniques absorption  -rays Mossbauer spectroscopy X-raysX-ray absorption spectroscopy UV/VisUV/Vis spectroscopy atomic absorption spectroscopy IRinfrared spectroscopy raman spectroscopy Microwavemicrowave spectroscopy Radio waveelectron spin resonance spectroscopy nuclear magnetic resonance spectroscopy Examples of Spectroscopic Techniques involving with energy transfer spectroscopy Continue 

18 Type of energy transfer Spectral region Spectroscopic techniques emissionUV/Visatomic emission spectroscopy photoluminescenceX-raysX-ray fluorescence UV/Visfluorescence spectroscopy phosphorescence spectroscopy atomic fluorescence spectroscopy chemiluminescenceUV/Vischemiluminescence spectroscopy Examples of Spectroscopic Techniques involving with energy transfer spectroscopy

19 Two major categories of spectroscopic techniques 2) Electromagnetic radiation undergoes a change in amplitude, phase angle, polarization, or direction of propagation as a result of refraction, reflection, scattering, diffraction, or dispersion refraction diffraction

20 Spectral regionType of Interaction Spectroscopic techniques X-rayDiffractionX-ray diffraction UV/Visrefractionrefractometry scatteringdynamic light scattering turbidimetry dispersionoptical rotary dispersion Examples of Spectroscopic Techniques that do not involve with energy transfer spectroscopy

21 Different spectral region : different energy levels of transition Radio Microwave Infrared Visible UV Energy (10 n scale)  E UV required for electronic transition is larger than  E vib required for transition from one vibrational state to another vibrational state.  E elec >>  E vib >>  E rot

22 The relationship between electronic, vibrational, rotational state energies Each electronic state will have a group of vibrational (and rotational) states. Vibrational transition takes a lot of energy more than rotational transition.

23 Pure electronic transition & the electronic transition couples with the vibrational transition

24 Transition from the ground to the first excited vibrational state. - N 1 /N 0 is very low. -All the molecules in a macroscopic sample are in their ground vibrational state (n=0) at room temperature (even at 1000K). -only the n = 0  n = 1 transition is observed in vibrational spectroscopy

25 Spontaneous emission vs Stimulated emission Random phase, random direction Incoherent wave Coherent wave Same phase, same direction Ex. Lightbulb Ex. Laser

26

27

28

29

30 Molecular motion Translation Vibration Rotation

31

Example: Using the following total energy eigenfunctions for the three-dimensional rigid rotor, show that the J=0 → J=1 transition is allowed, and that the J=0 → J=2 transition is forbidden: Providing the notation is used for the preceding functions. Assuming the electromagnetic field to lie along the z- axis, and the transition dipole moment takes the form

For the J=0 → J=1 transition,

Now consider Use reduction or substitution method Replace the result into the original integration

From the previous derivation: For the J=0 → J=1 transition, The J=0 → J=1 transition is allowed. Thus:

For the J=0 → J=2 transition, Let consider by dividing into two separate terms:

For the J=0 → J=2 transition, Consider Use the substitution method (similar to the previous one) Replace x with  and integrate from 0 to , we get: Do the same for

For the J=0 → J=2 transition, From the previous derivation: Therefore: Thus: Thus, the J=0 → J=2 transition is forbidden.

39

40

41

Solution Assuming the electromagnetic field to lie along the zaxis,, and the transition dipole moment takes the form For the J=0 → J=1 transition,

43

Solution For the J=0 → J=2 transition, The preceding calculations show that the J=0 → J=1 transition is allowed and that the J=0 → J=2 transition is forbidden. You can also show that is also zero unless MJ=0.

45

46

47

48

49