CHM 4412 Chapter 16 - University Of Illinois

CHM 4412 Chapter 16 - University Of Illinois

Lecture 34 Rotational spectroscopy: intensities Rotational spectroscopy In the previous lecture, we have considered the rotational energy levels. In this lecture, we will focus more on selection rules and intensities.

Selection rules and intensities (review) Transition Intensity dipole moment of transition Rotational selection rules

Transition moment Oscillating electric field (microwave) No electronic / vibrational transition x-dipole dipole

Rotational selection rules Gross selection rule: nonzero permanent dipole

Does H2O have microwave spectra? Yes Does N2 have microwave spectra? No Does O2 have microwave spectra? No Quantum in nature

Microwave spectroscopy How could astrochemists know H2O exist in interstellar medium? Public image NASA

Selection rules of atomic spectra (review) From the mathematical properties of spherical harmonics, this integral is zero unless Rotational selection rules

Specific selection rule: Spherical & linear rotors In units of wave number (cm1): Nonrigid rotor: Centrifugal distortion

Diatomic molecule Nonrigid rotor: Centrifugal distortion Diatomic molecule Vibrational frequency Nonrigid rotor: Centrifugal distortion

Nonrigid Rigid Appearance of rotational spectra Rapidly increasing and then decreasing intensities

Transition moment2 Degeneracy Boltzmann distribution (temperature effect) Rotational Raman spectra Gross selection rule:

polarizability changes by rotation Specific selection rule: x +y +z 2 2 2 xy, etc. are essentially Y0,0, Y2,0, Y2,1, Y2,2

Linear rotors: J = 0, 2 Spherical rotors: inactive (rotation cannot change the polarizability) ~ Y0,0 Rotational Raman spectra Anti-Stokes wing slightly less intense than Stokes wing why?

Boltzmann distribution (temperature effect) Rotational Raman spectra Each wings envelope is explained by

Degeneracy Boltzmann distribution (temperature effect) H2 rotational Raman spectra Why does the intensity alternate? H2 rotational Raman spectra Why

does the intensity alternate? Answer: odd J levels are triply degenerate (triplets), whereas even J levels are singlets. Nuclear spin statistics Electrons play no role here; we are concerned with the rotational motion of nuclei. The hydrogens nuclei (protons) are fermions and have / spins .

The rotational wave function (including nuclear spin part) must be antisymmetric with respect to interchange of the two nuclei. The molecular rotation through 180 amounts to interchange. Para and ortho H2 Singlet (para-H2) Sym.

Antisym. Y ( r1 ,r2 ) { spatial part of rotation} { a (1)b (2) - b (1)a (2)} Nuclear (proton) spins Triplet (ortho-H2) Antisym. Sym.

a (1)a (2) Y ( r1 ,r2 ) { spatial part of rotation} b (1)b (2) a (1)b (2) + b (1)a (2) With respect to interchange (180molecular rotation) Spatial part of rotational wave function

By 180 degree rotation, the wave function changes sign as (1)J (cf. particle on a ring) Para and ortho H2 Singlet (para-H2) Sym. Antisym.

Sym. a (1)a (2) Y ( r1 ,r2 ) { J =odd } b (1)b (2) a (1)b (2) + b (1)a (2) Antisym. Y ( r1 ,r2 ) { J =even} { a (1)b (2) - b (1)a (2)}

Triplet (ortho-H2) Summary We have learned the gross and specific selection rules of rotational absorption and Raman spectroscopies. We have explained the typical appearance of rotational spectra where the temperature

effect and degeneracy of states are important. We have learned that nonrigid rotors exhibit the centrifugal distortion effects. We have seen the striking effect of the antisymmetry of proton wave functions in the appearance of H2 rotational Raman spectra.

Recently Viewed Presentations

  • G.A. Farrell & Associates Limited CHARTERED VALUATION AND ...

    G.A. Farrell & Associates Limited CHARTERED VALUATION AND ...

    Leisure Industry. G.A. Farrell & Associates Limited. Financial Institutions. Colonial Life Ins. Co (T) Ltd. Others. Manufacturing. ABEL. Shopping Centres. Carlton Centre . First Citizens Bank Limited Home Mortgage Bank Intercommercial Bank Limited.
  • Case Study Follicular Lymphoma - haematologynursesireland.ie

    Case Study Follicular Lymphoma - haematologynursesireland.ie

    GCS 15/15, PEARL, no apparent injury. CTB - clear. Wanted to leave hospital to attend the hearing of his step-fathers court case. Treatment. 5/7/16 - 1st CHOP with Rasburicase (no GCSF-splenomegaly) ... Case Study Follicular Lymphoma Last modified by:
  • THE WALLINGFORD BURH TO BOROUGH RESEARCH PROJECT QUEENS

    THE WALLINGFORD BURH TO BOROUGH RESEARCH PROJECT QUEENS

    THE WALLINGFORD BURH TO BOROUGH RESEARCH PROJECT QUEEN'S ARBOUR EXCAVATIONS, 2010 The curving stone structure Back in 2003 a geophysical survey detected a buried stone structure in the Queens Arbour meadow, jutting out from Wallingford Castle earthworks towards the River...
  • MODEL OF DEMAND - Memorial University of Newfoundland

    MODEL OF DEMAND - Memorial University of Newfoundland

    Memorial University of Newfoundland ... be frequent assignments The aids We will use STATA 11 to work with empirical data It will be available through your LABNET accounts Make sure you get one! The aids We will use STATA to...
  • Responsible Investing: Aligning your financial goals with ...

    Responsible Investing: Aligning your financial goals with ...

    18-333 Financial planning offered through Northeast Planning Associates, Inc. (NPA), a registered investment adviser (RIA). Securities and advisory services offered through LPL Financial (LPL), an RIA and broker-dealer (BD), member FINRA/SIPC. Credit union is not an RIA or BD. Insurance...
  • Judicial Decisions - baroda-icai.org

    Judicial Decisions - baroda-icai.org

    -Definition inclusive and hence wider horizon-Services as managing agent covered for that reason. ... Ahmedabad Bench Pushpanjali Dyeing and Printing Mills P. Ltd.(72 TTJ 886). -No addition when no defect in books ... Judicial Decisions
  • ECE 448 FPGA and ASIC Design with VHDL

    ECE 448 FPGA and ASIC Design with VHDL

    You may be held financially responsible for any damage caused to your board FPGA available on the board Xilinx Spartan 6, XC6SLX16-CSG324C FPGA 2,278 CLB slices Programmable Interconnects Configurable Logic Block slices (CLB slices) Block RAMs 32 DSP units 32...
  • Grammar Unit - Reeds Spring High School

    Grammar Unit - Reeds Spring High School

    Robert ate worms. This is a clause. Robert. is the subject, and . ate . is the verb. This clause is "independent" because it can stand alone as a sentence. ... Juliet Tabor fails to take into account the spirit...