19_01fig_PChem.jpg Spectroscopy

18_12afig_PChem.jpg Rotational Motion Center of Mass Translational Motion r1r1 r2r2 Motion of Two Bodies Each type of motion is best represented in its own coordinate system best suited to solving the equations involved  k RcRc Internal coordinates Cartesian Internal motion (w.r.t CM) Motion of the C.M. Origin r Vibrational Motion

18_11fig_PChem.jpg Simple Harmonic Motion Hooks Law Max Min Max Min K V Still fast Still Conservation of Energy Kinetic Energy Potential Energy

18_01fig_PChem.jpg k Odd Even Symmetric Can be approximated by a quadratic Harmonic Approx. Hamiltonian of a Diatomic r

Vibrational Wavefunctions Hermite polynomials Gaussian Tunneling Oscillation Highly excited state n=12

19_02tbl_PChem.jpg Vibrational Spectroscopy D(t) r(t) Band structure

19_10fig_PChem.jpg Polyatomic Vibrations For an N atom molecule: 3 CM Coordinates (X,Y,Z) 3 Axes of Rotation Remaining coordinates are Vibrational modes Normal modes have a characteristic frequency,  i,determined by the motion they represent, and are independent of each other Total of 3N Coordinates (x,y,z)

19_04tbl_PChem.jpg Vibrational Spectra of Molecules

Modes of Vibration

Correlation Tables

Vibrational Spectroscopy E(n) Selection Rule For perfect Harmonic Behaviour 1 st Overtone 2 nd Overtone not exactly 2x due to anharmonicity

19_p08_PChem.jpg Selection Rules and Line Intensities Boltzmann DistributionAt ambient T, most are in the ground state: ex) k = 250 N/m,  = 2 x kg and  E(n) 94 % 5.4 % 0.3% 0.06% 0.003% x

19_02tbl_PChem.jpg Coupled Modes Mode i Mode j Combination Mode Difference Mode Fermi Resonance Causes linebroadening, and splitting

19_18fig_PChem.jpg Instrumentation Scanning Grating Orientation (  ) Absorption I0I0 I 

19_18fig_PChem.jpg Instrumentation FT Spectrum Inteferogram The reference and sample beams are coherent, therefore they can interfere with each other. The phase of the reference beam can be modulated by changing the mirror position Mirror Displacement