Rotational and Vibrational Spectroscopy

Rotational and Vibrational Spectroscopy Lecture Date: January 30th, 2008 Vibrational and Rotational Spectroscopy  Core techniques: – Infrared (IR) spectroscopy – Raman spectroscopy – Microwave spectroscopy 1 The Electromagnetic Spectrum  The basic!  Microwave  Infrared (IR) The History of Infrared and Raman Spectroscopy  Infrared (IR) Spectroscopy: – First real IR spectra measured by Abney and Festing in 1880’s – Technique made into a routine analytical method between 1903-1940 (especially by Coblentz at the US NBS) – IR spectroscopy through most of the 20th century is done with dispersive(grating) instruments, i.e. monochromators – Fourier Transform (FT) IR instruments become commonin the 1980’s, led to a great increase in sensitivity and resolution  Raman Spectroscopy: – In 1928, C. V. Raman discoversthat small changes occur the frequency of a small portion of the light scattered by molecules. The changes reflect the vibrationalproperties of the molecule – In the 1970’s, lasers made Raman much more practical. Near-IR lasers (1990’s) allowed for avoidance of fluorescence in many samples. W.Abney, E. R. Festing, Phil.Trans.Roy. Soc. London,1882,172,887-918. 2 Infrared Spectral Regions  IR regions are traditionally sub-divided as follows: Region Wavelength (),m Near 0.78to 2.5 Mid 2.5to 50 Far 50 to 1000 Wavenumber (),cm-1 12800 to 4000 4000 to 200 200 to 10 Frequency (),Hz 3.8x 1014 to 1.2x 1014 1.2x 1014 to 6.0x 1012 6.0x 1012 to 3.0x 1011 After Table 16-1 of Skoog, et al. (Chapter 16) What is a Wavenumber?  Wavenumbers (denoted cm-1) are a measure of frequency – For an easy way to remember,think “waves per centimeter”  Relationshipof wavenumbers to the usual frequency and wavelength scales:  Converting wavelength () to wavenumbers: 10000 cm−1  Image fromwww.asu.edu 3 Rotational and Vibrational Spectroscopy: Theory  Overview: – Separation of vibrationaland rotational contributions to energy is commonplaceand is acceptable – Separation of electronic and rovibrationalinteractions  Basic theoretical approaches: – Harmonic oscillator for vibration – Rigid rotor for rotation  Terminology: – Reduced mass (a.k.a. effectivemass): 1m2 m +m2 SeeE. B. Wilson, Jr., J. C. Decius, and P. C. Cross,“Molecular Vibrations”, Dover, 1955. Rotational Spectroscopy: Theory  Rotationalenergy levels can be described as follows:  (J) = (J +1)B −(J +1)3 D For J = 0,1, 2, 3… The rotational constant: B = h/8π 2r2c The centrifugal distortion coefficient: D = 4B3 /ω2 ωc = 2πc k u Where: c is the speed of light k is the Hooke’s law force constant r0 is the vibrationally-averaged bond length is the reduced mass h is Planck’s constant Example for HCl: B0 = 10.4398 cm-1 D0 = 0.0005319cm-1 r0 = 1.2887 Å ω0 = 2990.946cm-1 (from IR) k = 5.12436 x 105 dyne/cm-1 R.Woodsand G. Henderson,“FTIR Rotational Spectroscopy”,J. Chem.Educ., 64, 921-924 (1987) 4 Vibrational Spectroscopy: Theory  Harmonic oscillator – based on the classical “spring” m = 1 k m is the natural frequency of the oscillator (a.k.a. the fundamental vibrational wavenumber) u kis the Hooke’s law force constant (now for the chemical bond) Note – all E are 1 v is the vibrational quantumnumber potentialenergies(V)! 2 m h is Planck’s constant  Since v must be a whole number (see Ex. 16-1, pg. 386): ΔE = hm = h k  and  =5.310−12 (wavenumbers) k   The potential energy function is: EHO (r) = 1 k(r −r )2 or EHO(r) = 2 (2πcm )2 (r −r )2 r is the distance (bond distance) re is the equilibrium distance Vibrational Spectroscopy: Theory  Potential energy of a harmonic oscillator: Figure from Skoog et al. 5 ... - tailieumienphi.vn