L12_Molec_spectrII

L12_Molec_spectrII - Molecular Spectroscopy ­part II...

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Unformatted text preview: Molecular Spectroscopy ­part II Rota%onal spectra of polyatomic molecules The rota3on of a polyatomic can be described in terms of three mutually perpendicular axes: Iz = Σ mi (xi2 + yi2); etc. It is convenient to choose three perpendicular moments of iner3a Ia, Ib, Ic, such that their dot products are 0. They are called the principal moments of iner%a. Ia is smaller or equal than Ib which is smaller or equal than Ic. Ia =0 and Ib = Ic : molecule is linear Ia = Ib = Ic : molecule is a spherical top (spherical shaped). Two equal momenta of iner3a symmetric top: Ia ≠ Ib = Ic for prolate top R is the perpendicular to the axis. The I with respect to the major axis is the smallest. If Ia = Ib ≠ Ic it is an oblate top The I with respect to the major axis is the largest. Ia ≠ Ib ≠ Ic asymmetric top. Energies: Erot= where ω is the angular velocity in radians per second. Spherical top: Ixx=Iyy=Izz=I For a tetrahedral molecule, the moment of iner3a is I = (8/3) m R2. Since tetrahedral molecules do not have dipole moments, they don't have purely rota3onal transi3ons. Linear molecule: Ixx = Iyy and Izz = 0 Symmetric top: Ixx=Iyy≠Izz. moments of iner3a parallel and perpendicular to the principal axis. Selec3on rules for rota3onal spectra of symmetric top: Δ = ±1; Δk = 0. Examples of spherical tops: phosphorus tetramer (P4), carbon tetrachloride (CCl4), nitrogen tetrahydride (NH4), ammonium ion (NH4+), sulfur hexafluoride (SF6) Examples of asymmetric tops: anthracene (C14H10), water (H2O), nitrogen dioxide (NO2) Examples of symmetric tops: Oblate: benzene (C6H6), cyclobutadiene (C4H4), ammonia (NH3) Prolate: chloromethane (CH3Cl), propyne (CH3C≡CH) Polyatomic molecules and normal modes Separable Hamiltonian and normal modes Separable Hamiltonian Infrared spectrum •  Recorded by passing a beam of infrared light through the sample. Examina3on of the transmi\ed light reveals how much energy was absorbed at each wavelength. This can be done with a monochroma3c beam, which changes in wavelength over 3me, or by using a Fourier transform instrument to measure all wavelengths at once. •  A transmi\ance or absorbance spectrum can be produced, showing at which IR wavelengths the sample absorbs. •  Analysis of these absorp3on characteris3cs reveals details about the molecular structure of the sample. When the frequency of the IR is the same as the vibra%onal frequency of a bond, absorp%on occurs. Raman spectrum •  The Raman effect (or Raman sca\ering) occurs when light impinges upon a molecule and interacts with the electron cloud of that molecule: the photon excites the molecule from the ground state to a virtual energy state inelas3c process. When the molecule relaxes it emits a photon and it returns to a different rota3onal or vibra3onal state. The difference in energy between the original state and this new state leads to a shi> in the emi?ed photon's frequency away from the excita%on wavelength. The Raman effect, which is a light sca\ering phenomenon, should not be confused with absorp3on (and with fluorescence) where the molecule is excited to a discrete (not virtual) energy level. If the final vibra3onal state of the molecule is more energe3c than the ini3al state emi\ed photon shiaed to a lower frequency : shia in frequency = Stokes shia. If the final vibra3onal state is less energe3c than the ini3al state emi\ed photon shiaed to a higher frequency: shia in frequency = An3 ­Stokes shia. A change in the molecular polarizability — related to amount of deforma3on of the electron cloud — with respect to the vibra3onal coordinate is required for a molecule to exhibit a Raman effect. The amount of the polarizability change will determine the Raman sca\ering intensity. The pa\ern of shiaed frequencies is determined by the rota3onal and vibra3onal states of the sample. •  •  •  •  Symmetry and molecular vibra%ons A molecular vibra3on is IR ac3ve only if it results in a change in the dipole moment of the molecule A molecular vibra3on is Raman ac3ve only if it results in a change in the polarizability of the molecule = ra3o of the induced dipole moment (p) to the electric filed (E) In group theory terms: A vibra3onal mo3on is IR ac3ve if it corresponds to an irreducible representa3on with the same symmetry as an x, y, z coordinate (or func3on) and it is Raman ac3ve if the symmetry is the same as x2, y2, z2, or one of the rota3onal func3ons Rx, Ry, Rz Symmetry of molecular displacements of water Vibra4onal modes Which of these vibra3ons having A1 and B1 symmetry are IR or Raman ac3ve? Raman active IR active Interac%on of electromagne%c waves with molecules The dipole approxima%on: How does the uniform oscilla%ng electric field interact with the molecule? Rate of transi%on between ini%al and final states Ques%on: Consider a generic state, write as l.c. of eigenstates and insert in %me dep. Schroedinger eq. Insert expression of perturba%on: Approxima%ons: Main Approxima%ons in rate calcula%on: Ini%al cond.: Linear response: Probability of transi%on between ini%al and final state Integrate equa%on for cf : Probability: Probability of transi%on per unit %me between ini%al and final state Fermi golden rule Fermi golden rule: selec%on rules for allowed transi%ons Fermi golden rule: energy conserva%on Selec%on rules for allowed transi%ons: the Harmonic Oscillator i ini3al state f final state ...
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This note was uploaded on 04/04/2011 for the course CHE 110B taught by Professor Galli during the Winter '11 term at UC Davis.

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