* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Section 6 Raman Scattering (lecture 10)
Quantum key distribution wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Electron configuration wikipedia , lookup
Rigid rotor wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Wave–particle duality wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
Atomic theory wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Delayed choice quantum eraser wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
Two-dimensional nuclear magnetic resonance spectroscopy wikipedia , lookup
Cross section (physics) wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Chemical imaging wikipedia , lookup
Section 6 Raman Scattering (lecture 10) Quantum theory of atoms / molecules Previously: Quantum Mechanics Valence Atomic and Molecular Spectroscopy Raman Scattering The scattering process Elastic (Rayleigh) and inelastic (Raman) scattering Selection rules for Raman Similarities and differences with dipole allowed absorption 6.1 Scattering In addition to being absorbed and emitted by atoms and molecules, photons may also be scattered (approx. 1 in 107 in a transparent medium). This is not due to defects or dust but a molecular effect which provides another way to study energy levels. This scattering may be: Elastic and leave the molecule in the same state (Rayleigh Scattering) or Inelastic and leave the molecule in a different quantum state (Raman Scattering) Nobel Prize 1904 (physics) 6.2 Rayleigh Scattering Nobel Prize 1930 (physics) Lord Rayleigh calculated that a dipole scatterer << l scatters with an intensity: no. of scatterers wavelength polarizability 0 2 4 2 2 n.b., distance scatterer - observer 4 5 times more effective for 400nm than 600nm Hence the sky is blue! (and sunsets red) 6.3 Inelastic (Raman) Scattering Energy exchange between the photon and molecule leads to inelastic scatter. Anti-Stokes Rayleigh n0 Stokes Virtual state The strongest scattering is Rayleigh scatter In Raman Scattering the scattered photon has different energy (frequency, wavelength) than the incident photon: Stokes lines are those in which the photon has lost energy to the molecule n0 – nt Anti-Stokes lines are those in which the photon has gained energy from the molecule n0 + nt n0 n0 – nt n0 + nt n Since molecular energy levels are quantised this produces discrete lines from which we can gain info on the molecule itself. 6.4 Raman Scattering selection rules Scattering is not an oscillating dipole phenomenon! (no TDM) The presence of an electric field E induces a polarization in an atom/ molecule given by ind If the field is oscillating (e.g., photon) ind 0 polarizability n In atoms the polarizability is isotropic, and the atom acts like an antenna and reradiates at the incident frequency – Rayleigh Scattering only In molecules the polarizability may be anisotropic, and depends on the rotational and vibrational coordinates. This can also give rise to Raman Scattering. Gross Selection Rule: To be Raman active a molecule must have anisotropic polarizability [Less restrictive than the need for a dipole moment, symmetric molecules can be Raman active] 6.5 Rotational Raman 6.5.1 Linear Molecules: The polarizability tensor is anisotropic ( ||) Specific Selection Rule: Anti-Stokes Rayleigh n0 Stokes As a molecule rotates the polarizability presented to the E field changes: the induced dipole is modulated by rotation results in rotational transitions Effective two-photon process and Stokes lines J+2 J Anti-Stokes lines J J–2 Rayleigh Even non-polar molecules (O2, N2, CO2) exhibit rotational Raman Spectra 6.5.1 Rotational Raman spectra J Assuming a rigid rotor: F(J) = BJ(J+1) Stokes lines are observed at: n n 0 J J n 0 J J -2 and Anti- Stokes lines at: n n 0 J J n 0 n.b. 1st Anti-Stokes line is J = 2 i.e., a gap of 6B between n0 and 1st lines of each branch lines in each branch of equal spacing = 4B 6.5.1 Example Rotational Raman spectra Stokes H2 Anti-Stokes 3:1 intensity alternation observed due to nuclear spin-statistics (3 times as many ortho-H2 levels (odd J) as para-H2 (even J)) Spectrum allowed because all transitions connect levels of the same symmetry. Likewise the 14N2 Raman spectrum shows 2:1 aternations For the same reason, alternate lies are completely missing in the Raman spectra of 16O and C16O .(if the level doesn’t exist one can’t see transitions to and from it) 2 2 In deducing B from spacings, beware the possibility of missing lines in the spectrum. 6.6 Vibrational Raman Gross Selection Rule: The polarizability must change during the vibration q 0 In practice this means the normal mode must transform with the same symmetry as the quadratic forms (x2, xy, etc.) 6.6.1 Diatomics: Even homonuclear diatomics satisfy the gross selection rule and exhibit Raman spectra Specific Selection Rule: Dv = ± 1 (+ Stokes, – Anti-Stokes) n.b. Anti-Stokes rarely observed because v > 0 weakly populated 6.6.2 Polyatomics: Need to check each normal mode against the gross selection rule: H2O Raman Active Raman Active Raman Active CO2: Dh IR Inactive Raman Active u IR Active Raman Inactive u IR Active Raman Inactive g 6.7 The Rule of Mutual Exclusion In the case of CO2 it is not coincidence that those modes which are Raman active are IR inactive and vice versa. This is an example of the rule of mutual exclusion which states: In a centrosymmetric molecule (i.e., one with a centre of inversion symmetry) a vibrational mode may be either IR active or Raman active but not both. acetylene D h Raman Infra Red Raman Raman Infra Red 6.8 Vibration-Rotation Raman In the same way that rotational transitions accompany vibrational absorptions so rotational structure is observed in high resolution Raman spectra. Vibrational / Rotational Raman spectrum of CO. The Q-branch identifies the vibrational spacing (we -2wexe)