Chemistry 330

1. Chemistry 330 Vibrational and Rotational Spectroscopy

2. The electromagnetic spectrum and the classification of the spectral regions. The band at the bottom of the illustration indicates the types of transitions that absorb or emit in the various regions. The Electromagnetic Spectrum

3. The Electromagnetic Spectrum (Cont’d)

4. The intensity of a transition is the area under a plot of the molar absorption coefficient against the wavenumber of the incident radiation. Transition Intensity

5. Absorption and emission of radiation and the attainment of thermal equilibrium. The excited state can return to the lower state spontaneously stimulated by radiation already present at the transition frequency. Absorption and Emission

6. Forbidden Transitions • When a 1s electron becomes a 2s electron, there is a spherical migration of charge • There is no dipole moment associated with this migration of charge • This transition is electric-dipole forbidden

7. When a 1s electron becomes a 2p electron, there is a dipole associated with the charge migration This transition is allowed. Forbidden Transitions

8. The shape of a Doppler-broadened spectral line The distribution reflects the Maxwell distribution of speeds in the sample Lines broaden as T increases Doppler Broadening

9. In this molecule three identical atoms attached to the B atom three different but mutually identical atoms attached to the C atom. Centre of mass lies on the C3 axis Perpendicular distances are measured from the axis passing through the B and C atoms. The Definition of Moment of Inertia

10. An asymmetric rotor has three different moments of inertia; all three rotation axes coincide at the centre of mass of the molecule. Asymmetric Rotor

11. Types of Rigid Rotors • A schematic illustration of the classification of rigid rotors.

12. The rotational energy levels of a linear or spherical rotor. Note that the energy separation between neighbouring levels increases as J increases. Spherical Rotors

13. When |K| is close to its maximum value, J, most of the molecular rotation is around the principal axis. When K = 0 the molecule has no angular momentum about its principal axis: it is undergoing end-over-end rotation. The significance of the quantum number K.

14. When MJ is close to its maximum value, J, most of the molecular rotation is around the laboratory z-axis. An intermediate value of MJ. When MJ = 0 the molecule has no angular momentum about the z-axis. The significance of the quantum number MJ.

15. The effect of an electric field on the energy levels of a polar linear rotor. All levels are doubly degenerate except that with MJ = 0. Linear Rotor

16. The processes that account for absorption and emission of radiation and the attainment of thermal equilibrium. The excited state can return to the lower state spontaneously by stimulated emission Absorption and Emission

17. The effect of rotation on a molecule. The centrifugal force arising from rotation distorts the molecule, opening out bond angles and stretching bonds slightly. The effect is to increase the moment of inertia of the molecule and hence to decrease its rotational constant. Centrifugal Distortion

18. A rotating polar molecule looks like an oscillating dipole which can stir the electromagnetic field into oscillation. Classical origin of the gross selection rule for rotational transitions. The Gross Selection Rule for Rotations

19. When a photon is absorbed, the angular momentum of the combined system is conserved. If the molecule is rotating in the same sense as the spin of the incoming photon, then J increases by 1. Photon Absorption

20. The transitions allowed by the selection rule J = 1 The intensities reflect the populations of the initial level in each case and the strengths of the transition dipole moments. The Linear Rotor

21. An electric field applied to a molecule results in its distortion, and the distorted molecule acquires a contribution to its dipole moment Polarizability

22. Polarizability (cont’d) • The polarizability may be different when the field is applied • parallel • perpendicular to the molecular axis • The molecule has an anisotropic polarizability.

23. The distortion induced in a molecule by an applied electric field returns to its initial value after a rotation of only 180 Origin of the J = 2 selection rule in rotational Raman spectroscopy. The Raman Selection Rules

24. The rotational energy levels of a linear rotor and the transitions allowed by the J = 2 Raman selection rules. The form of a typical rotational Raman spectrum A Rotational Raman Spectrum

25. The energy may be approximated by a parabola near the bottom of the well. The parabolic potential leads to harmonic oscillations. A molecular potential energy curve

26. The force constant measures of the curvature of the potential energy close to the equilibrium extension of the bond. The Definition of the Force Constant

27. The oscillation of a molecule, even if it is nonpolar, may result in an oscillating dipole that can interact with the electromagnetic field. Nonpolar Species

28. The electric dipole moment of a heteronuclear diatomic molecule varies as shown by the green curve. For small displacements the change in dipole moment is proportional to the displacement.

29. The Morse potential energy curve reproduces the general shape of a molecular potential energy curve. The number of bound levels is finite. Note the relation between the dissociation energy, D0, and the minimum energy, De, of the curve. Morse Potentials

30. The dissociation energy is the sum of the separations of the vibrational energy levels up to the dissociation limit just as the length of a ladder is the sum of the separations of its rungs. The Dissociation Energy

31. The area under a plot of transition wavenumber against vibrational quantum number is equal to the dissociation energy of the molecule. The Birge-Sponer extrapolation. Birge-Sponer Plot

32. The HCl Spectrum • A high-resolution vibration-rotation absorption spectrum of HCl. • The lines appear in pairs because H35Cl and H37Cl both contribute! Note - no Q branch,

33. The formation of P, Q, and R branches in a vibration-rotation spectrum. The intensities reflect the populations of the initial rotational levels. P, Q, R Branches

34. The formation of O, Q, and S branches in a vibration-rotation Raman spectrum of a linear rotor. Note the frequency scale runs in the opposite direction to those of the P, Q, R branches. O, Q, S Branches

35. The Vibrations of CO2. • The stretching modes are not independent, and if one CO group is excited the other begins to vibrate. • The symmetric and antisymmetric stretches are independent, and one can be excited without affecting the other: they are normal modes. • The two perpendicular bending motions are also normal modes.

36. The three normal modes of H2O. The mode v2 is predominantly bending, and occurs at lower wavenumber than the other two. The Normal Modes of Water

37. The atomic displacements of CH4 and the symmetry elements used to calculate the characters. Symmetry and Normal Modes