Chem. 355B - 2010 Molecular Properties & Structure II (Molecular Spectroscopy)

1. Chem. 355B - 2010 Molecular Properties & Structure II (Molecular Spectroscopy) Prof. W. Galley email: william.galley@mcgill.ca Lectures: MWF 10:30AM OM 217 Tutorial: 1/wk to be arranged Midterm exam: Wed. Feb.18, 6:00-9:00 PM OM10 25% Assignments: 15% Final exam: 60%

2. Chem. 355B - 2010 Molecular Properties & Structure II (Molecular Spectroscopy) Study Materials: no required text. Some lecture notes available. Useful texts: Symmetry & Spectroscopy, Harris, D.C. & Bertolucci, M.D., Molecular Spectroscopy, Banwell, C.N. Physical Chemistry, Atkins, P.W. Quantum Chemistry, McQuarrie, Schulich Library, on reserve, iv).

3. Chem. 355B Course Outline I. Introduction a) Spectroscopy at the heart of chemistry b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De iii) atomic transitions X-rays to changes in nuclear spin . states iv) relative populations c) Dipole moments i) definition, ii) point dipole approximation iii) dipole moments of diatomic molecules iv) dipole moments of polyatomic molecules v) dipole moments and symmetry

4. vi) induced dipoles and polarizability vii) interaction of a dipole and a field viii) orientation and distortion ix) the Debye equation d) Transition probabilities i) conservation of angular momentum Laporte rule ii) transition dipoles, time-dependent perturbation . theory iii) Einstein coefficients iv) transition dipoles and symmetry ii) orientation dependence and absorption polarization II. Rotational Spectroscopy a) rigid rotor i) energies ii) populations

5. II. Rotational Spectroscopy a) rigid rotor i) energies ii) populations iii) transition probabilities iv) centrifugal distortion v) non-linear rotors III. Vibrational Spectroscopy a) harmonic oscillator energies b) relative populations c) transition probabilities d) symmetry c) polyatomic molecular and normal modes d) Raman spectroscopy

6. IV. Molecular Electronic Absorption spectroscopy a) energies b) electronic transitions n-p*, p-p* c) transition dipoles and symmetry d) vibronic bands and Franck-Condon principle c) Laser action V. Emission Spectroscopy a) excited-state processes b) Jablonsky diagram c) lifetimes and quantum yields d) emission depolarization VI Spin Resonance a) ESR b) NMR

7. References Symmetry and Spectroscopy, Harris & Bertolucci Molecular Spectroscopy, McHale J.L., QC454 H8 H65 2002b Basic Atomic and Molecular Spectroscopy, Hollas, J.M , QC454 MC 08313 2002 Fundamentals of Molecular Spectroscopy, Banwell, C.N., QD96 M65 B36 1994 Molecular Spectroscopy, Brown, J.W. Oxford Series? QD96 M65 B76 1998 Introduction to Molecular Spectroscopy, QC451 B33 1962 Gordon M. Barrow Physical Chemistry: R.A. Alberty and R.J. Silbey Physical Chemistry P. Atkins

8. I. Introduction a) Spectroscopy at the heart of chemistry

9. I. Introduction a) Spectroscopy at the heart of chemistry

20. b) States of a system and transitions i) Bohr frequency rule De = hn

21. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De

22. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De iii) atomic transitions (X-rays) to changes in nuclear . spin states (radiowaves)

23. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De iii) atomic transitions (X-rays) to changes in nuclear . spin states (radiowaves) iv) relative populations

24. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De iii) atomic transitions (X-rays) to changes in nuclear . spin states (radiowaves) iv) relative populations c) Dipole Moments (see notes: dipole moments p.1→16) i) Electric and magnetic dipole moments are associated with . interactions between radiation and matter, & therefore in . spectroscopy. ii) Electric dipoles also involved in interactions between . molecules: non-ideal gases, liquids, macromolecules etc. iii) Dipoles appear in the form of: permanent-, induced- or . transition dipoles.

25. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De . iii) atomic transitions (X-rays) to changes in nuclear . spin states (radiowaves) iv) relative populations c) Dipole Moments (see notes: dipole moments p.1→16) i) Electric and magnetic dipole moments are associated with . interactions between radiation and matter, & therefore in . spectroscopy. ii) Electric dipoles also involved in interactions between . molecules: non-ideal gases, liquids, macromolecules etc. iii) Dipoles appear in the form of: permanent-, induced- or . transition dipoles.

26. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De . iii) atomic transitions (X-rays) to changes in nuclear . spin states (radiowaves) iv) relative populations c) Dipole Moments (see notes: dipole moments p.1→16) i) Electric and magnetic dipole moments are associated with . interactions between radiation and matter, & therefore in . spectroscopy. ii) Electric dipoles also involved in interactions between . molecules: non-ideal gases, liquids, macromolecules etc. iii) Dipoles appear in the form of: permanent-, induced- or . transition dipoles.

27. b) States of a system and transitions i) Bohr frequency rule De = hn ii) range of frequencies, range of De . iii) atomic transitions (X-rays) to changes in nuclear . spin states (radiowaves) iv) relative populations c) Dipole Moments (see notes: dipole moments p.1→16) i) Electric and magnetic dipole moments are associated with . interactions between radiation and matter, & therefore in . spectroscopy. ii) Electric dipoles also involved in interactions between . molecules: non-ideal gases, liquids, macromolecules etc. iii) Dipoles appear in the form of: permanent-, induced- or . transition dipoles.

28. Transition dipoles. The latter have no simple classical analog, and are more to difficult to grasp. Transitiondipoles determine whether an interaction with radiation occurs or not, and if so, the intensity and polarization direction of the virtual or real transition involved.

29. Transition dipoles. The latter have no simple classical analog, and are more to difficult to grasp. Transitiondipoles determine whether an interaction with radiation occurs or not, and if so, the intensity and polarization direction of the virtual or real transitions involved.

30. Permanent electric dipole moments and point charges. An electric dipole moment m, a vector quantity, provides a measure of the asymmetry of a charge distribution resulting from a collection of positive and negative charges. Expressed as: q and r, individual charges and distances from an origin: (sum of the charges = 0). A single positive and negative charge separated by a distance r yields: Dipole moments are depicted with an arrow pointing from the center of negative to the center of positive charge.

31. Permanent electric dipole moments and point charges. An electric dipole moment m, a vector quantity, provides a measure of the asymmetry of a charge distribution resulting from a collection of positive and negative charges. Expressed as: q and r, individual charges and distances from an origin: (sum of the charges = 0). A single positive and negative charge separated by a distance r yields: Dipole moments are depicted with an arrow pointing from the center of negative to the center of positive charge.

32. Permanent electric dipole moments and point charges. An electric dipole moment m, a vector quantity, provides a measure of the asymmetry of a charge distribution resulting from a collection of positive and negative charges. Expressed as: q and r, individual charges and distances from an origin: (sum of the charges = 0). A single positive and negative charge separated by a distance r yields: Dipole moments are depicted with an arrow pointing from the center of negative to the center of positive charge.

33. Length of the arrow a measure of the magnitude of the dipole moment: Magnitude and direction are independent of the origin. Take origin at the center of the positive charge q+, q- is located at r, i.e. in the positive x-direction. m becomes: Negative charge indicates neg. charge in pos. x-direction. If origin chosen between 2 charges:

34. Length of the arrow a measure of the magnitude of the dipole moment: Magnitude and direction are independent of the origin. Take origin at the center of the positive charge q+, q- is located at r, i.e. in the positive x-direction. m becomes: Negative charge indicates neg. charge in pos. x-direction. If origin chosen between 2 charges:

35. Length of the arrow a measure of the magnitude of the dipole moment: Magnitude and direction are independent of the origin. Take origin at the center of the positive charge q+, q- is located at r, i.e. in the positive x-direction. m becomes: Negative charge indicates neg. charge in pos. x-direction. If origin chosen between 2 charges:

36. With 2-particle system above let q = a full electronic charge e, i.e. e and – e charge separated by 1A (1x10-10 m). Magnitude of m is: = 1.602x10-19 C x 1x10-10 m = 1.602x10-29 Cm Now in cgs units: = 4.803x10-10 esu x 1x10-8 cm = 4.803x10-18 esu cm = 4.803 D (Debye unit) † where 1D = 1x10-18 esu cm To convert SI units of Cm → Debye units, divide by 3.3356x10-30 Cm/D or: 1.602x10-29 Cm

37. With 2-particle system above let q = a full electronic charge e, i.e. e and – e charge separated by 1A (1x10-10 m). Magnitude of m is: = 1.602x10-19 C x 1x10-10 m = 1.602x10-29 Cm Now in cgs units: = 4.803x10-10 esu x 1x10-8 cm = 4.803x10-18 esu cm = 4.803 D (Debye unit) † where 1D = 1x10-18 esu cm To convert SI units of Cm → Debye units, divide by 3.3356x10-30 Cm/D or: 1.602x10-29 Cm

38. With 2-particle system above let q = a full electronic charge e, i.e. e and – e charge separated by 1A (1x10-10 m). Magnitude of m is: = 1.602x10-19 C x 1x10-10 m = 1.602x10-29 Cm Now in cgs units: = 4.803x10-10 esu x 1x10-8 cm = 4.803x10-18 esu cm = 4.803 D (Debye unit) where 1D = 1x10-18 esu cm To convert SI units of Cm → Debye units, divide by 3.3356x10-30 Cm/D or: 1.602x10-29 Cm

39. The percent ionic character: (m/mionic)x100 e.g. For HF: mHF = 1.83 D. rbond distance = 0.917A. With complete transfer of an electron from H → F:

40. The percent ionic character: (m/mionic)x100 e.g. For HF: mHF = 1.83 D. rbond distance = 0.917A. With complete transfer of an electron from H → F: mionic= exr = 4.803 DA-1 x 0.917 A = 4.40 D i.e. (4.803x10-10 esu x 0.917x10-8 cm = 4.40x10-18 esu cm)

41. The percent ionic character: (m/mionic)x100 e.g. For HF: mHF = 1.83 D. rbond distance = 0.917A. With complete transfer of an electron from H → F: mionic= exr = 4.803 DA-1 x 0.917 A = 4.40 D i.e. (4.803x10-10 esu x 0.917x10-8 cm = 4.40x10-18 esu cm) or mionic = 1.602x10-19 C x 0.917 x 10-10 m = 1.47x 10-29 Cm = (1.47x 10-29 Cm/3.3356x10-30 Cm/D) = 4.40 D

42. The percent ionic character: (m/mionic)x100 e.g. For HF: mHF = 1.83 D. rbond distance = 0.917A. With complete transfer of an electron from H → F: mionic= exr = 4.803 DA-1 x 0.917 A = 4.40 D i.e. (4.803x10-10 esu x 0.917x10-8 cm = 4.40x10-18 esu cm) or mionic = 1.602x10-19 C x 0.917 x 10-10 m = 1.47x 10-29 Cm = (1.47x 10-29 Cm/3.3356x10-30 Cm/D) = 4.40 D % ionic character =

43. A molecule with a dipole moment is said to be polar. Polarity, or dipole moments, depend on atoms with differing electronegativities in a molecule. Homonuclear diatomic molecules, e.g. N2, O2 etc. are non-polar, (dipole moment = 0). The electonegativity difference between C and H is small so that there are many organic molecules, e.g. hydrocarbons, which are non-polar. There can be charge separation between a pair of atoms in a bond, but due to symmetry the overall dipole moment is zero. Consider the CO2 molecule. Due to the more electronegative O atoms, electrons are drawn toward the O’s and away from the central C atom. This creates 2 bond dipoles but because of the linear nature of the molecule, the bond dipoles cancel.

44. A molecule with a dipole moment is said to be polar. Polarity, or dipole moments, depend on atoms with differing electronegativities in a molecule. Homonuclear diatomic molecules, e.g. N2, O2 etc. are non-polar, (dipole moment = 0). The electonegativity difference between C and H is small so that there are many organic molecules, e.g. hydrocarbons, which are non-polar. There can be charge separation between a pair of atoms in a bond, but due to symmetry the overall dipole moment is zero. Consider the CO2 molecule. Due to the more electronegative O atoms, electrons are drawn toward the O’s and away from the central C atom. This creates 2 bond dipoles but because of the linear nature of the molecule, the bond dipoles cancel.

45. A molecule with a dipole moment is said to be polar. Polarity, or dipole moments, depend on atoms with differing electronegativities in a molecule. Homonuclear diatomic molecules, e.g. N2, O2 etc. are non-polar, (dipole moment = 0). The electonegativity difference between C and H is small so that there are many organic molecules, e.g. hydrocarbons, which are non-polar. There can be charge separation between a pair of atoms in a bond, but due to symmetry the overall dipole moment is zero. Consider the CO2 molecule. Due to the more electronegative O atoms, electrons are drawn toward the O’s and away from the central C atom. This creates 2 bond dipoles but because of the linear nature of the molecule, the bond dipoles cancel.

46. A molecule with a dipole moment is said to be polar. Polarity, or dipole moments, depend on atoms with differing electronegativities in a molecule. Homonuclear diatomic molecules, e.g. N2, O2 etc. are non-polar, (dipole moment = 0). The electonegativity difference between C and H is small so that there are many organic molecules, e.g. hydrocarbons, which are non-polar. There can be charge separation between a pair of atoms in a bond, but due to symmetry the overall dipole moment is zero. Consider the CO2 molecule. Due to the more electronegative O atoms, electrons are drawn toward the O’s and away from the central C atom. This creates 2 bond dipoles but because of the linear nature of the molecule, the bond dipoles cancel.

47. The observation that SO2 has a dipole moment of 1.63 D indicates that the molecule is non-linear. Similarly, mH2O = 1.85 D resulting from the vector addition of the 2 O-H bond dipoles. Given the bond angle of 104.5o, the measured dipole can be decomposed into 2 bond dipoles. With r = 0.96 A (bond length) the fraction of an electronic charge on the H and O atoms can be found. = 1.51 D

48. The observation that SO2 has a dipole moment of 1.63 D indicates that the molecule is non-linear. Similarly, mH2O = 1.85 D resulting from the vector addition of the 2 O-H bond dipoles. Given the bond angle of 104.5o, the measured dipole can be decomposed into 2 bond dipoles. With r = 0.96 A (bond length) the fraction of an electronic charge on the H and O atoms can be found. = 1.51 D

49. The observation that SO2 has a dipole moment of 1.63 D indicates that the molecule is non-linear. Similarly, mH2O = 1.85 D resulting from the vector addition of the 2 O-H bond dipoles. Given the bond angle of 104.5o, the measured dipole can be decomposed into 2 bond dipoles. With r = 0.96 A (bond length) the fraction of an electronic charge on the H and O atoms can be found. = 1.51 D

50. The observation that SO2 has a dipole moment of 1.63 D indicates that the molecule is non-linear. Similarly, mH2O = 1.85 D resulting from the vector addition of the 2 O-H bond dipoles. Given the bond angle of 104.5o, the measured dipole can be decomposed into 2 bond dipoles. With r = 0.96 A (bond length) the fraction of an electronic charge on the H and O atoms can be found. = 1.51 D but