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

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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.

e.g. For HF: mHF = 1.83 D. rbond distance = 0.917A. With complete transfer of an electron from H → F:

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.

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.

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%

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).

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

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

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

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

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

a) Spectroscopy at the heart of chemistry

a) Spectroscopy at the heart of chemistry

b) States of a system and transitions

i) Bohr frequency rule De = hn

b) States of a system and transitions

i) Bohr frequency rule De = hn

ii) range of frequencies, range of De

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)

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

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.

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.

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.

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)

iii) Dipoles appear in the form of: permanent-, induced- or . 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.

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.

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.

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.

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.

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:

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:

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:

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

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

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

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:

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)

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

The percent ionic character: (m/mionic)x100

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 =

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.

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.

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.

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

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

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

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.

= 1.51 D

but

5.25 x 10-20 C

q =

= 0.328e

or 0.328 of an electronic charge missing on each H atom and 0.656 of an electronic charge on the central O atom.

Isomers can be distinguished from the magnitudes of their dipole moments. e.g. the 3 dichlorobenzenes possess different dipole moments.

chlorobenzene dichlorobenzenes

ortho- meta- para-

m = 1.57 Dm = 2.25 Dm = 1.48 Dm = 0

Differences in electronegativity of the atoms and their relative orientations are the main factors determining the magnitude and direction of m. Electron delocalization can also play a role.

The structure on the left emphasizes the electronegativity difference between C and N → m with the electron density shifted toward the N atom.

However, the lone pair of electrons from the N atom are not non-bonding, but p electrons that can be delocalized into the ring. This can be depicted with resonance structures shown on the right.

Differences in electronegativity of the atoms and their relative orientations are the main factors determining the magnitude and direction of m. Electron delocalization can also play a role.

The structure on the left emphasizes the electronegativity difference between C and N → m with the electron density shifted toward the N atom.

However, the lone pair of electrons from the N atom are not non-bonding, but p electrons that can be delocalized into the ring. This can be depicted with resonance structures shown on the right.

Differences in electronegativity of the atoms and their relative orientations are the main factors determining the magnitude and direction of m. Electron delocalization can also play a role.

The structure on the left emphasizes the electronegativity difference between C and N → m with the electron density shifted toward the N atom.

However, the lone pair of electrons from the N atom are not non-bonding, but p electrons that can be delocalized into the ring. This can be depicted with resonance structures shown on the right.

The effect is to shift electron density into the ring rather than drawing it away. The balance of these 2 effects makes the overall dipole moment smaller in magnitude than that found e.g. in aminoethane where there is no delocalization. A priori, it is unclear in which direction the overall dipole is pointing.

Molecular point groups and dipole moments. As indicated with the CO2 and the dichlorobenzenzes, a molecule might not have a dipole moment due to symmetry, despite significances differences in the electronegativity of the atoms involved. In order for a molecule to possess a dipole moment it cannot have a center of inversion, and must belong to the Cs, Cn or Cnv point groups.

The effect is to shift electron density into the ring rather than drawing it away. The balance of these 2 effects makes the overall dipole moment smaller in magnitude than that found e.g. in aminoethane where there is no delocalization. A priori, it is unclear in which direction the overall dipole is pointing.

Molecular point groups and dipole moments. As indicated with the CO2 and the dichlorobenzenzes, a molecule might not have a dipole moment due to symmetry, despite significances differences in the electronegativity of the atoms involved. In order for a molecule to possess a dipole moment it cannot have a center of inversion, and must belong to the Cs, Cn or Cnv point groups.

In the latter 2 groups the dipole moment must lie along the symmetry axis. The character table associated with the point group of a molecule can also be employed in relating symmetry and dipole moments. At least one of the translations Tx, and/or Ty, and/or Tz must be symmetric in order for the molecule to possess a dipole moment.

This examination also determines the direction of the dipole moment, if it exists, as well. For example in H2O the symmetry axis that bisects the bond angle is chosen as the z-axis. Inspection of the character table for the C2v point group reveals that it is Tz that remains unchanged in response to all 4 symmentry operations in the group.

Symmetry operations transform a molecule into itself, and as a result if that molecule possesses a dipole moment, it must remain unchanged by these operations.

In the latter 2 groups the dipole moment must lie along the symmetry axis. The character table associated with the point group of a molecule can also be employed in relating symmetry and dipole moments. At least one of the translations Tx, and/or Ty, and/or Tz must be symmetric in order for the molecule to possess a dipole moment.

This examination also determines the direction of the dipole moment, if it exists, as well. For example in H2O the symmetry axis that bisects the bond angle is chosen as the z-axis. Inspection of the character table for the C2v point group reveals that it is Tz that remains unchanged in response to all 4 symmetry operations in the group.

Symmetry operations transform a molecule into itself, and as a result if that molecule possesses a dipole moment, it must remain unchanged by these operations.

In the latter 2 groups the dipole moment must lie along the symmetry axis. The character table associated with the point group of a molecule can also be employed in relating symmetry and dipole moments. At least one of the translations Tx, and/or Ty, and/or Tz must be symmetric in order for the molecule to possess a dipole moment.

This examination also determines the direction of the dipole moment, if it exists, as well. For example in H2O the symmetry axis that bisects the bond angle is chosen as the z-axis. Inspection of the character table for the C2v point group reveals that it is Tz that remains unchanged in response to all 4 symmetry operations in the group.

Symmetry operations transform a molecule into itself, and as a result if that molecule possesses a dipole moment, it must remain unchanged by these operations.

E C2 sv(xy) sv’(yz)

A1 1 1 1 1 z x2,y2,z2

A2 1 1 -1 -1 Rz xy

B1 1 -1 1 -1 x,Ry xz

B2 1 -1 -1 1 y,Rx yz

Gx,y,z 3 -1 1 1

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