Chapter 13 - Molecular Spectroscopy 1: Rotational and Vibrational Spectra

Emission spectroscopy

A molecule undergoes a transition from a state of high energy E1 to a state of lower energy E2 and emits the excess energy as a photon

Absorption spectroscopy

The net absorption of nearly monochromatic (single frequency) incident radiation is monitored as the radiation is swept over a range of frequencies

Stokes radiation

When incident photons collide with the molecules, give up some of their energy, and emerge with a lower energy

Anti-Stokes radiation

When incident photons collect energy from the molecules (if they are already excited), and emerge with a higher frequency

Spectrometer

An instrument that detects the characteristics of light scattered, emitted, or absorbed by atoms and molecules

Dispersing element

It separates radiation into different frequencies

Transmittance

The ratio of the transmitted intensity to the incident intensity at a given frequency

Beer-Lambert law

Absorbance

Beer-Lambert law with absorbance

Integrated absorption coefficient

The sum of the absorption coefficients over the entire band

Stimulated absorption

The transition from a low energy state to one of higher energy that is driven by the electromagnetic field oscillating at the transition frequency

Transition rate

Total rate of absorption (W)

The transition rate of a single molecule multiplied by the number of molecules N in the lower state

Gross selection rule

It specifies the general features a molecule must have if it is to have a spectrum of a given kind

Specific selection rules

They express the allowed transitions in terms of the changes in quantum numbers

Doppler effect

In which radiation is shifted in frequency when the source is moving towards or away from the observer

Collisional deactivation

Arises from collisions between molecules or with the walls of the container

Collisional lifetime

The mean time between collisions

Moment of inertia

The mass of each atom multiplied by the square of its distance from the rotational axis through the center of mass of the molecule

Rigid rotors

Bodies that do not distort under the stress of rotation

Spherical rotors

They have three equal moments of inertia

Symmetric rotors

Two equal moments of inertia

Linear rotors

One moment of inertia

Asymmetric rotors

Three different moments of inertia

Stark effect

The splitting of states by an electric field

For a molecule to give a pure rotational spectrum

it must be polar.

Gross selection rule for rotational Raman transitions

The molecule must be anisotropically polarizable

Nuclear statistics

The selective occupation of rotational states that stems from the Pauli principle

Ortho-hydrogen

The form with parallel nuclear spins

Para-hydrogen

The form with paired nuclear spins

Vibrational terms

The energies of its vibrational states expressed in wavenumbers

Infrared active vibrations

Where the electric dipole moment of the molecule must change when the atoms are displaced relative to one another

Anharmonic motion

When the restoring force is no longer proportional to the displacement

Morse potential energy

Birge-Sponer plot

Graphical technique used to determine the dissociation energy of the bond when several vibrational transitions are detectable

Branches

Groups in which absorptions are divided

P branch

All transitions with J = -1

Q branch

All lines with J = 0

R branch

Lines with J = +1

Combination differences

A procedure used widely in spectroscopy to extract information about a particular state

Gross selection rule for vibrational Raman transitions

The polarizability should change as the molecule vibrates

Normal mode

An independent, synchronous motion of atoms or groups of atoms that may be excited without leading to the excitation of any other normal mode and without involving translation or rotation of the molecule as a whole

Gross selection rule for infrared activity

The motion corresponding to a normal mode should be accompanied by a change of dipole moment

Parallel bands

The transitions arising when the dipole moment change is parallel to the principal axis

Perpendicular bands

Transitions involving the perpendicular change of a dipole to the principal axis

Force field

The set of force constants corresponding to all the displacements of the atoms

Tumbling

The random change of orientation in molecules

Exclusion rule

If the molecule has a center of symmetry, then no modes can be both infrared and Raman active

Depolarization ratio

The ratio of the intensities of the scattered light with polarizations perpendicular and parallel to the plane of polarization of the incident radiation

Depolarized line

If the depolarization ratio is close to or greater than 0.75

Polarized line

If the depolarization ratio is less than 0.75

Resonance Raman spectroscopy

A modification of the basic Raman effect involves using incident radiation that nearly coincides with the frequency of an electronic transition of the sample

Infrared active mode

If the symmetry species of a normal mode is the same as any of the symmetry species of x, y, or z

Raman active mode

If the symmetry species of a normal mode is the same as the symmetry species of a quadratic form