Rotational and Vibrational Spectroscopy pdf

 Rayleigh scattering: – occurs when incident EM radiation induces an oscillating dipole in a molecule, which is re-radiated at the same frequency  Raman scattering: – occurs when mon

Lecture Date: January 30 th , 2008

Rotational and Vibrational

The Electromagnetic Spectrum

 The basic!

 Microwave

 Infrared (IR)

The History of Infrared and Raman Spectroscopy

 Infrared (IR) Spectroscopy:

– First real IR spectra measured by Abney and Festing in 1880’s

– Technique made into a routine analytical method between

1903-1940 (especially by Coblentz at the US NBS)

dispersive (grating) instruments, i.e monochromators

– Fourier Transform (FT) IR instruments become common in the

1980’s, led to a great increase in sensitivity and resolution

 Raman Spectroscopy:

– In 1928, C V Raman discovers that small changes occur the

frequency of a small portion of the light scattered by molecules

The changes reflect the vibrational properties of the molecule

– In the 1970’s, lasers made Raman much more practical

Near-IR lasers (1990’s) allowed for avoidance of fluorescence in

many samples

W Abney, E R Festing, Phil Trans Roy Soc London, 1882, 172, 887-918.

Infrared Spectral Regions

 IR regions are traditionally sub-divided as follows:

Region Wavelength

(), m

Wavenumber (), cm -1

Frequency (), Hz

 Wavenumbers (denoted cm-1) are a measure of frequency

– For an easy way to remember, think “waves per centimeter”

 Relationship of wavenumbers to the usual frequency and

Rotational and Vibrational Spectroscopy: Theory

 Overview:

– Separation of vibrational and rotational contributions to energy is

commonplace and is acceptable

– Separation of electronic and rovibrational interactions

 Basic theoretical approaches:

– Harmonic oscillator for vibration

– Rigid rotor for rotation

 Terminology:

– Reduced mass (a.k.a effective mass):

See E B Wilson, Jr., J C Decius, and P C Cross, “Molecular Vibrations”, Dover, 1955

2 1

2 1

m m

m m







Rotational Spectroscopy: Theory

 Rotational energy levels can be

described as follows:

R Woods and G Henderson, “FTIR Rotational Spectroscopy”, J Chem Educ., 64, 921-924 (1987)

D J

B J



c r h

B  / 8 2 02

2 3/

Where:

c is the speed of light

k is the Hooke’s law force constant

r 0 is the vibrationally-averaged bond length

The rotational constant:

The centrifugal distortion coefficient:

u

k c

Vibrational Spectroscopy: Theory

 Harmonic oscillator – based on the classical “spring”

mis the natural frequency of the oscillator (a.k.a the fundamental vibrational wavenumber)

k is the Hooke’s law force constant (now for the chemical bond)u

km

 Since v must be a whole number (see Ex 16-1, pg 386):

 The potential energy function is:

2 2

r is the distance (bond distance)

reis the equilibrium distance

Vibrational Spectroscopy: Theory

 Potential energy of a harmonic oscillator:

Figure from Skoog et al.

Anharmonic Corrections

 Anharmonic motion : when the restoring force is not

proportional to the displacement

– More accurately given by the Morse potential function than by the

harmonic oscillator equation

– Primarily caused by Coulombic (electrostatic) repulsion as atoms

approach

 Effects: at higher quantum numbers, E gets smaller, and

the ( = +/-1) selection rule can be broken

– Double ( = +/-2), triple ( = +/-3), and higher order transitions

2 ) (

) 1

( )

2

) 2

– In stretching vibrations, the strongest coupling occurs between

vibrational groups sharing an atom

– In bending vibrations, the strongest coupling occurs between

groups sharing a common bond

– Coupling between stretching and bending modes can occur when

the stretching bond is part of the bending atom sequence

– Interactions are strongest when the vibrations have similar

frequencies (energies)

– Strong coupling can only occur between vibrations with the same

symmetry (i.e between two carbonyl vibrations)

Vibrational Modes and IR Absorption

Asymmetric Change in dipole IR-active

Scissoring Change in dipole IR-active

 IR-active modes require dipole changes during rotations

Active

Inactive

InactiveActive

IR Spectra: Formaldehyde

 Certain types of vibrations have distinct IR frequencies – hence the

chemical usefulness of the spectra

 The gas-phase IR spectrum of formaldehyde:

Formaldehyde spectrum from: http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/InfraRed/infrared.htm#ir2

Results generated using B3LYP//6-31G(d) in Gaussian 03W.

 Tables and simulation results can help assign the vibrations!

(wavenumbers, cm -1 )

Rayleigh and Raman Scattering

 Only objects whose dimension is ~1-1.5  will scatter EM

radiation

 Rayleigh scattering:

– occurs when incident EM radiation induces an oscillating dipole in

a molecule, which is re-radiated at the same frequency

 Raman scattering:

– occurs when monochromatic light is scattered by a molecule, and

the scattered light has been weakly modulated by the

characteristic frequencies of the molecule

 Raman spectroscopy measures the difference between

the wavelengths of the incident radiation and the

scattered radiation.

The Raman Effect

are necessary to form

the virtual state and

hence the Raman

hv1

Ground state (vibrational)

or polarized states) that persist for the short timescale of

the scattering process.

Excited state (vibrational)

hv1 – hv2

Stokes line

hv 1 – hv 2

Anti-Stokes line

More on Raman Processes

 The Raman process: inelastic scattering of a photon

when it is incident on the electrons in a molecule

– When inelastically-scattered, the photon loses some of its energy

to the molecule (Stokes process) It can then be experimentally

detected as a lower-energy scattered photon

– The photon can also gain energy from the molecule (anti-Stokes

process)

 Raman selection rules are based on the polarizability of

the molecule

 Polarizability: the “deformability” of a bond or a molecule

in response to an applied electric field Closely related to

the concept of “hardness” in acid/base chemistry.

P W Atkins and R S Friedman, Molecular Quantum Mechanics, 3 rd Ed Oxford: 1997

More on Raman Processes

 Consider the time variation of the dipole moment induced

by incident radiation (an EM field):

) ( ) ( )

P W Atkins and R S Friedman, Molecular Quantum Mechanics, 3 rd Ed Oxford: 1997

EM field Induced dipole moment

 Expanding this product yields:

 If the incident radiation has frequency  and the

polarizability of the molecule changes between min and

maxat a frequency intas a result of this rotation/vibration:

The Raman Spectrum of CCl4

Figure is redrawn from D P Strommen and K Nakamoto, Amer Lab., 1981, 43 (10), 72.

-400

218 314

-314 -459 459

0 Rayleigh line (elastic scattering)

Raman-Active Vibrational Modes

 Modes that are more polarizable are more Raman-active

 Examples:

 cause no change in dipole (IR-inactive)

 cause a change in the polarizability of the bond – as the bond gets

longer it is more easily deformed (Raman-active)

 cause a change in dipole (IR-active)

 Polarizability change of one C=O bond lengthening is cancelled by

the shortening of the other – no net polarizability (Raman-inactive)

 Some modes may be both IR and Raman-active, others

may be one or the other!

The Raman Depolarization Ratio

 Raman spectra are excited by linearly polarized radiation

(laser).

 The scattered radiation is polarized differently depending

on the active vibration.

 Using a polarizer to capture the two components leads to

the depolarization ratio p:

 The depolarization ratio p can be useful in interpreting the

actual vibration responsible for a Raman signal.

Instrumentation for Vibrational Spectroscopy

 Absorption vs Emission for IR spectroscopy:

– Emission is seldom used for chemical analysis

– The sample must be heated to a temperature much greater than its

surroundings (destroying molecules)

– IR emission is widely used in astronomy and in space applications.

 Two IR Absorption methods:

– Dispersive methods: Scanning of wavelengths using a grating

(common examples are double-beam, like a spectrometer

discussed in the optical electronic spectroscopy lecture)

– Fourier-transform methods: based on interferometry, a method of

interfering and modulating IR radiation to encode it as a function

of its frequency

Radiation

Wavelength Selector

Detector (transducer)

Radiation

Detector (transducer)

Why Build Instruments for Fourier Transform Work?

 Advantages:

– The Jacqinot (throughput) advantage: FT instruments have

few slits, or other sources of beam attenuation

– Resolution/wavelength accuracy (Connes advantage):

achieved by a colinear laser of known frequency

– Fellgett (multiplex) advantage: all frequencies detected at

once, signal averaging

 These advantages are critical for IR spectroscopy

 The need for FT instruments is rooted in the detector

– There are no transducers that can acquire time-varying signals

 Why are FT instruments not used in UV-Vis?

– The multiplex disadvantage (shot noise) adversely affects

signal averaging – it is better to multiplex with array detectors

(such as the CCD in ICP-OES)

– In some cases, technical challenges to building interferometers

with tiny mirror movements

Inteferometers for FT-IR and FT-Raman

and white light

Figures from Wikipedia.org

 is the frequency of the radiation

c is the speed of light in cm/s

v m is the mirror velocity in cm/s

The Basics of the Fourier Transform

1 1.5 2

1 1.5 2 2.5

1 N k N ikn k

Beamsplitter

Detector

Interferogram

Fourier Transform - IR Spectrum

frequencies for some EM radiation (ex ICP-OES with CCD,

UV-Vis DAD)

interferometer, which modulates each IR individual

frequency with an additional unique frequency:

IR Sampling Methods: Absorbance Methods

 Salt plates (NaCl): for liquids (a drop) and small amounts of solids

Sample is held between two plates or is squeezed onto a single plate

 KBr/CsI pellet: a dilute (~1%) amount of sample in the halide matrix

is pressed at >10000 psi to form a transparent disk

– Disadvantages: dilution required, can cause changes in sample

 Mulls: Solid dispersion of sample in a heavy oil (Nujol)

– Disadvantages: big interferences

 Cells: For liquids or dissolved samples Includes internal reflectance

cells (CIRCLE cells)

 Photoacoustic (discussed later)

IR Sampling Methods: Reflectance Methods

 Specular reflection: direct

reflection off of a flat surface

– Grazing angles

 Attenuated total reflection

(ATR): Beam passed through

an IR-transparent material with

a high refractive index, causing

internal reflections Depth is

~2 um (several wavelengths)

 Diffuse reflection (DRIFTS): a

technique that collects IR

radiation scattered off of fine

particles and powders Used

for both surface and bulk

studies

Figures from http://www.nuance.northwestern.edu/KeckII/ftir7.asp

ATR

DRIFTS

IR Sources

 Nernst glower: a rod or cylinder made from several grams

of rare earth oxides, heated to 1200-2200K by an electric

current.

 Globar: similar to the Nernst glower but made from silicon

carbide, electrically heated Better performance at lower

frequencies.

 Incandescent Wires: nichrome or rhodium, low intensity

 Mercury Arc: high-pressure mercury vapor tube, electric

arc forms a plasma Used for far-IR

 Tungsten filament: used for near-IR

 CO2Lasers (line source): high-intensity, tunable, used for

quantitation of specific analytes.

IR Detectors

 Thermal transducers

– Response depends upon heating effects of IR radiation

(temperature change is measured)

 Slow response times, typically used for dispersive instruments or

special applications

 Pyroelectric transducers

– Pyroelectric: insulators (dielectrics) which retain a strong electric

polarization after removal of an electric field, while they stay

below their Curie temperature

– DTGS (deuterated triglycine sulfate): Curie point ~47°C

 Fast response time, useful for interferometry (FTIR)

 Photoconducting transducers

– Photoconductor: absorption of radiation decreases electrical

noise

– Mid-IR: Mercury cadmium telluride (MCT)

– Near-IR: Lead sulfide (NIR)

Raman Spectrometers

 The basic design dispersive Raman scattering system:

 Special considerations:

– Sources: lasers are generally the only source strong enough to

scatter lots of light and lead to detectable Raman scattering

– Avoiding fluorescence: He-Cd (441.6 nm), Ar ion (488.0 nm,

Selector

Detector (photoelectric transducer)

Radiation

source

(90° angle)

Modern Raman Spectrometers

 FT-Raman spectrometers – also make use of Michelson

interferometers

– Use IR (1 m) lasers, almost no problem with fluorescence for

organic molecules

– Have many of the same advantages of FT-IR over dispersive

– But, there is much debate about the role of “shot noise” and

whether signal averaging is really effective

 CCD-Raman spectrometers – dispersive spectrometers

that use a CCD detector (like the ICP-OES system

described in the Optical Electronic lecture)

– Raman is detected at optical frequencies!

– Generally more sensitive, used for microscopy

– Usually more susceptible to fluorescence, also more complex

 Detectors - GaAs photomultiplier tubes, diode arrays, in

addition to the above.

More on Raman

 Raman can be used to study aqueous-phase samples

intense in Raman

– However, the water can absorb the scattered Raman light and

will damp the spectrum, and lower its sensitivity

 Raman has several problems:

– Susceptible to fluorescence, choice of laser important

– When used to analyze samples at temperatures greater than

250C, suffers from black-body radiation interference (so does

IR)

– When applied to darkly-colored samples (e.g black), the Raman

laser will heat the sample, can cause decomposition and/or

more black-body radiation

Applications of Raman Spectroscopy

 Biochemistry: water is not strongly detected in Raman

experiments, so aqueous systems can be studied

Sensitive to e.g protein conformation.

 Inorganic chemistry: also often aqueous systems

Raman also can study lower wavenumbers without

interferences.

 Other unique examples:

– Resonance Raman spectroscopy: strong enhancement (102 –

to an electronic transition (Can detect umol or nmol of analytes)

– Surface-enhanced Raman (SERS): an enhancement obtained

for samples adsorbed on colloidal metal particles

– Coherent anti-Stokes Raman (CARS): a non-linear technique

using two lasers to observe third-order Raman scattering – used

for studies of gaseous systems like flames since it avoids both

fluorescence and luminescence issues

Applications of Raman Spectroscopy

 Raman in catalysis research (see C&E News, Oct 13,

2006, pg 59):

– Useful for the study of zeolite interiors

– Fluorescence can be a problem, but one approach is to use UV

light (257 nm) which avoids it just like switching to the IR (but at

the risk of decomposition) – See work from the Stair group at

Northwestern

– For uses of SERS: Catal Commun 3 547 (2002)

 Raman microscopy: offers sub-micrometer lateral

resolution combined with depth-profiling (when combined

with confocal microscopy)

Comparison of IR and Raman Spectroscopy

 Advantages of Raman over IR:

– Avoids many interferences from solvents, cells and sample

preparation methods

– Better selectivity, peaks tend to be narrow

– Depolarization studies possible, enhanced effects in some cases

– Can detect IR-inactive vibrational modes

 Advantages of IR over Raman:

– Raman can suffer from laser-induced fluorescence and

degradation

– Raman lines are weaker, the Rayleigh line is also present

– Raman instruments are generally more costly

– Spectra are spread over many um in the IR but are compressed

into several nm (20-50 nm) in the Raman

 Final conclusion – they are complementary techniques!