Vibrations

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Infra-Red (IR) Spectroscopy
or
Vibrational spectroscopy
Applied Chemistry
Course: CHY101
Electromagnetic Radiation
Frequency ()
Wavelength ()
Radio-waves
Region
Microwaves
Region
Infra-red
Region
Visible
Region
Ultra-violet
Region
X-ray
Region
-ray
Region
Frequency
(HZ)
106 - 1010
1010 - 1012
1012 - 1014
1014 - 1015
1015 - 1016
1016 - 1018
1018- 1020
Wavelength
10m – 1 cm
1 cm – 100µm
100µm – 1µm
700 – 400 nm
400-10 nm
10nm –
100pm
100pm –
1 pm
NMR, ESR
Rotational
Spectroscopy
Vibrational
spectroscopy
Electronic
Spectroscopy
Electronic
Spec.
0.001 – 10
J/mole
Order of some
100 J/mole
Some 104
J/mole
Some 100
kJ/mole
Some 100s
kJ/mole
107- 109
J/mole
109- 1011
J/mole
Energy
UHF TV, cellular,
telephones.
(300 MHz and 3 GHz)
FM Radio, VHF TV.
AM Radio
Microwave ovens,
Police radar, satellite
stations-- (3 to 30 GHz)
Table lamp,
Tube light (400
nm -800 nm or
400–790 THz)
Sun Lamp
X-ray
Electromagnetic Radiation
The interaction of radiation with matter
http://hyperphysics.phy-astr.gsu.edu/hbase/mod3.html
http://www1.lsbu.ac.uk/water/vibrat.html
Hook’s Law
Hook’s Law,
F=-kx
F is the restoring force
x is the displacement from equilibrium
k is the force constant
The restoring force proportional to the displacement of particle from its equilibrium
position and the force constant k of the spring.
Vibrational spectra: Harmonic oscillator model
The Simple Harmonic Oscillator Model: H2 molecule
H1
H2’
H2”
E2
In this case, energy curve is
parabolic,
E=
E1
H1
H2”
H2’
req
1
k (r – req)2
2
Harmonic Oscillator Model
The Simple Harmonic Oscillator Model: H2 molecule
H1
The compression & extension of a bond (like
a spring) obeys Hooke’s Law,
H2’
H2”
E2
E1
H1
H2”
H2’
req
f is the restoring force
k is the force constant
In this case, energy curve is
parabolic,
E=
1
k (r – req)2
2
Anharmonic Oscillator Model
Where a is a constant for a particular
molecule and Deq is the dissociation energy.
The Morse potential (blue) and harmonic oscillator potential (green). The potential at
infinite internuclear distance is the dissociation energy for pure vibrational spectra.
Anharmonic oscillator model
The actual potential energy of an anharmonic oscillator fits the parabolic function fairly well only near
the equilibrium internuclear distance.
The Morse potential function more closely resembles the
potential energy of an anharmonic oscillator model.
Where a is a constant for a particular
molecule and Deq is the dissociation energy.
Deq
req
Fig. The energy diagram of molecule’s vibrational model showing an (a) ideal diatomic or (b) anharmonic
diatomic oscillator.
http://www1.lsbu.ac.uk/water/vibrat.html
Vibrational spectra: Harmonic oscillator model
Oscillation Frequency,
k is the force constant
 = reduced mass,
Vibrational frequency only dependent on the mass of
the system and the force constant .
From Schrodinger equation, Vibrational energies for simple harmonic oscillator,
Vibrational spectra: Harmonic oscillator model
At
Zero-point energy
The implication is that the diatomic molecule
(and, indeed, any molecule) can never have
zero vibrational energy; the atoms can never
be completely at rest relative to each other.
The simple selection rule for the harmonic oscillator
undergoing vibrational changes
The allowed vibrational energy levels and transitions between them for a diatomic molecule
undergoing simple harmonic motion.
Anharmonic oscillator model
The Morse potential function more closely resembles the potential energy of an anharmonic oscillator
model.
Energy in a particular vibrational energy level of
an anharmonic oscillator is found to be (from
Schrodinger equation),
Deq
req
Where xe is the corresponding anharmonicity
constant which, for bond stretching vibrations,
is always small and positive (~ +0.01), so that
the vibrational levels are crowd more closely
together with increasing vibrational level v.
Fig. The energy diagram of molecule’s vibrational model showing an (a) ideal diatomic or (b) anharmonic
diatomic oscillator.
Vibrational spectra: Anharmonic oscillator model
Vibrational energies for simple harmonic oscillators,
………
A
………
B
Vibrational energies for anharmonic oscillators,
Vibrational spectra: Harmonic oscillator model
Oscillation Frequency,
k is the force constant
 = reduced mass,
The vibrational frequency is increasing with:
 increasing force constant k ( = increasing bond strength)
 decreasing atomic mass
• Example:
k cc > k c=c > k c-c
Infrared Spectroscopy
POSITION
REDUCED MASS
LIGHT ATOMS
HIGH FREQUENCY
BOND STRENGTH
(STIFFNESS)
STRONG BONDS
HIGH FREQUENCY
The vibrational frequency is increasing with:
• increasing force constant k (= increasing bond strength)
• decreasing atomic mass
Different types of Energy
Connecting macroscopic thermodynamics to a molecular understanding requires that
we understand how energy is distributed on a molecular level.
ATOMS:
The electrons: Electronic energy. Increase the energy of one (or more)
electrons in the atom.
Nuclear motion: Translational energy. The atom can move around
(translate) in space.
MOLECULES:
The electrons: Electronic energy. Increase the energy of one (or more) electrons in
the molecule.
Nuclear motion:
Translational energy. The entire molecule can translate in space.
Vibrational energy. The nuclei can move relative to one another.
Rotational energy. The entire molecule can rotate in space.
N2
CO2
Molecular vibrations
 How many vibrations are possible (= fundamental vibrations)?
A molecule has as many degrees of freedom as the total degree of freedom of its
individual atoms.
Each atom has three degrees of freedom (corresponding to the Cartesian
coordinates), thus in an N-atom molecule there will be 3N degree of freedom.
In molecules, movements of the atoms are constrained by interactions through
chemical bonds.
Molecular vibrations
Molecular vibrations
Molecular vibrations
Translation - the movement of the entire molecule while the positions of the atoms
relative to each other remain fixed: 3 degrees of translational freedom.
Rotational transitions – interatomic distances remain constant but the entire molecule
rotates with respect to three mutually perpendicular axes: 3 rotational freedom
(nonlinear), 2 rotational freedom (linear).
Fundamental Vibrations
Vibrations – relative positions of the atoms change while the average position and
orientation of the molecule remain fixed.
Molecular vibrations
Stretching and Bending
Types of Molecular Vibrations: Vibrations fall into the basic categories of stretching
and bending.
 Stretching vibration involves a continuous change in the inter-atomic distance
along the axis of the bond between two atoms.
 Bending vibrations are characterized by a change in the angle between two bonds
and are of four types: scissoring, rocking, wagging, and twisting.
Stretching Vibration
Bending Vibration
H2O: Stretching and Bending Vibrations
 Bending is easier than stretching -- happens at lower energy (lower wavenumber)
 Bond Order is reflected in ordering -- triple > double > single (energy)
with single bonds easier than double easier than triple bonds
 Heavier atoms move slower than lighter ones
Examples of Vibrational Modes
Example 1: Consider Water
Examples of Vibrational Modes
Example 1: Consider Water
Vibrations of water
Gas
H216O
3756 cm-1
v1, cm-1
3657.1
v2, cm-1
1594.7
3657 cm-1
v3, cm-1
3755.9
1595 cm-1
Examples of Vibrational Modes
Example 2: Consider Carbon Dioxide
Examples of Vibrational Modes
Example 3: The Methylene Group
It is important to note that there are many different kinds of bends, but due to the
limits of a 2-dimensional surface it is not possible to show the other ones.
A linear molecule will have another bend in a different plane that is degenerate or
has the same energy. This accounts for the extra vibrational mode.
Selection Rules
 A molecule will absorb infrared radiation if the change in vibrational states is
associated with a change in the dipole moment () of the molecule.
 Vibrations which do not change the dipole moment are Infrared Inactive
(homonuclear diatomics).
Homonuclear diatomic molecules (O2, N2, H2, Cl2) – IR Inactive
Heteronuclear diatomic molecules (HF, HCl) – IR Active
Dipole moment is greater when electronegativity difference between the atoms in a
bond is greater.
Some electronegativity values are:
H 2.2; C 2.55; N 3.04; O 3.44; F 3.98; P 2.19; S 2.58; Cl 3.16
Infrared Spectrum of Carbon Dioxide (CO2)
Stretching
Bending
Asymmetric Stretching Vibration of the CO2
Fig. The asymmetric stretching vibration of the CO2 molecule, showing the
fluctuation in the dipole moment.
The asymmetric stretch is infrared active because there is a change in the
molecular dipole moment during this vibration.
Symmetric Stretching Vibration of the CO2
To be "active" means that absorption of a photon to excite the vibration is allowed by the
rules of quantum mechanics.
[Aside: the infrared "selection rule" states that for a particular vibrational mode to be
observed (active) in the infrared spectrum, the mode must involve a change in the dipole
moment of the molecule.]
The symmetric stretch is not infrared active, and so this vibration is not observed in
the infrared spectrum of CO2.
Bending motion of the CO2
Fig. The bending motion of the carbon dioxide molecule and its associated
dipole fluctuation.
Infrared Spectroscopy
POSITION
STRENGTH
REDUCED MASS
LIGHT ATOMS
HIGH FREQUENCY
BOND STRENGTH
(STIFFNESS)
STRONG BONDS
HIGH FREQUENCY
CHANGE IN
‘POLARITY’
STRONGLY POLAR BONDS
INTENSE BANDS
The vibrational frequency is increasing with:
• increasing force constant k (= increasing bond strength)
• decreasing atomic mass
Calculated IR bands for CH2 in formaldehyde (CH2O)
Infrared Spectroscopy
4000-3000
cm-1
3000-2000
cm-1
2000-1500
cm-1
1500-1000
cm-1
1000- below
cm-1
O-H
N-H
C-H
C C
C N
C=C
C=O
C-O
C-F
C-Cl
C-C
deformations
Bending/other
stretching –
Fingerprint
region
increasing energy
increasing frequency
The vibrational frequency is increasing with:
• increasing force constant k = increasing bond strength
• decreasing atomic mass
• Example: k
c c
> k c=c > k c-c
Absorption Regions
Infrared Spectroscopy for Structure Determination
Divide the spectrum in to two regions:
4000 cm-1 1600 cm-1 most of the stretching bands, specific functional groups
(specific atom pairs). This is the “functional group” region.
1600 cm-1  400 cm-1 many bands of mixed origin. Some prominent bands are
reliable. This is the “fingerprint” region. Use for comparison
with literature spectra.
Alcohols
O–H stretch, hydrogen bonded 3500-3200 cm-1
C–O stretch 1260-1050 cm-1 (s)
C-C stretches
C–O stretch in same region as C–C but much more intense.
O-H
Infrared Spectrum of EtOH (Ethanol)
Alcohols
C–O–H stretch 3600 cm-1 in dilute
solution
phenethanol
Typically H-bonding and at lower
frequency ~3400 cm-1
Position is sensitive to subs. pattern
1-phenylethanol
RCH2–OH
1050 cm-1
R2CH–OH
1110 cm-1
R3C–OH
1175 cm-1
Why O-H peak is broad?
2-piperidinylethanol
Ketones
C=O stretch:
aliphatic ketones 1715 cm-1
alpha, beta-unsaturated ketones 1685-1666 cm-1
Carbonyl Compounds
All carbonyl compounds absorb in the region 1760-1665 cm-1 due to the stretching
vibration of the C=O bond.
Aldehydes
H–C=O stretch 2830-2695 cm-1
C=O stretch:
aliphatic aldehydes 1740-1720 cm-1
alpha, beta-unsaturated aldehydes 1710-1685 cm-1
The carbonyl stretch C=O of saturated aliphatic aldehydes appears from 1740-1720 cm-1. As in
ketones, if the carbons adjacent to the aldehyde group are unsaturated, this vibration is shifted
to lower wavenumbers, 1710-1685 cm-1.
Aldehydes
Note: The O=C–H stretches in both aldehydes in the region 2830-2695 cm-1, especially the
shoulder peak at 2725 cm-1 in butyraldehyde and 2745 cm-1 in benzaldehyde.
Carboxylic Acids
Carboxylic acids show a strong, wide band for the O–H stretch. Unlike the O–H stretch band
observed in alcohols, the carboxylic acid O–H stretch appears as a very broad band in the region
3300-2500 cm-1, centered at about 3000 cm-1.
O–H stretch from 3300-2500 cm-1
C=O stretch from 1760-1690 cm-1
C–O stretch from 1320-1210 cm-1
O–H bend from 1440-1395 and 950-910 cm-1
Esters
The carbonyl stretch C=O of aliphatic esters appears from 1750-1735 cm-1; that of
α, β-unsaturated esters appears from 1730-1715 cm-1.
C=O stretch
aliphatic from 1750-1735 cm-1
α, β-unsaturated from 1730-1715 cm-1
C–O stretch from 1300-1000 cm-1
Esters
Note: The C=O stretch of ethyl acetate (1752) is at a higher wavelength than that
of the α, β-unsaturated ester ethyl benzoate (1726). Also note the C–O stretches
in the region 1300-1000 cm-1.
Amines
The N–H stretches of amines are in the region 3300-3000 cm-1. These bands are weaker and
sharper than those of the alcohol O–H stretches which appear in the same region.
In primary amines (RNH2), there are two bands in this region, the asymmetrical N–H stretch
and the symmetrical N–H stretch.
Secondary amines (R2NH) show only a single weak band in the 3300-3000 cm-1 region, since
they have only one N–H bond.
Tertiary amines (R3N) do not show any band in this region since they do not have an N–H
bond.
N–H stretch 3400-3250 cm-1
1° amine: two bands from 3400-3300 and 3330-3250 cm-1
2° amine: one band from 3350-3310 cm-1
3° amine: no bands in this region
N–H bend (primary amines only) from 1650-1580 cm-1
C–N stretch (aromatic amines) from 1335-1250 cm-1
C–N stretch (aliphatic amines) from 1250–1020 cm-1
N–H wag (primary and secondary amines only) from 910-665 cm-1
Amines
The spectrum of aniline is shown below. This primary amine shows two N–H stretches (3442,
3360); note the shoulder band, which is an overtone of the N–H bending vibration. The C–N
stretch appears at 1281 rather than at lower wavenumbers because aniline is an aromatic
compound. Also note the N–H bend at 1619.
Amines
The spectrum of diethylamine is below. Note that this secondary amine shows only one N–H
stretch (3288). The C–N stretch is at 1143, in the range for non-aromatic amines (1250-1020).
Diethylamine also shows an N–H wag (733).
Amines
Triethylamine is a tertiary amine and does not have an N–H stretch, nor an N–H wag. The C–N
stretch is at 1214 cm-1 (non-aromatic).
Amines
R-NH2
3500, 3300 cm-1 doublet, frequently NH stretch
(without, with H-bonding effect)
1600 cm-1 NH2 scissoring - broad
700-900 cm-1 NH2 wagging - broad, strong
1080 cm-1 C–N str. --weak for alkyl
1300 cm-1 Ar–N str. strong
R–NH–R
3400 cm-1 singlet str. NH stretching
Weak C–N 1125 cm-1
R–NR–R
No IR band over 3000 cm-1, NO NH bond.
adjacent CH2 will shift to 2800 cm-1. A tert-amine salt NH strong
at 2500 cm-1
Alkanes
C–H stretch from 3000–2850 cm-1
C–H bend or scissoring from 1470-1450 cm-1
C–H rock, methyl from 1370-1350 cm-1
C–H rock, methyl, seen only in long chain alkanes, from 725-720 cm-1
Alkenes
C=C stretch from 1680-1640 cm-1
=C–H stretch from 3100-3000 cm-1
=C–H bend from 1000-650 cm-1
Alkynes
–C≡C– stretch from 2260-2100 cm-1
–C≡C–H: C–H stretch from 3330-3270 cm-1
–C≡C–H: C–H bend from 700-610 cm-1
Alkyl Halides
C–H wag (-CH2X) from 1300-1150 cm-1
C–X stretches (general) from 850-515 cm-1
C–Cl stretch 850-550 cm-1
C–Br stretch 690-515 cm-1
Alkyl Halides
Aromatics
C–H stretch from 3100-3000 cm-1
overtones, weak, from 2000-1665 cm-1
C–C stretch (in-ring) from 1600-1585 cm-1
C–C stretch (in-ring) from 1500-1400 cm-1
C–H "oop" from 900-675 cm-1
Out-of-plane CH bending
Nitro Groups
The N–O stretching vibrations in nitroalkanes occur near 1550 cm-1 (asymmetrical) and 1365 cm-1
(symmetrical), the band at 1550 cm-1 being the stronger of the two.
If the nitro group is attached to an aromatic ring, the N–O stretching bands shift to down to slightly
lower wavenumbers: 1550-1475 cm-1 and 1360-1290 cm-1.
N–O asymmetric stretch from 1550-1475 cm-1
N–O symmetric stretch from 1360-1290 cm-1
Nitro Groups
Compare the spectra of nitromethane and m-nitrotoluene: In nitromethane, the N–O stretches are
at 1573 and 1383, while in nitrotoluene, they are a little more to the right, at 1537 and 1358.
Nitro Groups
+
N
O
Analogous to Carboxylate ion. Strong bands
Aromatic nitro: 1520, 1350 cm-1
O
R
+
N
O
O
Aliphatic nitro: 1550, 1370 cm-1
Esters and Lactones
O
1735 cm-1
O
R
1300-1100 intense, often doublet
Determining benzene ring substitution
patterns from IR spectra
IR spectra provide valuable information about local configurations of atoms in molecules. The three
possible isomers are easy to differentiate by IR. It can be used to identify the relative positions of
the substituents on a disubstituted benzene ring. Examples are:
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