Transcript scat subject

Topic III: Spectroscopy
Chapter 12
Rotational and vibrational spectra
Spectroscopy
• The analysis of the EM radiations emitted, absorbed or
scattered by atoms, molecules or matter
• Photons of the radiation bring information to us about the
atom, molecule or matter.
• The difference between molecular and atomic
spectroscopy: a molecule can make a transition between
its electronic, rotational and vibrational states.
• The rotational and vibrational spectroscopy of a molecule
can provide information about the bond lengths, bond
angles and bond strength in the molecule.
Electromagnetic spectrum
General features of spectroscopy
h  | E1  E2 |
1 
~
 
 c
~
is called the wavenumber of the
photon and gives the number of
complete wavelengths per centimeter.
It is in the unit of cm-1.
Emission spectrum: A molecule returns to a state of lower energy
E1 from an excited state of energy E2 by emitting a photon.
Absorption spectrum: A molecule is excited from a lower energy
state to a higher energy state by absorbing a photon as the
frequency of the incident radiation is swept over a range
Raman spectrum
A monochromatic radiation is incident and scattered by the molecule. The
frequency of a scattered radiation is different from the frequency of the
incident radiation. The spectrum of the scattered radiation is called the
Raman spectrum.
Stokes Raman spectrum: The frequency of the scattered radiation is
lower than the frequency of the incident radiation.
Anti-Stokes Raman spectrum: The frequency of the scattered radiation is
higher than the frequency of the incident radiation.
Stimulated and Spontaneous emissions
Spontaneous emission:
A molecule in an excited state will decay to a lower
energy state without any stimulus from the outside.
Stimulated emission:
As an EM radiation incident upon a molecule in an
excited state can cause the molecule to decay to a
lower energy state. If the incoming photon has the
same frequency as the emitted photon, the incident
and emitted photons have the same wavelength and
phase and travel in the same direction. The
incoming photon is not absorbed by the molecule
but triggers emission of a second photon. The two
photons are said to be coherent.
The stimulated emission is the fundamental physical
process of the operation of the laser.
Experimental techniques
Absorption spectrometer
Raman spectrometer
Emission spectrometer
• Sample
• Source of radiation
• Dispersion elements
• Detector
Source of radiation
• To produce radiation, either monochromatic or polychromatic spanning a
range of frequencies.
• Tungsten-Lamps (for visible), LASER (almost monochomatic), a discharge
through deuterium gas or Xe in quartz (for near ultraviolet), a mercury arc
in a guartz (for far infrared), a heated ceramic filament containing rareearth oxides (for mid infrared)
• Synchrotron radiation emitted from an electron beam traveling in a storage
ring
Dispersion element and Detector
• Dispersing element: To separate the radiation
into different frequencies
Diffraction grating
Glass, quartz prism, diffraction grating and
Fourier transform spectrometer (Michelson
interferometer)
• Detector: To convert the scattered radiation into
an electric current for the appropriate signal
processing by radiation-sensitive semiconductor
devices, photodiode or Si (for the visible
region).
A charge-coupled device (CCD) is a twodimensional array of photodiode detectors.
The mercury cadmium telluride (MCT) is a
photovoltaic device for mid infrared.
Michelson interferometer
Samples
• For rotational spectroscopy, the samples are in a gas phase in
which molecules are almost in free rotation and infrequently
collide.
• For infrared spectroscopy, the samples are embedded in a
condensed phase (liquids or solids).
• The measured spectroscopy depends on the number of
molecules in the initial state. For samples at thermal
equilibrium, the populations of the initial states follow the
equilibrium statistics. For samples at non-equilibrium
thermodynamic state , the populations of the initial states do
not follow the statistics.
The Beer-Lambert law for absorption
The intensity of radiation transmitted by an absorbing sample decreases
exponentially with the path length through the sample.
T
I
I0
I0
  [ J ]L
I
I  I 010  [ J ] L
A  log
[J ] 
A
L
I0 and I : Intensities of the incident and transmitted radiations
A : Absorbance of the sample, T: Transmittance
L : Length of the sample
[J] : Concentration of the absorbing species in the sample
 : Molar absorption coefficient or the extinction coefficient
 depends on
wavelength of the
incident radiation.
Transition dipole moment and selection rules
• Transition dipole moment
The strength with which individual molecules are able to interact with the EM
radiation and generate or absorb photons. The transition dipole moment
depends on the initial and the final states of the molecules
μ fi   ψ *f μˆ ψ i dτ
μ̂ : Electric dipole moment operator
• Selection rules: Rules for non-zero transition dipole moments.
Two kinds of selection rules:
Gross selection rules: the general features that a molecule must have to cause
the spectrum of a given kind. Example: A molecule gives a rotational spectrum
only if it has a permanent electric dipole moment.
Specific selection rules: statements about which changes in quantum numbers
may occur in a transition.
An allowed transition (1s→2p) is permitted by a specific selection rule
A forbidden transition (1s→2s) is disallowed by a specific selection rule
Exception: A forbidden transition sometimes may occur weakly.
The absorption spectrum
• The molar absorption coefficient  of
an radiation by a sample generally
spreads over a range of wavenumber
(or frequency), with a maximum at
certain wavenumber. The spread
molar absorption coefficients are
referred as a band of absorption
spectrum of the sample.
• The integrated absorption coefficient
A is the sum of absorption over the
entire band and gives the total
absorption intensity.
• The spreading of the spectrum is
indicated by the full width at half
maximum (FWHM) or the half width at
half maximum (HWHM).
A   ( ~
 ) d~

For a Gaussian spectrum,
( ~
 ~
m ) 2 / 22
~
I ()  e
HWHM  2 ln 2  
FWHM  2  HWHM
1/ 2
The spectral linewidths
I. Doppler broadening: the frequency of a radiation is shifted when the
source of the radiation is moving toward or away from the observer.
This effect is important for samples in a gas phase.
2  2k BT ln 2 



c 
m

1/ 2
obs
T: temperature of the sample
m : Mass of the molecule
In a gas phase, the velocities of the
molecules follow the Maxwell-Boltzmann
distribution. Some move toward the
detector and some move away. The
linewidth of the detected spectrum is
resulted from all of the Doppler shifts. The
spectrum is generally a Gaussian. The full
width of the spectrum is defined at half of
its maximum, denoted as FWHM.
Decreasing temperature of the sample
reduces the Doppler broadening
II. Lifetime broadening: line broadening due to the lifetime of
the states involved in the transition.
• According to the uncertainty principle, the state of a
system that is changing with time do not have
precisely defined energies. If the system in an excited
state that exponentially decays with a time constant t,
which is called the lifetime of the state, the energy
level of the excited state is blurred by E.

 hcδν~
t
1
5.3
cm
δν~ 
t / ps
E 
Two processes are responsible for the finite lifetime of the excited states
I. Collision deactivation: Collisions between molecules or with the wall of the
container (In gas phase, this effect can be minimized by working at low
pressures.)
II. Spontaneous emission: The emission of radiation as the system in the excited
state collapses into a lower state. The rate of the emission depends on the
wavefunctions of the excited and lower states. The linewidth of spontaneous
emission increases as 3 ( is the frequency). This broadening is the nature
linewidth of the transition and is not avoidable by modifying T or P of the system.
Rigid-rotor models of molecules
• Rigid-rotor model of molecules: The relative distances and orientations of
atoms in a molecule do not change during the rotational motion of the
molecule
• A rigid rotor has three orthogonal axes passing through the center of mass
of the rotor, which are called the principal axes of the rotor.
• Corresponding to each principal axis, a moment of inertia of the molecule
is defined. A rigid rotor has three principal moments of inertia, Ix, Iy and Iz.
Ix 
2
2
m
(
y

z
 j j j)
j
The moment of inertia of a molecule
about a rotational axis is a sum of the
mass of each atom multiplied by the
square of its distance from the axis.
Three principal moments of inertia of a rigid molecule
An asymmetric rotor has three different moments of inertia.
Ix = Iy= Iz
Ix = Iy  Iz
Ix  Iy  Iz
Rotational energy levels of a rigid rotor
The kinetic energy of a rigid rotor with
angular momentum Jx, Jy and Jz. with respect
to the three principal axes of the rotor.
J y2
J x2
J z2
E


2I x
2I y
2I z
Classical
description
For a linear or spherical rigid rotor with a
moment of inertia I
J2
E
, J 2  J x2  J y2  J z2
2I
Quantum
description
~
E J  hcB J ( J  1),
J  0, 1, 2, 3, ....

~
B
4πcI
EJ  E J 1  EJ
~
 2 B ( J  1)
Rotational energy levels of a symmetric rotor
E
J
2
||
2 I ||

2

J
2I 
I|| > I⊥, for a oblate rotor
like a pancake.
I|| < I⊥, for a prolate rotor
like a cigar.
~ ~
~
E J,K  hcBJ(J  1 )  hc(A  B)K 2
J  0, 1, 2, 3,....
K  J, J - 1, J - 2, ........,-J
~
A


~
, B
4πcI||
4πcI 
I|| : The moment of inertia about the axis
parallel to the molecular axis
I⊥ : The moment of inertia about the axis
perpendicular to the molecular axis
K: the quantum number to specify the component
of angular momentum parallel to the symmetric
axis. There are two special cases
Case I: As the rotational axis is parallel to the
molecular axis, K = ± J.
Case II: As the rotational axis is perpendicular to
the molecular axis, K = 0.
Centrifugal distortion
• In real molecules, the atoms of
rotating molecules are subject
to centrifugal forces due to the
rotation. The centrifugal forces
tend to distort the molecule
geometry by stretching the
bonds between atoms and
increase the moment of inertia
about the rotational axis. Hence,
the molecular distortion due to
the centrifugal effect reduces
the separations of energy levels
predicted by the rigid-rotor
models.

~
~
E J  hc BJ ( J  1)  DJ J 2 ( J  1) 2
~3
4
B
~
DJ  ~ 2


The centrifugal distortion constant
Rotational spectroscopy
• Gross selection rule: The molecules must have a permanent electric dipole
moment so that the molecules are polar.
Classical description
Rotational-inactive molecules: Molecules
without rotational spectrum
Homonuclear diatomic molecules: N2, O2
Symmetric linear molecules: CO2
Tetrahedral molecules: CH4
Octahedral molecules: SF6, C6H6
Rotational-active molecules: Molecules
with rotational spectrum
Heteronuclear diatomic molecules: HCl
Less symmetric polar molecules: NH3, H2O
To an observer, a rotating polar
molecule has an electric dipole that
appears to oscillate. This oscillating
dipole can interact with the EM field.
Specific selection rules for rotational transition
J = 1 and K = 0
• Conservation of angular momentum for J = 1
A photon is a spin-1 particle. When the molecule
absorbs one photon, the angular momentum of the
molecule must increase to conserve the total angular
momentum, so J increases by one. When the
molecule emits a photon, the angular momentum of
the molecule must decreases, so J decreases by one.
• For symmetric rotors, K = 0
The dipole moment of a polar molecule does not
move when a molecule rotates around its symmetric
axis and, therefore, there is no absorption or
emission of the EM radiation by the rotation of the
molecule about the axis.
Quantum description
Absorption of allowed rotational transitions
A rigid molecule with K=0 makes a
transition from J to J+1
~
E  EJ 1  EJ  2hcB ( J  1)
~
~
  2 B ( J  1)
Rigid-rotor model
~
~
~
  2 B ( J  1)  4DJ ( J  1)3
• The rotational spectrum consists of a series of lines at frequencies
separated by 2 B~ .
• The rotational spectra of gas-phase samples are microwave
spectroscopy.
~
• We can use the value of B obtained from the rotational spectrum to
estimate the bond length of a heteronuclear diatomic molecule.
Intensity of rotational spectrum: Populations of rotational states
•
Intensity of absorption spectrum
is proportional to the population
of molecules in the absorbing
state.
N J  Ng J e
~
 hcBJ(J 1 )/kBT
•
The temperature effect arises
from Boltzmann statistics.
•
The degeneracy of a rotational
state gives a factor gJ = 2J+1.
The maximum intensity for
linear rotors is at
1/ 2
J max
 k BT 

~
 2hcB 
1

2
Rotational Raman spectroscopy
Visible or
ultraviolet
Lasers
Rayleigh line
Stokes lines: the scattered lines shifted to lower frequency than
the incident radiation (scat < inc)
Anti-Stokes lines: the scattered lines shifted to higher
frequency than the incident radiation (scat > inc)
Rayleigh lines: the scattered lines in the forward direction and
with the same frequency as the incident radiation (scat  inc)
Gross selection rule
• The molecules must have anisotropic polarizability.
The polarizability of a molecule is a measure of the extent to which an
applied electric field can induce an electric dipole moment m in addition to
any permanent dipole moment. The anisotropy of the polarizability is its
variation with the orientation of the molecule.
  
μ  E
μx   x Ex , μ y   y E y , μz   z Ez
 || >  
x   y  z
All spherical rotors, like tretrahedral (CH4), octahedral (SF6) and icosahedral
molecules (C60), are both rotationally and rotationally Raman inactive.
All homonuclear diatomic molecules and linear molecules are rotationally
inactive but rotationally Raman active.
Specific selection rules of rotational Raman spectroscopy
The distortion induced in a molecule by an applied
electric field returns to its initial value after a rotation
of only 180°.
Rotational Raman scattering is associated with the
variation of molecular polarizability due to rotational
motions of the molecule.
(t )   0   cos( 2B t )
  ||   
B: Angular frequency of molecular rotation
J =  2 for linear rotors
Positive for Stokes lines
Negative for Anti-Stokes lines
Stokes and anti-Stokes lines of rotational Raman spectrum
For Stokes lines
~
 2hcB (2 J  3)
E  E J  E J  2
~
  2 B (2 J  3), J  0, 1, 2, 3,..
For anti-Stokes lines
~
E  E J  E J  2  2hcB (2 J  1)
~
  2 B (2 J  1), J  2, 3,..
Stokes lines
Anti-Stokes lines
 : frequency shift relative to the incident radiation.
• The rotational Raman spectrum consists of a series of lines at frequencies of
6 B~ , 10 B~ and 14 B~ … , which are separated by 4 B~ .
• We can use the value of B obtained from the rotational Raman spectrum to
estimate the bond length of a homonuclear diatomic molecule.
• The intensities of the Stokes lines are generally stronger than those of the
Anti-Stokes lines.
Rotational Raman spectrum of a diatomic
molecule with two identical nuclei of spin ½
For H2 molecules with nonzero nuclear spins,
the intensities of the odd-J lines are three
times more than those of the even-J lines.
Under rotation through 180°,
Wavefunctions with even J do not change sign.
Wavefunctions with odd J do change sign.
Nuclear statistics must be taken into
account whenever a rotation
interchanges equivalent nuclei.
ψtotal  ψnucψrot
Ortho- and Para-hydrogen molecules
•
If the nuclear spin I is a half-integer, the total
wavefunction should be antisymmetric. The
even-J rotational states are associated with
the antisymmetric nuclear wavefucntions
and the odd-J rotational states are with the
symmetric nuclear wavefunctions.
Podd  J I  1

Peven  J
I
•
•
•
Ortho-hydrogen molecule
(Ortho-H2): Molecule with
parallel nuclear spin
Para-hydrogen molecule
(Para-H2): Molecule with
antiparallel nuclear spin
If the nuclear spin I is an integer, the total
wavefunction should be symmetric. The
even-J rotational states are associated with
the symmetric nuclear wavefucntions and
the odd-J rotational states are with the antisymmetric nuclear wavefunctions.
Podd  J
I

Peven  J I  1
For H2, I=1/2
For D2, I=1
Podd  J
3
Peven  J
Podd  J 1

Peven  J 2
Vibrations of diatomic molecules
Harmonic approximation around the equilibrium
1  d 2V
V ( R)  
2  dR 2

 ( R  Re ) 2    
0
 d 2V
k f  
2
 dR
1
k f ( R  Re ) 2
2
1
En  (n  )  , n  0,1,2,3,....
2
Vhar ( R) 
 kf

m
 eff
1/ 2

 ,


meff 
m A mB
m A  mB


0
A diatomic molecule has three
translational modes, two rotational
modes and one vibrational mode.
kf : force constant of the bond,
the curvature of the potential at Re
Infrared spectroscopy: Vibrational transitions
• Gross selection rule
The molecule need not to have a permanent dipole moment but
the electric dipole moment of the molecule must change during
the vibration. The rule only requires a change in electric dipole
moment, possibly from zero.
The typical vibrational frequency of a molecule
is about 1013~1014 Hz. The vibrational
spectroscopy of molecules is in the infrared
region, which normally lies in 300 ~ 3000 cm-1.
Homonuclear diatomic molecules are infrared
inactive, because their dipole moments remain
zero as they vibrate.
Bending motion of CO2
Heteronuclear diatomic molecules are infrared
active, because their dipole moments change as
they vibrate.
Specific selection rules for infrared spectroscopy
Electric dipole moment
1  k f
~
~
n  1, E  hcv , ν 
2c  meff
1/ 2




• Molecules with stiff bonds joining atoms
with low masses have high vibrational
wavenumbers.
• The bending modes of a linear molecule
 dmˆ 
are usually less stiff than stretching modes.
mˆ ( x)  mˆ 0    x    
So, the bending modes usually occur at
 dx 0
lower wavenumbers than the stretching
modes in a spectrum.
Transition dipole element
• At room temperatures, almost all molecules
are in their vibrational ground states (n = 0).
μ fi  ψ*f μˆ ψi dτ
So, the most probable transition is from n =
0 to n = 1.
 dmˆ 
 μ0    ψ*f xˆψi dτ     • For n = 1, the molecule absorbs one
 dx  0
photon and, for n = -1, the molecule emits
one photon.


Anharmonicity
• The harmonic approximation is only good for
the potential in the region near Re but is poor as
the molecule is deviated far from Re.
• Morse potential is an anharmonic potential but
the Schrodinger’s equation of the model is
exactly solvable.
• The transition moves to lower wavenumbers as
n increases.
• Anharmonicity also accounts for the appearance
of weak absorption lines corresponding to n = 0
to n = 2 and n = 0 to n = 3, 
2
1
1


En   n     n   x e 
2
2


~
a 2

xe 
 ~
2meff  4 De

~
V (r )  hcDe 1  e  a ( R  Re )

2
1/ 2
 meff 2 
a
~ 
 2hcD
e 

De: Depth of the potential minimum
ce : Anharmonicity constant
En  hc~
  2(n  1) xe ~

Vibration-rotation spectrum of HCl
Each line of the high-resolution
vibrational spectrum of a gasphase heteronuclear diatomic
molecule is found to consist of a
large number of closely spaced
components in the order of 10
cm-1, which suggests that the
structure is due to the rotational
transitions accompanying the
vibrational transitions.
• There is no Q branch.
• The lines appear in pair,
because both H35Cl and
H37Cl contribute in their
abundance ratio 3:1.
Vibration-rotation spectra
• In reality, the vibrational spectra of gas molecules are
complicated as the excitation of a vibration also results in the
excitation of rotation.
The rotational and vibrational energy levels of a linear molecule
En , J
1
~

  n    hcB J ( J  1)
2

Two quantum numbers n and J
n : quantum number for vibration
J : quantum number for rotation
Selection rules
J = 0 or ±1
n = ±1
Transition wavenumber
E  hc~
( J )
Vibration-rotation absorption spectrum
P branch: J = -1
~
~
~
 P ( J )    2 B ( J  1)
Q branch: J = 0
~
Q ( J )  ~

R branch: J = +1
~
~
~
 R ( J )    2 B ( J  1)
Electric dipole moment
2. Unit of dipole moments
1. Definition

m  QR


An electric dipole m is composed of two
charges, Q and –Q, separated by
 a distance
R. The electric
 dipole moment m is defined
as Q times R , which is a vector pointing from
the negative charge to the positive one.
1 D (debye) = 3.3564 × 10-30 C·m
The electric dipole moment of two
charges e and –e separated by
100 pm is 4.8D.
3. Addition
The electric dipole moment is a vector.
The addition of two dipole moments
follows the law of vector addition.
mres  m  m  2m1m2 cos 
2
2
1
2
1/ 2
Polar and nonpolar molecules
A polar molecule has a permanent dipole moment arising from
the partial charges of its atoms.
A nonpolar molecules has no permanent dipole moment.
All homonuclear diatomic molecules are nonpolar molecules.
All heteronuclear diatomic molecules are polar molecules.
Whether a polyatomic molecule is polar or
not is strongly related to the geometric
symmetry of the molecule.
O3 is polar.
CO2 is nonpolar.
Electric dipole moments of dichlorobenzene isomers
Benzene is a nonpolar molecule, due to its molecular symmetry.
Dipole moments of molecules
without geometric symmetry
mx   Qj x j
my  Qj y j
mz   Qj z j
j
j
j
Qj is the partial charge of atom j.
xj, yj and zj are the Cartesian coordinates of atom j.

m  m m m
2
x

2
2 1/ 2
y
z
Multipoles of point charges
An n-pole is an array of point charges with an n-pole
moment but no lower moment.
Induced dipole moment
• Physical reason:
Without an external electric field, the centers of the negative
and positive charge distributions of a nonploar molecule are at
the same place, so there is no permanent dipole moment. But,
in an external electric field, the centers of the negative and
positive charge distributions are separated by a distance and
give rise to an induced dipole moment. The proportional
constant between the induced dipole mement and the external
field is called the electric polarizability.
• A nonpolar molecule may acquire a temporary induced dipole
moment m* by the electric field E generated by a nearby ion or
polar molecule.
Electric polarizability
• The polariability depends on the orientation of the molecule with respect
to the electric field.
• In general, the polarizability is a 3 × 3 matrix. Except for atoms,
tetrahedral, octahedral and icosohedral molecules, the polarizabilities of
all other molecules have anisotropic polarizabilities, corresponding to the
off-dagonal element of the matrix.
• A large polarizability means the electronic density can undergo relatively
large fluctuation. The polarizability is inversely proportional to the
ionization energy.
Polarizability tensor of a nonpolar
molecule
*  
m  E
m x*   xx E x
m   yx E x
*
y
m z*   zx E x
Polarizability volume (in unit of
volume)

 
40
[ ]  [V ]  L3
Vibrational Raman spectroscopy
• The incident photon leaves some of its energy in the vibrational modes of
the molecule it strikes (Stokes lines), or collects additional energy from a
vibration that has already been excited (Anti-Stokes lines).
• Gross selection rule: The molecular polarizability must change as the
molecule vibrates.
Both homonuclear and heteronuclear diatomic molecules are vibrationally
Raman active.
• Specific selection rules:
J = 0 or ±2, n =  1
Induced dipole moment



min ( x)  ( x) E(t )
• The Stokes lines are more intense than the Anti-Stokes lines, because very
few molecules are in an excited vibrational state initially.
Vibration-rotation Raman spectrum of a linear rotor
O branch: J = -2
~
~
~
~
O ( J )    2B  4BJ
Q branch: J = 0
~
Q ( J )  ~

S branch: J = +2
~
~
~
~
 S ( J )    6 B  4 BJ
Vibration-rotation Raman spectrum of CO
J=-2
J=0
J=+2
Normal modes of polyatomic molecules
The motions of a non-rigid polyatomic
molecule of N atoms have 3N degrees
of freedom, including three
translational and three rotational
modes of the center of mass and 3N-6
vibrational modes among atoms.
Translational motions:
Motion of center of mass of the
molecule.
Rotational motions:
Motion of the molecule with all bond
lengths and bond angles among atoms
unchanged.
Vibrational motions:
Internal relative motions among atoms
of the molecule with changing bond
lengths (stretching) or bond angles
(bending).
• Harmonic approximation:
Deviated not too far away from the
equilibrium of a molecule, the
vibrational motions of the molecule
can be described as a linear
combination of normal modes.
• The number of normal modes
should equal the number of
degrees of freedom.
• Number of vibrational modes:
3N-6 for nonlinear molecules
3N-5 for linear molecules
Features of normal modes
A vibrational normal mode describes
a specific collective motion of atoms,
with each atom in a harmonic
oscillation of the same frequency. The
collective motion of a normal mode is
called a vibrational excitation.
In the harmonic approximation, all
normal modes of a molecule are
independent from one another. Each
normal mode behaves like an
independent harmonic oscillator. The
energies of the vibrational levels of
the i-th normal mode with frequency
i are
1

Eni   ni  h i
2

Symmetric atretching and antisymmetric
stretching modes of CO2 molecule

Symmetric
Stretching mode
Antisymmetric
stretching mode
Four vibrational modes of CO2
Symmetric stretching and antisymmetri stretching modes
The frequency of symmetric
stretching mode is higher
than that of the antisymmetric
stretching mode.
Two bending modes
The frequencies of bending
modes are double degeneracy.
Typically, the frequencies of
bending modes are smaller than
those of stretching modes.
Three vibrational modes of H2O
Symmetric stretch
Bending mode
Antisymmetric stretch
http://www1.lsbu.ac.uk/water/water_vibrational_spectrum.html
Typical vibrational modes of a tetrahedral molecule
Typical vibrational wavenumbers
Vibration type
V/cm
C–H
28502960
C–H
13401465
C–C stretch, bend
1
7001250
CC stretch
16201680
CC stretch
21002260
O–H stretch
35903650
CO stretch
16401780
CN stretch
22152275
N–H stretch
32003500
Hydrogen bonds
32003570
Gross selection rules of vibrational normal modes
• The collective motion of a vibrational normal mode must give
rise to a change in dipole moment of the molecule.
• The symmetric stretching mode of CO2 leaves the dipole moment
unchanged, so this mode is infrared inactive.
• The antisymmetric stretching mode of CO2 makes the dipole moment
changed, so this mode is infrared active.
• The two bending modes of CO2 are infrared active.
The solar energy strikes the top of the Earth’s
atmosphere and 30 percent of the energy is reflected
back into space. The Earth atmosphere absorbs the
remaining energy, with most of the intensity in the
infrared range. The trapping of the infrared radiation by
certain gases in the atmosphere is the greenhouse effect.
O2 and N2 in the atmosphere do not contribute to the
greenhouse effect. H2O and CO2 do absorb infrared
radiation and are responsible for the greenhouse effect.
Fingerprint of infrared absorption spectrum
The infrared absorption spectrum of a molecule is a characteristic
of the molecule and can be used as a fingerprint to identify the
presence of the molecule in a particular substance.
A sample (O2N-C6H4-CC-COOH)
Vibrational Raman spectra of polyatomic molecules
Gross selection rule: The vibrational normal mode is
accompanied by a change in the polarizability of the molecule.
• The symmetric stretch of CO2 is Raman active, and the other are
Raman inactive.
• A general exclusion rule: If the molecule has a center of
inversion, then no modes can be both infrared and Raman active.
Resonant Raman spectroscopy
In the conventional Raman spectroscopy, the incident radiation
does not match an electronic absorption frequency of the molecule
and there is only a virtual transition to an excited state. In the
resonant Raman spectroscopy, the incident radiation has a
frequency that nearly coincides with a molecular electronic
transition. This resonant Raman spectroscopy gives a much greater
intensity in the scattered radiation and is used to study biologic
molecules that absorb strongly in the ultraviolet and visible regions.
Exercises of Chapter 12
•
•
•
•
•
12A.2(a), 12A.9(b)
12B.1(a), 12B.4(a)
12C.2(a), 12C.8(a)
12D.2(a), 12D.3(a)
12E.1(a), 12E.5(a)