Vibrational Spectroscopy Flashcards
What is meant by vibrational spectroscopy?
This is the study of how EM radiation interacts with a molecule to change its vibrational energy
What is molecular vibration?
Vibrations involve the motion of atoms in individual chemical bonds
The atoms in a molecule vibrate around their equilibrium positions and the bonds act like springs
What region of the EM does vibrational spectroscopy correspond to?
They correspond to the IR region
What is the purpose of vibrational spectroscopy?
It is used to identify functional groups in molecules, to confirm the structure of compounds and to measure concentrations
- it can also measure vibrational frequencies and force constants of chemical bonds
What is the equation for the restoring force (Hooke’s law)?
F= -k (r-re)
K is the force constant which is the stiffness of spring/ strength of bond (Nm-1)
(r-re) is the distance from equilibrium (m)
PE is the potential energy= J (Nm)
What is the equation for potential energy?
PE= 1/2 k(r-re) ^2
K is the force constant which is the stiffness of spring/ strength of bond (Nm-1)
(r-re) is the distance from equilibrium (m)
PE is the potential energy= J (Nm)
What happens when a diatomic molecule vibrates?
- stretching or compression
- atoms are connected by a ‘spring’
- when molecule vibrates the string stretches and contracts around equilibrium position
(Corresponds to equilibrium bond length ro)
What is simple harmonic motion?
- motion of the spring
- spring vibrates because there is a restoring force that pulls it back to the equilibrium position
- restoring force is proportional to displacement
What is the equation for vibrational frequency?
Vvib= 1/ 2pi {k/RM}
{}= square root
RM= reduced mass (kg)
Vvib= s-1
Vibrational wavenumber= cm-1
What happens during the vibration of a heavy atom and a light atom?
During the bond vibrations, the heavy atom stays almost still with the light atom moving much larger distances
What is the equation for reduced mass?
RM= m1 x m2/ m1 + m2
Units are kg
What does quantum mechanics tell us about the vibrational energy levels?
-Energy levels are quantised
- moderately spaced (moderate difference in energy between levels)
- v is quantum number
Ev is the energy of the vth level
V=0 is equal to 1/2 hv
Vibrational energy levels are non degenerative
How do you calculate the energy of vibrational level?
Ev= (v+ 1/2) x vibrational wavenumber
Where v= 0, 1,2,3…
V= vibrational quantum number
Vvib determines the actual energy levels for a specific molecule
You can define the energy in terms of Vvib (wavenumber)
What is the energy at the lowest level?
Lowest level for v=0 is Eo= 1/2 Vvib (wavenumber)
This means the molecule is not permitted to have no vibrational energy and so atoms are always moving
What happens to the energy levels as you increase v ?
The gaps between the energy levels are constant
What is the equation for the vibrational wavenumber?
VW= 1/2piC x {k/RM)
VW= cm-1
Force constant is k (Nm-1)
Reduced mass is in kg
Speed of light is c = (ms-1 or cms-1)
What is the equation for Ev ( energy of level)?
Ev= (v+ 1/2) VW
For a small light molecule what would the force constant, RM, vibration wavenumber, energy and energy gap be like?
Force constant would be high Reduced mass would be low VW would be high Energy would be large Energy gap would be large
For a large heavy molecule what would the force constant, RM, vibration wavenumber, energy and energy gap be like?
The force constant would be low The reduced mass would be high The VW would be low The energy would be small The energy gap would be small
What are the gross selection rules?
There must be a change in dipole during the vibration to give a peak
In diatomics this means it needs a permanent dipole
(Homonuclear have no dipole therefore no peak)
What is the specific selection rule?
Transitions can only take place between adjacent vibrational energy levels
^V=+-1
Vibrational energy levels are moderately spaced, what does this mean?
This means most molecule are in the lowest level V=0 at room temperature
Only one transition can occur ( to V=1)
( absorb photon equal to this gap)
Spectrum shows one band
Why would you expect the same peak in the spectrum, irrespective of the level from which the transition originates?
This is because the energy gap is the same for all adjacent energy levels (hv)
What is the major application for IR?
To determine the force constant for bonds
You can find this from experimental data by using the wavenumber equation and rearranging
FC is the stiffness of the bond (related to bond strength)
