Vibrational (Infrared) spectroscopy Flashcards
What does the absorption involve?
Absorption of infrared energy involves the vibrations of chemical bonds, vibration means lots of things: stretch, bend etc
What unit used on spectra?
Typically uses wavenumber on the “energy” axis – 4000 cm -1 – 400 cm -1, corresponding to the change in energy 12 kJ mol-1
Vibration of a chemical bond?
Treat the chemical bond as a spring, If the spring is extended or compressed, there is a restoring force, F, Simple harmonic motion: Hookes Law, Force, F, is proportional to the extension, x F = -kx
Energy, E = 1⁄2 k x2
k is the force constant of the spring
What is force constant?
related to the stiffness of the spring (or strength of bond); how easy it is to set into motion
Typical molecular vibrational energies?
10-19 - 10-20 J, infrared frequencies
Energy level of a harmonic oscillator?
Energy levels are equally separated
All vibrational levels have degeneracy =1
The lowest energy possible, v=0, is NOT zero
This is called zero point energy
Gross selection rule in vibrational spectroscopy?
The dipole moment of a molecule must change during the vibration
Specific selection rule in vibrational spectroscopy?
Only transitions between adjacent energy levels can occur, delta v = ±1
Homonuclear diatomics?
Not IR active
Heteronuclear diatomics?
IR active
Polyatomics?
Some modes IR active some IR inactive
How do we find the number of vibrational modes?
We use a 3-D geometry to define molecules in space, the position of each atom in a molecule can be given in terms of three measurements,
1 atom = 3 degrees of freedom
2 atoms = 6 degrees of freedom
3 atoms = 9 degrees of freedom
N atoms = 3N degrees of freedom
A degree of freedom (DOF) is an independent mode of position or motion in a molecule
Translational motion?
Always 3 modes of translational motion (doesn’t matter how many atoms)
Rotational motion?
2 cases
Non linear, 3 axes = 3 DOF
Linear, 2 axes = 2 DOF
rotation about the x axes does not change positions of any atoms
Vibrational motion?
The other degrees of freedom (to make total up to 3N) are taken up by vibrational motion within molecules Total Degrees of freedom = 3N for N atoms Always 3 trans.+ either 2 or 3 rot = 5 or 6 (trans. + rot.) Linear (3N – 5) vibrational modes Non linear (3N – 6) vibrational modes An independent mode of vibration (one that does not influence another mode) is called a normal mode
Vibrational spectroscopy for complex molecules?
As the number of atoms increase, the number of peaks increases rapidly, Usually not possible to assign all the peaks but can use the fingerprint region to identify characteristic frequencies
Effect of isotopic substitution?
As for rotational spectroscopy, E vibrational depends on reduced mass so will change if different isotopes are present, k depends on the electron distribution in the bond - adding neutrons to a nucleus has little effect on electron density, assume isotopic substitution does not change the force constant
How does changing from H to D affect the reduced mass?
The bond vibration of HCl gives an absorption at 2990 cm–1, replacing H by deuterium, D (2H), changes the reduced mass, this gives the D–Cl absorption at lower wavenumber, 2140 cm-1, Largest shifts occur for H → D but significant for other elements – can be used to confirm the presence or otherwise of elements in a compound
The selection rule for anharmonic motion?
The selection rule delta v = ± 1 strictly works only for harmonic motion, weak bands can be seen at 2hv0 3hv0 etc these are overtone bands
Motion of a bond?
The motion of a bond is not harmonic. At large displacements, atoms repel (at short distances) or bonds break (at long distances).
Anharmonicity effects –> separation between levels is not constant
More realistic motion of bond?
Anharmonic not harmonic as classically thought
Anharmonic effect on the curve of energy levels?
Energy – distance curve isn’t a true parabola - ”Morse” curve
If push the atoms together, repulsion increases - steeper slope
If we pull the atoms apart, the bond breaks - dissociation energy
What does solution of the Schrödinger equation for the Morse potential show for the selection rule?
The selection rule delta v = ± 1 is not strictly obeyed, overtones appear with delta v = ± 2 and delta v = ± 3
What does solution of the Schrödinger equation for the Morse potential show for the vibrational levels?
Vibrational levels are not equally spaced, separation gets smaller with increasing v and becomes = 0 at the limit
Equation for better description of energy levels?
Ev = (v + 1⁄2) hv – A (v + 1⁄2)2 hv
Why So Many Peaks for Vibrational-Rotational Spectra?
Transitions occur simultaneously between vibrational and rotational levels
What does IR detect?
Detects changes in the vibrational energy of molecules
How can diatomic molecules be treated?
Diatomic molecules can be treated as harmonic or (better) anharmonic oscillators which allows calculation of bond force constant and bond dissociation energy
What do triatomic molecules show?
Triatomic molecules show overtone and combination bands
What do polyatomic molecules show?
Polyatomic molecules with N atoms vibrate in 3N-5 (for linear) or 3N-6 (for non-linear) normal modes
What do complex molecules show?
Complex molecules show characteristic frequencies for certain functional groups and a fingerprint region
What do vibrational rotational spectra give?
Can give access to previously forbidden rotational signals, line-spacing in (high resolution) rotational fine structure allows calculation of the bond length
How can a bond be treated like a spring of simple harmonic motion?
The greater the masses of the atoms the more slowly the spring vibrates, stiffness of the bond the bond is less easily deformed and vibrates more quickly, the bond vibrates because there is a restoring force when it is displaced from equilibrium position, as the bond is stretched the force pulls it back towards the equilibrium position as the bond is compressed the force pushes it back, the restoring force is proportional to the displacement the further the bond is stretched or compressed the large the force that restores it
What does the penitential energy of the bond depend on?
The square of the extension x, at the extremes of the vibration when the bond is fully extended or compressed the kinetic energy is zero and all the energy of the spring is in the form of potential energy, as the spring passes through its equilibrium length the kinetic energy is at its maximum
Constant k?
Force constant of the bond and is related to its stiffness as k increases the bond becomes stiffer the frequency of the vibration increases, as the reduced mass increases and the masses of the atoms become larger the frequency decreases
Why is reduced mass used?
Since the frequency depends on the masses of both atoms, during bond vibration the heavy atom stays almost still while the light atom moves much larger distances
Different isotopes?
Since the energy of a vibration depends on the masses of the atoms the energy will change if different isotopes are present in the molecules, the shift of the peak wavenumber due to isotopic substitution is largest for h and D but is significant for other elements and can be used to confirm the presence or otherwise of elements in a compound
