Rotation-vibration Spectra Flashcards
What is a diatomic vibrating rotor?
This is a diatomic molecule that is both vibrating and rotating
What is the total energy for a molecule that is both vibrating and rotating?
Vibration and rotational energies are different and can be considered independent so Etotal is the energies added together
= (v + 1/2)VW + BJ(J+1)
(Harmonic oscillator + rigid rotor)
What is the relation between vibrational and rotational energy levels?
In each vibrational level a molecule might have different amounts of vibrational energy
What are the specific selection rules?
^V= +/-1
^J= +/- 1
-1 is called p, 0 is called Q and +1 is called R
Describe the spacing between vibrational and rotational levels
Vibrational levels are moderately spaced. This means that most molecules occupy V=0
Rotational levels are closely spaced so a range of J levels are occupied
Describe the spectrum of rotational and vibrational lines
The spectrum will have one overall band due to V=0->1 transition
There will be several lines due to J->J+/-1 rotational transitions that occur simultaneously
What is the energy gap in a vibrational and rotational spectra?
^Ev,J= VW +- 2Bm
Where m= 1,2,3…
What is rotational fine structure?
This is observed in a vibration-rotation spectra
- at high resolution you can see the two peaks in the low resolution spectrum are made up of a series of closely spaced peaks
- you can measure B and hence fine bond length
- the lines are from a transition between a rotational energy level in the lower vibrational state to one of the upper vibrational states
What is a diatomic anharmonic oscillator?
This is not a harmonic oscillator (that is an approximation)
At high vibrational energies, the bond lengthens more
As the bond in a real molecule is stretched, it becomes weaker until it eventually breaks
What is a morse curve?
This is the variation of potential energy with bond lengths in a real molecule
This does not correspond to the graph of harmonic oscillator although for low vibration quantum numbers, there is agreement
What is the equation for vibrational energy level for anharmonic oscillator?
Ev= (v+1/2)VW - (v+1/2)^2 x Xe
Xe is the anharmonicity constant
How does the anharmonic oscillator selection rule differ to Harmonic oscillator?
The selection rule ^V=+-1 only works for Harmonic
In a real system (anharmonic) you can have transitions from v=0 to 2 and v=0 to 3
These are called overtone bands
^V= +1 is still the strongest band
How many vibrational modes does a diatomic molecule have?
One mode of vibration
The bond can stretch and compress
How many vibrational modes can a polyatomic molecule have?
Several
A molecule contains N atoms
The position can be specified by 3 coordinates
The position of atoms is specified by 3N
The molecule has 3N degrees of freedom
It can move by translation (xyz)- 3 translational degrees of freedom
It can move by rotation or vibration
How many rotational degrees of freedom do polyatomic molecules have?
Non linear have 3 rotational degrees of freedom
Linear have 2
