Rotation-vibration Spectra Flashcards

1
Q

What is a diatomic vibrating rotor?

A

This is a diatomic molecule that is both vibrating and rotating

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2
Q

What is the total energy for a molecule that is both vibrating and rotating?

A

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)

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3
Q

What is the relation between vibrational and rotational energy levels?

A

In each vibrational level a molecule might have different amounts of vibrational energy

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4
Q

What are the specific selection rules?

A

^V= +/-1
^J= +/- 1
-1 is called p, 0 is called Q and +1 is called R

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5
Q

Describe the spacing between vibrational and rotational levels

A

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

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6
Q

Describe the spectrum of rotational and vibrational lines

A

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

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7
Q

What is the energy gap in a vibrational and rotational spectra?

A

^Ev,J= VW +- 2Bm

Where m= 1,2,3…

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8
Q

What is rotational fine structure?

A

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
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9
Q

What is a diatomic anharmonic oscillator?

A

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

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10
Q

What is a morse curve?

A

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

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11
Q

What is the equation for vibrational energy level for anharmonic oscillator?

A

Ev= (v+1/2)VW - (v+1/2)^2 x Xe

Xe is the anharmonicity constant

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12
Q

How does the anharmonic oscillator selection rule differ to Harmonic oscillator?

A

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

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13
Q

How many vibrational modes does a diatomic molecule have?

A

One mode of vibration

The bond can stretch and compress

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14
Q

How many vibrational modes can a polyatomic molecule have?

A

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

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15
Q

How many rotational degrees of freedom do polyatomic molecules have?

A

Non linear have 3 rotational degrees of freedom

Linear have 2

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16
Q

How can you work out the number of vibrational modes of a polyatomic molecule?

(Depends on number of atoms)

A

Non linear
3N, 3 translational, 3 rotational
So you use 3N-6

Linear
3N, 3 translational, 2 rotational
So you use 3N-5

17
Q

What types of vibrations are there?

A

There are stretching vibrations (symmetric or asymmetric) and there are bending vibrations

18
Q

What happens if a molecule contains similar or identical groups?

A

They couple together to give symmetric vibrational (in phase) and asymmetric vibrations (out of phase)

19
Q

What is normal mode of vibration?

A

This is where the atoms oscillator in sync

They pass through their equilibrium positions at the same time

20
Q

When does each normal mode of vibration occur?

A

Each normal mode occurs all the time and independently from the others at its own frequency
This means it will give its own specific band in a spectrum