Vibrational Spectroscopy

What is vibrational spec

• Vibrational spec is the study of how EM radiation interacts with a molecule to change its vibrational energy 

• Atoms in a molecule vibrate  around their equilibrium positions, and the bonds act like springs 

How do we observe vibrations of bonds

• Apply classical mechanics to them, Hooke’s Law

Give Hooke’s law to describe bond vibrations, stating each coponant

Draw a graph of energy against bond length for a simple harmonic oscillator, stating energies at equilibrium and turning points

Draw graph of harmonic oscillators with big vs small k values

Give equation for Vibrational frequency

Give equation for vibrational wave number, giving units and definitions for each part

What does quantized and moderately spaced refer too

• Molecule can only vibrate with discrete amounts of energy, meaning they are quantized 

• Molecules have moderate differences in energy between different vibrational levels. They are moderately spaced meaning we need to look at photons of higher energy looking at the infrared region rather than microwaves 

What are diatomic harmonic oscillators

Refers to diatomic molecules that obey Hooke’s Law

Give equation for the energy of vibrational levels, describing all components and their units

Give the three different variations for the E_V equation

What does quantum theory tell us of Vibrational energy levels

quantum theory tells us that vibrational energy levels are quantized 

• Vibrational Quantum Number defines the permitted energy levels Ev, in general, for all molecules 

• Vibrational Wave number  determines the actual energy levels for a specific molecule 

Draw a graph of energy against bond length displaying energy levels of a harmonic oscillator

What is the lowest level for v and what does this mean for the molecule

Lowest level for v = 0, is E0 = ½ x Vibrational wave number,

This will still have a numerical value, as seen on the graph previously meaning we can see here that the atoms are always moving's, they are not permitted to have 0 vibrational energy 

Give equation for Vibrational wavenumber describing each component and giving units, state what it is dependant on.

• Constant for a specific molecules 

• Depends on the force constant and mass 

Consider relationship between the Force constant and mass of molecules, what this means for energy and wavenumber

Describe the Gross selection rule, draw diagrams displaying this

• For absorption or emission, there must be a change in dipole on vibration

• The oscillating electric field needs to interact with the molecule and to let it do so its required to interact with the molecules oscillating dipole and it vibrates

Describe the specific selection rule

• Delta V = + - 1

• Transitions only allowed to next level.

Describe vibrational transitions

Vibrational energy levels are moderately spaced 

• most molecules are in the lowest level, v = 0, at room temperature 

• only ONE transition can occur, to v = 1 

• by absorbing a photon ONLY of energy equal to the gap ΔEv = 0→1 

• a vibrational absorption spectrum shows ONE band 

What does an infrared spectrum show

• That a molecule has a change in dipole on vibration

What is a diatomic vibrating rotor

• A diatomic that is both vibrating and rotating

Describe how vibrational and rotational energies are observed together

• Because the vibrational and rotational energies are very different from each other.

• As such, the two types of motion can be considered to occur independently of each other, the total energy is the sum of the individual energies

Give the BORN-OPPENHEIMER approximation

Give the general equation for E_VJ

ΔE_v,J = v^~_obs = v^~_vib ± 2 Bm

What is a diatomic anharmonic oscillator

Not a harmonic oscillator

At high vibrational energies, the bond lengthens more

What does quantum mechanics tell us about the anharmonic oscillators energy

What is the selection rule for anharmonic oscillators

Selection rule relaxed to: Δv = ±1, ±2, ... but Δv = +1 still the strongest band

Describe how vibration differs between diatomic and polyatomic

• For diatomics the bond can only stretch and compress. (One mode of vibration)

• For polyatomics the modes of vibration differ and are calculated by 3N

  • As a molecule can contains N atoms, and there are 3 positions each atom can be specified by

  • It can move by translation (X,Y,Z)

  • It can move by rotation

  • It can move by vibration

How do you calculate number of vibrational modes in polyatomics

3N - (modes of rotation + modes of translation)

Name the two main types of vibrations

• Stretching vibrations

• Bending vibrations

Give the two types of vibration for when a molecule contains similar or identical groups

• Vibrations do not occur independently, they couple to give

• Symmetric vibrations (In-Phase)

• Asymmetric vibrations (Out-Phase)

What do normal modes of vibration refer to, what does this mean for frequency and vibrations.

Normal modes of vibration refer to when : 

• All atoms oscillating synchronously  

• All atoms passing through their equilibrium position at the same time 

• They occur all the time in this state 

• Each of these vibrations are independent from each other 

• Each will also have its own specific frequency and as such each of the normal modes of vibration will generate its own specific band in the spectrum  

What does a transition being IR active mean

• The transition is allowed

• There is a chance in dipole upon vibration giving an IR band

• The large the change the stronger the band

Describe why we prefer either the condensed or the gas phase for rotational spectroscopy

• Gas Phase

  • Preferred for more high resolution studies, this is due to its free rotation meaning there is rotational fine structure rather than just vibrational data

• Condensed Phase

  • Much simpler spectra 

  • Band positions may be shifted 

  • Not free rotating 

  • Hydrogen bonding causes a broad band due to forming many different structures and interactions 

  • No fine structure

what are skeletal vibrations, what region do they occupy

Skeletal vibrations 

• involve SEVERAL or ALL atoms within a molecular skeleton 

• bands may occur in the FINGERPRINT region at ca. 700 - 1500 cm-1  

• characteristic pattern for "fingerprint" identification  

What are group vibrations

Group vibrations 

• are LOCALISED on a specific bond or group  

• give bands at a SIMILAR wavenumber regardless of the molecule 

• Excellent for identifying specific groups