EPR Spectroscopy| Count Hyperfine line and relative intensities

The primary condition for EPR: One or more number of unpair electrons. Radical: Methyl radical, carbene, Transition metal ions, Hydrogen atom.

EPR (Electron Paramagnetic Resonance)

Hello everyone today we will discuss Inorganic Spectroscopy. First of all, we are talking about ESR Spectroscopy (Electron Spin Resonance) or EPR Spectroscopy (Electron Paramagnetic Resonance).

EPR Spectroscopy: Chemarticle


 Electron Spin Resonance Spectroscopy (ESR) or Electron Paramagnetic Resonance (EPR)

Similar to NMR spectroscopy – NMR (Nuclear Magnetic Resonance) resonating by Nucleus. In case EPR spectroscopy resonating by electron.

The primary condition for EPR

  • One or more number of unpair electrons.

In presence of one or more unpair electrons can produce Electron Spin Resonance, such as Hydrogen atom, O2 (two unpair electrons), NO, NO2, etc.

  • Radical: Methyl radical (one unpair electron), carbene (two unpair electrons)
  • Transition metal ions: (one to five unpair electrons)
  • Hydrogen atom (one unpair electron)

EPR in Organic Reaction

Where free radical or free unpair electron presence the EPR spectrum will be determent. The organic reaction such as Free Radical mechanism, Polymerization reaction, etc.

EPR spectrum intensity

The EPR spectrum line intensity depends on the concertation of free radicals. The peak intensity is directly proportional to the concentration of free radicals or the concentration of the paramagnetic species.

Intensity   α   concentration of the free radicals

Intensity   α   concentration of the paramagnetic species

That is why increasing the concentration of free electrons corresponds to an increase in the intensity of the EPR spectrum line. Corresponding to decreases the concentration of free radical decreases the spectrum intensity.

Sensitivity of EPR spectrum

Use of 10-13 mole of free radical

Spectrum width

The electron paramagnetic resonance spectrum width depends on the relaxation time of the spin states. Spectrum width insertional proportional to relaxation time. In the case of EPR spectroscopy, the relaxation time is very small. The relaxation time (τ) is approximately 10-7 seconds = 100 ns.

Δv=1/2πτ=1/(2π×10^(-7) )=10^6 Hz≅1MHz

That is why the EPR spectrum gives a broad peak.

Advantage and Disadvantage of EPR spectrum broader

  • Advantage: Homogeneity of the magnetic field is less critical. 
  • Disadvantage: Detection of the peak location is uncertain.

Devolve the detection of the peak location during derivative plots. And find out the peak potion of ESR spectroscopy.

What is deferent between EPR Spectrum and the NMR spectrum?

 

NMR spectrum EPR or ESR spectrum
1. Nuclear Magnetic resonance by the nucleus. 1. Electron spin resonance by free electrons or unpair electrons.
2. Relaxation time is high. 2. Relaxation time is very small.
3. Due to higher relaxation time (τ) spectrum peak is broader 3. Due to lower relaxation time (τ) spectrum peak is narrow.

4. According to Heisenberg uncertainty principle:  

Δv=1/2πτ

Δv. τ = Constant

In case τ is high, Δv is low.

where Δv is the Width of the spectrum and τ is the relaxation time.

4. According to Heisenberg uncertainty principle:  

Δv=1/2πτ

Δv. τ = Constant

In case τ is low, Δv is high.

where Δv is the Width of the spectrum and τ is the relaxation time.


Hyperfine splitting constant

The distance between two hyperfine lines is called a hyperfine splitting constant. Which is determined by A term. Hyperfine splitting constant detects the space between two spectrum lines. 

This is just like a coupling constant (J) in NMR spectroscopy.

Number of hyperfine line determination

We have considered hydrogen atom, this has one unpair electron. The hydrogen atom, H2+ (hydrogen cation radical), H2- (hydrogen anion radical) all are EPR active.

Number of hyperfine lines = (2nI + 1)

Where n = number of nuclei involved, I = Spin of nuclei involved.

Hyperfine line of H2+ cation

This cation has one single electron. And spin of hydrogen nucleus (I) =1/2. In case two hydrogen nuclei are involved n = 2.

Number of hyperfine lines = (2 x 2 x 1/2 + 1) = (2+1) = 3, triplet signal.

A total of three hyperfine lines are present in EPR spectroscopy for Hydrogen cation.

Similarly, 

Hyperfine line calculated for H2- anion

In this hydrogen, anion has one single electron. And spin of nuclei = ½. In case two hydrogen nuclei are involved n =2.

Number of hyperfine lines of EPR or ESR spectrum = (2 x 2 x 1/2 + 1) = (2+1) = 3, triplet signal.

Calculation of hyperfine lines for methyl radical

We know that Carbon atoms are two isotopes 13C and 12C. In case compered to natural abound of 12C is very high (98.9%), on the other hand, natural abounds of 13C is very low (0.1%).

See the EPR spectroscopy: 12C isotope is EPR inactive, due to nuclear spin (I) of 12C = 0. On the other hand, 13C isotope EPR is active, (where I = ½) but natural abounds are very low.

Now consider the methyl radical, three hydrogens, and one carbon. We have to remark by the percent of hydrogen is 75% and carbon is 25%. 

Now compared to natural abounds hydrogen is all almost 100%. That is why we have to negligible the carbon nuclei. In case carbon is called dilute nuclei

Note: in the case of methyl radical, carbon radical does not involve due to hydrogen 100% a boundness in this radical. So, carbon nuclei do not count in the number of hyperfine line calculations. This is called dilute nuclei.

Number of hyperfine lines of Methyl radical = (2 x 3 x ½ + 1) = 4, Quadrat signal. A total of four hyperfine lines are produced.

Where the number of hydrogen nuclei (n) = 3

The intensity of spectrum line

When nuclear spin (I) = 1/2 

For intensity ratio of spectrum line of EPR, using Pascale triangle rules…

Singlet; 1

Doublet; 1: 1

Triplet; 1: 2: 1

Quadrat; 1: 3: 3: 1

Quintet; 1: 4: 6: 4: 1



Q.1. In the EPR spectrum of a methyl radical, the number of lines and relative intensities, respectively, are

A. 1 and 1

B. 3 and 1: 2: 1

C. 4 and 1: 2: 2: 1

D. 4 and 1: 3: 3: 1

Answer: (D) 4 and 1: 3: 3: 1

Hints: 

In methyl, radicals have one unpair electron are present.

.CH3

In case one types of protons are present, the number of nuclei (n) = 3. In case carbon nuclei do not count due to less natural abounds (0.1%) of EPR active 13C.

Number of hyperfine lines for methyl radical = (2 x 3 x ½ + 1) = 4, Quadrat signal.

Using Pascal triangle rules: - Intensity of the EPR spectrum lines for methyl radical 1: 3: 3: 1

Singlet 1

Doublet 1: 1

Triplet 1: 2: 1

Quadrat 1: 3: 3: 1

The intensity ratio of the EPR spectrum lines for methyl radical 1: 3: 3: 1
The intensity ratio of the EPR spectrum lines for methyl radical 1: 3: 3: 1


Q.2. In the EPR spectrum of an ethyl radical, the number of lines and relative intensities, respectively, are

(a). 12 and 1: 2: 1: 3: 6: 3: 3: 6: 3: 1: 2: 1

(b). 12 and 1: 3: 3: 1: 3: 5: 5: 3: 1: 3: 3: 1

(c). 12 and 1: 3: 3: 1: 2: 6: 6: 2: 1: 3: 3: 1

(d). 8 and 1: 3: 3: 1: 1: 3: 3: 1 

Which statement is correct?

(A) a and b

(B)a and c

(C) a b and c

(D) all are incorrect 


Answer: (B) a and c

Hints:

Ethyl radicals have one unpaired electron.

.CH2CH3

In the case of ethyl radical, have two different types of protons in is the presence of a total of three numbers of hydrogen-1 and two numbers of hydrogen-2. Where n1 = 3, n2 = 2, I = 1/2.

Number of hyperfine lines for ethyl radical = (2n1I +1) (2n2I +1) = (2 x 3 x ½ + 1) (2 x 2 x ½ + 1) = 4 x 3 = 12. Total 12 hyperfine lines are produced. That means quadrat of triplet signal or triplet of quadrat.

In case 

When we consider:  CH2 < CH3 

would produce a quadrat of triplet (12 lines)

Intensity using Pascale triangle:

(Quadrat) 1: 3: 3: 1

(Triplet) 1: 2: 1

(Quadrat of triplet) 1: 2: 1: 3: 6: 3: 3: 6: 3: 1: 2: 1


When we consider:  CH2 > CH3 

would produce a triplet of quadrat (12 lines)

Intensity using Pascale triangle:

(Triplet) 1: 2: 1

(Quadrat) 1: 3: 3: 1

(Triplet of Quadrat) 1: 3: 3: 1: 2: 6: 6: 2: 1: 3: 3: 1

Q.3. Find out The EPR spectrum of benzene radical, the number of lines, and relative intensities

Ans:

In benzene, radicals have one free electron present.

.C6H6

In case, Benzene is a symmetrical molecule. In Benzene, the molecule has six, which are symmetric. That means six hydrogens are given the same EPR spectrum line.

Number of hyperfine lines of benzene radical = (2 x 6 x ½ + 1) = 7. Produced the septet signal.

The intensity of the septet line for EPR spectroscopy is 1: 6: 15: 20: 15: 6: 1. We have used the Pascal triangle rule easy to find the intensity of the EPR spectroscopy for benzene radical.