NMR SPECTROSCOPY.pptx

Nmr spectroscopy

1. NMR SPECTROSCOPY A Seminar Presented on Partial Fulfilment of the requirement of internal assessment of Physical Chemistry- III Presented by, SHORABHJIT HAZARIKA M.Sc. 3 rd Semester Enrollment No. : ACAS510850 DEPARTMENT OF CHEMISTRY ARUNACHAL UNIVERSITY OF STUDIES, NAMSAI, AP 20, DECEMBOR 2021

2. CONTENTS INTRODUCTION LARMOR PRECESSION SPIN-SPIN AND SPIN-LATTICE RELAXATION RELATIVE INTENSITIES OF LINES QUANTUM MECHANICAL TREATMENT OF THE AB SYSTEM CONCLUSION 2 DEPARTMENT OF CHEMISTRY

3. INTRODUCTION Nuclear magnetic resonance, or NMR, is a technique which utilizes the nuclear properties to obtain an NMR spectrum. Only the nucleus which I >0 shows NMR spectra. The protons in a nuclei spin about an axis and thus possesses a circular electric current. The spinning proton behaves as tiny bar magnet placed along the spin axis as shown in figure 3 DEPARTMENT OF CHEMISTRY

4. The size of the dipole is proportional to the spin angular momentum. where γ is a fundamental constant, called the magnetogyric ratio , and has characteristic values for each nucleus. Due to electromagnetic radiation, resonance in the small magnet take place and this process is known as NMR spectroscopy. T he resonance frequency for protons falls within the radio-wave range, anywhere from  100 MHz to 800 MHz  depending on the strength of the magnet . 4 DEPARTMENT OF CHEMISTRY

5. Larmor Precession The precession angular frequency, ω , is proportional to the magnetic field strength and is given by It is expressed in rad s -1 . 5 DEPARTMENT OF CHEMISTRY

6. QUANTUM MECHANICAL TREATMENT Quantum mechanical considerations show that, like many other atomic properties, the angular momentum is quantized . T he magnitude of the angular momentum is given by where I takes, for each nucleus with spin I ≠ can produce an NMR spectrum. Like other angular momenta, not only is the magnitude of the angular momentum quantized, but also its component along a reference direction, usually taken as z , is quantized , i.e. 6 DEPARTMENT OF CHEMISTRY

7. Where m I : Intrensic magnetic quantum number. In the absence of an external field, all mI values have the same energy. This degeneracy is lifted and 2 I + 1 different energy levels result if an external magnetic field is applied to define the reference direction. Effect of magnetic field: The magnetic moment is proportional to the magnitude of the angular momentum. For a point charge of charge e and mass m , it can be shown that For a proton where g N is the nuclear g factor. 7 DEPARTMENT OF CHEMISTRY

8. Above equation can be rewrite as where is the nuclear magneton akin to the Bohr magneton for electrons. Its value is 5.05078353×10-27 J T -1 . Application of a magnetic field causes an interaction between the magnetic moment and the field . The interaction energy is given by 8 DEPARTMENT OF CHEMISTRY

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10. SPIN-SPIN AND SPIN-LATTICE RELAXATION RELAXATION : Absorption of radiation causes the spins in the lower energy state to flip to the upper energy state until the populations of the two states becomes equal. This disturbs the equilibrium population. Relaxation is the process by which the spins return to equilibrium, i.e. the state in which the populations are those determined by the Boltzmann distribution law. RELAXATION TIME : The time taken to established the equllibrium , i.e. the state in which the populations are those determined by the Boltzmann distribution in the presence of external magnetic field is called relaxation time. There are two types of relaxation processes. These are Spin- lattice Relaxation Spin- spin Relaxation 10 DEPARTMENT OF CHEMISTRY

11. Spin-Lattice or Longitudinal Relaxation  Relaxation process occurs along z-axis  Transfer of the energy to the lattice or the solvent material Coupling of the nuclei magnetic field with the magnetic field of the ensemble of the vibrational and rotational motion of the lattice or the solvent .  Results in a minimal temperature increase in sample . Relaxation time (T1 ) Where n : T he population difference between  and β n : population difference at time zero, i.e. before the application of the radiofrequency. 11 DEPARTMENT OF CHEMISTRY

12. T 1 : Relaxation time where P ↓ and P ↑ , probability rates of the transitions from the upper state to the lower state and vice versa. Spin-spin or Transverse Relaxation  Relaxation process in the X-Y plane  Exchange of energy between excited nucleus and low energy state nucleus . Randomization of spins or magnetic moment in X-Y plane 12 DEPARTMENT OF CHEMISTRY

13.  Related to NMR peak line-width. Relaxation time T 2 T 2 may be equal to T 1 , or differ by orders of magnitude RELATIVE INTENSITIES OF LINES the peak multiplicity depends on the combination of the interacting spins. In general, n equivalent spin-½ nuclei split the resonance of a neighbouring spin or group of equivalent spins into n +1 lines with an intensity distribution that obeys Pascal’s triangle rule 13 DEPARTMENT OF CHEMISTRY

14. QUANTUM MECHANICAL TREATMENT OF THE AB SYSTEM SHIELDING AND DESHIELDING 1.INDUCED MAGNETIC FIELD :  In the applied magnetic field, the valence electrons around the nucleus are cause to circulates and they generates their own secondary magnetic field is known as induced magnetic field . 2.SHIELDING :- The circulation of electron around the protons itself generates field in a such way that , it oppose the applied field. The magnetic field at the nucleus (the effective field) is therefore generally less than the applied field by a fraction σ where σ is a dimensionless quantity known as the shielding or screening constant, As a result, the resonance condition is met at a lower frequency than might be expected. (A) 14 DEPARTMENT OF CHEMISTRY

15. DESHIELDING :- DESHIELDING If the induced magnetic field reinforced the applied magnetic field ,then the field felt by the proton is augmented and the proton is said to be deshielded . CHEMICAL SHIFT The chemical shift δ is defined as W here υ is the frequency of the line in the sample we are interested in and υ TMS is the corresponding quantity for TMS, both expressed in Hz. The quantity in above equation is small, so this can be rewrite as where υ is reference frequency of the spectrometer. 15 DEPARTMENT OF CHEMISTRY

16. Let us now consider the two-spin AB system . Since the two protons are in different environments, we have from equation (A). In terms of the frequencies, and the two protons therefore appear at different frequencies. δ AB is expressed in parts per million as This is the difference in the chemicals shifts of protons A and B with reference to TMS, since 16 DEPARTMENT OF CHEMISTRY

17. Four possibilities arise: α (A) α (B), α (A) β (B), β (A) α (B) and β (A) β (B), each with a different energy. For simplicity, in what follows, we shall drop A and B and take it that the first spin corresponds to A and the second to B. For example, αβ refers to A having α spin and B having β spin, i,e . α (A) β (B). The NMR Hamiltonian is a sum of three terms: The Zeeman Hamiltonian is given by In NMR spectroscopy, it is more convenient to express the energies in frequency units. Therefore 17 DEPARTMENT OF CHEMISTRY

18. The scalar coupling term is given by . The third term in the Hamiltonian is the dipolar term, which depends on the relative orientation of spins. In liquids, this averages to zero and here we ignore it. Hence, Application of this Hamiltonian to the four wave functions yields the energies given in Table 1. 18 DEPARTMENT OF CHEMISTRY

19. CONCLUSION Nuclear magnetic resonance spectroscopy is one of the most powerful tools that use to determine the structure of compounds. Generally, NMR spectroscopy gives the information about organic and inorganic compound. 19 DEPARTMENT OF CHEMISTRY

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