ANISOTROPY IN HYPERFINE COUPLING AND ITS APPLICATIONS

1. KASHMIR UNIVERSITY DEPARTMENT OF CHEMISTRY ANISOTROPY IN HYPERFINE COUPLINGANDITS APPLICATIONS BY Touseef Ahmad Dar M.Sc 3rd Semester Batch 2012-13 touseefdar97@gmail.com

2. ANISOTROPY • Having different properties when measured along different axis. (or) • State or quality of having different properties along different directions.

3. HYPERFINE COUPLING • The interaction between the spin magnetic moment of an unpaired electron and nuclear spin magnetic moment resulting in the splitting of α and β energy levels in an external magnetic field and thus in the multiplet pattern of the ESR spectra of radical like species and transition metal compounds.

4. Two main contributions to hyperfine coupling are considered usually- 1. Fermi contact 2. Dipolar interaction Fermi contact is isotropic one and is related to the unpaired spin density at the nucleus. The dipolar interaction is anisotropic and is related to rˉ³ where r is the distance between the atom having the unpaired electron and nucleus with non zero spin. Besides Fermi contact, isotropic contribution is also due to Spin Polarization exchange effect. Contributions to hyperfine coupling

5. In rigid systems like NO2,KNO3 the interaction between the electron and nuclear dipoles gives rise to anisotropic interaction. • The interaction of these two moments can be represented as- Ĥdipolar = gBgNBN[Ŝ.Î/rˉ³-3(Ŝ.r)(Î.r)/r^5] g = gyromagnetic ratio Ŝ = spin function of electron Î = nuclear spin state B = Bohr magneton r = distance between unpaired electrons and nucleus

6. On substituting Ŝ = Ŝx+Ŝy+Ŝz, Î=Îx+Îy+Îz, and r=x+y+z. we get a Ĥdipolar interms of r and Î matrix*, that finally leads to- Ĥdipolar = hŜTÎ Where T = dipolar interaction tensor (in Hz), that gauges the nuclear anisotropic hyperfine interactions. • In terms of spherical polar coordinates T is given by- TZZ = gBgNBN‹(3cos²ѳ-1)/r³› TXX = -1/2gBgNBN‹(3cos²ѳ-1)/r³› TYY = -1/2gBgNBN‹(3cos²ѳ-1)/r³› * see Physical Methods for Chemistry by R.S.Drago… 2nd Ed. Page 384

7. The solution of above Hamiltonian leads to the following equation- Ĥ =gBHŜ+ gNBHÎ +AÎŜ gBHŜ = electron Zeeman term (interaction between magnetic field and spin function of electron) gNBHÎ=Nuclear Zeeman term (interaction of nuclear spin state with the magnetic field) AÎŜ = interaction of electron and nuclear spin magnetic moment A = Hyperfine coupling constant

8. The energy corresponding to the above Hamiltonian is- E = gBHms + gNBHmi + Amims In organic free radicals nuclear Zeeman effect gives rise to a small energy term compared to the others and also g-anisotropic is less. So, we can treat g as isotropic only while discussing hyperfine interactions.

9. The electron Zeeman term is considered to be the dominant energy term. So electron spin is quantized along H labeled as z-axis • And nuclear moment will not be quantized along z-axis but along effective field Heff. Which is sum of direct external field H and hyperfine field produced by electrons

10. If hyperfine interaction is large(100gauss), the hyperfine field at this nucleus is about 11700gauss. Thus we can ignore nuclear Zeeman term from above equation of energy. So, the Hamiltonian of most of the organic free radicals is of the form- Ĥ= gBHms + Amsmi • The hyperfine coupling constant A has two contributions one is called isotropic(AIso) and another anisotropic (AAniso) A = AIso + AAniso

11. In solution phase anisotropic components are averaged to zero so A is taken as1/3 of trace of A to decompose A into AIso and AAniso • The energy of hyperfine coupling is given by- ∆Ehf = 1/2√Azx² + Azy² + Azz² • The hyperfine coupling constant observed experimentally is the difference between the appropriate levels and is given by- A = h [(AIso – AAniso )²+ 3AAniso (2 AIso + AAniso )cos²ѳ]½ Ѳ is the angle that z axis makes with field

12. If there is an unpaired electron in pz orbital of ¹³C nucleus 12 + + + - - - - - - + + H + fig.(C) fig.(A) fig.(B) Visual representation of dipolar averaging of the electron & nuclear moments 12

13. As the pz orbital is aligned with the field fig.(A) almost entire averaging of the dipolar interaction of the nuclear moment over the pz orbital will occur in the positive region of cone. Thus a large positive value of Tzz is expected. • For the orientation along x-axis fig.(B) the dipolar interaction, Txx , will be large and negative; same is the case with Tyy, for the orientation shown in fig.(C)

14. Anisotropic hydrogen hyperfine components of a C-H radical + + + + C - - - - - C H - H C H + + H + Fig.(i) Fig.(ii) Fig.(iii) Visual representation of the dipolar averaging of the nuclear moment on the hydrogen with electron moment on p-orbital of carbon 14

15. From the Fig.(i),(ii),(iii) it is evident that Tzz is small, whereas Tyy is positive & Txx is negative. • For ¹³C the anisotropic hyperfine coupling constant is given by- -B -B +2B

16. APPLICATIONS • Anisotropic together with isotropic hyperfine coupling constants have provided considerable information about molecular orbital containing unpaired electrons. • Anisotropic & isotropic hyperfine coupling constant have helped in determining structure of free radicals like CH3 (Aiso =38.5gauss) is planar & CF3 (Aiso =271.6gauss) is pyramidal with s-character in the orbital containing unpaired electron. Also Aiso of N-14 in NO2 is 151 MHz & AAnso is 12 MHz & on the basis of spin density of s & p orbitals it is predicted that more p character is being used in the orbitals to bond oxygen & at an angle of 120º.

17. THANK YOU