1. Matrix representation of Spin Operator

2. J. I kz I l z 2 I ky I l z I kx

3. xx t1t1 t2t2 Correlation Spectroscopy (COSY) Considering two spin k and l

6. Heteronuclear Single Quantum Correlation Spectroscopy (HSQC) ϕ 1 = x, -x, x, –x ϕ 2 = x, x, -x, –x ϕ R = x, -x, -x, x yy t2t2 ϕ1ϕ1 y y y ϕ2ϕ2 y I S ϕRϕR ABCDE F -y

7. Heteronuclear Single Quantum Correlation Spectroscopy (HSQC) I S y y AB

8. y y I S AB y ϕ1ϕ1 y ϕ2ϕ2 CDE -y ϕ 1 = x, -x, x, –x ϕ 2 = x, x, -x, –x

9. Heteronuclear Single Quantum Correlation Spectroscopy (HSQC) yy ϕ1ϕ1 y y ϕ2ϕ2 I S ABCDE -y y y F

10. Heteronuclear Single Quantum Correlation Spectroscopy (HSQC) yy ϕ1ϕ1 y y ϕ2ϕ2 I S ABCDE -y y y F t2t2 ϕRϕR ϕ 2 = x, x, -x, –x ϕ 1 = x, -x, x, –x ϕ R = x, -x, -x, x

11. Heteronuclear Single Quantum Correlation Spectroscopy (HSQC) yy t2t2 ϕ1ϕ1 y y y ϕ2ϕ2 y I S ϕRϕR ABCDE F -y For protons NOT coupled to S spin We need two step phase cycle to get rid of this magnetization ϕ 1 = x, -x ϕ R = x, -x Steps ϕ1ϕ1 ϕRϕR Magnetization at point F Protons coupled to S spinProtons NOT coupled to S spin Step Ixx Step II-x

12. Heteronuclear Single Quantum Correlation Spectroscopy (HSQC) yy t2t2 ϕ1ϕ1 y y y ϕ2ϕ2 y I S ϕRϕR ABCDE F -y For complete removal of multiple quantum term we need four step phase cycle to get rid of this magnetization ϕ 1 = x, -x, x, -x ϕ 1 = x, x, -x, -x ϕ R = x, -x, -x, x Steps ϕ1ϕ1 ϕ2ϕ2 ϕRϕR Magnetization at point F Protons coupled to S spinProtons NOT coupled to S spin Step Ixxx Step II-xx Step IIIx-x Step IV-x x

13. Sensitive enhanced Heteronuclear Single Quantum Correlation Spectroscopy (SE-HSQC) yy t2t2 ϕ1ϕ1 y y y ϕ2ϕ2 y I S ϕRϕR A -y ϕ 3 = y, -y, y, –y ϕ3ϕ3 -y y yy

14. SE- Heteronuclear Single Quantum Correlation Spectroscopy (SE-HSQC) yy t2t2 ϕ1ϕ1 y y y ϕ2ϕ2 y I S ϕRϕR -y D A BC ϕ3ϕ3 y yy ϕ 3 = y, -y, y, –y

15. SE- Heteronuclear Single Quantum Correlation Spectroscopy (SE-HSQC) yy t2t2 ϕ1ϕ1 y y y ϕ2ϕ2 y I S ϕRϕR D -y A BC ϕ3ϕ3 y yy ϕ 3 = y, -y, y, –y