Lecture 37 Nuclear magnetic resonance

Nuclear magnetic resonance The use of NMR in chemical research was pioneered by Herbert S. Gutowski of Department of Chemistry, University of Illinois, who established the relationship between chemical shifts and molecular structures. He also discovered spin- spin coupling. Foundation of magnetic spectroscopy. Proton NMR.

Circular electric current = magnet Electrons in p, d, f orbitals Electron spin Nuclear spin angular momentum charge magnetic moment mass

Magnet-magnetic-field interaction high energy low energy Classical Magnetic moment Magnetic field Quantum

Tesla Nikola Tesla Public domain image from Wikipedia kgm 2 /s C J kg T (Tesla) 1 T = 1 V s / m 2 Field strength in 500 MHz NMR ($0.5M) = 11.7 T Field strength in 1 GHz NMR ($20M) = 23.5 T Strongest continuous magnetic field = 45 T (National High Magnetic Field Lab at Tallahassee, FL)

Electrons in p, d, f orbitals First-order perturbation theory Bohr magneton 9.724×10 −24 J/T (2 l + 1)-fold degeneracy (field off) Zeeman effect (field on)

Quantum electrodynamics g-value … 2-fold degeneracy (field off) Electron spin α β ESR or EPR (field on)

Nuclear g-factor proton: fold degeneracy (field off) Nuclear spin α β NMR (field on) Nuclear magneton 1800 times smaller than Bohr magneton Proton mass Negative sign positive nuclear charge

Proton NMR α β Sample Sweep coils Radio freq

Proton NMR spectra (1)Overall intensity (2)Groups of peaks (3)Relative intensities of groups of peaks (4)Pattern in each group (hyperfine structure)

Overall intensity α β Intensity of a NMR signal ~ energy of RF radiation absorbed / time ~ ΔE × number of excess α spins ~ B 2 / T Stronger magnet + lower temperature excess α spins

Group of peaks: chemical shifts Resonance freq. Chemical shift Resonance freq. of TMS Si(CH 3 ) 4 “ppm” α β

Group of peaks: chemical shifts Resonance freq. Chemical shift Shielding constant

Group of peaks: chemical shifts Shielding constant +

Group of peaks: chemical shifts Shielding constant

Group of peaks: chemical shifts δ -COOH -CHO Ar-H ArOH ROH -CH- -CH 2 - RCH 3

Relative intensities C2H6OC2H6O HH2H2 H3H3 OH CH 2 CH 3 CH 3 CH 2 OH ROH -CH 2 - RCH δ

Hyperfine structure CH 3 CH 2 OH OHCH 2 CH 3 α β α α β β Hnearby H Spin-spin coupling:

Hyperfine structure CH 3 CH 2 OH OHCH 2 CH 3 α β α α ββ H H Spin-spin coupling: ββ αα βα, αβ H2H2 αβ, βα ββ αα

Hyperfine structure CH 3 CH 2 OH OHCH 2 CH Pascal’s triangle nearby H nearby H 2 nearby H 3 nearby H 4

CH 3 CH 2 OH OHCH 2 CH 3 Q: Why doesn’t the proton in the OH group cause splitting? A: The proton undergoes a rapid exchange with protons in other ethanol or water molecules; its spin is indeterminate in the time scale of spectroscopic transitions; this causes lifetime broadening of spectral line rather than splitting. ? Hyperfine structure

CH 3 CH 2 OH OHCH 2 CH 3 Q: Why is there no spin-spin coupling between the two protons in the CH 2 group? A: There is spin-spin coupling between them; however, its effect on the peaks is null and undetectable; this is because these protons are chemically and magnetically equivalent. ?? Hyperfine structure

CH 3 CH 2 OH Triplet magnetic Singlet non-magnetic no spin-spin coupling with spin-spin coupling No change in spacing

Spin-spin coupling constant HH HCH HCCH

HH Fermi contact Fermi contact Covalent bond singlet-coupling higher energy?? Fermi contact lower energy! higher energy??

Spin-spin coupling constant HC Fermi contact Fermi contact Covalent bond singlet coupling H Covalent bond singlet coupling Hund

Spin-spin coupling constant HCCH H CH Martin Karplus Department of Chemistry University of Illinois ILLIAC Karplus equation Image (c) University of Illinois

Magnetic resonance imaging: MRI Paul Lauterbur (far right) Department of Chemistry University of Illinois Magnetic field gradient Intensity ~ number of protons (in water) at x x Resonance frequency ~ location (x) Public domain image from Wikipedia

Summary We have studied the foundation of magnetic interactions and magnetic spectroscopy. We have learned the theory of proton NMR as an essential tool for chemical structural analysis. The origins of chemical shifts, hyperfine structures, and spin-spin coupling constants are discussed as well as their relation to molecular structures.