Chemistry 125: Lecture 59 March 21, 2011 Precession and MRI NMR Spectroscopy Chemical Shift and Spin-Spin Coupling Preliminary This For copyright notice see final page of this file

90° RF Pulse and the “Rotating Frame” Applied Magnetic Field Precessing proton gives rise to constant vertical field Will rotating horizontal field generate 100 MHz RF signal? No, because there are many precessing protons with all possible phases. Consider a “rotating frame” in which the observer orbits at 100 MHz - protons seem to stand still as if no applied field. (just long enough to rotate all nuclear spin axes by 90°). Fast precession (~100 MHz) Slow precession (~0.1 MHz) Horizontal fields cancel. Subsequent precession generates 100 MHz RF signal in lab frame. 100 MHz RF in lab frame Until “relaxation” reestablishes equilibrium. and rotating horizontal field. Pulse a very weak magnetic field fixed in this rotating frame

A 90° pulse makes spinning nuclei ( 1 H, 13 C) “broadcast” a frequency that reports their local magnetic field.

MRI: locating protons within body using non-uniform field

X-Ray Tomography

MRI: find protons in body (e.g. fluid H 2 O) BzBz wrap in several miles of special wire at 4K ~1.5 Tesla (15,000 Gauss) Superconducting Solenoid protons precess at 63 MHz So there are protons in the body, but where?

How to locate Crickets, if you can’t see them: Establish a temperature gradient and listen with a stopwatch. P. LeMone (2007)

subtract from B z on left MRI: find protons in body (e.g. fluid H 2 O) add to B z near head const H z MHz MHz const B z subtract from B z near feet dB z /dz BzBz add to B z on right dB z /dx ~1.5 Tesla (15,000 Gauss) protons precess at 63 MHz 40  T/mm (~30 ppm/mm) MHz Superconducting Solenoid Four analogous top/bottom coils establish These three gradients allow slicing in all directions to construct a 3D tomograph. dB z /dy So there are protons in the body, but where?

Functional MRI: locating protons whose signal strength is being fiddled with

BOLD Imaging Subject Fasting Functional MRI (fMRI) e.g. Blood Oxygen-Level Dependent (BOLD) Imaging Spatial Resolution ~1 mm Temporal Resolution 2 sec Subject recently fed Difference Map with permission of Dr. Tony Goldstone, Imperial College minus Cell activity increases blood oxygen supply, speeds relaxation.

NMR: locating protons within molecules using uniform field ?

HO-CH 2 -CH 3 Oscilliscope Trace (1951) The “Chemical” Shift 2.48 ppm Fractional difference in applied field ! Requires very high uniformity of field to avoid “MRI” BoBo Listen at fixed frequency. Tune B o to “hear” precession.

In the late 1950s chemistry departments began buying NMR spectrometers with fields homogeneous enough to determine molecular structures from chemical shifts (and spin-spin splittings). With multi-user equipment, it was a challenge to keep the fields sufficiently homogeneous to obtain sharp lines. At SUNY-Stony Brook in 1972 physical chemist Paul Lauterbur would take over the departmental machine nightly and destroy the field inhomogeneity. By establishing gradients in different directions he located two 1 mm tubes of H 2 O within a 5 mm tube of D 2 O, and published this “zeugmatogram” in Nature in years later he shared the Nobel Prize in Physiology or Medicine for inventing MRI. Do Not Touch These Gradient Knobs!!! or this one!

have put classical structure proof by chemical transformation (and even IR!) out of business. One Yale “natural products” organic professor, whose research used chemical transformations to puzzle out molecular structures, abandoned organic chemistry to take up fundamental research on quantum theory (and later became a professional studio photographer). Magnetic Resonance Spectrometers (and X-ray Diffractometers)

Some of the Magnetic Resonance Spectrometers in Yale's Chemistry Department

500 MHz

600 MHz

800 MHz ~8 3 = 512 times as sensitive as 100 MHz (not to mention the chemical shift advantage discussed below) * 1) Boltzmann factor 2) Energy quantum 3) Electronics sensitivity *

EPR (Electron Paramagnetic Resonance) (for Free Radicals with SOMOs) e magnet is 660x H + !

EPR (Electron Paramagnetic Resonance) 9 GHz ~3000 Gauss (0.3 Tesla)

New 1000 MHz (23.5 Tesla) NMR Spectrometer NHFML - Florida State University now has a pulsed field NMR at 45 Tesla (there is no charge for use, but you have to have a great experiment

HO-CH 2 -CH 3 Oscilliscope Trace (1951) Area (integral) Which peak is which set of protons?  number of protons, because they are so similar (not like IR)

Advertisement 1) O 3 2) H 2 O 2 C-OH HO-C OO cis-caronic acid 1:11:1 Structural proof by chemical degradation (venerable) 3:13:1 ? ? O O O O O O O O H C C H

 (ppm) in CDCl 3 solvent at 5.9T (250 MHz) CH 3 C OCH 2 CH 3 O ppm × 250 MHz 7.3 Hz CHCl 3 “Low” Resolution (~0.3 ppm) High Resolution (~3 ppb, sample spun) ? Triplet (1:2:1) Quartet (1:3:3:1) Peak Width ~3 ppb 7.3 Chem 220 NMR problem 7

A 90° pulse makes spinning nuclei ( 1 H, 13 C) “broadcast” a frequency that tells their LOCAL magnetic field.

Components of Effective Magnetic Field. Inhomogeneous ~ 30,000 G for MRI CAT scan. (4 G/cm for humans, 50 G/cm for small animals) Applied Field: Homogeneous for Chemical NMR Spectroscopy (spin sample) Molecular Field: Net electron orbiting - “Chemical Shift” (Range ~12 ppm for 1 H, ~ 200 ppm for 13 C) Nearby magnetic nuclei - “Spin-Spin Splitting” (In solution J HH 0-30 Hz ; J CH Hz) B effective B molecular (diamagnetic) B applied

The Chemical Shift

Chemical Shift and Shielding high electron density shielded upfield high e - density low chemical shift low frequency deshielded downfield low e - density high chemical shift high frequency CH 3 C C-H ? ! ??? TMS B effective B molecular (diamagnetic) B applied Note: Electron orbiting to give B is driven by B; so B  B.  (ppm) Alkyl R-H H C H CHCH X X = O, Hal, N RC CHCH O H O OHOH O R-OH (depends on conc, T) ++ --

ZERO! Suppose molecule in fluid undergoes rotational averaging. net from average over sphere net from average around circle  1/r 3 Electrons Orbiting Other Nuclei Diamagnetism from Orbiting Electrons Ignore electrons on other atoms! B applied PPM Suppose the studied nucleus is fixed relative to the other nucleus by bond(s).

ZERO! net from average over sphere Electrons Orbiting Other Nuclei Unless orbiting depends on molecular orientation B applied Diamagnetic “Anisotropy” (depends on orientation) NOT suppose less orbiting for this molecular orientation reinforces B applied

B0B0 Diamagnetic Anisotropy Benzene “Ring Current” B 0 can only drive circulation about a path to which it is perpendicular. If the ring rotates so that it is no longer perpendicular to B 0, the ring current stops. Net deshielding of aromatic protons; shifted downfield

Aromaticity: PMR Chemical Shift Criterion HCCl 3 TMS   electrons (4  3) + 2 DIAMAGNETIC ANISOTROPY! ? DIAMAGNETIC ANISOTROPY 8 H2 H TMS 10  electrons (distorted – less overlap & ring current)  (ppm) Boekelheide (1969)

HCCl TMS Aromaticity: PMR Chemical Shift Criterion   electrons (4  3) + 2 DIAMAGNETIC ANISOTROPY! DIAMAGNETIC ANISOTROPY Metallic K adds 2  electrons to give 16 (4n) -2 CH 3 signals shift downfield by 26 ppm despite addition of “shielding” electrons. “Anti-Aromatic” Dianion  (ppm) Shrink Scale Boekelheide (1969) THF solvent

Diamagnetic Anisotropy Acetylene “Ring Current” H H H H The H nuclei of benzene lie beside the orbital path when there is ring current. (B 0 at H reinforced; signal shifts downfield). The H nuclei of acetylene lie above the orbiting path when there is ring current. (B 0 at H diminshed; signal shifts upfield). H H Warning! This handy picture of diamagnetic anisotropy due to ring current may well be nonsense! (Prof. Wiberg showed it //to be nonsense for 13 C.)

Spin-Spin Splitting

 (ppm) CH 3 C OCH 2 CH 3 O Triplet (1:2:1) C. C. H H Four (2 2 ) sets of molecules that differ in spins of adjacent H nuclei “Spin Isomers” so similar in energy that Boltzmann makes them equally abundant Chem 220 NMR Problem 1 (of 40)

CH 3 C OCH 2 CH 3 O C. C. H H H  (ppm) Quartet (1:3:3:1) 7.3 Triplet (1:2:1) Eight (2 3 ) sets of molecules that differ in spins of adjacent H nuclei 7.3 Influence of CH 2 on CH 3 must be the same as that of CH 3 on CH 2 and independent of B o J in Hz vs. Chemical Shift in binomial coefficients (Orbiting driven by B o ) Chem 220 NMR Problem 1 (of 40)

DMSO-d 5 CD 3 SCD 2 H O HO-CH 2 -CH Hz5.1 Hz Doublet of Quartets 1.8 Hz ? Hz 13 CH 3 1:4:6:4:1 Quintet? ?  ppm × 400 MHz J = 7.2 Hz 1.1% of C D is a weaker magnet than H. ? H2OH2O 1:2:3:2:1 Quintet Subtle Asymmetry  (ppm)  D can be oriented 3 ways in B o.

What determines the Strength of Spin-Spin Splitting?

Isotropic J H-H is mediated by bonding electrons (through-space part is anisotropic, averaged to zero by tumbling)

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