Nuclear Magnetic Resonance (NMR)

NMR arises from the factthat certain atomic nucleihave a property called “spin”

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Technically, spin arises from the

fact that some nuclei possess a

magnetic moment, μ →

, and angular

momentum, I→

In analogy with other formsof spectroscopy, like UV-VIS,for example, where the electron can occupy either a ground state or excited state, certaintypes of NMR spins can assumetwo possible possible orientations,aligned or opposed to the staticmagnetic field, Bo. Aligned state is designated , opposed state isdesignated .

Excitation of NMR Spin

ΔE

α

β

ΔE

α

βIrradiate with Frequency so as

to satisfy Planck'sLaw

ΔE=hυ

Frequency (Hz)

Energy

NMR Chemical Shifts

= physical constant for a given type of nucleus (ratio of magnetic moment and angular momentum)

h = Planck’s constant

Bo = static magnetic field strength€

ν ∝Bo

€

ΔE = γhBo 2π = hν

Predictions Do Not Match Reality

Bo

Bo(1-σa)Bo(1-σb)

Bo €

Beff = Bo(1−σ )

€

ν eff ∝ Bo 1−σ( )

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ΔE = γhBo 1−σ( ) 2π = hν

σ = chemical shielding tensor

Frequency

+D3N

HO

O-CH

H3CCH2

CH3

Ile in D2O

12

1

HDO

1

2 1

(Acquisition time = 4 hr)

Chemical Shielding

Shielding arises from the various ways by which electrons“shield” the nuclear spin from the external magnetic field (Bo)

Physical mechanism relates to induced circulation of electrons that oppose static magnetic field (Lentz’ Law)

Shielding (tensors) can in principle be determined through ab initio calculations. This, however, is computationally expensive, and realistically not applicable to large molecules

Classic Approaches to Shielding Local electronic structure; electronegativity of attached groups, bond lengths, bond angles, and conformation (dihedral angles)

Anisotropy of local groups (circulating electrons from aromatic rings for example)

Hydrogen bonds

Electric field effects that polarize bonds

Chemical Shielding Trends for Protons

Functional Groups

Proteins

1234567891011

R

CH3

R

CH2

R'

R

CH

R''R'

C

C

H

R

RCH2C6H5

RCH2XRCH2OR'H

RC6H5RCHO

Frequency

1234567891011

H Aliphatic MethylAromaticAmide

Frequency

Chemical Shifts Can Change Dramatically with Changes in Conformation

8 M Urea

Chemical Shielding & Chemical Shifts

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ν eff ∝ Bo 1−σ( )Recall

Bo field dependence of frequency makes comparison of spectradifficult from one instrument to another

Hence, report relative ν’s, not absolute ν’s

Chemical Shift (ppm) = =

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ν peak −ν ref

ν ref

x 106

νpeak = frequency of signal of interestνref = frequency of reference signal

IUPAC-IUB Shift Standard for Proteins

Sodium-2,2-dimethyl-2-silapentane-5-sufonate (DSS)

CH3

SiH3C

CH3

SO3-

J-coupling

Ha

Ha R

Hb

R'' R'

Ha Hb+ =

Hb

Ha

+ =Ha

Ha

J-couplings in Ile

+D3N

HO

O-CH

H3CCH2

CH3

Ile in D2O

1

2

1

1

2 1

1

NMR Active Nuclei

Isotope Natural Abundance (r adHz T-1) spin

1H 99.985 % 26.75 x 107 1/22H 0.02 % 4.12 x 107 1

12C 98.9% nmr-inactive nmr-inactive13C 1.1 % 6.73 x 107 1/2

14N 99.63 % 1.93 x 107 115N 0.37 % -2.71 10x 7 1/2

16O 99.9 nmr-inactive nmr-inactive17O 0.04% -3.63 10x 7 -5/2

31P 100 % 10.83 x 107 1/2

Sensitivity of NMR

€

ΔE = γhBo 2π

& spin states willassume a Boltzman distribution

Implications: Highest sensitivity w/ higher & higher Bo€

Nα /Nβ = expΔE

kT

⎛

⎝ ⎜

⎞

⎠ ⎟= exp

hγBo /2π

kT

⎛

⎝ ⎜

⎞

⎠ ⎟=1.0018 (γ = 2.67x108, Bo =11.7 T)

1D 13C Natural Abundance Spectrum of Ile

+D3N

HO

O-CH

H3CCH2

CH3

Ile in D2O (1H Decoupled)

(Acquisition time = 4 hr)

1

2 1

13C ppm13C ppm

112

CO

1030507090110130150170190210

Aliphatic MethylAromaticCarbonyl C

13C ppm