CHAPTER 14 1

CHAPTER 14 Molecular Spectroscopy 3: Magnetic Resonance

I. Magnetic Resonance Spectroscopy - General Idea.

A. Excite Nuclear and electron spin state transitions. (NMR, ESR)

B. In absence of magnetic field, spin states are degenerate. States split by constant magnetic field. (Stark field)

-the energy of a magnetic moment µ in a magnetic field B; is :

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E = − µ • B

C. A second oscillating magnetic field (sweep field) can then excite spin flips,

which lead to absorption of the secondary field energy. This field oscillation frequency is varied (scanned).

D. Splitting depends not only on Stark field strength, but on presence of

other electrons and nuclei near one of interest. So frequency at which transition occurs reflects “chemical environment” in neighborhood of nucleus undergoing transition.

Probe of structure of molecules.

II. Effect of Magnetic Fields on Electrons and Nuclei A. Electrons

1. The orbital angular momentum of the electron produces a magnetic moment that interacts with the external field B and gives energies:

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Em =mµBBo

m =magnetic quantum number

µB = Bohr magneton

Bo =magnetic field magnitude

µB = −γe =e

2me= 9.724x10−24J /T

so :Em = −γemBo

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2. The spin angular momentum also interacts with the magnetic field with energy:

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Ems= gemsµBBo

ms = spin quantum number(±1/2)

ge = g-value = 2.0002319so :Ems

= −geγemsBo

3. These equations are useful in interpreting ESR spectra, which

observes electron spin state changes for unpaired electrons only.

B. Nuclei. 1. The spin quantum number I of a nucleus is a fixed property

depending on number of protons and neutrons in the nucleus: Table 14A.1 Nuclear constitution and the nuclear spin quantum

number

2. Spin angular momentum of the nucleus is, as usual:

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I(I+1) 3. For a given I there are spins states mI = -I, …. +I representing

orientation of the nuclear magnetic moment relative to the external field.

4. Energy of interaction of nuclear magnetic moment with the field B is:

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EmI

= −µzB

o

µz= nuclear magnetic moment along field direction

EmI

= −γmI!B

o

mI= spin orientation quantum number( ±1/2 for proton)

γ = magnetogyric ratio for specified nucleusE

mI

= −gµNm

IB

o

g = nuclear g-factor

µN=

e!2m

proton

= 5.051×10−27J / T

(nuclear magneton constant)For proton:

E = ±gµ

NB

o

2

Table 14A.2 Nuclear spin properties

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III. NMR - nuclear magnetic resonance spectroscopy.

A. Field strengths and frequencies involved. 1. An external magnetic field of strength B (typically magnitude ~ 10

Tesla (T)) produces a splitting of the spin states (for a spin 1/2 nucleus) given by

ΔE = E−1/2

−E+1/2

= −gµNBo(−12−12)

ΔE = gµNBo

2. So now, what sweep field frequency is needed to cause spin state

changes from +1/2 to -1/2 in this diagram?

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hν = ΔE = gµNBo

ν = gµNBo /h

3. Work it out, for proton NMR; for C-13 NMR:

ν = 425 MHz for protons; 107 MHz for C-13 nuclei These are the resonance frequencies for an isolated nucleus in a field of 10 Tesla.

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B. The Chemical Shift. 1. Nuclei interact not just with the external field Bo, but with the local

magnetic field B. 2. Local field B is combination of external field Bo plus field induced in

the neighborhood Bind.

3. External field induces electronic orbital angular momenta giving rise to a field of its own. (field due to circulation of electronic currents)

4. Induced field Bind = -σBo

where σ = shielding constant Bo = external field magnitude

5. So local field felt by nuclei is:

Bloc = Bo + Bind =(1-σ) Bo

6. The chemical shift δ of a particular nucleus is then defined:

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δ =ν − ν°ν°

×106ppm

where ν = actual resonance freq ν° = resonance freq in a reference standard compound (TMS)

7. Relation of δ to σ.

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ν =gµN

hBloc =

gµN

h1−σ( )Bo

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νo =gµN

hBloc TMS( ) =

gµN

h1−σo( )Bo

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δ =

gµN

h1−σ( )Bo − 1−σo( )Bo{ }

gµN

hBo

×106

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δ = σo −σ( ) ×106 ppm

where σo is the shielding constant in TMS σ is the shielding constant in actual environment

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Notice δ is independent of magnitude of external field Bo. 8. Deshielding:

As shielding σ gets smaller, chemical shift δ gets larger.

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9. Typical chemical shifts δ in proton and C-13 NMR.

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10. Contributions to shielding. σ = σ(local) + σ(neighbor) + σ(solvent) e- on e- in other same atom parts of molecule σd + σp diamagnetic paramagnetic contrib contrib

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σd ∝1r

r = e- nuclear distance; depends on e- density close to nucleus σp only contributes if unpaired e- present on the atom, or if molecule

has low-lying excited states. σ(neighbor) - arises from field-generated e- currents in neighboring

groups of atoms.

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∝1r3 where r = distance to neighbor atoms

Particularly strong around aromatic groups because B induces a ring

current.

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C. The Fine Structure. (spin-spin coupling)

1. Splitting of NMR lines due to effect of the other nuclei. 2. Strength of interaction expressed as scalar coupling constant J (Hz). 3. J is independent of field B. 4. For two interacting nuclei A...X with coupling J, each is split by the

other by J Hz.

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ν = νo ± 12 J

in absence of neighbor nucleus One line is split into two for each nucleus.

5. For nuclei A interacting with two equivalent nuclei X, in other words

A...X2, the equivalent X nuclei resonate like a single nucleus but with double the intensity.

So the lines due to X are a doublet still.

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6. The nucleus A however is split into a 1:2:1 triplet. 7. For a nucleus A interacting with 3 equivalent nuclei A...X3 the

spectrum of A is a 1:3:3:1 quartet.

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8. Now interpret ethanol splitting pattern.

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9. Magnitudes of coupling constants J.

1J means only 1 bond separates the two interacting nuclei.

e.g. 13C - 1H is 1JCH (~120 to 250 Hz) 2J means 2 bonds separate. e.g. 13C - C - 1H is 2JCH (~10 to 20 Hz) 3J means 3 bonds separate. e.g. NJ for N>4 are negligible.

10. The Karplus Equation = three-bond coupling constant depends on dihedral angle as:

3J = A + B cos φ + C cos 2φ

Important for 3JHH coupling:

C— C is J (~1 to 15 Hz) 3

HH

1H 1H

C— C

1H 1H

φ