Advanced Nuclear Magnetic Resonance Spectroscopy

Ala-Arg-Pro-Tyr-Asn-Phe Cpa -Leu-NH 2 Cpa Pro Ala

Guillermo Moyna - Spring 1999

Why bother learning NMR?

• Structural (chemical) elucidation • Natural product chemistry.

• Synthetic organic chemistry. Analytical tool of choice of synthetic chemists.

• Study of dynamic processes • Reaction kinetics.

• Study of equilibrium (chemical or structural).

• Structural (three-dimensional) studies • Proteins.

• DNA. Protein/DNA complexes • Polysaccharides • Drug design • S tructure A ctivity R elationships by NMR • Medicine - MRI

The gory details

• Absorption (or emission) spectroscopy, as IR or UV. Detects the absorption of radiofrequencies (electromagnetic radiation) by certain nuclei in a molecule.

• Unfortunately, some quantum mechanics are needed to understand it (a lot to really understand it…).

• Only nuclei with

spin number

(

I

)  0 can absorb/emit electro magnetic radiation.

• Even atomic mass & number 

I

= 0 ( • Even atomic mass & odd number 

I

12 C, 16 O) = whole integer ( 14 N, 2 H, 10 B) • Odd atomic mass 

I

= half integer ( 1 H, 13 C, 15 N, 31 P) • The

spin states

of the nucleus (

m

) are

quantified

:

m = I, (I - 1), (I 2), … , -I

• Properly,

m

is called the

magnetic quantum number

.

Background (continued)

• For 1 H, 13 C, 15 N, 31 P (biologically relevant nuclei) then:

m = 1/2, -1/2

• This means that only two states (energy levels) can be taken by these nuclei.

• Another important parameter of each particular nuclei is the

magnetic moment

( m ), which can be expressed as: m

=

g

I h / 2

p • It is a vector quantity that gives the direction and magnitude (or strength) of the ‘nuclear magnet’ •

h

is the Planck constant • g is the gyromagnetic ratio, and it depends on the nature of each nuclei.

• Different nuclei have different magnetic moments.

Effect of a magnetic field (for

I

= 1/2)

• In the ground state all nuclear spins are disordered, and there is no energy difference between them. They are

degenerate

:

=

g

h / 4

p • Since they have a magnetic moment, when we apply a strong external magnetic field (

B o

), they orient either against or with it:

B o

• There is always a small excess of nuclei (

population

excess) aligned with the field than pointing against it.

Energy and populations

• Upon application of the external magnetic field we create an energy difference between nuclei aligned and against

B o

: b

B o > 0

D

E = h

n a

B o = 0

• Each level has a different

population

(

N

), and the difference between the two is related to the energy difference by the Boltzmman distribution:

N

a

/ N

b

= e

D

E / kT

• The D E for 1 H at 400 MHz (

B o

= 9.5 T) is 3.8 x 10 -5 Kcal / mol

N

a

/ N

b

= 1.000064

• The surplus population is small when compared to UV or IR.

Energy and sensitivity

• The energy (for a single spin) is proportional to the magnetic moment of the nuclei and the external magnetic field:

E = -

m .

B o



E

(up)

=

g

h B o / 4

p

--- E (

down

) = -

g

h B o / 4

p D

E =

g

h B

o

/ 2

p • This has implications on the energy (i.e., the intensity of the signal and sensitivity) that each nuclei can absorb: • Bigger magnets (bigger

B o

) make more sensitive NMR instruments.

• Nuclei with larger g absorb/emit more energy and are therefore more sensitive. Sensitivity is proportional to m , to

N

a

- N

b , and to the ‘coil magnetic flux’, which are all dependent on g . Therefore, it is proportional to g

3

.

g 13

C = 6,728

rad / G g 1

H = 26,753

rad / G 1 H is ~ 64 times more sensitive than 13 C just because of the g • If we consider natural abundance, 13 C (~1%) ends up being 6400 times less sensitive...

Energy and frequency

• Since energy is related to frequency, we can do some insightful math… D

E = h

n n

=

g

B

o

/ 2

p D

E =

g

h B

o

/ 2

p • For 1 H in normal magnets (2.35 - 18.6 T), this frequency is in the 100-800 MHz range. For 13 C, 1/4 of that… g -rays x-rays UV VIS IR m -wave radio 10 -10 10 -8 10 -6 10 -4 10 -2 wavelength (cm) 10 0 10 2 • To explain certain aspects of NMR, we need to refer to circular motion. Hz are not the best units to do so. We define the

precession

or

Larmor

frequency, w : w

= 2

pn  w

o =

g

B o

(radians)

Precession and spinning tops

• What precession is w

o

associated with? One thing that we left out from the mix is the

angular momentum

,

l

, which is associated with all nuclei:

l

• Crudely, we can think of the nuclei as being spinning around its z axis. If we now consider those nuclei that have also a non zero m , we have little spinning atomic magnets.

• Now, if we bring about a big

B o

, there will be an interaction between m and

B o

that generates a torque. No matter which is the original direction of m , it will tend to align with

B o

: m

B o or...

m

B o

Precession (continued)

• Now it starts getting exciting (?). Since the nuclei associated with m is spinning due to

l

, there are two forces acting on it.

One that wants to bring it towards

B o

, and one that wants to keep it spinning. m ends up precessing around

B o

: w

o

m

B o

• The best way to picture it is to imagine a spinning wooden top under the action of gravity.

• The frequency at which m precesses around Bo is the same as the one derived from energetic considerations. • Although there is no apparent connection between these two frequencies, the relationship comes about automatically if we do a rigorous quantum mechanical derivation. Some of the phenomena are a black box for the classical NMR model...

Bulk magnetization

• We see the effects on macroscopic magnetization,

M o

, which is directly proportional to the population difference (

N

a

- N

b ), in which contributions from different m s have been averaged:

z z

M o

x x y y

B o B o

• We can decompose each little m in a

z

contribution and an

plane contribution. The components in the

plane are randomly distributed and cancel out. For the ones in

z

, we get a net magnetization proportional to

N

a

- N

b .

• Since this is (more or less) the situation in a real sample, we will from now on use

M o

in all further descriptions/examples.

• There is an important difference between a m and

M o

. While the former is ( a

quantized

and can be only in one of two states or b ), the latter tells us on the whole spin population. It has a

continuous

number of states.

Next class topics • Bulk magnetization and vector models.

•

Simple excitation of average magnetization.

•

Laboratory and rotating frames.

•

Chemical shift ( d )

•

Spin-spin coupling (J). Energy diagrams for systems of two coupled spins.