1D Pulse sequences •

We now have most of the tools to understand and start analyzing pulse sequences. We’ll start with the most basic ones and build from there. The simplest one, the sequence to record a normal 1D spectrum, will serve to define notation:

Vectors:

z z

M o

x

90 y pulse

y

M xy

x

acquisition

y

Shorthand:

90 y 90 y n

•

According to the direction of the pulse, we’ll use

90 x

or

90 y

(or

90

f if we use other phases) to indicate the relative direction of the

B 1

field WRT

M o

in the rotating frame.

•

The acquisition period will always be represented by an FID for the nucleus under observation (the triangle).

Inversion recovery •

Measurement of

T 1

is important, as the relaxation rate of different nuclei in a molecule can tell us about their local mobility. We cannot measure it directly on the signal or the FID because

T 1

affects magnetization we don’t detect.

•

We use the following pulse sequence:

180 y (or x) 90 y t D

• If we analyze after the p pulse:

z z x

180 y (or x)

x

t D

y y

•

Since we are letting the signal decay by different amounts exclusively under the effect of longitudinal relaxation (

T 1

), we’ll see how different

t D

’s affect the intensity of the FID and the signal after FT.

Inversion recovery (continued)

t D = 0

z z x

90 y

x

FT

y y

t D > 0

z z x

90 y

x

FT

y y

t D >> 0

z z x

90 y

x

FT

y y

•

Depending on the

t D

delay we use we get signals with varying intensity, which depends on the

T 1

relaxation time of the nucleus (peak) we are looking at.

Inversion recovery (continued) at 40

o

C

N N

•

If we plot intensity versus time (

t d

), we get the following:

I(t) = I



* ( 1 - 2 * e - t / T 1 )

•

It’s an exponential with a decay constant equal to

T 1

.

time

Spin echoes •

In principle, to measure

T 2

we would only need to compute the envelope of the FID (or peak width), because the signal on

M xy

, in theory, decays only due to transverse relaxation.

•

The problem is that the decay we see on

M xy

is not only due to relaxation, but also due to inhomogeneities on

B o

(the dephasing of the signal). The decay constant we see on the FID is called

T 2 *

. To measure

T 2

spin echoes

.

properly we need to use

•

The pulse sequence looks like this:

90 y 180 y (or x) t D t D

•

Spin echos are probably the first pulse sequences developed, even before FT NMR existed. Although they are very simple, spin echoes are used as blocks in almost all complex pulse sequences to refocus

M xy

magnetization.

Spin echoes (continued) •

We do the analysis after the

90 y

pulse:

z y y x



x

t D

y y y dephasing x

t D

refocusing

•

Now we return to

coordinates:

y z x

180 y (or x)

x x



y

Spin echoes (continued) •

If we acquire an FID right after the echo, the intensity of the signal after FT will affected only by

T 2

relaxation and not by dephasing due to an inhomogeneous

B o

. We repeat this for different

t D

’s and plot the intensity against

2 * t D

. In this case it’s a simple exponential decay, and fitting gives us

T 2

.

at 90

o

C

N N

I(t) = I o * e - t / T 2 time

Applications of spin echo sequences •

So far we haven’t discussed how chemical shift and coupling constants behave during spin echos. Here we’ll start seeing how useful they are...

•

A pretty anoying thing we have to do in NMR spectroscopy is ‘phase the spectrum. Why do we have to do this? We have to think on the effects of chemical shift on different components of

M xy

during a ‘short’ time or delay.

•

This short delay, called the

‘pre-acquisition delay’

(

DE

), is needed or otherwise the ‘remants’ of the high power pulse will give us artifacts in the spectrum or burn the receivers.

y y x

...

x



•

During this pre-acquisition delay all the spins have the opportunity to evolve under the effects of chemical shifts, and when we finally turn on the receiver all of them will have a certain

phase

with respect to the carrier. It will be a mixture of

absortive

and

dispersive

signals...

Spectrum phasing •

The phase of the lines appears due to the contribution of

absorptive or real

(cosines) and

dispersive or imaginary

(sines) components of the FID. Depending on the relative frequencies of the lines, we’ll have more or less sine/cosine components:

S(

w

) x =

S

cosines(

w

)

- real spectrum

S(

w

) y =

S

sines(

w

)

- imaginary spectrum •

What we want is the purely absorptive spectrum, so we combine different amounts of the

real

(cosine) and the

imaginary

(sine) signals obtained by the detector. The combination depends on the frequency of the spectrum:

S(

w

) = S(

w

) x + [

f

o +

f

1 (

w

) ] * S(

w

) y

•

f

o

is called the

zero order

phase and f

1

the

first order

phase. The correction is usually done by hand. In some cases (nuclei with low g ), it’s pretty much impossible...

•

There is one experiment using spin-echoes that

theoretically

allows us to avoid this. We’ll see later why it is actually not that useful...

Spin-echoes on chemical shift •

Now we go back to our spin-echoes. The effects on elements of

M xy

with an offset from the

B 1

those seen for dephased

M xy

frequency are analogous to after the p

/ 2

pulse:

z y y x



t D

x

f

y

w

eff

•

After a time

t D

, the magnetization precesses in the

plane w

eff * t D

( f ) radians, were w

eff

= w

-

w

o

. After the p pulse and a second period

t D

, the magnetization precesses the same amount

back

to the

x

axis.

x y y

180

f

x

t D

x

 w

eff

•

Apart from being upside down, we have no dephasing if we start acquisition immediately after the second

t D

. In principle, this sequence would give a purely absorptive spectrum...

Spin-echoes and heteronuclear coupling •

We now start looking at more interesting cases. Consider a 13 C nuclei coupled to a 1 H:

13 C

b C b H

J (Hz)

a C b H

1 H 1 H

b C a H

I

a C a H

13 C

•

If we took the 13 C spectrum we would see the lines split due to coupling to 1 H. The 1

J

CH couplings are from 50 to 250 Hz, and make the spectrum really complicated and overlapped.

We usually decouple the 1 H, which means that we saturate 1 H transitions. The 13 C multiplets are now single lines:

13 C

b C b H a C b H

1 H 1 H

b C a H a C a H

13 C I

Spin echoes and heteronuclear coupling (…) •

We modify a little our pulse sequence to include decoupling:

90 y 180 y (or x) t D t D 13 C: { 1 H} 1 H:

•

Now we analyze what this combination of pulses will do to the 13 C magnetization in different cases. We first consider a CH (a methine carbon). After the p

/ 2

pulse, we will have the 13 C

M xy

evolving under the action of vector is said to be

labeled

coupled to, a and b :

J

coupling. Each by the states of the 1 H it is

z y y

- J / 2

(a)

x



x

t D

f

x y

(b)

J / 2

•

Remember that under

J

-coupling f

=

p

* t D * J

.

Spin echoes and heteronuclear coupling (…) •

We now apply the p pulse, which inverts the magnetization, and start decoupling 1 H. This removes the labels of the two vectors, and effectively ‘stops’ them. They collapse into one, with opposing components canceling out:

y y y x



x



x

•

In this case the second

t D

under decoupling of refocus chemical shift and get nice phasing… 1 H is there to

•

Now, if we take different spectra for several

t D

values and plot the intensity we get something that looks like this for a CH:

t D = 1 / 2J t D = 1 / J t D

Spin echoes and heteronuclear coupling (…) •

The signal intensity varies with the cosine of

t D

, is zero for

t D

values equal to multiples of

1

/

2J

and maximum/minimum for multiples of

1

/

J

.

•

If we are looking at a CH 2 (methylene), the analysis is similar, and we obtain the following plot of amplitudes versus delay times:

t D = 1 / 2J t D t D = 1 / J

• Analogously, for CH 3 (methyl), we have:

t D = 1 / 2J t D = 1 / J t D

Spin echoes and heteronuclear coupling (…)

• Now, if we make the assumption that all 1

J

CH couplings are more or less the same (true to a certain degree), and use the pulse sequence on the following molecule with a

t D

of

1

/

J

, we get (don’t take the d values for granted…):

HO 2 1 3 4 OH 5 6 7

1,4 6 150 100 50 0 ppm 5 2,3 7

•

The experiment can discriminate between C, CH, CH 2 , and CH 3 , and we identify all the carbon types in the molecule.

•

This experiment is called the

attached proton test

(

APT

).

It is one of the first multiple pulse sequences, and has been superseded by the

INEPT

and

DEPT

pulse sequences.

Spin-echoes and homonulcear coupling •

Here we’ll see why spin echoes won’t work if we want to get our perfectly phased spectrum. The problem is that so far we have only used single lines (no homonuclear

J

coupling) or systems that have heteronuclear coupling.

•

Lets consider a 1 H that is coupled to another 1 H, and that we are exactly on resonance. After the p

/ 2

pulse of the spin echo sequence and the td delay we have evolution under the effects of

J

coupling. Each vector will be labeled by the state of the 1 H it is coupled to. We have:

z y y

J / 2

(a)

y x



x

t D

x

(b)

J / 2

•

The problem is that if we now put the p pulse, we invert the populations of all protons in the sample. Therefore, we

invert the labels

of our protons:

Spin echoes and homonulcear coupling (…) •

The p pulse flips the vectors and inverts the labels:

y

J / 2

(a)

180 y (or x) J / 2

(b)

x

(b)

J / 2

(a)

J / 2

y x

•

Now, instead of refocusing, things start moving

backwards

, and we will have even more separation of the lines of the multiplet during the second evolution period. If we then take the FID, the signal will be completely dispersive (although this depends on the length of the

t D

periods…):

y

t D

x

FID, FT

Spin echoes and homonulcear coupling (…) •

We see why this is not all that useful. For different

t d

values we get the following lineshapes for a doublet coupled with a triplet (both have the same

J

value…): QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

•

Despite of its patheticness, understanding how this works is crucial to understand

2DJ

spectroscopy. The phenomenon is known as

J-modulation

.

Binomial pulses •

Binomial pulses are examples of

pulse trains

which we can explain with vectors. Among other things, we can use them to eliminate solvent peaks (see

T 1

…).

•

The simplest binomial pulse is the

1:1

, two p

/ 2

pulses with opposite signs, separated by a certain interval

t d

, and exactly on resonance with the peak we want to eliminate:

90 y 90 -y t D

•

The first p

/ 2

puts everything on

. After

t d

, signals/spins precess to one side or the other of

x

. All except the signal we are interested in eliminating from the spectrum:

z z y

M o 90 y t D

x x x y y

Binomial pulses (continued) •

The next p

/ 2

return everything on

x

to the

z

axis. This includes all the signal corresponding to the peak to eliminate, as well as the

x

components of the remaining signals:

y y x

90 -y

x



y

•

The resulting FID only has signals corresponding to peaks that aren’t in resonance with the carrier. They will all be in phase with the receiver, but signals on each side of the carrier will have opposite signs:

y x x

FID (y) FT

•

Due to

t d

, both peaks on resonance and those from signals at multiples of

1 / (2*t d )

Hz will be nulled (any signal with that frecuency with turn half a cycle in

t d

…).

Binomial pulses (…) •

As mentioned before, they are used to eliminate solvent peaks, particularly water in cases that other secuences could perturb protons that exchange with water (NHs, OHs, etc.).

~ 50 mM sucrose in H 2 O/D 2 O (9 to 1).

1

H spectrum:

1

H spectrum with 1:1 pulse (

t d

= 200



S):

Binomial pulses (…) •

To avoid the sign change we can use other binomial pulse trains, such as the

1:3:3:1

:

1 / 8 90 y 3 / 8 90 -y 3 / 8 90 y 1 / 8 90 -y t D t D t D

•

You also get artifacts. None of these pulse trains, nor experiments that take advantage on

T 1

differences, give results as good as those that are obtained with secuences using gradients, such as

WEFT

or

WATERGATE

.

•

For the same sample this is what we get with

WEFT

: