1D Pulse sequences1D 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:

Shorthand:

• According to the direction of the pulse, we’ll use 90x or 90y

(or 90 if we use other phases) to indicate the relative

direction of the B1 field WRT Mo in the rotating frame.

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

90y 90y

n

z

x

y

z

x

Mxy

y

Mo90y

acquisition

pulse

Inversion recoveryInversion recovery

• Measurement of T1 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 T1 affects magnetization we don’t detect.

• We use the following pulse sequence:

• If we analyze after the pulse:

• Since we are letting the signal decay by different amounts exclusively under the effect of longitudinal relaxation (T1), we’ll see how different tD’s affect the intensity of the FID and the signal after FT.

180y (or x) 90y

tD

z

x

y

z

x

y

180y (or x) tD

Inversion recovery (continued)Inversion recovery (continued)

• Depending on the tD delay we use we get signals with varying intensity, which depends on the T1 relaxation time of the nucleus (peak) we are looking at.

z

x

y

tD = 0

z

x

y

tD > 0

z

x

y

tD >> 0

z

x

y

z

x

y

z

x

y

90y

90y

90y

FT

FT

FT

• It’s an exponential with a decay constant equal to T1.

Inversion recovery (continued)Inversion recovery (continued)

NN

• If we plot intensity versus time (td), we get the following:

at 40oC

time

Inte

nsi

ty (

)

I(t) = I * ( 1 - 2 * e - t / T1 )

Spin echoesSpin echoes

• In principle, to measure T2 we would only need to compute the envelope of the FID (or peak width), because the signal on Mxy, in theory, decays only due to transverse relaxation.

• The problem is that the decay we see on Mxy is not only due

to relaxation, but also due to inhomogeneities on Bo (the

dephasing of the signal). The decay constant we see on the FID is called T2*. To measure T2 properly we need to use

spin echoes.

• The pulse sequence looks like this:

• 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 Mxy magnetization.

180y (or x)90y

tD tD

Spin echoes (continued)Spin echoes (continued)

• We do the analysis after the 90y pulse:

• Now we return to <xyz> coordinates:

z

x

y

x

y

x

y

x

y

x

y

tD

180y (or x)

tD

dephasing

refocusing

z

y

x

y

I(t) = Io * e - t / T2

NN at 90oC

Spin echoes (continued)Spin echoes (continued)

• If we acquire an FID right after the echo, the intensity of the signal after FT will affected only by T2 relaxation and not by dephasing due to an inhomogeneous Bo. We repeat this for

different tD’s and plot the intensity against 2 * tD. In this case

it’s a simple exponential decay, and fitting gives us T2.

time

Inte

nsi

ty (

)

Applications of spin echo sequencesApplications 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 Mxy 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.

• 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...

x

y

x

y

...

Spectrum phasingSpectrum 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()x = cosines() - real spectrum

S()y = sines() - 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() = S()x + [ o + 1() ] * S()y

• o is called the zero order phase and 1 the first order phase. The correction is usually done by hand. In some cases (nuclei with low ), 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 shiftSpin-echoes on chemical shift

• Now we go back to our spin-echoes. The effects on elements of Mxy with an offset from the B1 frequency are analogous to those seen for dephased Mxy after the / 2 pulse:

• After a time tD, the magnetization precesses in the <xy>

planeeff * tD () radians, were eff = - o. After the pulse and a second period tD, the magnetization precesses the same amount back to the x axis.

• Apart from being upside down, we have no dephasing if we start acquisition immediately after the second tD. In principle, this sequence would give a purely absorptive spectrum...

z

x

y

x

y

x

y

tD

eff

x180 tD

x

y

y

eff

Spin-echoes and heteronuclear couplingSpin-echoes and heteronuclear coupling

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

• If we took the 13C spectrum we would see the lines split due to coupling to 1H. The 1JCH couplings are from 50 to 250 Hz, and make the spectrum really complicated and overlapped. We usually decouple the 1H, which means that we saturate 1H transitions. The 13C multiplets are now single lines:

I

J (Hz)

I

1H

13C

1H

13C

CH

CH

CH

CH

CH

CH

CH

CH13C

13C

1H

1H

Spin-echoes and heteronuclear coupling (…)Spin-echoes and heteronuclear coupling (…)

• We modify a little our pulse sequence to include decoupling:

• Now we analyze what this combination of pulses will do to the 13C magnetization in different cases. We first consider a CH (a methine carbon). After the / 2 pulse, we will have the 13C Mxy evolving under the action of J coupling. Each vector is said to be labeled by the states of the 1H it is coupled to, and :

• Remember that under J-coupling = * tD * J.

180y (or x)90y

tD tD

{1H}1H:

13C:

x

y

x

y

tD

J / 2

z

x

y

- J / 2

Spin-echoes and heteronuclear coupling (…)Spin-echoes and heteronuclear coupling (…)

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

• In this case the second tD under decoupling of 1H is there to refocus chemical shift and get nice phasing…

• Now, if we take different spectra for several tD values and plot the intensity we get something that looks like this for a CH:

x

y

x

y

x

y

tD

tD= 1 / 2J tD= 1 / J

Spin-echoes and heteronuclear coupling (…)Spin-echoes and heteronuclear coupling (…)

• The signal intensity varies with the cosine of tD, is zero for tD

values equal to multiples of 1 / 2J and maximum/minimum for multiples of 1 / J.

• If we are looking at a CH2 (methylene), the analysis is similar, and we obtain the following plot of amplitudes versus delay times:

• Analogously, for CH3 (methyl), we have:

tD

tD= 1 / 2J

tD

tD= 1 / 2J tD= 1 / J

tD= 1 / J

Spin-echoes and heteronuclear coupling (…)Spin-echoes and heteronuclear coupling (…)

• Now, if we make the assumption that all 1JCH couplings are more or less the same (true to a certain degree), and use the pulse sequence on the following molecule with a tD

of 1 / J, we get (don’t take the values for granted…):

• The experiment can discriminate between C, CH, CH2, and CH3, 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.

2

1

43 5

67

OH

HO

1,4

2,35

6

7

0 ppm150 100 50

Spin-echoes and homonulcear couplingSpin-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 1H that is coupled to another 1H, and that we are exactly on resonance. After the / 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 1H it is coupled to. We have:

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

x

y

x

y

tD

J / 2

z

x

y

J / 2

Spin-echoes and homonulcear coupling (…)Spin-echoes and homonulcear coupling (…)

• The pulse flips the vectors and inverts the labels:

• 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 tD periods…):

x

y

J / 2

J / 2

x

y

J / 2

J / 2

180y (or x)

x

y

tD FID, FT

Spin-echoes and homonulcear coupling (…)Spin-echoes and homonulcear coupling (…)

• We see why this is not all that useful. For different td values we get the following lineshapes for a doublet coupled with a triplet (both have the same J value…):

• Despite of its patheticness, understanding how this works is crucial to understand 2DJ spectroscopy. The phenomenon is known as J-modulation.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Binomial pulsesBinomial 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 T1…).

• The simplest binomial pulse is the 1:1, two / 2 pulses with opposite signs, separated by a certain interval td, and exactly on resonance with the peak we want to eliminate:

• The first / 2 puts everything on <xy>. After td, signals/spins precess to one side or the other of x. All except the signal we are interested in eliminating from the spectrum:

90y

tD

90-y

z

y

x

y

tD

z

x

y

Mo90y

x

Binomial pulses (continued)Binomial pulses (continued)

• The next / 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:

• 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:

• Due to td, both peaks on resonance and those from signals at multiples of 1 / (2*td) Hz will be nulled (any signal with that frecuency with turn half a cycle in td…).

x

y

x

y

90-yx

y

FID (y)

FTx

y

Binomial pulses (…)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 H2O/D2O (9 to 1).

1H spectrum:

1H spectrum with 1:1 pulse (td = 200 S):

1/8 90y

tD

3/8 90-y

tD tD

3/8 90y1/8 90-y

Binomial pulses (…)Binomial pulses (…)

• To avoid the sign change we can use other binomial pulse trains, such as the 1:3:3:1:

• You also get artifacts. None of these pulse trains, nor experiments that take advantage on T1 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: