Part 7: Pulse Sequences


Introduction

Modern ft-nmr spectrometers are controlled almost entirely by computers. The technique for doing the complex experiments that have arisen over the past two decades involves the use of a sequence of rf pulses issued before and after certain time delays. These, of course, are controlled by the computer and the operator can write and use her/his own pulse sequences to accomplish whatever nmr task is required. One example of a simple pulse sequence exists in the hardware document.

We can break down the typical pulse sequence into several sections, preparation, mixing and acquisition times. In the preparation section the spin system is being prepared, as the name suggests, to yield a specific type of information. The mixing time, which may or may not be present, is used to allow for mixing of density matrix terms and is ended with a 'read' pulse which reads the state of the spin system. The acquisition time is ... well ... the acquisition time during which signal from the spin system is being recorded. In the simple 1D pulse sequence shown in the hardware section, the preparation time consists of an interpulse delay which allows for the spin system to relax towards equilibrium. This is followed directly by a read pulse and the aquisition time ... about the simplest pulse sequence there is.

Basic 1D pulse sequence

The basic one dimensional nmr experiment consists of a very simple pulse sequence:

The interpulse delay serves to allow the spin system to relax back towards equilibrium. This is important for achieving the maximum signal-to-noise ratio. If the spin system doesn't relax sufficiently the relative intensity of the observed nmr peaks will suffer. You can see this effect if you observe the fid being accumulated. If DS (dummy scans) is 0 and D1 is very short, the second fid acquired will be appreciably smaller than the first, since sufficient relaxation hasn't occurred yet. The longer the relaxation delay the closer the spin system gets to equilibrium. Of course, a long relaxation delay means a long experiment so some type of compromise is made in practice. D1 is generally about 4-5 times the T1 value for the spin with the longest T1 value in the spin system. For protons this is about 2-4 seconds. The spin system is also relaxing during the aquisition time, AQ, so that the total relaxation time is really D1 + AQ. This means that you can usually get away with a fairly short value of D1 ... 100 msec or so, provided that AQ is long enough. The pulse, P1, is ... well ... the pulse. It usually has a duration in the 5-15 microsecond range. What actually happens is that the rf generator, which is always on and generating an rf frequency, is suddenly turned on ('gated on' in electronics jargon) for a few microseconds and then shut off. The effect of this is that a range of frequencies is irradiated simultaneously. The dead time, DE, is a short delay between the end of the pulse and the beginning of acquisition. This is needed for the electronics of the system to stabilize (prevents 'ringing', again electronics jargon). Unfortunately, this introduces frequency dependent phase errors into the resulting spectrum but fortunately they can be compensated for if DE is not too large.

Spin Echo Pulse Sequence

One of the beautiful things about pulse sequences is that you can use a 'building block' approach to constructing a sequence. That is, if a specific effect is needed you simply build in the pulse sequence that accomplishes that effect. One of the most commonly used of these is the spin echo pulse sequence.

As you can see this is a very simple sequence ... a delay followed by a 180o pulse followed by a delay equivalent in length to the first delay.  The utility of this pulse sequence lies in its ability to refocus dephasing magetization and eliminating chemical shift effects from a pulse sequence. Let's see what will happen if we insert this into our simple 1D pulse sequence:

The first 90o pulse rotates the magnetization into the transverse plane (the xy plane, see the theory section). During the delay time, d2, chemical shift and coupling evolution take place.  For a doublet with a heteronuclear coupling constant of w hz, this can be pictured via the vector model as two vectors rotating in the transverse plane at a frequency difference of w hz.

Here, vector a is rotating with a frequency that is w hz. higher than vector b. A 180ox pulse will rotate vectors a and b around the x axis by 180 degrees:

Note that vector b is now ahead of a but both are still rotating with their original frequencies so that a will catch up with b during the second delay period, d2:


The vectors a and b are said to be "refocussed". Also, note that at the end of the pulse sequence the vectors will always be aligned along the same axis regardless of precession frequency or, what is equivalent, regardless of chemical shift. Recall that one of the sources of phase error that is corrected by software means is the frequency dependent phase error (see hardware-phase correction). This phase error is removed by the refocussing of the multiplet vectors onto the -y axis. Chemical shift effects are said to be removed. This can be seen using a product operator analysis of the pulse sequence:

Note that there are no chemical shift terms, only coupling terms. Also, note that the preceding analysis assumes heteronucear coupling with pulses being applied only to one nucleus. The picture changes if we consider homonuclear coupling. Application of the same pulse sequence (this time with the rotating frame frequency the same as the doublet chemical shift frequency) with the spin echo building block gives, after a delay time, d2:

After a 180o x pulse:

As before,  the vectors have rotated 180o about the x axis but this time, since the 180o pulse has been applied to all nucleii, the labels  on the vectors have changed (reference 1). The vectors will rotate in the same directions as before the 180o pulse to give, after the second delay time:

Antiphase magnetization is created instead of refocussed magnetisation. This is used to advantage in the INEPT experiment.
 

BIRD

This is the BIlinear Rotational Decoupling pulse sequence. The fundamental idea here is that there is ususally a substantial difference between one bond coupling constants and two, three or four bond coupling constants.  The pulse sequence is as follows:

Where tau = 1/(2J CH). The actions of these pulses can be visualized by the vector method:


After the first tau delay time, the one bond couplings have evolved to become antiphase magnetization but the 2-4 bond couplings, which are smaller, have not appreciably evolved. The concurrent 1H and 13C pi pulses serve to rotate the 2-4 bond couplings about the x axis and exchange the labels on all vectors so that they now rotate in the reverse sense. The one bond couplings end up being refocussed after the second tau delay and are then rotated onto the -z axis by the final pi pulse.

What is a series of BIRD pulses called, you ask? Well a FLOCK, of course.

TANGO

Testing for Adjacent Nucleii with a Gyration Operator is a pulse sequence that is similar to the BIRD sequence in that it takes advantage of differences in coupling constants.


Vector analysis of the pulse sequence, similar to that for the BIRD sequence, results in a final state:

Here, the one bond coupling is refocussed and aligned along the +y axis
 

Z-Filter

Bruker AMX pulse programming
  Bruker AMX pulse programming is accomplished by using the built-in proprietary Bruker pulse programming language. There are keywords for everything needed to accomplish most tasks. Here is an example program (the simple program to acquire a proton spectrum):
;zg
;amx-version
;1D sequence


1 ze
2 d1
p1 ph1
go=2 ph31
wr #0
exit

ph1=0 2 2 0 1 3 3 1
ph31=0 2 2 0 1 3 3 1


;hl1: ecoupler high power level
;p1 : 90 degree transmitter high power pulse
;d1 : relaxation delay; 1-5 * T1


We can follow what the program is doing by a stepwise analysis. The first three lines beginning with ';' are comment lines. Anything following the ';' character is simply ignored by the pulse program compiler. Many programming languages have comments in order to make the flow of the program more legible to the casual reader (and easier to maintain).

Now the actual program begins at the line with '1' in the first column. 'ze' means zero the memory ... ie. wipe out any data in the memory and start fresh. The next line with a '2' in the first column is 'd1' which means execute delay d1. This is the interpulse relaxation delay. In textbooks it is generally shown at the end of a pulse sequence but it actually is at the beginning. The '1' and the '2' just referred to are line markers that are used by other commands in the program.

The next line is 'p1 ph1'. 'p1' means issue a pulse of 'p1' microseconds on the transmitter using phase program 'ph1'. Looking down several lines we see the definition of phase program 'ph1'. In this case it is 0 2 2 0 1 3 3 1 or in vector model terminology, x -x -x x y -y -y y.

Next line ... 'go=2 ph31'. This is the "loop" portion of the program. 'go=2' means loop back to the line that begins with '2', which as we have seen is the second line of the program. At the same time the receiver is turned on using the phase program 'ph31', which as with 'ph1' is listed below the program. The number of times that the program will loop is defined by the parameter 'ns' (number of scans).

'wr #0' means write all of the data that have been collected in memory to a file. 'exit' means ... exit.

At the end of the file there are some more comment lines. These generally tell what is required in the way of parameter setup for the program. In this case, 'hl1' is the power setting for the transmitter, 'p1' is the 90 degree pulse width and 'd1' is the relaxation delay.

Examples

JMOD
DEPT
INEPT
COSY
CAPT
HMQC

Coherence Mapping