5. COMMON PARAMETERS

• 5.1 TRANSMITTER FREQUENCIES (tof, satfrq, dof, dof2)
• 5.2 SPECTRAL WIDTHS (sw, sw1, sw2)
• 5.3 ACQUISITION TIMES (np and at)
• 5.4 SIGNAL AVERAGING (d1, nt and ss)
• 5.5 PULSE LENGTHS AND FIELD STRENGTHS (pw, pwx, dmf, dmf2)
• 5.6 POWER LEVELS
• 5.6.1 Pulse Power Levels (tpwr, pwxlvl, pwylvl)
• 5.6.2 Decoupler Power Levels (dpwr, dpwr2, satpwr)
• 5.6.3 Calculating Power Levels and Field Strengths
• 5.6.4 WALTZ and GARP Decoupling (dm, dmm, dmf)
• 5.7 FOURIER TRANSFORM AND WEIGHTING FUNCTIONS
• 5.7.1 Fourier Transforms (ft, df, ds)
• 5.7.2 Weighting Functions (wti, wft, lb, gf, gfs, sb, sbs)
• 5.7.3 Phasing (rp and lp)
• 5.7.4 Alfa and the Flat Baseline (alfa)

This section gives some background and a few guidelines to setting some of the common parameters which are used in almost every experiment. It is put here to prevent repetition in later sections. Each separate heading is followed by the parameters that are most relevant to that topic.

The transmitter frequency is normally placed in the center of the spectrum and is the frequency at which the RF pulses are applied. The values of tof, dof and dof2 correspond to the frequencies for the observe channel, decoupler channel and the second decoupler channel respectively. The parameter satfrq is used in some experiments where saturation of the solvent is required however, this is normally set to the same value as tof. The values of tof, dof etc. are not the absolute frequencies, rather they are a "fine tuning" of the transmitter frequencies. The absolute frequencies are given by the parameters sfrq, dfrq and dfrq2 respectively. The value for each parameter will depend on which machine you are using. Typical settings for the transmitter frequencies are given below

5.2 SPECTRAL WIDTHS (sw, sw1, sw2)

The spectral width is the frequency range of the spectrum that you wish to record. The three parameters sw, sw1 and sw2 refer to the settings for the spectral widths of the first, second and third dimensions respectively. The spectral width is given in Hertz and should be optimized after recording a 1D spectrum of the sample. It is always better to start with a large spectral width and then narrow it down later. This reduces the chances of making mistakes. As a guide 1 ppm is the 10^-6*spectrometer frequency. e.g. 1 ppm 1H at 400 MHz is 400 Hz. Suggested starting values for the spectral widths for 1D experiments are given below:
1H 14 ppm for Proteins
20 ppm for DNA/RNA
C13 200 ppm for Proteins
250 ppm for RNA/DNA
P31 10-20 ppm depending on structure
{N15 100 ppm for Proteins } Do not normally run 1Ds on N15
{ 150-200 for RNA/DNA}

The length of the acquisition time (at) used in an experiment depends on several factors. Firstly, theory dictates that in order to discriminate two signals that are [Delta] Hz apart, the interval between sequential data points (the dwell time) must be 1/[Delta] seconds. Secondly, to discriminate between signals that are much closer together (e.g. 1-10 Hz) we have to sample our data for a sufficiently long period of time to allow the phases of the separate signals to have evolved away from each other. However in most NMR experiments on biological macromolecules, relaxation destroys most of our signal before the latter can happen. Normally we collect between 2048 or 4096 data points (np) using the typical spectral widths given above. This results in acquisition times of between 100-300 ms. For smaller molecules where relaxation is not a limiting factor it is not unusual to collect up to 64000 data points. It is usual to set sw and np to the desired values and let the computer work out the value of at.. The number of points collected should be adjusted for each sample. If the T2 relaxation rates are fast the signal will decay very quickly and in such cases there may be no point in collecting 4096 points if all the signal has decayed within the first 1024.

A single pass through a pulse sequence including the period of data acquisition is called a transient or scan. The amount of signal in a single transient may often be too small to be distinguished from the noise. However, because the noise is essentially random we can repeat the experiment a large number of times and signal will add up after each scan but the noise will cancel. In fact the noise does not cancel exactly but rather adds up proportionally to [radical]2 times the number of transients (nt). This means that in order to double the signal to noise in the final spectrum I would have to collect four times the number of scans, i.e. if I acquire 256 scans in an experiment, to improve the signal to noise ratio by a factor of two I would have to collect an additional 768 scans, making a total of 1024.
Most experiments require that you set the number of transients to a multiple of 16 or 32 which is determined by the phase cycle (See section 4.2). After each scan there is a relaxation period (d1) during which the system is allowed to return to equilibrium. For protein samples this delay is typically 1-1.5s. However, this delay is a compromise between the full relaxation time and the time constraints placed on the user. As a result the system does not return to equilibrium after each scan but enters a "steady-state". In many experiments this may lead to unwanted artifacts if data is collected immediately after the first scan. Therefore the system can be set to perform a number of "steady-state" scans (ss). During these scans the spectrometer executes all the pulses and delays in the pulse sequence but does not collect any data. The value of ss depends on the sequence. For simple 1D Proton experiments ss can be set to 4 or 8. For experiments with decoupling it may be necessary to set ss to 64 or 128 or even higher to allow the temperature to reach equilibrium

NMR experiments use the magnetic component of a short pulse of Radio Frequency (RF) fields to manipulate nuclear spins. The RF field rotates the spins away from their equilibrium positions and the angle of rotation depends on both the duration of the RF field and its magnetic field strength (Eqn 1). The success of many NMR experiments depends on the correct calibration of these radio frequency fields.
(Eqn 1) [tau] [gamma] B₁ = [phi]_R Tip angle in radians
Where [tau] = duration of pulse, B₁ is field strength of RF pulse (Tesla), [phi]_R = tip angle (in radians) and [gamma] = Gyromagnetic Ratio (rad T^-1 s^-1 ). It is more usual to find the field strength expressed in Hertz which is essentially the effective excitation range of the RF pulse. The field strength in Hertz is calculated from the time required to rotate the magnetization through 360[ring]. (Eqn 2 and 3). NMR spectroscopists also refer to the duration of the 90[ring] pulse which is directly related to the field strength.
(Eqn 2) [tau] [gamma]B₁/2[pi] = [phi] Tip angle in degrees
(Eqn 3) 1/[tau]₃₆₀ = [gamma]B₁/2[pi] Field Strength in Hertz
For many experiments it is necessary to know the field strength of the pulse at a given power level. From the above equations it can be seen that this is easily derived after determining the duration of a 360[ring] pulse, 180[ring] or a 90[ring] pulse. It is usually more accurate and easier to determine the value a 360[ring] or a 180[ring] pulse than a 90[ring] pulse but it is not always possible to do so.
The parameters pw, pwx and pwy are used to represent the 90[ring] pulse lengths of the observe, 1st decoupler and 2nd decoupler channels respectively. The parameters dmf and dmf2 are the so called "decoupler modulation frequencies". These are in fact measures of the field strength of a pulse but are expressed as 1/pw90 where pw90 is the 90[ring] pulse width at the power level being used for decoupling.

WARNING The power levels are set in units of dB which is a logarithmic scale. An increase of 20 dB increases the power to the probe by a factor of 100. When using decoupling sequences do not set the power above 50 dB.

The parameter tpwr controls the power of the observe channel for the application of pulses. In this laboratory pwxlvl and pwylvl are used for controlling the power for pulses on the first and second decoupler although these can be interchanged depending on context. Generally pulses are applied at power levels of 60 dB unless otherwise instructed. The exception is P31 which should not be used at power levels above 55 dB

Unlike pulses which only last for a few microseconds, decoupler sequences and solvent saturation can last 0.2-2 seconds. If the decoupler is turned on for this period of time at full power serious damage can be casued to the probe. Consequently decoupler power is limited to a maximum of 50 dB. dpwr and dpwr2 control the power level setting for decoupling on the first and second decoupler channels respectively. The parameter satpwr is used for irradiation of solvent and is typically set to 10 dB for H₂O and 1-4 dB for D₂O.

Once you have calibrated the 90[ring] or 360[ring] degree pulse width at 60 dB for each channel, you can calculate what the pulse width will be at different power level settings from the following relationship (Eqn 4) which is rearranged to give Eqn 5
(Eqn 4) [Delta]dB = 20 log (RF_Measured/RF_Required)
(Eqn 5) log(RF_Required) = log(RF_Measured) - [Delta]dB/20
Where [Delta]dB is the change in power level, RF_Measured is the field strength of the calibrated pulse and RF_Required is the field strength of the pulse at the new power level. This may appear complex but it has a very simple result. Each change of 6 dB in power changes the field strength by a factor of 2. So a change in 12 dB will change the field strength by a factor of 4. Some other useful steps to remember are:

dB Change Factor

As an example, if the 90[ring] pulse is 12.5 µs at 60 dB then the field strength is 20 KHz. Therefore at 48 dB, the field straight will be 5 KHz and my 90[ring] pulse will be 50 µs. At 42 dB the field strength is 2.5 KHz and the 90[ring] pulse is 100 µs. These simple relationships will prove very useful in the following sections.

A nucleus with a magnetic dipole (1H, C13, N15 and P31) perturbs the energy of neighbouring dipoles depending on its orientation within the magnetic field. This phenomenon is called coupling and causes the neighbouring dipole to appear as two lines in the NMR spectrum. The frequency separation of these lines is the coupling constant. In many experiments with labeled samples the coupling between the 1H and the heteronucleus (C13, N15 or P31) makes the spectrum harder to interpret. Consequently we use decoupling techniques to remove these effects in order to simplify the spectrum and increase the signal to noise ratio.
There are presently two widely used techniques for broad band decoupling. Both techniques use a series of RF pulses to achieve good decoupling and consequently are known as Composite Pulse Decoupling Schemes. WALTZ-16 produces high quality decoupling over 2xB₁ field strength and is used primarily to decouple Protons from C13/N15 and P31. Its limited range makes it unsuitable for decoupling the wide spectral width of C13. In this case we use GARP which provides adequate decoupling over 5xB₁ Field Strength although it is not recommended for small molecules. The following parameters must be set up for decoupling:
dm The "Decoupling Mode" is status parameter that controls whether decoupling is on or off. e.g. dm=`nny' sets decoupler on during status C
dmm "Decoupler Modulation Mode" sets the decoupling sequence. e.g. dmm=`ccg' sets GARP decoupling during status C and "continuous" or "pulse" mode at all other times. dmm=`ccw' sets WALTZ decoupling. The first entry in dmm should always be `c'
dpwr The power used for the decoupling period on the first decoupler channel
dmf "Decoupler modulation frequency" is a measure of the field field strength in Hertz. dmf should be set =1/pw90 where pw90 is the 90[ring] pulse at the power level set in dpwr.
dres "Decoupler Resolution" This parameter is used to calculate the length of a 90[ring] pulse on the decoupler. For WALTZ set dres=90 for GARP set dres=1.0

5.7 FOURIER TRANSFORM AND WEIGHTING FUNCTIONS

5.7.1 Fourier Transforms (ft, df, ds)

The fourier transform (FT) is the mathematical process that converts Free Induction Decay (FID) into the more common NMR spectrum. The FID represents the signal amplitude as a function of time whilst the spectrum represents the signal amplitude as a function of frequency. Consequently the FID is sometimes referred to as the "time domain" and the spectrum as the "frequency domain". The mathematics behind the FT process is beyond the scope of this handout but essentially it can be thought of as a series of frequency deconvolutions over all possible frequencies. The FID can be displayed using the command "df" and is converted into a spectrum using the command "ft". The resulting spectrum is displayed using the command "ds".

An FID which decays exponentially to zero contains most of its signal intensity in its first part. The first part of the FID also contains the broader signals which arise from the rapidly decaying components of the sample whilst only signals from the narrower components extend into the later parts of the FID. It is these narrower components which allow us to resolve signals that have similar frequencies. Sometimes it is desirable to study only these narrow components and so obtain well resolved spectra. Unfortunately the intensity of these narrow components is very small and often cannot be distinguished from the noise. The weigthing process multiplies the raw FID data by a simple function prior to Fourier transformation before the FT procedure to enhance its appearance and can be used to enhance these narrow components and at the same time reduce the contribution that the broader components make to the spectrum. In addition weighting functions can be used to correct artifacts e.g. if the acquisition time was too short and the FID did not decay to zero (this often happens if there is unsuppressed solvent resonances). They can also be used when the acquisition time was too long. In these latter cases the later parts of the FID contain only noise and can be ignored. Weighting functions provide an easy way to do this.
There are many different weighting functions that can be applied to an FID and nearly every user has their own favourite and so no rules are given about which ones to use. The following guidelines set up a weighting function that removes any truncation artifacts and provides a reasonable resolution enhancement without throwing out too much signal. This example uses the very powerful interactive routine wti (which stands for "Weight Transients Interactively"). The Interactive display has three panels, the lower one shows the FID, the middle one the weighting function and the upper panel shows the spectrum (the spectrum is turned on by clicking the right mouse button). The Buttons in the Command window show the weighting function parameters whilst the bottom line of the graphics display shows the current settings of those parameters. To adjust a parameter, click on the parameter Button and then click the mouse in the function window. To turn a parameter off, click on the parameter Button twice.
- After acquiring an FID type "wti" to enter the interactive routine
- Turn all functions off
- Click on "sb" and then click in the function window
- Adjust the appearance of the function so it has a maximum just before or at the end of the FID
- Now click on "sbs" to adjust the location of the maximum
- Adjust the function so that the maximum is near the beginning of the FID and it reaches zero at or just before the end of the FID
- Now activate "gf" and click towards the right edge of the function window.
- Activate "gfs" and adjust the maximum so that it is about 1/4 to 1/3 in from the beginning of the FID. You may have to readjust "gf" to achieve this.
- You can now display the spectrum full size by typing "wft". This applies the function that you set up and FTs the data. This command will apply the weighting function to all subsequent FIDs in the same job until you change it.
NOTE.
Weighting functions must always be used with caution. The inappropriate usage of weighting functions will introduce artifacts into the processed spectrum. Therefore you should always be fully aware of the consequences of applying a particular function. For example, if the first point of the FID is made zero by application of an unshifted sine-bell function it is a mathematical consequence that the total signal intensity in the spectrum is also zero. This means that for every positive intensity there must be an equal and opposite negative intensity. This may lead to the cancelation of smaller signals by the artifacts associated with stronger signals. In addition some weighting functions can introduce artefacts that may appear like real signals. These effects may lead to the mis-interpretation of your data.

A newly transformed spectrum very rarely looks right. The peaks will have different amplitudes relative to each other and may appear to be twisted. A distortion arises when the phase of the transmitter signal is shifted relative to the receiver signal. This occurs in almost every spectrum because of the construction of the electronic circuitry. This shift is constant over the whole spectrum and and can be corrected by applying a "Zero order phase correction" (rp). An additional phase correction must be applied to each signal which depends on its chemical shift. Each component of the net magnetization will precess at a different frequency in the XY plane as soon as the magnetization has been displaced from the Z axis. Consequently after a pulse and prior to data acquisition the relative phase of each signal (i.e. its position in the XY plane) depends on the chemical shift difference from the reference frequency. This correction is called the First order phase correction (lp). The paramter rp and lp stand for "right phase" and "left phase" respectively
- After FTing the FID click the "Phase" button on the menu line
- If "Phase" is not visible, click on the "Main Menu" button on the top line,
- Click on "Display" then click on "Interactive", the "Phase" Button should now be visible
- Place the cursor above a peak on the right hand side of the spectrum and click.
- Hold down the left mouse button and move the mouse up or down to adjust the appearance of this peak . The selected peak should be all positive. Release the cursor
- Move the cursor to the left side of the spectrum and click it above an isolated peak
- Hold down the left mouse button and adjust the appearance of the spectrum so that the remaining peaks appear in-phase
- When you have finished click the "Return" button
It may be necessary to repeat this process to get the best phasing. If the baseline is not flat you may need to adjust the pre-acquisition delay: see below.

Following the last pulse of an experiment there is a series of small delays to allow various parts of the hardware to settle prior to acquisition. These delays are imposed by the computer and some of these cannot be changed. The receiver is then gated on and the data is collected. During these delays the magnetization will dephase. A parameter, alfa, has been provided to allow the user to adjust the total time after the last pulse to correct this dephasing. The delays are adjusted by use of the macro "ca180". This macro calculates the value of alfa based on the phase corrections that must be applied to the spectrum:
- Record and phase a spectrum making sure the baselines on either side of the spectrum are as flat as possible.
- Enter the command "ca180"
- Re-record the spectrum
- Set lp=-180 and then phase the spectrum. You should only need to adjust the zero order correction (rp) to obtain a properly phased spectrum.
- If you need to adjust lp to correct the phasing the ca180 command again and repeat the process setting lp back to -180 each time before you phase the spectrum. At this point the baseline may appear curved.
- You can correct this curvature by adjusting the value of "fpmult" before transforming the spectrum. Try setting fpmult=0.7 and retransforming the spectrum. If the baseline improves continue to decreease the value of fpmult. If it gets worse adjust fpmult in the opposite direction. The default value of fpmult is 1.0

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