Revised January 24, 1991. RN.
Acquisition parameters require careful optimization for achieving the best possible signal-to-noise ratio (S/N) in a given amount of time. While low S/N rarely presents a problem in routine 1H NMR, it is much more important for 13C spectra. Careful optimization of acquisition parameters can reduce the experimental time required by a factor of two or more over "routine parameters". While the following is mostly true for any nucleus, only 13C is discussed as it is the most commonly measured X-nucleus. Since 13C spectra typically require 1 to 12 or more hours of acquisition time, the savings can be significant.
(A) Choice of the flip angle ,ø , of the carbon observe pulse, and the repetition rate, R, as a function of the spin lattice relaxation, T1.
(B) Line width and S/N; factors contributing to line widths.
(C) Choice of the acquisition time (block size).
(D) Decoupling parameters.
(E) Temperature stability and temperature gradients.
T1 - Spin lattice relaxation time. T2 - Transverse relaxation time. T2* - Transverse relaxation time including contributions by the instrument due to inhomogeneity of the static magnetic field B0, incomplete decoupling, field instability, temperature gradients or instability. Wex - Width at half height of the observed line, =1/p(ie)T2*. ø - Flip angle of the rf-pulse. R - Repetition time, acquisition time plus delay between scans. AT - Acquisition time, time during which the FID is being collected.
A paper by Becker and co-workers (1) analyzes the relationships of the flip angle ,ø , the pulse repetition time, R, and the final signal-to-noise ratio. Table 1 has been constructed for selection of ø for a range of T1.
It is assumed that T1 = T2. This is usually the
case for small organic molecules. The experiment consists of one pulse
followed by the acquisition of the FID and a recycle delay. Decoupling
has no effect on the choice of ø .
Base the selection of ø on the longest T1 of interest.
For 13C spectra, this usually pertains to quaternary carbons.
In addition to long T1's, there is usually little NOE.
If quaternary carbons are acquired with optimal parameters, the protonated
carbons will generally show more than adequate S/N. If only protonated
carbons are of interest, a DEPT experiment should be used in the first
place!
As a rule of thumb one can argue that, with ø and R optimized
for a slowly relaxing quaternary carbon, protonated carbons cannot be more
than three times as intense. This limit is derived from the fact that the
maximum NOE results in triple the intensity.
Assuming full relaxation and no NOE on the quaternary carbons, the intensities
of protonated carbons thus should not be more than three times larger than
quaternary carbons. In practice, the protonated carbons may exhibit less
than maximum NOE and quaternary carbons frequently show a partial NOE,
reducing the ratio even more.
Table 1 ø vs. R T1: 2 5 10 15 25 50 100 Seconds R = 2s, ø ° : 70 50 35 30 25 20 R = 5s, ø ° : 70 55 45 35 25 R = 10s, ø ° : 70 60 50 35 25
R = Acquisition time AT, plus Delay between scans.
No angles larger than 70° are listed.
If the repetition time R exceeds T1, the S/N per unit time will
decrease considerably (1)!
The values for ø are only approximate and rounded to the nearest
5 ° .
Since the integral of an NMR resonance is independent of its line width, it follows that the intensity must be inversely related to the width. In other words, the narrower the line, the better the S/N. For organic molecules up to the size of steroids, the width is expected to range from about 0.01 Hz to 1.0 Hz (2). This corresponds to a range of T1 from 0.3 to 30 seconds.
Assuming T1 = T2, every effort should be made to assure that the observed line width Wex is as narrow as possible compared to the intrinsic line width. The following factors contribute to the observed line width, Wex, measured at half-height:
Careful shimming can minimize this contribution. Note that the contribution is scaled by the ratio of g of 1H and g of the X-nucleus. For example, if a proton resonance is broadened by 0.4 Hz due to field inhomogeneity, a 13C line is broadened only by about 0.1 Hz , and 31P by about 0.15 Hz.
Incomplete decoupling results in residual coupling. While the resonance is not necessarily visibly split, it is broadened. Current decoupling schemes can limit the contribution to the l ine width to about 0.2 Hz to 0.5 Hz.
Decoupling leads to sample heating. The heating, especially on large sample tubes (=> 10 mm) may not be uniform. Using V.T. air to cool the probe and sample can worsen the situation if the flow rate is too low! The gas-stream usually is directed to the bottom of the sample and flows upwards along the sample. Low flow removes heat more efficiently near the bottom, thus creating a temperature gradient along the sample.
The temperature rise is a function of the decoupler power, the probe characteristics (i.e., how much heat is transferred to the sample by convection from the decoupling coil), and the sample's absorption of rf-energy and conversion to heat. A large sample tube filled with, e.g., saline solution will heat considerably more than a 5 mm tube filled with chloroform. At higher frequencies, the heating increases (the reason for the high operating frequency of microwave ovens).
Since chemical shifts are temperature dependent, spins in different
regions of the sample may resonate at slightly different frequencies. The
average of these shifts then broadens the observed line. At 50.3 MHz, 13C
frequency (200 MHz 1H) shifts at 0.2 to 1 Hz/° C have been observed
(2). If a CO resonance is broadened to e.g. 2 Hz (a factor 10 to 20!),
the S/N will be severely reduced.
While the homogeneity itself is usually quite adequate, it may be affected by changes in ambient temperature and, quite severely, by changes in probe and sample temperature. A sample undergoing c hanges (solvent evaporation, precipitation, etc.) can itself adversely affect the magnetic field homogeneity. If an automatic shim device is available (and functioning!), it should be used.
A change in temperature will lead to an average of chemical shifts, causing a broadening of the observed line width.
The spectrometer itself contributes to the line width. The lock system
may not stabilize the field as well as could be.
The variable temperature unit may not regulate well enough. Fluctuations
in gas flow can lead to temperature instability. The user may not have
much, if any, control over these factors.
The instrumental contributions can be checked by observing a small spectral
region, comparing the line width after a single scan to the width obtained
during an overnight run.
The stability may also be reduced by traffic near the magnet. Although the lock system may not fail, it usually cannot prevent momentary field shifts; it may take several seconds until it settles back to normal.
One of the parameters most often ignored is the acquisition time (AT) of each scan. Assuming the observed width of the signals to be 0.5 Hz, which for quaternary carbons should always be attainable, a minimum acquisition time of 2 seconds is needed (1,3). Briefly, the best S/N is achieved when a resonance is observed during 1/Wex followed by sensitivity enhancement by exponential multiplication with a line broadening factor of LB = Wex. The lower limit of LB is equal to 1/AT.
If the sum of Wex and LB are less than 2/AT , the intensity of the line can become dependent on the phase correction. With perfect phasing , the intensity may well be considerably reduced. In extreme cases, the signal may vanish altogether.
According to (1) an LB either too large or too small by a factor of
two results in a loss of S/N of less than 5% for an acquisition time of
2 x T2*. For shorter acquisition times the loss increases more
drastically if the minimum LB is given by the acquisition time. Assuming
a Wex of 0.1 Hz, the S/N is calculated to be reduced to 70% for a 1 second
AT and to about 85% for a 2 second AT.
Assuming an observed window of 230 ppm, the minimum block size for a 200
MHz (1H) NMR would be 32 k, for 300 MHz at least 64 k. For 500 MHz, 128
k should be chosen.
Proton Broad Band decoupling ideally results in complete removal of J-coupling. The result should be a line of a width at half-height of 1/pT2, ignoring contributions from inhomogeneity from the magnetic field and temperature gradients. In practice, the lines appear broader than predicted. The cause is residual coupling. The residual coupling is larger for large JX-H. Since one-bond JC-H averages about 150 Hz and two-bond JP-H about 10 Hz, it can easily be seen that efficient decoupling is more important for 13C spectra. It also explains why TMS (JC-H = 200 Hz) frequently shows a larger line width than most other resonances.
The decoupler modulation normally is efficient only over a range of +/- 5 ppm. For small J's, e.g., 31P, the efficiency may still be sufficient for a 10 ppm offset, but this cannot be assumed to be true in all cases. Consequently, the decoupler frequency must be centered in the middle of the proton region. For most practical samples, this may actually be closer to 3.8 ppm rather than the customarily assumed 5 ppm.
If the field is changed for locking on a different solvent, the Larmor frequency of protons naturally will also change. For example, if 5 ppm in the proton spectrum corresponds to 500.138'000 MHz while locked on CDCl3, the Decoupler frequency therefore needs to be increased by 5 ppm for a solvent resonating at 2.25 ppm. Deuteron and proton shifts can be assumed to be the same in ppm for this calculation. The decoupler frequency needs to be increased by 2500 Hz to 500.140,500 MHz. If all protons resonate between 0 and 7.6 ppm, a 1.2 ppm decrease (600 Hz) would result in the optimal setting of 500.139,900 MHz.
The modulation scheme commonly used is called WALTZ-16 (4). 90° decoupler pulses are phase-shifted by 180° according to a fairly complicated scheme. The main advantage over older schemes is its much higher efficiency. Decoupling power can be up to 10 times lower using WALTZ-16. It is implemented in hardware and may also have a software control (P9 on Bruker spectrometers) to adjust the width of the nominal 90° decoupler pulse. With hardwired units the pulse width is set once and the strength of the decoupler field is adjusted for the strength to match the 90° pulse length.
Deviation by more than 10% (1 dB) either way may result in observable degradation of decoupling. Residual coupling leads to additional line broadening. Although once the optimal conditions are set, they may need fine adjustments due to improperly tuned decoupling coils and changes in decoupler output with time. Note that no two probes can be expected to show the same decoupler field B2 for a given input power. To measure the performance of the modulation, one can use a sample where the X-nucleus signal can easily be seen in a single scan . With the decoupler on resonance, take a scan and measure to the line width. Repeat the procedure for several decoupler offsets up to 5 ppm. To quickly check the set-up for proper power level set the decoupler 5 ppm away from proton resonance. Adjust the power for slowest decay of the carbon FID. This can conveniently be done in GS (Bruker) or SK (Nicolet). The response number increases with slower decay. B e careful though to avoid saturation by too long a carbon pulse. For a final check, measure the line width. The observed width Wex should be less than 0.5 Hz. Using 39% Dioxane in C6D6 in a 5 mm tube, 0.08 Hz on-resonance and 0.26 Hz off-resonance has been observed on a 300 MHz (1H) NMR.
As pointed out by Allerhand (2), chemical shift for 13C NMR
resonances can change from 0.2 to 1 Hz/° C as measured on a 200 MHz
(1H) NMR. Some compounds may shift even more. Some 31P resonances
have been observed to shift an estimated 5 Hz/° C, but no accurate
measurements have been done. To minimize temperature gradients along the
sample, the V.T. unit should be used at a high flow rate. For long term
temperature stability, it is recommended to use temperature regulation.
With 5 mm probes and WALTZ decoupling, the temperature rise is usually
below 2° C up to 300 MHz. Setting the V.T. to regulate 2 or 3°C
above normal probe temperature should be sufficient. For best results,
shimming should be done at the temperature at which the spectrum will be
measured. Consequently, the V.T. should be turned on immediately after
the sample is placed in the magnet. Unless a proton spectrum will be measured,
the spectrometer should be immediately set up for x-nucleus observation
and decoupling at the power level to be used. In a few minutes, the temperature
should be equilibrated.
Since the temperature instability will impact S/N more than a 2 or 3°
C increase in temperature, it is most likely preferable to use single level
decoupling throughout the experiment. Otherwise the temperature will change
once a two-level decoupling sequence is started. Furthermore, it is conceivable
that during a scan, the temperature might change although the effect most
likely would be small.
The effect of the absolute temperature cannot be entirely neglected. The signal intensity is inversely proportional to the temperature (arising from the Boltzman factor) Therefore, at lower temperature, a higher S/N is expected. Lowering the temperature from 300° K to 270° K would theoretically increase S/N by about 10%. T1 decreases with temperature in small organic molecules. Lowering the temperature can provide faster repetition while providing increased S/N. Unfortunately, the probe tuning changes with temperature for both the observe and the decoupler circuits. The de-tuning effects cannot easily be predicted and vary from probe to probe. Therefore, it follows that probe tuning should be checked at the temperature at which the sample is run. At low temperature this is frequently impractical due to the tuning elements freezing. Repeated tuning as the probe is cooling might help. At least, the tuning should be closer to the final of the temperature if the tuning elements should freeze.
A concentrated sample of camphor was run in a 5 mm tube on a 300 MHz spectrometer. All spectra are the result of 32 scans.
Spectrum a was obtained with a ø of 25° (4 us) and 2 seconds repetition time, corresponding to optimal parameters for a T1 of about 25 seconds. 64 k points were acquired, AT = 1.9 seconds. Total time = 64 seconds.
Spectrum b was acquired with a ø of 45° (7 us) and a repetition time of 4.9 seconds, corresponding to optimal parameters for a T1 of about 15 seconds. 64k points were acquired, AT = 1.9 seconds. Total time = 157 seconds.
Comparison of a and b shows that there is little, if any, increase in S/N for the quaternary carbons C1-C3 despite an increase of total time by about a factor of 2.5!
Spectra a and b are processed using a line broadening LB of 0.5 Hz. Using an LB = 1 Hz and processing only 32 k points results in plots c and d. For comparison of the intensity, C1 is expanded for both plots. C1 shows a slight decrease in S/N. Note though that the intensity of C3 is much reduced! The S/N for the protonated carbons C4-C9 is somewhat improved.
Plots a1 and b1 show that, in addition to the loss of intensity of C3 the peaks, the peaks C4, C5 are no longer resolved.
The plots e and f are the result of using an LB = 6 Hz on the same FID's as in a and b to obtain intensities less dependent on the line width. Note the ratios of C1-3 versus C4-8. The ratios in e are much closer to what would be expected.
As a rule of thumb one can argue that if ø and R are optimized for quaternary carbons, protonated carbons cannot be more than three times more intense (assuming equal line width). This limit can be predicted by the fact that with maximum NOE the intensity will be tripled. A carbon with full NOE thus cannot be more than three times as intense as a carbon without any NOE. In practice, it is possible for a quaternary carbon to show NOE of up to 50% and protonated carbons to show less than 100% NOE. In such cases the ratio will be even lower.
Taking into account all the factors discussed, it is possible to more than double the S/N compared to an non-optimized "Routine Parameter" - type experiment.
For successful observation of quaternary carbons and 31P, all the parameters except proton decoupling need to be considered.
For protonated carbons, the decoupling parameters should be optimized.
While the line width Wex has been optimized for reasons of S/N, it also follows that closely spaced resonances are better resolved.
By using too short an acquisition time (number of points) S/N will be affected more than generally recognized while improper LB has a relatively small effect.
1. E. Becker et al. Anal. Chem. 51, 1413 (1979).
2. A. Allerhand et al. J. Am. Chem. Soc. 107, 5809 (1985).
3. M. L. Martin, G. T. Martin, J. J. Delpuech "Practical NMR Spectroscopy"
Heyden, London, 1980.
4. A. Shaka, J. Keeler and R. Freeman, J. Magn. Reson. 53, 313 (1983).
Last Update: 9/25//95 RN.