T1 Anisotropy

In the solid state, in the absence of magic angle spinning, the frequency of NMR lines depends on the orientation of the molecules with respect to the static magnetic field. For powdered samples, all orientations are represented in the sample and one obtains a broad envelope of peaks resulting from all possible orientations. Such broad resonance are called powder patterns and are said to be anisotropic. The frequency is not necessarily the only orientation dependant parameter. In some cases, the T₁ relaxation time also depends on the orientation of the molecules with respect to the magnetic field. In such cases the T₁ is said to be anisotropic. In contrast to the NMR resonances in solution which are characterized with a single T₁, the powder pattern can be characterized with many different T₁ relaxation times. Furthermore, the presence or absence of anisotropy in the T₁ can help discriminate between certain types of molecular motion. An example of an anisotropic T₁ is illustrated in the figure below for the wide line ²H inversion recovery spectra of acetone-d6 trapped in an organic inclusion compound. The line shape indicates that the acetone molecules undergo both fast methyl group rotation and fast two-fold flips about he carbonyl bond. One can see that the entire powder pattern does not have the same T₁ as the line shapes are a function of the inversion recovery delay, tau. The T₁ depends on the frequency within the powder pattern which in turn depends on the orientation of the molecules with respect to the magnetic field.

The Effect of Dissolved Oxygen on Relaxation Times

Proton T₁ relaxation occurs, to a very large extent, due to inter-proton dipole-dipole interactions and their time dependence as a result of molecular motion. Potentially, there is also dipole-dipole interactions between protons and unpaired electrons which also contribute greatly to proton relaxation. In fact, for ¹³C NMR, paramagnetic materials are sometimes added to the sample to make relaxation more efficient. Dissolved molecular oxygen from air is a paramagnetic material that is often overlooked. Like other paramagnetic materials it contributes significantly to the relaxation rate of protons. It can be eliminated from NMR samples by simply bubbling nitrogen through the sample for a few minutes or freeze-pump-thawing the sample a few times. The following data show the effect of dissolved oxygen on the proton relaxation times of ethyl acetate in acetone-d6.

T₁'s for sample under air 
quartet = 8.7 seconds
singlet = 7.7 seconds
triplet = 6.9 seconds
T₁'s for sample under nitrogen
quartet = 17.7 seconds
singlet = 13.2 seconds
triplet = 12.5 seconds

One can see that the relaxation times are nearly 100% longer when oxygen is eliminated from the sample. The figure below shows the proton T₁ inversion recovery measurement for the acetate methyl singlet of ethyl acetate for the same sample before and after nitrogen was bubbled through the solution.

Fast Molecular Motions and Solid State Wide Line 2H NMR

On occasion, I have been asked why people make such a big deal about solid state wide line ²H NMR. After all, ²H has a low natural abundance and isotopic labelling is necessary to collect the data. The answer is that the ²H line shapes depend on the interaction between the ²H quadrupole moment and the electric field gradient tensor surrounding the ²H nucleus. The electric field gradient tensor is dramatically affected by the averaging of different types of molecular motions and this effect is readily observed in the NMR line shapes. The line shapes are sensitive to the rates, order and axes defining the motion. For molecular motions occurring at rates fast with respect to the width of the static ²H NMR spectrum, one can determine the type of molecular motion by doing reasonably straight forward calculations or often simply by inspecting the motionally averaged spectrum. The figure below shows the effects that some common fast molecular motions have on ²H NMR line shapes. The same static quadrupolar coupling constant of 160 kHz was used in the calculation of all of the spectra in the figure.

The line shapes observed for molecules undergoing motions at rates comparable to the width of the static ²H NMR spectrum can also be calculated however, the calculations are a bit more involved.

Baseline Correction in 2D NMR Spectra

Sometimes a 1D NMR spectrum will have a baseline roll. One way of correcting this is to fit the baseline of the spectrum (between two limits) to a polynomial and then subtract the polynomial from the spectrum to produce a flat baseline. Baseline roll is not an exclusive problem to 1D data. It can also be present in each domain of a 2D data set. Baseline orrection can be applied to each of the dimensions. The figure below shows a proton NOESY spectrum which is uncorrected (top left), baseline corrected in the rows (top right), baseline corrected in the columns (bottom left) and baseline corrected in both domains (bottom right).

Output Power Expressed in decibels (dB)

It is often very confusing for students to know exactly how much RF power (in Watts) they are using in their NMR experiments, especially since the two major instrument manufacturers express the output power differently. It is very expensive to use a power level too high as NMR probes can be damaged if proper safety measures are not taken. Both Varian and Bruker express the output power of their instruments in decibels (dB). The maximum power level (pl1, pl2, pl3 .... etc) on a Bruker spectrometer is -6 dB and the minimum power is 120 dB. On Varian spectrometers (at least our INOVA), the maximum power (tpwr, dpwr etc) is 63 dB and the minimum power is 0 dB. Because of amplifier non-linearity, one may get maximum power below 63 dB on a Varian instrument (perhaps 55 dB to 60 dB) with no further gain at higher settings. On Bruker instruments, the non-linearity can be taken into account by calibrating with known attenuators and creating a correction table (CORTAB). If one is using an amplifier with a maximum output power of 100 Watts and the effects of amplifier non-linearity are neglected, the output power will be approximately:

100 W @ 63 dB (Varian) and -6 dB (Bruker)
1 W @ 43 dB (Varian) and 14 dB (Bruker)
1 mW @ 13 dB (Varian) and 44 dB (Bruker)

The figure below shows a plot of the power level in dB vs. the fraction of total amplifier power. The expressions in the figure do not take into account amplifier saturation.

CAUTION : Exact output power on any particular instrument must always be measured and calibrated.

Thank you to Victor Terskikh of the National Ultra-high Field NMR Facility for Solids for suggesting this post.

Double Quantum Filtered COSY

COSY spectra are very useful in structure elucidation as they provide correlations between coupled spins. Often, NMR spectra have large singlet signals from uncoupled protons (such as t-butyl methyls, methoxy protons, excess water or a solvent signal) which provide no information in the COSY spectrum and perhaps even get in the way of looking for smaller coupled spins. In such cases one can use a double quantum filtered COSY sequence rather than a standard COSY 90 or COSY 45 sequence. Double quantum filtered COSY spectra filter out uncoupled singlets. A comparison of a standard COSY 90 and a double quantum filtered COSY sequence for ethyl acetate is shown below. One can see that the singlet is present in the COSY 90 spectrum but absent in the double quantum filtered COSY spectrum.

Backward Linear Prediction to Correct for Receiver Saturation

If the receiver gain is set too high the initial portion of the FID is clipped and the NMR spectrum is distorted. In such cases the spectrum should be run again with an appropriate receiver gain setting. Sometimes however, this may not be convenient as the sample may have decomposed. One way to improve the quality of the data is to take a close look at the FID, discard the initial clipped points, use backward linear prediction to calculate the discarded points and then do the Fourier transform. An example of the improvement you can expect is shown in the figure below.

Echoes and Fourier Transforms

NMR data are often collected using pulse sequences involving echoes. These sequences are usually of the form:

pulse1 - delay1 - pulse2 - delay 2 - acquire data

In theory the echo occurs when delay1 = delay2. Often, this is not quite correct in practice due to the pulses having finite duration and short hidden pre-acquisition delays before the receiver is turned on. It is a good idea to set delay2 < delay1 so that the entire echo is captured. In such cases it is important to discard the data before the top of the echo before Fourier transformation. Failure to do so will result in improper line shapes (in the case of broad lines) or phasing errors. The figure below shows the ²H quadrupolar echo data for perdeuterated PMMA. The effect on the line shape is shown when the data are Fourier transformed before the echo (top trace) and after the echo (bottom trace). The correct line shape is only obtained when the data are Fourier transformed precisely at the top of the echo (middle trace).