Gradients for coherence selection

In addition to artifact suppression and removing solvent peaks, gradient pulses can be used for coherence selection. Traditionally, this was done by phase cycling but using gradients for coherence selection allows cleaner spectra to be obtained more quickly. In this post the use of gradients to select coherences in heteronuclear experiments is discussed.

When using gradients for artifact suppression a pair of gradients of equal strength and duration are employed. The first gradient twists the orientation of the nuclear magnetisation vectors depending upon the location of the vectors in the sample tube. After inverting all the vectors with a 180^o pulse, applying the same gradient again will remove the twist imposed by the first gradient. Only those vectors experiencing a perfect 180^o pulse are refocused for detection.

A similar strategy can be used for heteronuclear experiments. By applying a gradient pulse before polarization transfer and one afterwards one can select only coherences that are transferred between the desired nuclei. The complication is that the gyromagnetic ratios of the desired nuclei must be taken into account. For example, in a ¹H-¹³C HSQC experiment if the first, encoding gradient is applied to the ¹³C magnetisation and the second, decoding gradient to ¹H, then the strengths of the two gradients must have the ratio γ_¹H:γ_¹³C, or roughly 4:1. This is because the rate at which the nuclei precess depends on the gyromagnetic ratio. Applying a gradient to the ¹³C magnetisation induces a twist proportional to the ¹³C gyromagnetic ratio and the strength of the applied gradient. After the polarisation transfer the magnetisation vectors are now precessing with the ¹H gyromagnetic ratio, i.e. four times faster. To undo the twist created by the first gradient the second gradient need only be one fourth the strength of the first gradient.

The figure below shows the first row of two ¹H-¹³C HSQC experiments collected using a 100 mg/ml sample of cholesteryl acetate in deuterated chloroform. The top, blue spectrum was acquired using gradients for coherence selection, while the lower, red one used a phase cycled pulse sequence. All acquisition parameters were the same, except for the receiver gain which was much higher for the blue, gradient selected spectrum. The red spectrum is scaled up by a factor of 32 relative to the blue spectrum.

The spectra are fairly similar except for the intensity. Using gradients excludes artifacts before the signal is digitised so that the entire dynamic range can be used for the desired signals. Without gradients, large artifacts that cancel out during phase cycling have to be digitised along with the desired signals and so the receiver gain must be reduced. This is one of the major advantages of gradient selected experiments. The other main advantage is that the number of scans does not have to be a multiple of the number of steps in the phase cycle. If the sample is concentrated enough then the number of scans can be reduced, enabling experiments to be collected more rapidly.

There are some disadvantages to gradient coherence selection as well. Gradients can only select one coherence pathway at a time, whereas phase cycling can be designed to select more than one. Selecting multiple coherence pathways means greater signal to noise can be obtained in some phase cycled experiments compared to their gradient selected versions, e.g. DQF-COSY. The other disadvantage of gradient selection, and of all experiments that use gradients, is that it is assumed that in the time between the two gradients the nuclei do not move very far, i.e. the rate of diffusion is small. If the nuclei do move significantly between gradients then signal will be lost. To reduce signal loss, pulse sequences are designed so that the time in between gradient pairs is minimised. This loss of signal due to molecular diffusion can actually be taken advantage of. Diffusion Ordered Spectroscopy, or DOSY, uses the loss of signal between a pair of gradients to measure the rate of molecular diffusion, the topic of the next post.