Symmetry-based Sequences for Singlet-Triplet Excitation (PulsePol)

In 2016 a Master’s student at Ulm’s Institute of Theoretical Physics, by the name of Benedikt Tratzmiller, described a simple yet powerful control sequence for optical DNP in diamond NV centres. The pulse sequence had the attractive name of PulsePol. The sequence made further appearances in an excellent paper and Tratzmiller’s PhD thesis.

Some time ago I listened to an inspiring online talk by Nino Wili (who quite convincingly spoke about cross-pollination between different fields of magnetic resonance) and we got to talking. After a few discussions/simulations eventually we realized that the PulsePol sequence could be applied to singlet NMR, and that application forms the basis of our paper, which chose to explain PulsePol using the language of symmetry-based sequence design borrowed from solid-state NMR.

PulsePol has some advantages over the M2S sequence, which was essentially a “default” option in NMR groups for generating nuclear singlet order (alongside variations of the arguably more elegant SLIC method invented by DeVience, Walsworth, and Rosen). These advantages include superior robustness (PulsePol is generally less sensitive to rf errors than M2S), simplicity, and even a small time advantage (PulsePol is ~1.21x faster than M2S). One should expect PulsePol to replace M2S in the future.

Here I provide some ready-to-use pulse programs, written for Bruker TopSpin, that the NMR community may use to actually implement the PulsePol sequence.

The pulse programs have a number of features:

1. The so-called “riffling” 180 phase shift modification on the central 180° pulses, which improves robustness against pulse strength (Rabi frequency) and resonance offset (detuning) errors.
2. A T₀₀ gradient filter for selective filtration of singlet order, and a z-filter to select longitudinal magnetization.
3. A singlet order destruction (SOD) element before the relaxation delay to purge residual singlet order, which may interfere with experiments.
4. Wimperis’ BB1 composite pulse (in the symmetrized implementation) replacing the pulses in the filters, improving robustness against pulse strength errors.

The pulse sequences can be downloaded here:

1. R4₃¹
2. R8₇³
3. R4₁¹
4. R6₁²
5. R8₁³
6. R10₁⁴

I also attach a quick reference table which provides the 2 experimental parameters that are actually relevant for optimal excitation of singlet order, because it has always annoyed me that the first one was not explicitly stated in our somewhat cryptic original paper:

Note that I have given the total duration of the PulsePol in terms of the SLIC duration 1/(√2 Δ) – which is the fastest currently known way to fully excite singlet order from longitudinal magnetization. The minimum of the total duration is around n = 3, N = 4, where the total evolution is ~1.38x longer than the SLIC sequence. The (fixed) total duration of the M2S sequence (~1.67x longer than SLIC) is given for comparison.

The “default” sequence for most people working with nearly equivalent spin-1/2 pairs would be R4₃¹ – or possibly R8₇³, which is only ~3.5% slower than R4₃¹ but provides improved robustness against resonance offset/detuning errors. However, in the common case where a spin system is at intermediate inequivalence (the chemical shift has a comparable magnitude with respect to the J coupling), one can benefit from the sequences in the series R4₁¹, R6₁², R8₁³, R10₁⁴… which perform over an increasingly wider range of inequivalence angles at the expense of being increasingly slower, as I discussed in the appendix to this paper.