Comparison of various NMR methods for the indirect detection of nitrogen-14 nuclei via protons in solids

We present an experimental comparison of several through-space Hetero-nuclear Multiple-Quantum Correlation experiments, which allow the indirect observation of homo-nuclear single- (SQ) or double-quantum (DQ) ¹⁴N coherences via spy ¹H nuclei. These ¹H-{¹⁴N} D-HMQC sequences differ not only by the order of ¹⁴N coherences evolving during the indirect evolution, t1, but also by the radio-frequency (rf) scheme used to excite and reconvert these coherences under Magic-Angle Spinning (MAS). Here, the SQ coherences are created by the application of center-band frequency-selective pulses, i.e. long and low-power rectangular pulses at the ¹⁴N Larmor frequency, ν0(¹⁴N), whereas the DQ coherences are excited and reconverted using rf irradiation either at ν0(¹⁴N) or at the ¹⁴N overtone frequency, 2ν0(¹⁴N). The overtone excitation is achieved either by constant frequency rectangular pulses or by frequency-swept pulses, specifically Wide-band, Uniform-Rate, and Smooth-Truncation (WURST) pulse shapes. The present article compares the performances of four different ¹H-{¹⁴N} D-HMQC sequences, including those with ¹⁴N rectangular pulses at ν0(¹⁴N) for the indirect detection of homo-nuclear (i) ¹⁴N SQ or (ii) DQ coherences, as well as their overtone variants using (iii) rectangular or (iv) WURST pulses. The compared properties include: (i) the sensitivity, (ii) the spectral resolution in the ¹⁴N dimension, (iii) the rf requirements (power and pulse length), as well as the robustness to (iv) rf offset and (v) MAS frequency instabilities. Such experimental comparisons are carried out for γ-glycine and l-histidine.HCl monohydrate, which contain ¹⁴N sites subject to moderate quadrupole interactions. We demonstrate that the optimum choice of the ¹H-{¹⁴N} D-HMQC method depends on the experimental goal. When the sensitivity and/or the robustness to offset are the major concerns, the D-HMQC sequence allowing the indirect detection of ¹⁴N SQ coherences should be employed. Conversely, when the highest resolution and/or adjusted indirect spectral width are needed, overtone experiments are the method of choice. The overtone scheme using WURST pulses results in broader excitation bandwidths than that using rectangular pulses, at the expense of reduced sensitivity. Numerically exact simulations also show that the sensitivity of the overtone ¹H-{¹⁴N} D-HMQC experiment increases for larger quadrupole interactions.

The parametric making of geometry: the platonic solids

Geometry is a source of inspiration in the design and making of the manmade world. Computing techniques provide tools to explore complex forms: the research question is how computational tool can be systemised to assist with the translation of geometric concepts into physical objects. The purpose is to describe computational/manufacturing methods for creating digital models and physical objects from regular geometric configurations. The methods are based on parametric design, assisting from ideation to the generation of digital models with material specifications – using the five regular convex polyhedra as a case study. The results are comprised of digital models used for prototyping with 3D printing technologies and hybrid fabrication processes: the products are built geometric shapes ranging from body ornaments to sculptures. These procedures can be extended to generate designs based on irregular geometric shapes. Parametric-based methods are recommended in the digital modeling and fabrication of any geometric form.