Optimized Excitation and Automation for High-Resolution NMR Using B1-Insensitive Rotation Pulses

Multipurpose Broadband NMR Inversion Sequences

Solution-state 2D correlation experiments increase signal-to-noise, provide improved resolution, and inform about molecular connectivity. NMR experiments are compromised when the nuclei have broad chemical shift ranges that exceed the bandwidth of the experiment. Spectra acquired under these conditions are unphasable and artifact-prone, and peaks may disappear from the spectrum altogether. Existing remedies provide usable spectra only in specific experimental contexts. Here, we introduce a general broadband strategy that leads to a library of high performing NMR experiments. We achieve arbitrary and independent evolution of NMR interactions by only changing delays in our pulse block, letting the block replace inversion elements in any NMR experiment. The experiments improve the experimental bandwidth for both nuclei by an order of magnitude over conventional sequences, covering chemical shift ranges of most molecules, even at ultrahigh field. This library enables robust spectroscopy of molecules such as perfluorinated oils (¹⁹F{¹³C}) and fluorophosphorous compounds in battery electrolytes (¹⁹F{³¹P}).

Spin dynamics during chirped pulses: applications to homonuclear decoupling and broadband excitation

Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems during these pulses plays a vital role, not only in describing the mechanism of techniques, but also in enabling new methodologies. In magnetic resonance spectroscopy, broadband inversion, refocusing, and excitation using these pulses are among the most used applications in NMR, ESR, MRI, and in vivo MRS. In the present survey, a general expression for chirped pulses will be introduced, and some numerical approaches to calculate the spin dynamics during chirped pulses via solutions of the well-known Liouville-von Neumann equation and the lesser-explored Wei-Norman Lie algebra along with comprehensive examples are presented. In both cases, spin state trajectories are calculated using the solution of differential equations. Additionally, applications of the proposed methods to study the spin dynamics during the PSYCHE pulse element for broadband homonuclear decoupling and the CHORUS sequence for broadband excitation will be presented.

Robust INEPT and refocused INEPT transfer with compensation of a wide range of couplings, offsets, and B1-field inhomogeneities (COB3)

Following the two-step optimization procedure previously introduced with the COB-INEPT (Ehni and Luy, 2012), a corresponding inphase-to-antiphase transfer element with close to optimal transfer efficiencies over a coupling range comprising approximately J-6J has been derived. The hard pulse sequence length is only 5.5 ms for coupling constants within 125-750 Hz. Robustness with respect to an offset range of 37.5 kHz on carbon (corresponding to 250 ppm on a 600 MHz spectrometer) and 10 kHz on protons (16.6 ppm at 600 MHz) is achieved with corresponding BUBI and BURBOP broadband pulses. As the sequence achieves a three times higher upper limit of J-compensation compared to the COB-INEPT, we name the transfer element COB3-INEPT. Next to the description of optimization and pulse sequence details, the performance of the resulting element is demonstrated on a test sample and partially aligned sample with actual total couplings in the range of 134 Hz⩽(1)TCH⩽391 Hz. The sequence can also be used for inphase-to-antiphase transfer starting from carbon, where the upper limit of J-compensation is 6J for CH-groups, 3J for CH2-groups, and slightly less than 2J for CH3. Theoretical transfers and experimental verification for the different multiplicities in an refocused INEPT are given.

HCNMBC--a pulse sequence for H-(C)-N Multiple Bond Correlations at natural isotopic abundance

We propose a pulse sequence, HCNMBC for multiple-bond H-(C)-N correlation experiments via one-bond (1)J(C,H) and one- or multiple bond (n)J(N,C) coupling constants (typically n=1-3) at the natural isotopic abundance. A new adiabatic refocussing sequence is introduced to provide accurate and robust refocussing of both chemical shift and J-evolution over wide ranges of C-13 and N-15 frequencies. It is demonstrated that the proposed pulse sequence provides high quality spectra even for sub-milligram samples. We show that when a 1.7 mm cryoprobe is available as little as 10 μg of glycine in D2O is sufficient to obtain the HCNMBC spectrum in ca. 12 h. The preliminary results indicate that the pulse sequence has a great potential in the structure determination of nitrogen heterocycles especially in cases where synthesis produces regioisomers.

A systematic approach for optimizing the robustness of pulse sequence elements with respect to couplings, offsets, and B1-field inhomogeneities (COB)

Robust experiments that cover a wide range of chemical shift offsets and J-couplings are highly desirable for a multitude of applications in small molecule NMR spectroscopy. Many attempts to improve individual aspects of the robustness of pulse sequence elements based on rational and numerical design have been reported, but a general optimization strategy to cover all necessary aspects for a fully robust sequence is still lacking. In this article, a viable optimization strategy is introduced that covers a defined range of couplings, offsets, and B(1)-field inhomogeneities (COB) in a time-optimal way. Individual components of the optimization strategy can be optimized in any adequate way. As an example for the COB approach, we present the (1)H -(13)C-COB-INEPT with transfer of approximately 99% over the full carbon and proton bandwidth and (1)J(CH) -couplings in the range of 120-250 Hz, which have been optimized using efficient algorithms derived from optimal control theory. The theoretical performance is demonstrated in a number of corresponding COB-HSQC experiments.

Implementation equations for HS n RF pulses

Implementation equations for the family of stretched hyperbolic secant (HS(n)) pulses are derived in the linear adiabatic range for inversion of spins. These master equations provide convenience relations for relating the peak amplitude RF(max) of the pulse to the frequency sweep (bwdth) range of the pulse and its duration T(p). The bandwidth of the pulse can also be related to the effective coverage (bw(eff)) of the pulse to a defined or chosen spectral region. The choice of pulse determined by the use of these derived expressions guarantees uniform inversion to a prescribed efficiency across the selected spectral region. The performance of HS(n) pulses in determining the cut-off region between spectral regions was also examined. It is found that beyond a unique T(p)bwdth product no additional gain may be obtained by extending pulse durations for a chosen bwdth of pulse. An example of practical implementation of the inversion pulses is presented for adiabatic decoupling using HS(7) and HS(8) pulses. It is shown that despite added B(1) inhomogeneity in the form of additional amplifier power to 400% from optimal, these pulses can still yield reproducible decoupled spectra.

Doubly compensated multiplicity-edited HSQC experiments utilizing broadband inversion pulses

We propose a family of doubly compensated multiplicity-edited heteronuclear single quantum coherence (HSQC) pulse sequences. The key difference between our proposed sequences and the compensation of refocusing inefficiency with synchronized inversion sweeps (CRISIS)-HSQC experiments they are based on is that the conventional rectangular 180 degrees pulses on the proton channel in the latter have been replaced by the computer-optimized broadband inversion pulses (BIPs) with superior inversion performance as well as much improved tolerance to B(1) field inhomogeneity. Moreover, all adiabatic carbon 180 degrees pulses during the INEPT and reverse-INEPT periods in the CRISIS-HSQC sequences have also been replaced with the much shorter BIPs, while the adiabatic sweeps during the heteronuclear spin echo for multiplicity editing are kept in place in order to maintain the advantage of the CRISIS feature of the original sequences, namely J-independent refocusing of the one-bond (1)H--(13)C coupling constants. These modifications have also been implemented to the preservation of equivalent pathways (PEP)-HSQC experiments. We demonstrate through a detailed comparison that replacing the proton 180 degrees pulses with the BIPs provide additional sensitivity gain that can be mainly attributed to the improved tolerance to B(1) field inhomogeneity of the BIPs. The proposed sequences can be easily adapted for (19)F--(13)C correlations.

The CLIP/CLAP-HSQC: pure absorptive spectra for the measurement of one-bond couplings

Heteronuclear residual dipolar one-bond couplings of organic molecules at natural abundance are most easily measured using t2 coupled HSQC spectra. However, inevitably mismatched transfer delays result in phase distortions due to residual dispersive antiphase coherences in such experiments. In this article, slightly modified t2 coupled HSQC experiments with clean inphase (CLIP) multiplets are introduced which also reduce the intensities of undesired long-range cross peaks. With the corresponding antiphase (CLAP) experiment, situations where alpha and beta components overlap can be resolved for all multiplicities in an IPAP manner. A comparison of the experiments using hard pulses and shaped broadband excitation and inversion pulses on the heteronucleus is given and potential spectral artefacts are discussed in detail.

Frequency-swept HSQC sequences for high-throughput NMR analysis

This article describes new versions of the DEPT phase-edited heteronuclear single quantum correlation (HSQC) pulse sequence with sensitivity enhancement. The sequences incorporate frequency-swept carbon and proton pulses. The new experiments are inherently robust, well-suited for a high-throughput setting in which sample-to-sample variations may be ignored. The observed signal has the obvious benefit of sensitivity enhancement resulting from the preservation of two magnetization transfer pathways. The two pathways are maintained even in the version of the sequence in which all pulses are frequency-swept. There is an additional signal gain of roughly 10% that derives from the use of both proton and carbon frequency-swept pulses. Furthermore, the sequences use J compensation to provide optimal signal over a range of heteronuclear coupling constants. We demonstrate that the new sequences offer good sensitivity and perform well even when the NMR probe is deliberately mistuned.

Frequency-swept HMQC sequences for high-throughput NMR analysis

We describe here new versions of the DEPT phase-encoded HMQC experiment that offer robust performance and improved sensitivity. The new sequences rely on frequency-swept proton and carbon pulses to minimize signal losses from miscalibrated pulses while providing 'J compensation' to optimize the signal strength over a range of heteronuclear coupling constants. By including both proton and carbon-swept pulses, the new sequences also offer an additional signal gain of roughly 10% over well-calibrated hard-pulse experiments. The new sequences also demonstrate that one can construct a sequence that incorporates both 90 degrees and 180 degrees frequency-swept pulses. Although individual pulses in the sequence cause severe phase roll, the phase roll can be eliminated by the proper choice of pulse lengths and sweep directions.

Compensated adiabatic inversion pulses: broadband INEPT and HSQC

When adiabatic fast passage is used to flip nuclear spins, sites with different chemical shifts are inverted at different times, causing refocusing errors. By mapping the phase evolution diagrams, we show that these effects can be accurately compensated with matched pairs of adiabatic pulses, either opposed or in the same sense, depending on the application. Applied to well-known heteronuclear polarization transfer experiments such as INEPT and HSQC, the requisite evolution of J-vectors is achieved irrespective of chemical shift or the duration of the adiabatic sweeps. By replacing conventional 180 degrees pulses, these new adiabatic sequences offer an order of magnitude improvement in effective bandwidth for the X-spins. Alternatively the experiments can be carried out with significantly reduced radiofrequency power. One- and two-dimensional spectra of (13)C in 13-cis-retinal at 600MHz have been used to demonstrate these advantages.

Optimal control design of constant amplitude phase-modulated pulses: application to calibration-free broadband excitation

An optimal control algorithm for generating purely phase-modulated pulses is derived. The methodology is applied to obtain broadband excitation with unprecedented tolerance to RF inhomogeneity. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-25 kHz for constant RF amplitude anywhere in the range 10-20 kHz, with a pulse length of 1 ms. Simulations transform Iz to greater than 0.99 Ix over the targetted ranges of resonance offset and RF variability. Phase deviations in the final magnetization are less than 2-3 degrees over almost the entire range, with sporadic deviations of 6-9 degrees at a few offsets for the lowest RF (10 kHz) in the optimized range. Experimental performance of the new pulse is in excellent agreement with the simulations, and the robustness of the excitation pulse and a derived refocusing pulse are demonstrated by insertion into conventional HSQC and HMBC-type experiments.

Universal equations for linear adiabatic pulses and characterization of partial adiabaticity

A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RF(max)) required for a preselected degree of inversion across a chosen effective bandwidth (bw(eff)) and for a chosen pulse length (T(p)). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bw(eff) being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bw(eff) is < or =bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, iota(bw), at the boundaries of bw(eff), two basic linear equations are found for both types of pulse and these are of the form (RF(max)T(p))(2)=m(1)T(p)bwdth+c(1) and T(p)bwdth=m(3)T(p)bw(eff)+c(3). The different behavior of the two pulses is expressed as different dependencies of the slopes m(n) and intercepts c(n) on iota(bw) and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of "linear adiabaticity." At low values of T(p)bwdth or T(p)bw(eff) the linear equations no longer apply, defining a region of "partial adiabaticity." Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RF(max) or T(p) but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RF(max) or T(p) efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of T(p)bw(eff), and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RF(max)T(p))(2) or (Total Power) T(p) versus T(p)bw(eff).

The return of the frequency sweep: designing adiabatic pulses for contemporary NMR

Frequency-modulated (FM) pulses that function according to adiabatic principles are becoming increasingly popular in many areas of NMR. Often adiabatic pulses can extend experimental capabilities and minimize annoying experimental imperfections. Here, adiabatic principles and some of the current methods used to create these pulses are considered. The classical adiabatic rapid passage, which is a fundamental element upon which all adiabatic pulses and sequences are based, is analyzed using vector models in different rotating frames of reference. Two methods to optimize adiabaticity are described, and ways to tailor modulation functions to best satisfy specific experimental needs are demonstrated. Finally, adiabatic plane rotation pulses and frequency-selective multiple spin-echo sequences are considered.

Asymmetric adiabatic pulses for NH selection

Many types of NMR experiments demand the use of frequency-selective pulses to invert magnetization within discrete frequency limits. For certain experiments, only one side of the inversion band must be sharply demarcated, in which case this transition bandwidth can be narrowed when using an asymmetric adiabatic full passage. In the present study, a highly efficient asymmetric adiabatic full passage was created from a combination of two adiabatic half passages which used different modulation functions (HS12 and tanh/tan). Each adiabatic half passage occupied a different amount of time in the total pulse and performed one-half of the inversion. On one side, HS12 produced a sharp transition between inverted and noninverted states which was approximately 2.5 times narrower than the transition bandwidth afforded by a symmetric hyperbolic secant pulse of equal length. On the other side of the narrow transition band, the tanh/tan pulse achieved broadband inversion. These asymmetric pulses were applied to select NH groups immediately adjacent to the water signal in water-flip-back HSQC experiments using a double spin echo for the reverse INEPT step.

New approaches to structure determination by NMR spectroscopy

New strategies have recently been developed for studying biological macromolecules of large size (beyond 100 kDa) in order to both improve the quality of the structures and make structure determination more efficient. This has been achieved by utilizing cross-correlation effects and novel labeling strategies, and developing novel NMR spectroscopy experiments.

Adiabatic pulses

Adiabatic pulses are sometimes considered to be mysterious and exotic entities which are difficult to understand, complex to generate and impractical to implement. This work is an attempt to bring familiarity and to fulfill the preliminary needs of anyone interested in learning more about this subject. The response of magnetization to stimuli produced by adiabatic pulses is analyzed using vector representations in a frequency modulated rotating frame. The first section deals with basic principles of amplitude and frequency modulated pulses and a vector representation in a second rotating frame is used to explain how the adiabatic condition can be satisfied. The subsequent section explains the principles of offset independent adiabaticity. These principles are then used to design optimal functions for the amplitude, frequency, and magnetic field gradient modulations for adiabatic inversion pulses. The last section considers some practical aspects for those who want to develop methodologies involving adiabatic pulses.