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Acquisition scheme for noise-detected two-dimensionalNMR. The general scheme consists of an evolution time t1 sandwiched between two mixing periods τ1 and τ2 and two noise acquisition periods t0 and t2, duringwhich the noise blocks m0(t0) and m2(t2) are acquired in an identical manner. In the spin-noise-HMQC(snHMQC) pulse sequence, used to demonstrate and test the conceptof spin-noise-detected two-dimensional NMR spectra, black rectangularbars represent 90x hard pulses onthe 13C channel. The hatched rectangles represent periodsof heteronuclear decoupling (WALTZ). No pulses are applied on the 1H channel.
where a0(ta) describes the complex-valuedrandom emission amplitude of an emission event (we do not distinguishbetween induced and spontaneous emission in the present context) attime point ta, ΩI isthe I-spin resonance frequency, R2 = 1/T2 or 1/T2* depending on which regime applies, and n0(t0) is the background broad-bandnoise (which may be assumed to be white noise over the observed spectralwidth) amplitude from the instrument or other sources. Heteronucleardecoupling of spin-noise signals works as expected; therefore, thereis no coupling modulation in eq 1. It was shownpreviously that heteronuclear decoupling does not cause spectral interferencewith the hardware used.16
where t0max is themaximum acquisition time, which is equal for the periods t0 and t2 in this experiment,and ΩS is the Larmor frequency of spin S. The transfer coefficient f(τ1, τ2) includes the effects of deviations from ideallymatched delays. RDQ and RZQ are the double- and zero-quantum relaxation rates,respectively, n2(t2) is the background noise amplitude from the instrument orother sources, b represents the contributions tothe signal from the emission events occurring in the period betweenthe two direct acquisition periods t0 and t2, and the integral encompassing c represents contributions to the signal from emission events originatingat time tc within the t2 period. Decoupling of the S spins isswitched on during t0 and t2. Hence, there is no coupling evolution during this period.
Because the repetition interval of spin-noise-detected experimentsis completely independent of the 1H longitudinal relaxationtime T1, the acquisition schemes can berepeated as fast as the hardware allows. Still, the per root-of-transient-numbersignal-to-noise ratio in the spectra obtained is very low comparedto pulse excitation spectra because the separation of the small amountof correlated noise from uncorrelated noise depends on the amountof signal averaging. Several enhancements to the efficiency of theacquisition scheme are currently under investigation. However, oneshould bear in mind that by extrapolating to lower spin numbers, noisepower amplitudes will exceed pulse excitation amplitudes originatingfrom natural polarization.17,24
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