Appendices A and B with mathematical derivations as referred to in the text (10 pages)

ARTICLE INFORMATION

EPAPS Document No.: E-JCPSA6-129-617827

Journal: J. Chem. Phys. 129, 044505 (2008)

All Authors: Stefan Kirsch, William E. Hull

Title: Quantitative time- and frequency-domain analysis of the two-pulse
CRAZED NMR experiment; theoretical and experimental aspects, time-zero
data truncation artefacts, and radiation damping

Deposit Information

Description: Appendices A and B with mathematical derivations as referred
to in the text (10 pages)

Total No. of Files: 2

File Names: Readme.txt, 617827JCP appendices.pdf

File Types: .txt and .pdf

Contact:
Dr. William E. Hull (PhD)
Core Facility: Molecular Structure Analysis (W160)
German Cancer Research Center (DKFZ)
Im Neuenheimer Feld 280
Postfach 101949
D-69009 Heidelberg

Fax: +49-6221-42-4554
Tel: +49-6221-42-4515 / -4544 / -4542

Quantitative time- and frequency-domain analysis of the two-pulse COSY revamped by asymmetric Z-gradient echo detection NMR experiment: Theoretical an

Stefan Kirsch and William E. Hull
J. Chem. Phys. 129, 044505 (2008)

The two-pulse COSY revamped by asymmetric Z-gradient echo detection (CRAZED) NMR experiment has the basic form 90°−G−t_rec−−nG−t_rec-FID, with a phase-encoding gradient pulse G of length applied during the evolution time for transverse magnetization, readout pulse , rephasing gradient nG, and recovery time t_rec prior to acquisition of the free-induction decay. Based on the classical treatment of the spatially modulated dipolar demagnetizing field and without invoking intermolecular multiple-quantum coherence, a new formulation of the first-order approximation for the theoretical solution of the nonlinear Bloch equations has been developed. The nth-order CRAZED signal can be expressed as a simple product of a scaling function C_n(,) and a signal amplitude function A_n(t), where the domain t begins immediately after the pulse. Using a single-quantum coherence model, a generalized rf phase shift function has also been developed, which explains all known phase behavior, including nth-order echo selection by phase cycling. Details of the derivations are provided in two appendices as supplementary material. For n>1, A_n(t) increases from zero to a maximum value at t=t_max before decaying and can be expressed as a series of n exponential decays with antisymmetric binomial coefficients. Fourier transform gives an antisymmetric binomial series of Lorentzians, where the composite lineshape exhibits negative wings, zero integral, and a linewidth that decreases with n. Analytical functions are presented for t_max and A_n(t_max) and for estimating the maximal percent error incurred for A_n(t_max) when using the first-order model. The preacquisition delay =+t_rec results in the loss of the data points for t=0 to . Conventional Fourier transformation produces time-zero truncation artifacts (reduced negative wing amplitude, nonzero integral, and reduced effective T2 ^*" align="middle" border="0">), which can be avoided by time-domain fitting after right shifting the data by . A doped water sample (9.93 mM NiSO₄, 10 mm sample tube) was used to study the behavior of the CRAZED signal for n=1–4 with =90° at 7 T (300 MHz ¹H frequency) as a function of , with and without radiation damping. Pulse-acquire experiments were used to determine the relaxation times (T₁=61.8 ms and T2 ^*" align="middle" border="0">=29.7 ms), and the radiation damping time constant T_rd=18.5 ms. When experimental CRAZED data sets were right shifted by , excellent least-squares fits to the first-order model function were obtained for all n using a minimal set of free variables. Without radiation damping the fitted T2 ^*" align="middle" border="0">values (29.7–30.2 ms) agreed with the reference value. With radiation damping the fitted effective T2 ^*" align="middle" border="0"> values were 16.2 ms for a 90° pulse-acquire experiment and 18.8–20.2 ms for the CRAZED experiment with n=1–4 and signal amplitudes spanning a range of 10⁵. ©2008 American Institute of Physics