Analytical treatment of proton double-quantum NMR intensity build-up: multi-spin couplings and the flip-flop term

This Dataset comprises the simulation code as well as the calculated raw data and contained in the figures of our journal article in Magnetic Resonance 6 (2025). A preprint is available here: https://doi.org/10.5194/mr-2024-15. For copyright details and licensing we refer to the published article and the publisher. Here is the abstract of the article:

A modified Anderson-Weiss approximation for describing double quantum (DQ) NMR experiments in systems with many I = 1/2 spins is proposed, taking inter-spin flip-flop processes into special consideration. In this way, an analytical result is derived for multi-spin systems for the first time. It is shown that in the initial stages of DQ intensity build-up, the probability of flip-flop processes in DQ experiments is half as large as in analogous Hahn-echo or free-induction-decay experiments. Their influence on the experimentally observed DQ NMR signal becomes dominant at times t > 2.12 T_2^eff , where T_2^eff is the effective spin-spin relaxation time measured by the Hahn echo. Calculations and a comparison with spin-dynamics simulations of small spin systems up to 8 spins reveal a satisfactory agreement.

The two .csv tables contain the numerical data contained in Figs. 1 and 2, separated into the two different spin systems (all-trans alkyl cut-outs and gg-propyl fragment with up to 2 extra spins). Each spin configuration has up to 3 columns, the first being always the DQ build-up curve, the second the FID (both from density matrix simulations) and the third and sometimes the sole column is from the analytical calculation, which can handle no more than 8 spins.

The two simulation codes are dmsim_statmq.cc and analytical_statmq.cc written in (GNU) C++ with the following include files:dynmatrix2+.hxxdynmatrix2+.ihxxdynvector2+.hxxdynvector2+.ihxx

Example for compile.bat, assuming an instance of the MinGW C++ compiler on a Windows PC in C:\MinGQ\ and additional include files in C:\sim\utils\:

set djgpp=C:\MinGW\djgpp.env set path=C:\MinGW\bin;%PATH%gcc -O2 -IC:\sim\utils -c %1.ccgcc %1.o -lm -lstdc++ -o %1.exedel %1.o

Such a compile.bat is called with either of the simulation codes without extension ".cc", e.g.compile dmsim_statmq

The simulation is called with either one of the include files (inCH2alkyl.txt or inCH2propgg.txt), e.g.dmsim_statmq inCH2alkyl.txtrequiring one of the powder averaging angle lists (angles.beta40b or angles.383, the former being for a z-symmetric spin system and the latter being a REPULSION set for full 3D) and possibly a file with Euler angles specifying fast rotational averaging (either rotz or rot20) being present in the same directory. Both lists contain space-seperated Euler angles alpha and beta in radians and a (relative) weighting factor.

We cannot provide a documentation of this home-written code, but provide a commented input file (inCH2propgg.pdf) to highlight the flexibility on the level of the input parameters (spin system and simulation options).