The density matrix theory of triple‐quantum filtered COSY (TQF‐COSY) NMR experiments applied to an AX system of spins S=1: An example of passive coupling in two‐dimensional NMR spectroscopy

Abstract

The 2D Triple-Quantum Filtered ( TQF ) COSY NMR spectrum of an AX spin system of spin-1 has been calculated by numerical density matrix calculations. The basic phase cycle to achieve triple quantum filtration and phase-modulation of the signal during t 1 consists of 12 steps. If nuclei A and X are not coupled, the calculations predict no peaks at all. If nuclei A and X are coupled and the multiplets are not resolved in the conventional 1D spectrum, two diagonal peaks are detected. If nuclei A and X are coupled and the multiplets are resolved in the conventional 1D spectrum, only diagonal and near-diagonal peaks are detected. One does not observe cross peaks if nuclei A and X are coupled because the coupling is passive. It is believed that the calculations presented here will be needed to calculate the Exclusive Correlation Spectroscopy (E. COSY ) of an AX system of spins S=1. K E Y W O R D SAX spin system , NMR , passive coupling , quadrupolar nuclei , spin-1 , TQF -COSY | INTRODUCTIONThe standard homonuclear COSY experiment 1 is probably the most popular two-dimensional (2D) NMR experiment and has been used for the detection of scalar coupling interaction in spin systems of NMR active quadrupolar nuclei such as 11 B, 2-10 51 V, 11 6 Li, 12-14 7 Li, 13,14 59 Co 15-17 and 2 H. 18From a COSY experiment it is possible to assign signals to individual substituents in a molecular structure and using the coupling constants the coupling interaction can be interpreted to describe the whole molecular structure. However, the COSY experiment does have some disadvantages. The magnitude mode of the standard sequence causes relatively broad cross and diagonal peaks making the determination of coupling constants impossible. In addition the intensive diagonal peaks can overlap with the cross peaks arising between signals with a small chemical shift difference. Also, it has been shown recently experimentally 17 that it is not always possible to observe cross peaks when dealing with quadrupolar nuclei relaxing usually very quickly and relatively small coupling constants. Different variants of the COSY NMR experiment have been developed to overcome some of these problems. The 2D experiment can for instance include a double quantum filter (DQF) or even a triple quantum filter (TQF) which reduces the intensity of the diagonal peaks such that cross peaks very near to the spectrum diagonal are better resolved. By contrast to what happen with the conventional COSY experiment, it is also sometimes possible to observe cross peaks with a DQF-COSY experiment when dealing with quadrupolar nuclei relaxing usually very quickly and relatively small coupling constants. 17,19 The density matrix theories of the COSY experiment for an AX system of spin-1/2 20 and for an AX or AMX system 2 | KEMPGENS AND PINCHUCK of any spin number 21 have been described elsewhere. The density matrix theory of the DQF-COSY NMR experiment for an AX or AMX system of any spin number has also been described elsewhere. 22,23 It is the purpose of this paper to desc...