Perturbation Approach for NMR Signals with Infinite-Order Corrections and Its Application to Solid-State MAS INADEQUATE Spectra Exhibiting Auto-Correlation Peaks due to Chemically-Equivalent Spin Pairs: Analogy to Renormalization Theory

Abstract

Abstract A perturbation approach comprehending infinite-order corrections is proposed so that NMR signals may be simulated without approximations. The present theoretical treatments based on Average Hamiltonian Theory put all the perturbative corrections into several tentative variables and eventually replace them by values resulting from experiments, as the renormalization theory does. The Hamiltonian for strongly-coupled two-spin-1/2 systems and the time evolutions of their coherences are analytically expressed using the proposed theory. The double-quantum excitation functions in 29Si solid-state MAS INADEQUATE measurements are observed for a zeolite sample and reproduced using the formula derived from the present theory. Thereby, it is proved to be possible to determine the internal spin interaction parameters including the J couplings between chemically-equivalent nuclei hidden in solution-state NMR spectroscopy, in addition to the parameters reflecting the high-order solid-state effects.