Coherence Pathways with Cartesian Product Operators. The C3PO Method

Abstract

Abstract The product-operator formalism using the Cartesian operator basis was modified, and the notation of Ix(φ) = Ixcos φ + Iysin φ and Iy(φ) = Iycos φ − Ixsin φ simplified the product-operator description of uncoupled or weakly coupled spins in multipulse sequences with arbitrary pulse phases and chemical-shift precessions. The compact Cartesian coordinate product-operator (C3PO) formalism is more compact than any other proposed basis set, easily provides complete coherence-pathway information, and provides better visualization than the original Cartesian basis set. Formulas for evolution under radiofrequency pulses, chemical-shift precession with spin-spin coupling, and multiple-quantum coherences are provided for weakly coupled IS and I3S spin systems (I = S = 1 2 ) and for a strongly coupled IS (AB) spin system. Formulas are also provided for a spin coupled to an S = 1 spin. The C3PO formalism is compared with the spherical basis set, and examples are provided for STEAM-localized spectroscopy, COSY, and a strongly coupled AB spin system.