Multipole NMR

Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software

“…Steps 1 and 2 are concerned with the preparation of the Hamiltonian, which may vary from one spin system to another, and generally follow the irreducible spherical tensor formalism pioneered by Freed [19,20] and Sanctuary [21][22][23][24][25]. Steps 3 and 4 then detail the automated BRW theory processing steps.…”

“…Consequently, the rotational modulation of these interactions may be treated in a very uniform and general way using the irreducible spherical tensor operator formalism [19][20][21][22][23][24][25].…”

Multiple quantum NMR spectroscopy onI> 1 nuclei in anisotropic systems

“…Both static couplings may be spatially inhomogeneous. We describe the dynamic state of the spin system in terms of the state multipole components Pqk(t) of multipole rank k = 1,..., 21 and quantum order q = -k,..., k [40][41][42][43][44][45], which are the coefficients in the expansion of the spin density operator in the complete orthonormal basis of irreducible spherical spin tensor operators spanning the spin Liouville space.…”

“…For the spin dynamics calculation we use the irreducible spin tensor operator (multipole) formalism [40][41][42][43][44][45], with our previous notation [23][24][25] suitably generalized to handle MQC evolution. Though most previous MQ spin dynamics calculations were performed in other bases [3,36,37], the multipole basis is probably the most convenient one for isolated quadrupolar nuclei and nonselective r.f.…”

Isotropic filtering using polyhedral phase cycles: Application to singlet state NMR

“…The natural language for a complete rotational classification is that of irreducible spherical tensor operators (ISTOs), since these span the irreducible representations of the full rotation group [10,11]. Irreducible spherical tensor operators are described by two quantum numbers, called the rank, denoted k, and the component index l, which takes 2k þ 1 values l 2 fÀk; Àk þ 1; .…”