Spinach – A software library for simulation of spin dynamics in large spin systems

Systematics of BX3 and BX2+ Complexes (X = F, Cl, Br, I) with Neutral Diphosphine and Diarsine Ligands

“…To test this interpretation the 31 P NMR spectrum was simulated using Spinach. 28 The predicted spectrum with JAX = JA'X' = 160 Hz, JAA' = 30 Hz (to match the experimentally observed coupling constants) and all other couplings at zero can be seen in Fig. 3 NMR spectrum ( Fig.…”

“…The phosphine complexes all show very large high frequency shifts relative to free ligand in their 31 P{ 1 H} NMR spectra, which are much larger in magnitude than those observed in the corresponding AlX3 systems. 28 In the 11 B NMR spectra 1 JBP decreases as the atomic number of the halogen increases, a trend that has been reported for a number of neutral phosphine adducts of BX3. 20,25,26 were found to be more prone to hydrolysis in solution.…”

On the accuracy of the state space restriction approximation for spin dynamics simulations

“…This estimate agrees perfectly with Figure 4 (which is discussed in detail in Section 3) and the empirical observations made when running the Spinach library 10 . In the case of the systems studied by Suter et.…”

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

“…For a publicly available simulation package that must preserve sparsity (matrix dimensions for large NMR systems are in the millions 25 ) and run reliably in a large variety of settings 14,19 , these considerations are decisive.…”

“…In this communication we propose a solution to this problem, based on the observation that matrix exponentiation, when used judiciously, does not require factorizations and preserves spin operator sparsity 13,14 and on the auxiliary matrix technique [15][16][17] for the evaluation of the integrals given in * An "expensive" matrix operation in this context is defined as requiring computational or storage resources that grow faster than quadratically with the dimension of the matrix; a "cheap" matrix operation is defined as the one with approximately linear resource requirements. Equation (1).…”