2007
DOI: 10.1016/j.jmr.2007.09.014
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Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction

Abstract: We report progress with an old problem in magnetic resonance -- that of the exponential scaling of simulation complexity with the number of spins. It is demonstrated below that a polynomially scaling algorithm can be obtained (and accurate simulations performed for over 200 coupled spins) if the dimension of the Liouville state space is reduced by excluding unimportant and unpopulated spin states. We found the class of such states to be surprisingly wide. It actually appears that a majority of states in large … Show more

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Cited by 85 publications
(136 citation statements)
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“…Whereas in strong fields, semiclassical approaches allow reliable simulations to be performed at a cost that rises only polynomially with the number of magnetic nuclei, current approaches for weak fields scale exponentially. A reliable method for low-field calculations with polynomial scaling would be a significant development (109). Now that a model system has been shown to respond to Ͻ50-T fields (14), it ought to be possible to explore experimentally as well as theoretically the design constraints imposed on a chemical compass by molecular disorder and motion.…”
Section: Future Workmentioning
confidence: 99%
“…Whereas in strong fields, semiclassical approaches allow reliable simulations to be performed at a cost that rises only polynomially with the number of magnetic nuclei, current approaches for weak fields scale exponentially. A reliable method for low-field calculations with polynomial scaling would be a significant development (109). Now that a model system has been shown to respond to Ͻ50-T fields (14), it ought to be possible to explore experimentally as well as theoretically the design constraints imposed on a chemical compass by molecular disorder and motion.…”
Section: Future Workmentioning
confidence: 99%
“…More details on the spin system and the relaxation theory problem in question are available from our recent paper on the subject 28 . The calculation uses the restricted state space approximation 43,44 with IK-0(4) basis set 25 …”
Section: Discussionmentioning
confidence: 99%
“…Besides the analytical insight which can be helpful to develop improved pulse schemes, the effective Hamiltonian found by analytical means can be determined independently for larger multi-spin systems by calculating and collecting the various terms separately. Combining such an approach with sparse matrix algorithms, as has been done for liquid-state NMR [28], may be useful to perform approximate simulations for larger spin systems in solids than is possible by direct numerical propagation procedures of the time-dependent Hamiltonian.…”
Section: Introductionmentioning
confidence: 99%