2014
DOI: 10.1016/j.jmr.2014.04.002
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Quantum mechanical NMR simulation algorithm for protein-size spin systems

Abstract: Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch-Redfield-Wangsness theory) on isotopically enriched human u… Show more

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Cited by 36 publications
(59 citation statements)
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“…In particular, SPINACH [101] supports all forms of magnetic resonance spectroscopy under the same roof, implements sophisticated spin relaxation theories as well as most mainstream optimal control algorithms that are presently used in magnetic resonance spectroscopy: GRAPE [92], GRAPE-BFGS [93,94], Krotov [96] and Krotov-BFGS [99]. Another advantage of SPINACH is the availability of polynomially scaling spin dynamics simulation algorithms that make previously intractable NMR and EPR simulation (and therefore control) problems accessible [121,328]. In the solidstate NMR community, the SIMPSON software package (SIMulation Program for SOlid state Nuclear magnetic resonance) has been the most extensively used generalpurpose software.…”
Section: State Of the Artmentioning
confidence: 99%
“…In particular, SPINACH [101] supports all forms of magnetic resonance spectroscopy under the same roof, implements sophisticated spin relaxation theories as well as most mainstream optimal control algorithms that are presently used in magnetic resonance spectroscopy: GRAPE [92], GRAPE-BFGS [93,94], Krotov [96] and Krotov-BFGS [99]. Another advantage of SPINACH is the availability of polynomially scaling spin dynamics simulation algorithms that make previously intractable NMR and EPR simulation (and therefore control) problems accessible [121,328]. In the solidstate NMR community, the SIMPSON software package (SIMulation Program for SOlid state Nuclear magnetic resonance) has been the most extensively used generalpurpose software.…”
Section: State Of the Artmentioning
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%
“…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.…”
Section: Exponentials Of Auxiliary Matricesmentioning
confidence: 99%
“…44 We use Krylov propagation 45 for short events and shaped pulses, and scaling and squaring matrix exponential propagation 46 for extended evolution periods. The primary technical problem is the generation of sufficiently small and accurate matrix representations for all operators involved, 33,47 which is the subject of the next section.…”
Section: Fokker-planck Formalism For Mri and Spatially Encoded Nmrmentioning
confidence: 99%
“…Larger spin systems are best handled with the restricted state space approximation; 49 technical details of the spin operator generation process in restricted state spaces are given in our recent paper. 47 The most straightforward practical way of generating matrix representations for spatial derivative operators occurring in eqn (3) and (4) is to discretise the spatial coordinates on finite grids. For periodic boundary conditions, Fourier differentiation matrices on uniform grids 50 are convenient:…”
Section: Numerical Implementationmentioning
confidence: 99%