Dual Lanczos simulation of dynamic nuclear magnetic resonance spectra for systems with many spins or exchange sites

Journal of Chemical Physics

Volumn 113, Issue 8, 2000, Pages 3270-3281

  Dumont, Randall S ^a   Hazendonk, Paul ^a   Bain, Alex ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON SPIN RESONANCE SPECTROSCOPY; FOURIER TRANSFORMS; MAGNETIZATION; NUMERICAL METHODS;

CHEBYCHEV POLYNOMIAL APPROXIMATION; LANCZOS ITERATIONS; SPIN DYNAMICS IDENTITY OPERATOR;

NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY;

EID: 0034702669     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1287327     Document Type: Article

References (38)

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23. Two groups of spins are treated as different type if all couplings between the constituent spins are weak - i.e., small compared with the chemical shift difference.
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32. Rate broadening - as a fullwidth at half maximum - is simply given by k when k is small compared with Δω. Division by 2π is required when the spectrum is given as a function of ν in Hz.
33. ω= 8192 frequencies for mutual exchange systems with 1 Hz line broadening, the direct spectrum portion of the computation constitutes a significant fraction of the total CPU time only for systems with fewer than nine spins. Since the simulation of a smaller spin system spectrum is reasonably fast, the elimi-nation of overhead in this part of the computation is not critical to the usefulness of the methodology.
34. T.
35. 2n√πn. Compare this with Eq. (1) which gives the size of the largest sub-block of this Liouvillian. The sub-block is thus a factor, 2/√πn, smaller. This factor exactly affords an additional spin - with the same computation time - when n ≅ 20. Note that the asymptotic form given here for the number of coherence level 1 transitions differs from that given in Sec. II of Ref. 1. The formula given there [the unlabeled equation after Eq. (14)] is incorrect. It is based on an inappropriately simplified Sterling formula. The conclusions of Ref. 1, based on this formula, are nevertheless still valid.
36. Eight spins is beyond the scope of the Householder method, implemented on our computer, due to the requirement of about 6 days of CPU time - this is not viable in a shared departmental facility. The memory requirements of the Householder method are not out of scope until nine spins are considered - more than 4 gigabytes random access memory is needed in this case.
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