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Fast simulation of dynamic two-dimensional nuclear magnetic resonance spectra for systems with many spins or exchange sites
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2.R. S. Dumont, P. Hazendonk, and A. D. Bain, J. Chem. Phys. (in press).
3.P. Hazendonk, A. D. Bain, H. Grondey, P. H. M. Harrison, and R. S. Dumont, J. Magn. Reson. (in press).
4.See, for example, S. A. Smith, T. O. Levante, B. H. Meier, and R. R. Ernst, J. Magn. Reson., Ser. A 106, 75 (1994).
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8.Sparse storage of a vector means storage of only the non-negligible vector components and their indices.
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9.a method based on magic-angle spinning is presented in M. Ernst, A. P. M. Kentgens, and B. H. Meier, J. Magn. Reson., Ser. A 138, 66 (1999).
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11.The Chebychev method provides efficient computation of any function of a Hermitian operator—e.g., the complex exponential of the Liouvillian in the case of unitary time evolution.
12.See, e.g., C. F. Gerald, Applied Numerical Analysis, 2nd ed. (Addison-Wesley, Reading, MA, 1978), p. 19.
13.Analysis of terms in the Taylor and Chebychev series for reveals similar convergence properties. In particular, in case of large the number of iterations to converge to machine accuracy is near and for nested applies and Chebychev approximation, respectively.
14.The block diagonal form of the Liouvillian results from the block diagonal form of the Hamiltonian which arises because of the large Zeeman term. The latter gives rise to in an average Hamiltonian which conserves total z magnetization. See R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Clarendon, Oxford, U.K., 1987), p. 81.
15.J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalues Computations (Birkhäuser, Boston, MA 1985).
16.Soft pulses can be treated via time evolution broken into a series of short time steps, each followed by the corresponding fraction of the total pulse implemented as a hard pulse. Such a treatment requires convergence with respect to time increment. This approach should be well suited to most soft pulses which generally do not span a long time—simulations should converge in few steps.
17.See, e.g., R. N. Zare, Angular Momentum (Wiley, New York, 1988), p. 78.
18.See, e.g., W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, U.K., 1992).
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22.A. D. Bain and I. W. Burton, Concepts Magn. Reson. 8, 191 (1996).
23.J. Shriver, Concepts Magn. Reson. 4, 1 (1992).
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