An algorithm to produce acceptably accurate Fourier transform NMR spectra using many fewer transients
than commonly obtained is introduced and applied to 13C chemical shift and one-dimensional INADEQUATE
Lorentzian type spectra. The algorithm supplies criteria to recognize when to stop transient collection at a
time too early for an acceptable spectrum to be produced by Fourier signal processing but not by harmonic
inversion signal processing.
A recently developed signal processing method has been applied to a time evolved Gaussian wave packet
roughly corresponding to the ground vibrational state of protonated methane at time zero. The time evolution
of the wave packet was described by semiclassical initial value representation theory where classical trajectories
are used to evaluate the quantum mechanical propagator, exp[−iĤt/ℏ]. We show that only about 25 000
relatively short time trajectories are necessary to yield a well converged eigenvalue of the ground vibrational
state. The calculations reveal an unusually large red shift of 448 cm-1 from the harmonic zero point level
placing the ground state at 10 973 cm-1, with a statistical error of ±30 cm-1. These results agree remarkably
well with full-dimensionality quantum mechanical calculations.
The new harmonic inversion noise reduction method was applied to (15)N natural-abundance NMR spectroscopy and N(5)SbF(6). This method is superior to conventional Fourier transform methods for processing FIDs and permits the detection of natural abundance (15)N NMR signals with significantly reduced numbers of scans and improved sensitivity. In addition to the confirmation of the previously reported chemical shifts for N(5)(+), the one bond coupling between N(beta) and N(gamma) could be observed for the first time. Its absolute value is compared to known coupling constants of other covalent azides and the free azide ion.
ABSTRACT:The asymptotic convergence characteristics with respect to the number of included path variables of the partial average and reweighted Fourier path integral methods are numerically compared using a Gaussian fit to the one-dimensional Lennard-Jones potential. Using harmonic inversion to determine the parameters of the Gaussian fit potential appropriate for neon, the energy eigenvalues and thermodynamic properties of the Gaussian fit and the Lennard-Jones interaction agree to better than 1%. Using Monte Carlo methods to study the Gaussian fit potential, the systematic error associated with the truncation of the number of path variables is found to be larger for the reweighted method than the partial average method for the same number of path variables actually used.
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