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A fortran program to simulate quadrupole-distorted NMR powder patterns
C-418 Computer Physics Communications 13 (1977) 107 -115 © North-Holland Publishing Company
A F O R T R A N P R O G R A M TO S I M U L A T E Q U A D R U P O L E - D I S T O R T E D NMR P O W D E R P A T T E R N S E.D. yon M E E R W A L L Physics Department, The University o f Akron, Akron, Ohio 44325, USA Received 3 January 1977
PROGRAM SUMMARY
Title o f program : H EQSIM 2 Catalogue number: ABMW Computer: IBM 370• 158; h~stallation: The University of Akron, Akron, Ohio 44325, USA Operath~g system: OS/MVT; OS/VS2 Programming language used: FORTRAN IV ~G) High-speed store required: 25 000 words (101 kbt) exclusive of loader Number o f bits in a word: 32 Overlay structure: none Number o f magnetic tapes required: none Other peripherals used: card reader, line printer, Calcomp incremental plotter Number o f cards in combflled program and test deck: 988
Keywords: nuclear magnetic resonance, spectrum, powder pattern, line shape, simulation, quadrupole distortion, dipolar broadening, chemical shift, absorption, dispersion, derivative Nature o f physical problem The effects of a quadrupole interaction, dipolar broadening, and a chemical shift on the NMR spectrum (static) of a nucleus of arbitrary spin 1 ~ I ~ 5 are simulated and plotted.
Method o f solution Perturbation results are used to produce satellite powder patterns and central transition (m = 1/2 to - I / 2 ) in second order quadrupolar theory, and anisotropic chemical shift in first order. The Kramers-Kronig relations are used to transform absorption to dispersion mode, and gaussian or lorentzian convolution functions simulate dipolar broadening. Histographic techniques are used for the central trnasition. Inhomogeneities in the quadrupolar interaction are simulated by adding discrete component spectra. Restrictions on program complexity Within the limitations of the program, no extensions are appropriate.
Typical nlnning time On the IBM 370/158, execution per case ranges from about 15 sec for I = 1 or 3/2 and low, homogeneous quadrupole interaction to over 4 rain for inhomogeneous anisotropic cases of high quadrupole interaction per dipolar broadening, and dispersion mode. Compilation (FORTRAN G compiler) takes about 16 CPU sec. Unusual features o f the program To maximize the utility and flexibility of the program, the following features are provided: (1) most aspects of the simulations are self-scaling with optional enlargement factors; (2) up to five VQ-Valuesper simulation provide inhomogcneity; five simulations with different rl are produced per case, with derivatives; absorption or dispersion mode may be selected; lorentzian or gaussian dipolar broadening may be of different size for central transition and satellites; (3) full chemical shift (3 components) is simulated; shift effects should be smaller than quadrupole effects; and (4) a plot of resonance derivative vs. field, scalable for direct comparison with experiment, is optional, and consists of the components of different asymmetry.
A F O R T R A N P R O G R A M TO S I M U L A T E Q U A D R U P O L E - D I S T O R T E D NMR P O W D E R P A T T E R N S E.D. yon M E E R W A L L Physics Department, The University o f Akron, Akron, Ohio 44325, USA Received 3 January 1977
PROGRAM SUMMARY
Title o f program : H EQSIM 2 Catalogue number: ABMW Computer: IBM 370• 158; h~stallation: The University of Akron, Akron, Ohio 44325, USA Operath~g system: OS/MVT; OS/VS2 Programming language used: FORTRAN IV ~G) High-speed store required: 25 000 words (101 kbt) exclusive of loader Number o f bits in a word: 32 Overlay structure: none Number o f magnetic tapes required: none Other peripherals used: card reader, line printer, Calcomp incremental plotter Number o f cards in combflled program and test deck: 988
Keywords: nuclear magnetic resonance, spectrum, powder pattern, line shape, simulation, quadrupole distortion, dipolar broadening, chemical shift, absorption, dispersion, derivative Nature o f physical problem The effects of a quadrupole interaction, dipolar broadening, and a chemical shift on the NMR spectrum (static) of a nucleus of arbitrary spin 1 ~ I ~ 5 are simulated and plotted.
Method o f solution Perturbation results are used to produce satellite powder patterns and central transition (m = 1/2 to - I / 2 ) in second order quadrupolar theory, and anisotropic chemical shift in first order. The Kramers-Kronig relations are used to transform absorption to dispersion mode, and gaussian or lorentzian convolution functions simulate dipolar broadening. Histographic techniques are used for the central trnasition. Inhomogeneities in the quadrupolar interaction are simulated by adding discrete component spectra. Restrictions on program complexity Within the limitations of the program, no extensions are appropriate.
Typical nlnning time On the IBM 370/158, execution per case ranges from about 15 sec for I = 1 or 3/2 and low, homogeneous quadrupole interaction to over 4 rain for inhomogeneous anisotropic cases of high quadrupole interaction per dipolar broadening, and dispersion mode. Compilation (FORTRAN G compiler) takes about 16 CPU sec. Unusual features o f the program To maximize the utility and flexibility of the program, the following features are provided: (1) most aspects of the simulations are self-scaling with optional enlargement factors; (2) up to five VQ-Valuesper simulation provide inhomogcneity; five simulations with different rl are produced per case, with derivatives; absorption or dispersion mode may be selected; lorentzian or gaussian dipolar broadening may be of different size for central transition and satellites; (3) full chemical shift (3 components) is simulated; shift effects should be smaller than quadrupole effects; and (4) a plot of resonance derivative vs. field, scalable for direct comparison with experiment, is optional, and consists of the components of different asymmetry.